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UBC Theses and Dissertations

Strategic positioning in product-service firms Vandenbosch, Mark B. 1991

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S T R A T E G I C POSITIONlNG IN P R O D U C T - S E R V I C E FIRMS by M A R K V A N D E N B O S C H B.A.(Hons. Bus. Admin.), University of Western Ontario, 1984 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y i n T H E F A C U L T Y O F G R A D U A T E STUDIES (Commerce and Business Administration) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I H S H C O L U M B I A S E P T E M B E R 1991 © Mark B. Vandenbosch, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date NOJ n. l^f^J DE-6 (2/88) abstract T h i s d i sser ta t i on consists of three essays r e la ted to p o s i t i o n i n g issues i n product - serv i ce f irms. A produc t - se rv i ce firm is defined as a c o m p a n y w h i c h is responsible for p r o v i d i n g b o t h the p h y s i c a l p r o d u c t a n d the associated services of an offering. T h i s s i t u a t i o n is t y p i c a l of m a n y companies m a n u f a c t u r i n g i n d u s t r i a l a n d c o m m e r c i a l p roduc t s . T h e first essay develops a game theoret i c analysis of two firms compet ing i n a t w o - d i m e n s i o n a l p r o d u c t m a r k e t . F i r m s compete o n pr ice a n d b o t h product d imensions . M o d e l s i n -c o r p o r a t i n g a l t e r n a t i v e d i f ferent iat ion assumpt ions (ver t i ca l , h o r i z o n t a l , and m i x e d ) are ana lyzed w i t h the results i n d i c a t i n g the prevalence of m a x i m u m di f ferent iat ion o n one p r o d u c t d i m e n s i o n a n d m i n i m u m di f ferent iat ion o n the other . I n the second essay, m a n y of the assumpt ions of the economic models are re laxed i n the development of a m o d e l w h i c h assesses the issue of how a product - serv i ce firm should choose its offering improve -ment strategy. T h e m o d e l addresses the s trateg ic quest ion of whether to invest i n p r o d u c t or service i m p r o v e m e n t s . In the t h i r d essay, one component of the mode l o u t l i n e d i n the second essay is deve loped fur ther a n d an e m p i r i c a l a p p l i c a t i o n is under taken . T h i s es-say develops a n i n d i v i d u a l level customer dec is ion m o d e l w h i c h est imates a n i n d i v i d u a l ' s b r a n d preferences as a f u n c t i o n of b r a n d s ' p e r c e p t u a l locat ions a n d prices. T h e m o d e l per formed we l l i n a n e m p i r i c a l s t u d y of the western C a n a d a combine harvester market . T a b l e of C o n t e n t s abstract i i L i s t of F i g u r e s iv Lis t of Tables v 1 I n t r o d u c t i o n 1 2 P r o d u c t a n d P r i c e C o m p e t i t i o n in a T w o - D i m e n s i o n a l M a r k e t 7 2.1 I n t r o d u c t i o n 7 2.2 L i t e r a t u r e R e v i e w 9 2.2.1 H o r i z o n t a l D i f f e rent ia t i on 10 2.2.2 V e r t i c a l D i f f e rent ia t i on 13 2.2.3 C o m b i n e d V e r t i c a l a n d H o r i z o n t a l D i f f e rent ia t i on 15 2.2.4 C o m p e t i t i v e M o d e l s i n M u l t i - d i m e n s i o n a l P r o d u c t Space 16 2.2.5 S u m m a r y of L i t e r a t u r e R e v i e w 18 2.3 T h e M o d e l s 19 2.3.1 T w o - D i m e n s i o n a l V e r t i c a l D i f f e rent ia t i on M o d e l 19 2.3.2 T w o - D i m e n s i o n a l H o r i z o n t a l D i f f e rent ia t i on M o d e l 27 2.3.3 M i x e d V e r t i c a l - H o r i z o n t a l D i f f e rent ia t i on M o d e l 32 2.3.4 G e n e r a l F o r m of the Indifference L i n e 36 2.4 A G e n e r a l i z e d P r i c e E q u i l i b r i u m 40 2.4.1 C h a r a c t e r i s t i c x D o m i n a n c e 41 2.4.2 C h a r a c t e r i s t i c y D o m i n a n c e 53 2.4.3 D o m i n a t e d Charac te r i s t i c s C o m p e t i t i o n 58 2.5 P r o d u c t E q u i l i b r i u m for the T w o - D i m e n s i o n a l V e r t i c a l M o d e l 65 2.5.1 A s y m m e t r i c Charac te r i s t i c s 66 2.5.2 D o m i n a t e d Charac te r i s t i c s 68 2.5.3 P r o d u c t E q u i l i b r i a 70 2.5.4 S u m m a r y a n d Impl i ca t i ons 80 2.6 P r o d u c t E q u i l i b r i u m for the T w o - D i m e n s i o n a l H o r i z o n t a l M o d e l 84 2.7 P r o d u c t E q u i U b r i u m for the M i x e d V e r t i c a l - H o r i z o n t a l Di f ferent iat ion M o d e l 88 2.7.1 P r o d u c t E q u i l i b r i a 91 2.7.2 S u m m a r y a n d Impl i ca t i ons 99 2.8 S u m m a r y 1 0 1 . 3 Set t ing the Strategic D i r e c t i o n i n a P r o d u c t - S e r v i c e F i r m 103 3.1 I n t r o d u c t i o n 103 3.2 L i t e r a t u r e R e v i e w 105 3.2.1 G l o b a l M a r k e t i n g 105 3.2.2 Services M a r k e t i n g 108 3.2.3 O p t i m a l P r o d u c t P o s i t i o n i n g 110 3.3 S t r u c t u r e of the S D M M o d e l 120 3.3.1 P r o d u c t - S e r v i c e Se t t ing 123 3.3.2 Deve lopment of a C u s t o m e r D e c i s i o n M o d e l 125 3.3.3 Of fer ing Improvement 130 3.3.4 M a p p i n g P o t e n t i a l Improvements in to P e r c e p t u a l Space 133 3.3.5 E s t i m a t i n g P r i c e and Share of D e m a n d for a n Improved Offer ing . 137 3.3.6 Assess ing R e t u r n on Investment 143 3.3.7 Strateg i c D i r e c t i o n Dec i s i on 145 3.4 C o n t r i b u t i o n s , F u t u r e Research a n d S u m m a r y 149 4 A n I n d i v i d u a l L e v e l C u s t o m e r D e c i s i o n M o d e l 154 4.1 I n t r o d u c t i o n 154 4.2 M o d e l Deve lopment 157 4.2.1 A F r a m e w o r k for M u l t i - a t t r i b u t e C u s t o m e r Dec i s i on M o d e l D e v e l -opment 157 4.2.2 P e r c e p t u a l S t r u c t u r e 158 4.2.3 Preference Measurement 166 4.2.4 C u s t o m e r C h o i c e R u l e 173 4.2.5 W h y N o t Use C o n j o i n t A l o n e 173 4.2.6 S u m m a r y of the C u s t o m e r D e c i s i o n M o d e l 175 4.3 A n E m p i r i c a l A p p l i c a t i o n of the I n d i v i d u a l L e v e l C u s t o m e r Dec i s i on M o d e l 176 4.3.1 T h e N o r t h A m e r i c a n C o m b i n e I n d u s t r y 176 4.3.2 D a t a C o l l e c t i o n Procedures 178 4.3.3 Ques t i onna i re Des ign 179 4.3.4 C o m p u t e r Interv iew Pretest 190 4.3.5 Secondary Q u e s t i o n n a i r e 190 4.4 Resu l t s of the E m p i r i c a l S t u d y 191 4.4.1 Sample 191 4.4.2 Resul ts of the Secondary Survey 195 4.4.3 C r e a t i o n of P e r c e p t u a l Space 197 4.4.4 Preference Measurement 208 4.4.5 E s t i m a t i o n of Preferences for B r a n d s 216 4.5 C o n t r i b u t i o n s a n d Conc lus ions 230 5 C o n c l u s i o n s a n d C o n t r i b u t i o n s , L i m i t a t i o n s a n d F u t u r e Research 233 5.1 P r i c e a n d P o s i t i o n i n g C o m p e t i t i o n i n a T w o - D i m e n s i o n a l M a r k e t . . . . 233 5.1.1 C o n c l u s i o n s a n d C o n t r i b u t i o n s 233 5.1.2 L i m i t a t i o n s 235 5.1.3 F u t u r e Research 237 5.2 S e t t i n g the S t ra teg i c D i r e c t i o n i n a P r o d u c t - S e r v i c e F i r m 239 5.2.1 C o n c l u s i o n s a n d C o n t r i b u t i o n s 239 5.2.2 L i m i t a t i o n s 240 5.2.3 F u t u r e Research 241 5.3 A n I n d i v i d u a l L e v e l C u s t o m e r Dec i s i on M o d e l 243 5.3.1 C o n c l u s i o n s a n d C o n t r i b u t i o n s 243 5.3.2 L i m i t a t i o n s 245 5.3.3 F u t u r e Research 247 B i b l i o g r a p h y 249 A P r i c e E q u i l i b r i u m A n a l y s i s 259 A . l A s y m m e t r i c C h a r a c t e r i s t i c s 259 A . 1.1 P r i c e E q u i l i b r i u m in Rl 260 A . 1.2 P r i c e E q u i l i b r i u m i n i ^ ^ 263 A . 1.3 P r i c e E q u i l i b r i u m in Rl 266 A . 2 C a s e 2: C h a r a c t e r i s t i c s y D o m i n a n c e 267 A . 2 . 1 P r i c e E q u i l i b r i u m in Rl 268 A . 2 . 2 P r i c e E q u i l i b r i u m in Rl 271 A . 2 . 3 P r i c e E q u i l i b r i u m i n itî^ 271 A . 3 D o m i n a t e d C h a r a c t e r i s t i c s 272 A . 3 . 1 P r i c e E q u i l i b r i u m in dRl 273 A . 3 . 2 P r i c e E q u i l i b r i u m in ^Rl 276 A . 3 . 3 P r i c e E q u i l i b r i u m in Rl 279 A . 4 Case 2: C h a r a c t e r i s t i c s y D o m i n a n c e 280 A . 4 . 1 P r i c e E q u i l i b r i u m i n ^Rl 281 A . 4 . 2 P r i c e E q u i l i b r i u m in Rl 283 A . 4 . 3 P r i c e E q u i l i b r i u m in Rl 284 B P r o o f of L e m m a 285 C C o m p u t e r - D r i v e n Q u e s t i o n n a i r e 290 D S e c o n d a r y Q u e s t i o n n a i r e 316 L i s t of F i g u r e s 2.1 A l t e r n a t i v e P r o d u c t Pos i t i on ings 23 2.2 R e l a t i o n s h i p Between C h a r a c t e r i s t i c s Space a n d P a r a m e t e r Space i n the T w o - d i m e n s i o n a l V e r t i c a l M o d e l w i t h A s y m m e t r i c C h a r a c t e r i s t i c s . . . . 24 2.3 R e l a t i o n s h i p Between C h a r a c t e r i s t i c s Space a n d P a r a m e t e r Space i n the T w o - d i m e n s i o n a l V e r t i c a l M o d e l w i t h D o m i n a t e d C h a r a c t e r i s t i c s 26 2.4 Jo in t Space Representa t i on of the T w o - D i m e n s i o n a l H o r i z o n t a l Di f feren-t i a t i o n M o d e l 31-2.5 Representat i on of the Indifference L i n e i n the M i x e d V e r t i c a l - H o r i z o n t a l Di f f erent ia t ion M o d e l 35 2.6 C h a r a c t e r i s t i c s Space Representa t i on of the M i x e d V e r t i c a l - H o r i z o n t a l D i f -ferent iat ion M o d e l 37 2.7 L o c a t i o n of the Indifference L i n e at B o u n d a r y Levels of pi (g iven ^2) • • 39 2.8 Three D e m a n d Regions U n d e r C h a r a c t e r i s t i c x D o m i n a n c e 43 2.9 D e t e r m i n a t i o n of D e m a n d in Rl 44 2.10 D e t e r m i n a t i o n of D e m a n d in Rl 46 2.11 D e t e r m i n a t i o n of D e m a n d in Rl 47 2.12 D e m a n d as a F u n c t i o n of p i (g iven P2) U n d e r C h a r a c t e r i s t i c x D o m i n a n c e 49 2.13 Three D e m a n d Regions U n d e r C h a r a c t e r i s t i c y D o m i n a n c e 54 2.14 D e t e r m i n a t i o n of D e m a n d i n 55 2.15 T h r e e D e m a n d Regions U n d e r D o m i n a t e d C h a r a c t e r i s t i c s C o m p e t i t i o n 61 2.16 S u m m a r y of P r o d u c t E q u i l i b r i a for the T w o - D i m e n s i o n a l V e r t i c a l M o d e l 81 2.17 S u m m a r y of P r o d u c t E q u i l i b r i a for the M i x e d V e r t i c a l - H o r i z o n t a l M o d e l 100 3.1 A J o i n t Space P e r c e p t u a l M a p I l l u s t r a t i n g P r o d u c t Locat i ons and C o n -sumer Ideal Po in ts I l l 3.2 Levels of A n a l y s i s i n the S D M M o d e l 122 3.3 O v e r v i e w of the S D M M o d e l 124 3.4 A n I n d i v i d u a l ' s P e r c e p t u a l M a p 126 3.5 A n I n d i v i d u a l ' s P e r c e p t u a l M a p F o l l o w i n g a Service Improvement . . . . 136 3.6 A n I n d i v i d u a l ' s V a l u a t i o n of the Offerings 142 4.1 P e r c e p t u a l M a p s I l l u s t r a t i n g O r t h o g o n a l Versus C o r r e l a t e d Factors . . . 164 4.2 C o n f i r m a t o r y F a c t o r A n a l y s i s P a t h D i a g r a m 184 4.3 Scree P l o t of the V a r i a n c e E x p l a i n e d by C o m m o n Factors and P r i n c i p a l J C o m p o n e n t s 203 4.4 P e r c e p t u a l M a p s 207 4.5 D i s t r i b u t i o n of Product P a r a m e t e r Values 213 4.6 D i s t r i b u t i o n of Service P a r a m e t e r Values 214 4.7 D i s t r i b u t i o n of Price P a r a m e t e r Values 215 4.8 L e v e l of Agreement Between F i r s t C h o i c e Preferences a n d M o d e l P r e d i c -t ions for A l t e r n a t i v e P r i c i n g s of C o m b i n e B r a n d s 228 4.9 J o h n Deere's Share of Preference at V a r i o u s Pr i ces 229 List of Tables 3.1 C o m p a r i s o n o f the S D M m o d e l w i t h O p t i m a l P r o d u c t P o s i t i o n i n g M o d e l s 150 4.1 Q u e s t i o n n a i r e O u t l i n e 180 4.2 B r a n d - P r i c e P a i r s 187 4.3 C o m b i n e Pro f i les U s e d i a C o n j o i n t A n a l y s i s 189 4.4 D e m o g r a p h i c s of P r i m a r y a n d Secondary Samples 194 4.5 C o m b i n e Inventory 195 4.6 A t t r i b u t e - F a c t o r Assoc ia t i ons i n the Secondary Survey 196 4.7 C o m b i n e A t t r i b u t e C o r r e l a t i o n M a t r i x 199 4.8 C o n f i r m a t o r y F a c t o r A n a l y s i s Resu l t s 202 4.9 L o a d i n g s for C o m m o n Fac tor a n d P r i n c i p a l C o m p o n e n t s Ana lyses . . . . 204 4.10 F a c t o r Score Coeff ic ients F r o m C F A l 206 4.11 M e a n a n d S t a n d a r d D e v i a t i o n of M a n u f a c t u r e r Pos i t ions 208 4.12 A T w o - W a y T a b l e that Serves as a B a s i s for De f in ing Agreement Measures 217 4.13 T w o - W a y T a b l e C o m p a r i n g F i r s t C h o i c e Preferences w i t h M o d e l P r e d i c t i o n s 2 1 9 4.14 E x t e n t of Agreement Between R a n k O r d e r Preferences a n d M o d e l P r e d i c -t ions 220 4.15 T w o - W a y T a b l e C o m p a r i n g F i r s t C h o i c e Preferences w i t h M o d e l P r e d i c -t ions U s i n g Respondents W h o O w n O n e of the Four Survey B r a n d s . . . 222 4.16 T w o - W a y T a b l e C o m p a r i n g C o m b i n e Inventory w i t h M o d e l P r e d i c t i o n s U s i n g Respondents W h o O w n O n e of the F o u r Survey B r a n d s 223 4.17 T w o - W a y T a b l e C o m p a r i n g C o m b i n e Inventory w i t h F i r s t C h o i c e Prefer-ences U s i n g Respondents W h o O w n O n e of the F o u r Survey B r a n d s . . . 224 4.18 Aggregate L e v e l M o d e l P r e d i c t i o n s Versus F i r s t Cho i ce Preferences and S a m p l e Inventory U s i n g Respondents W h o O w n One of the F o u r Survey B r a n d s 225 4.19 T w o - W a y T a b l e C o m p a r i n g F i r s t Cho i ce Preferences w i t h M o d e l P r e d i c -t ions U s i n g the B r a n d - P r i c e P a i r s In format ion 226 C h a p t e r 1 I n t r o d u c t i o n P r o d u c t p o s i t i o n i n g has been a m a j o r focus for m a r k e t i n g researchers a n d pract i t ioners for over 20 years. T h r o u g h o u t the years, interest i n pos i t i on ing issues has remained h igh . I n this d i s ser ta t i on , three essays concerned w i t h pos i t i on ing issues i n product -serv ice f i rms are presented. T h e n o t i o n of a product-service firm is an i m p o r t a n t component of this research. A product - serv i ce f i r m is defined as a c ompany w h i c h is responsible for p r o v i d i n g b o t h the p h y s i c a l p r o d u c t a n d the associated services of an offering. T h i s s i t u a t i o n is t y p i c a l of m a n y companies m a n u f a c t u r i n g i n d u s t r i a l a n d c o m m e r c i a l p roduc t s . For example , the e m p i r i c a l s t u d y descr ibed i n C h a p t e r 4 focuses o n a single of fering, combine harvesters, i n the f a r m equipment i n d u s t r y . M a n u f a c t u r e r s of combines , hke J o h n Deere, manufacture combines i n centra l i zed p r o d u c t i o n faci l it ies a n d market t h e m t h r o u g h a propr i e tary dealer network . In the J o h n Deere combine example , poor service at the dealer level causes customers to have a lower eva luat i on of the J o h n Deere offerings. Contras t this s i t u a t i o n w i t h a shoe manufac turer . To the customer , service m a y be an i m p o r t a n t feature w h e n p u r c h a s i n g shoes. However , when poor service is deUvered, i t is a t t r i b u t e d to the re ta i ler , not the manufac turer . T h e customer m a y choose to b u y the same shoes f r o m a different reta i ler . Hence , at this l eve l , the shoe m a n u f a c t u r e r is not responsible for service. T h e need to s t u d y p o s i t i o n i n g issues i n product - serv i ce firms is based on the premise that there is a di f ferential i m p a c t of p roduc t a n d service changes w i t h i n the company. These differences i m p l y that i t is necessary to a n a l y z e p o s i t i o n i n g issues f r o m b o t h the customer and c o m p a n y perspect ives . T r a d i t i o n a l l y , p o s i t i o n i n g research i n m a r k e t i n g has concentrated on the customer ' s v iew of the offerings i n a m a r k e t . Cus tomers are assumed to consider a n u m b e r of features or a t t r i b u t e s of the offerings. W h e t h e r the a t t r ibutes are re lated to the p r o d u c t features or service has very l i t t l e i m p a c t on the na ture of the a n a l y t i c a l procedures employed . However , f r o m the company ' s perspect ive , the d i s t i n c t i o n between p r o d u c t a n d service features is very i m p o r t a n t . For example , i n a p r o d u c t or iented company , the a b i l i t y to i m p r o v e the service component of an offering requires the development of new ski l l s a n d capab i l i t i e s . T h i s impl ies costs over a n d above the var iable costs assoc iated w i t h the service i m p r o v e m e n t . In a d d i t i o n , the t r a n s i t i o n towards a more service or iented c o m p a n y m a y be i m p e d e d by an entrenched corporate cu l ture . In order to bet ter u n d e r s t a n d the i m p a c t of these di f ferential changes, i t is i m p o r t a n t to look at p o s i t i o n i n g strategy f r o m several more general p r o d u c t a n d service d imens ions . T h i s level of analys is enables the research to concentrate on some of the i m p o r t a n t s trateg ic tradeoffs are faced by product service f irms. T h i s d i sser ta t i on consists of three essays re lated to p o s i t i o n i n g issues i n p r o d u c t -service f i rms. These essays are presented i n chapters 2-4. E a c h of these chapters can be considered as an independent research paper . However , there are s trong l inks between each chapter . In chapter 2, en t i t l ed Product and Price Competition in a Two- Dimen-sional Market, three economic models are a n a l y z e d to assess the e q u i l i b r i u m p o s i t i o n i n g i m p l i c a t i o n s of a l t ernat ive p r o d u c t d i f ferent iat ion assumpt i ons . In chapter 3, ent i t l ed Setting the Strategic Direction in a Product-Service Firm, m a n y of the assumpt ions of the economic models are re laxed i n the development of a m o d e l w h i c h assesses the issue of how a product - serv i ce f i r m should choose i ts of fering improvement strategy. F i n a l l y , i n chapter 4 , e n t i t l e d An Individual Level Customer Decision Model, one component of the m o d e l developed i n chapter 3 is developed fur ther a n d a n e m p i r i c a l a p p l i c a t i o n is u n d e r t a k e n . E a c h of these chapters w i l l be descr ibed i n more d e t a i l below. T h e economic models developed i n chapter 2 e x p a n d o n recent a n a l y t i c a l m a r k e t i n g models w h i c h s tudy product and price c o m p e t i t i o n i n markets character ized by m u l t i p l e p r o d u c t d imensions (e.g., Hauser 1988; K u m a r a n d S u d h a r s h a n 1988; C a r p e n t e r 1989; C h o i , D e S a r b o and H a r k e r 1990, H o r s k y a n d N e l s o n 1989). In these art ic les , the o p t i m a l c o m p e t i t i v e behavior w i t h respect to produc t p o s i t i o n i n g has not been fu l l y addressed. N o n e of the current models character ize a p r o d u c t e q u i l i b r i u m where firms are able to choose freely i n the al lowable produc t space. In a d d i t i o n , there has been very l i t t l e research into the compet i t i ve i m p l i c a t i o n s of various produc t d i f ferent iat ion assumpt ions w h e n produc t s are character ized by m u l t i p l e d imens ions . It is on these p o s i t i o n i n g issues that the models developed i n chapter 2 concentrate . A n economic analysis of a market w i t h two compet i tors c o m p e t i n g on pr i ce a n d t w o p r o d u c t d imensions is under taken . A l t h o u g h the two p r o d u c t d imensions can repre-sent p r o d u c t and service character ist ics of a n offering, the models are general enough to represent any produc t w h i c h can be descr ibed o n two character is t i cs . B o t h the one-d i m e n s i o n a l ver t i ca l d i f ferent iat ion m o d e l (Shaked a n d S u t t o n 1982, M o o r t h y 1988) and o n e - d i m e n s i o n a l h o r i z o n t a l d i f ferent iat ion m o d e l ( H o t e U i n g 1929, d ' A s p r e m o n t et a l 1979) are ex tended to two dimensions a n d a n analysis of p r o d u c t a n d price c o m p e t i t i o n is u n d e r t a k e n . In a d d i t i o n , the h y b r i d m o d e l c o n t a i n i n g one v e r t i c a l a n d one h o r i z o n t a l charac ter i s t i c is ana lyzed . A two-stage game theoret ic analys is i n w h i c h two firms c o m -pete first o n p r o d u c t pos i t ions a n d t h e n on pr i ce is u n d e r t a k e n for each of the models . C l o s e d f o r m e q u i l i b r i u m solutions are o b t a i n e d for each stage i n w h i c h compet i tors are unres t r i c t ed i n the ir choices of price or p r o d u c t pos i t i ons . C h a p t e r 3 develops a m o d e l w h i c h can be used to a i d a firm d e t e r m i n i n g the strategic d i r e c t i o n i t shou ld pursue. A strategic direction is defined as the company ' s overr id ing focus for improvements r e l a t i n g to i ts p roduc t - serv i ce offering(s). For example , a com-p a n y m a y choose a service or iented s trateg ic d i r e c t i o n . T h i s impl i es t h a t , i n the m e d i u m t e r m , the m a j o r i t y of offering i m p r o v e m e n t s w i l l be re la ted to service. T h e development of a t e chn ica l service d e p a r t m e n t , a n i m p r o v e m e n t i n the parts de l ivery sys tem a n d / o r an increase the n u m b e r of dealerships m a y a l l be p a r t of this "serv ice" emphasis . T h e need for a strategic d i r e c t i o n stems f r o m the a s s u m p t i o n t h a t companies must cont inuous ly i m p r o v e the i r offerings i n order to r e m a i n c o m p e t i t i v e . In a w o r l d of increas ing g loba l c o m p e t i t i o n , th is a s s u m p t i o n appears to be reasonable . T h e strategic d i r e c t i o n m o d e l ( S D M mode l ) considers b o t h the customer and company perspect ive i n d e t e r m i n i n g the o p t i m a l s trategic d i r e c t i o n for a f i r m . A t the customer leve l , customer percept ions a n d preferences for the offerings i n the market are assessed. A t the c o m p a n y leve l , i m p l e m e n t a t i o n managers propose p r o m i s i n g p r o d u c t a n d service improvements to the ex i s t ing produc t - se rv i ce offering. T h e strategic d i re c t i on decision is based on the expec ted market i m p a c t of these proposed improvements . T h i s incre -m e n t a l i s m a p p r o a c h to offering i m p r o v e m e n t recognizes the need to consider the current pos i t i on ing of the c o m p a n y ' s offering i n any i m p r o v e m e n t strategy. T h e S D M m o d e l relaxes m a n y of the assumpt ions used i n the economic models de-ve loped i n chapter 2. C u s t o m e r preferences are descr ibed by a ver t i ca l d i f ferentiat ion (vector) m o d e l w h i c h inc ludes p r o d u c t , service a n d pr ice factors. U n l i k e the economic mode ls , the m e t h o d o l o g y al lows customers to have heterogeneous percept ions of the of-ferings. In a d d i t i o n , the S D M m o d e l al lows for m u l t i p l e compet i tors , m u l t i p l e regions a n d the i n c l u s i o n of b o t h f ixed a n d var iab le costs i n the profit a n d r e t u r n ca lcu lat ions . T h i s added genera l i ty prevents the d e t e r m i n a t i o n of a pos i t i on ing e q u i l i b r i u m , but is appropr ia te for the assessment of o p t i m a l s trateg ic d i r e c t i on . C h a p t e r 4 develops a n d e m p i r i c a l l y tests an i n d i v i d u a l level customer dec is ion mode l w h i c h can be used as p a r t of the S D M m o d e l . T h e customer decis ion m o d e l is unique i n a n u m b e r of respects. F i r s t , c o n f i r m a t o r y factor analys is is used to define the perceptual space. L i k e o ther factor a n a l y t i c techniques , c o n f i r m a t o r y factor analys is allows for het-erogeneous percept ions t h r o u g h the e s t i m a t i o n of i n d i v i d u a l factor scores. In a d d i t i o n , c on f i rmatory factor analys is al lows for a p r i o r i spec i f i cat ion of n u m b e r of perceptual d i -mensions and the measurement of the i r i n t e r - c o r r e l a t i o n . Second, the m o d e l uses conjoint measurement to es t imate cus tomers ' preference weight ings for each of the perceptua l d i -mensions a n d price . P a r a m e t e r s are e s t i m a t e d at the i n d i v i d u a l level a n d app l i ed to an i n d i v i d u a l ' s b r a n d percept ions to de termine the i n d i v i d u a l ' s re lat ive preference for each of the brands i n the m a r k e t . F i n a l l y , the m o d e l al lows for the i n c o r p o r a t i o n of price c o m p e t i t i o n between brands . Because the price p a r a m e t e r is e s t imated over a range of price levels, the customer dec is ion m o d e l is s t i l l v a l i d as current prices are adjusted to N a s h e q u i U b r i u m prices . B u i l d i n g on the S D M m o d e l developed i n chapter 3, the customer decis ion mode l is speci f ical ly designed for markets w h i c h are charac ter i zed by product - serv i ce firms. However , its general f o r m u l a t i o n al lows it to be a p p l i e d i n m a n y sett ings. T h e e m p i r i c a l a p p l i c a t i o n of the customer dec is ion m o d e l focuses on a single offering, combine harvesters , i n the f a r m equipment i n d u s t r y . A computer d r i v e n quest ionnaire was a d m i n i s t e r e d to c ombine owners a t t e n d i n g the 1990 C a n a d a W e s t e r n A g r i b i t i o n i n R e g i n a , Saskatchewan. T h e A g r i b i t i o n is a m a j o r a g r i c u l t u r a l t rade show w h i c h is at -tended by an e s t i m a t e d 30,000 farmers annua l ly . U s i n g this d a t a , the customer decision m o d e l is parameter i zed . T h e pred i c t ive a b i l i t y of the m o d e l is assessed t h r o u g h a com-p a r i s o n w i t h respondents choices on a number of preference questions. T h e d isser tat ion concludes w i t h a s u m m a r y chapter . In this chapter (chapter 5) , c o n t r i b u t i o n s , l i m i t a t i o n s a n d future research are d iscussed for each of the essays. T o date , research o n p o s i t i o n i n g issues i n produc t - se rv i ce firms has been h m i t e d . Yet , as the i m p o r t a n c e of services i n t r a d i t i o n a l m a n u f a c t u r i n g operat ions increases, the c ompet i t i ve success ( a n d poss ib ly the surv iva l ) of m a n y companies depends on an u n -ders tand ing of these issues. It is be l ieved that the research developed in this d issertat ion contr ibutes to our u n d e r s t a n d i n g of th is research top i c . C h a p t e r 2 P r o d u c t a n d P r i c e C o m p e t i t i o n i n a T w o - D i m e n s i o n a l M a r k e t 2.1 I n t r o d u c t i o n Recent ly , a n u m b e r of a n a l y t i c a l m a r k e t i n g models have been developed to s tudy produc t a n d pr i ce c o m p e t i t i o n i n markets character ized by m u l t i p l e p r o d u c t d imensions (Hauser 1988; K u m a r a n d S u d h a r s h a n 1988; C a r p e n t e r 1989; C h o i , D e S a r b o and H a r k e r 1990, H o r s k y a n d N e l s o n 1989). Co l lec t ive ly , these models prov ide a n u m b e r of i m p o r t a n t ins ights i n t o the o p t i m a l behav ior of c o m p e t i n g f irms w i t h respect to p r i c i n g , p r o d u c t p o s i t i o n i n g a n d , i n some models , adver t i s ing a n d d i s t r i b u t i o n . I n t u i t i v e l y , i t w o u l d seem that one of the p r i m a r y reasons for deve lop ing a n a l y t i -ca l models i n a m u l t i d i m e n s i o n a l context w o u l d be to s t u d y produc t design decis ions. However , the o p t i m a l c o m p e t i t i v e behavior w i t h respect to produc t p o s i t i o n i n g has not been sat i s fac tor i ly addressed. N o n e of the current models character ize a p r o d u c t equiUb-r i u m where f irms are able to choose freely i n the a l lowable p r o d u c t space. In a d d i t i o n , there has been very l i t t l e research into the c o m p e t i t i v e i m p l i c a t i o n s of various produc t d i f ferent iat ion assumpt ions when products are character ized by m u l t i p l e d imens ions . In th is chapter , a general ized t w o - d i m e n s i o n a l m o d e l of p r o d u c t a n d pr i ce c o m p e t i t i o n is developed. B o t h the one -d imens iona l ve r t i ca l d i f ferent iat ion m o d e l (Shaked a n d S u t t o n 1982, M o o r t h y 1988) a n d one -d imens iona l h o r i z o n t a l d i f ferent iat ion m o d e l ( H o t e l l i n g 1929, d ' A s p r e m o n t et a l 1979) are extended to two d imensions a n d a n analys is of p roduc t a n d pr i ce c o m p e t i t i o n is under taken . In a d d i t i o n , the h y b r i d m o d e l c o n t a i n i n g one ver t i ca l a n d one h o r i z o n t a l character is t i c is ana lyzed . A two-stage game theoret ic analysis i n w h i c h two firms compete first o n p r o d u c t pos i t ions a n d then on price is under taken for each of the models . C losed f o rm e q u i l i b r i u m solut ions are o b t a i n e d for each stage i n w h i c h compet i tors are unres t r i c ted i n the ir choices of price or produc t pos i t ions . A l t h o u g h there are s u b s t a n t i a l differences i n the s tructures of the three models , there are s t rong s imi lar i t i es i n the nature of the ir e q u i h b r i u m so lut ions . T h e most s igni f i -cant finding is that there is a prevalence of MaxMin p roduc t d i f ferent iat ion . T h a t i s , i n e q u i l i b r i u m , the two firms tend to choose pos i t ions w h i c h w i l l represent m a x i m u m di f ferent iat ion on one d imens ion a n d m i n i m u m di f ferent iat ion on the other d i m e n s i o n . T h e notable except ion to this type of e q u i l i b r i u m occurs i n the t w o - d i m e n s i o n a l v e r t i c a l d i f ferent iat ion m o d e l where , under ce r ta in cond i t i ons , m a x i m u m p r o d u c t d i f ferent iat io i i occurs. I n a d d i t i o n to generat ing s i m i l a r produc t e q u i l i b r i a , the pr ice e q u i l i b r i a for the three models share a general ized f o r m w i t h some parameter values depend ing o n the produc t d i f ferent iat ion assumpt ions used. C o m p a r i s o n s are made between these models a n d the ir one -d imens iona l counterparts as we l l as o ther t w o - d i m e n s i o n a l models of p r o d -uct p o s i t i o n i n g a n d pr i ce (e. g. E c o n o m i d e s 1986b; Hauser 1988; C a r p e n t e r 1989; L a n e 1980). In order to h igh l ight b o t h the s imi lar i t i e s a n d differences, each of the models is de-veloped i n t a n d e m . Speci f ical ly , the chapter is s t r u c t u r e d as fol lows. Sect ion 2.2 reviews the relevant l i t e r a t u r e i n b o t h economics a n d m a r k e t i n g . Sect ion 2.3 develops the three different models by o u t l i n i n g the i r assumpt ions a n d c o m p a r i n g t h e m to e x i s t i n g models . Sec t i on 2.4 develops the pr ice e q u i l i b r i u m whi l e sections 2.5-2.7 develops the produc t e q u i l i b r i a for each of the three models . I m p l i c a t i o n s a n d m o d e l summar ies are also i n -c l u d e d i n these sections. Sec t i on 2.8 summar izes the chapter . 2.2 L i t e r a t u r e R e v i e w In m a r k e t i n g , the L a n c a s t e r i a n v iew of product space is w i d e l y accepted (Lancaster 1966, 1971, 1979). Lancas ter pos i ted t h a t produc ts are c ompr i sed of a set of character-ist ics a n d that the consumer 's u t i l i t y for this produc t is a f u n c t i o n of the levels of these character is t i cs . T h i s a s s u m p t i o n is the basis for m a n y m a r k e t i n g research techniques i n c l u d i n g conjoint analysis a n d m u l t i d i m e n s i o n a l sca l ing . U s i n g Lancaster ' s no t i on of p roduc t space, two variants of p r o d u c t d i f ferent iat ion can be d i s t ingu ished : h o r i z o n t a l d i f ferent iat ion a n d ver t i ca l d i f f erent iat ion . In a h o r i z o n t a l l y d i f ferent iated p r o d u c t space, tastes vary across the p o p u l a t i o n r e s u l t i n g i n a d i s t r i b u t i o n of i n d i v i d u a l idea l charac-ter is t i c levels. T h u s , this type of d i f ferent iat ion has been te rmed var iety d i f ferent iat ion . Charac te r i s t i c s l ike sweetness, color a n d phys i ca l l o c a t i o n are h o r i z o n t a l i n nature . In a v e r t i c a l l y di f ferentiated p r o d u c t space, a l l consumers agree that more of a character is t i c is a lways better . T h i s results i n a n a t u r a l o rder ing over the character i s t i c space ( T i r o l e 1988). Charac ter i s t i c s Hke q u a l i t y a n d efficacy are ve r t i ca l i n nature . A c c o r d i n g l y , this type of d i f ferent iat ion has been t e r m e d q u a l i t y d i f ferent iat ion . M a r k e t e r s have t r a d i t i o n a l l y mode led h o r i z o n t a l a n d v e r t i c a l character ist ics us ing the vector m o d e l and the idea l po int m o d e l respect ive ly (Shocker a n d S r i n i v a s a n 1979). R a t c h f o r d (1979) shows how the development of these e m p i r i c a l l y based models are l inked to Lancaster ' s goods- character ist ics theory. T h e models based o n these two types of p roduc t d i f ferent iat ion are reviewed i n more d e t a i l . T h i s is fol lowed by a rev iew of c o m p e t i t i v e mode ls i n w h i c h markets are char-acter ized by a m u l t i d i m e n s i o n a l p r o d u c t space. Interested readers are also d i rec ted to L a n c a s t e r (1990) and R a t c h f o r d (1990) who review the l i t e r a t u r e o n p r o d u c t di f ferentia-t i o n i n economics and m a r k e t i n g respectively. 2.2.1 H o r i z o n t a l Di f ferent iat ion T h e h o r i z o n t a l d i f f e rent ia t ion m o d e l was developed by HoteUing (1929). Indeed, his ar t i c l e " S t a b i l i t y i n C o m p e t i t i o n " has i n s p i r e d m u c h of the research i n spa t ia l economics. T h e basic a s s u m p t i o n b e h i n d a h o r i z o n t a l d i f ferent iat ion m o d e l is that consumers are heterogeneous w i t h respect to the ir i dea l level of a character is t i c . C o n s u m e r s decrease the i r v a l u a t i o n of a p r o d u c t as a f u n c t i o n of "d i s tance " f r o m their i dea l level of the character i s t i c to the p r o d u c t ' s l eve l . T h o u g h they vary w i t h respect to the i r not ion of a n idea l p r o d u c t , a l l consumers value a n i dea l p r o d u c t equal ly a n d have the same u t i l i t y r educ ing d istance f u n c t i o n . T h u s , consumers use b o t h produc t prices a n d distance f rom the i r respect ive i d e a l po in ts to decide w h i c h p r o d u c t to purchase. T h e basic ideas b e h i n d H o t e l l i n g ' s h o r i z o n t a l d i f ferent iat ion m o d e l are as follows. T w o firms, se l l ing the same p h y s i c a l g o o d w i t h equa l (zero) p r o d u c t i o n costs, compete on store l o c a t i o n a n d pr i ce . T h e env i ronment for c o m p e t i t i o n is a linear city, represented by a l ine of l e n g t h 1. T h e two firms are l o ca ted at respect ive distances X i a n d I 2 f rom the zero end of this l ine such t h a t : X2 > X i , 0 < X i , X 2 < 1. C o n s u m e r s , who purchase one un i t of the g o o d each p e r i o d , are assumed to be u n i f o r m l y " l o c a t e d " a long the line a n d value a firm's of fering based o n a c o m b i n a t i o n of i ts price a n d the d is tance to the store. T h u s , each consumer has an i dea l store l o c a t i o n (where the d istance to the store is zero) . Let pi a n d p2 represent the respect ive prices of the two produc ts and let c represent the t r a n s p o r t a t i o n rate . T h e n consumers choose the p r o d u c t w h i c h min imizes the i r t o t a l cost for the p r o d u c t : M i n C = pi-\- c|x* — Xi\, for i = 1, 2. T h e m a i n finding of H o t e l l i n g ' s paper is the e q u i l i b r i u m choice of l o c a t i o n for the two firms. A t equa l pr ices , consumers l o ca ted to the left o f X i (between 0 and X i ) w o u l d always purchase f r o m firm 1. T h i s region can be termed firm I's h i n t e r l a n d . A s Xi moves t oward X 2 , firm I 's market share w o u l d increase as more consumers wou ld be i n its h i n t e r l a n d . T h e same force w o u l d draw f i r m 2 towards firm 1 m a k i n g the produc t e q u i l i b r i u m Xi = X2 ( i . e. m i n i m u m di f ferent iat ion) . T h i s Principle of Minimum Differentiation has been used wide ly to e x p l a i n w h y some businesses (l ike banks and gas stat ions) seem to locate very close to one another a n d w h y p o l i t i c a l parties tend to have s i m i l a r p la t f o rms . Hote l l ing ' s l o c a t i o n result was generated when prices were equal . T h o u g h H o t e l l i n g discussed the poss ib i l i t y of price c u t t i n g i n his a r t i c l e , he d i d not e laborate . A s i l l u s t r a t e d by d ' A s p r e m o n t , G a b s z e w i c z and T h i s s e (1979), m i n i m u m di f ferent iat ion i n a H o t e l l i n g env ironment leads to severe price c u t t i n g a n d a pr ice e q u i l i b r i u m on ly at pl = p2 = 0 (assuming m a r g i n a l cos t=0) . T h e no t i on here is that because the products are phys i ca l l y i d e n t i c a l a n d at the same l o c a t i o n , B e r t r a n d pr i ce c o m p e t i t i o n w i l l result . In a d d i t i o n , these researchers prove t h a t a pr ice e q u i l i b r i u m ( w i t h prices > 0) w i l l not exist unless^ the firms are l o ca ted far enough f rom each other . D ' A s p r e m o n t et a l m o d i f y the consumer 's m i n i m i z a t i o n f u n c t i o n to M i n C = pi + c\x' - Xi\^, for i = 1, 2 T h i s m o d i f i c a t i o n of the d istance f u n c t i o n obta ins a un ique l o c a t i o n a l e q u i l i b r i u m w h i c h impl ies m a x i m u m p r o d u c t d i f ferent iat ion . T h i s result is p r i m a r i l y due to a strategic force: the desire to reduce price c o m p e t i t i o n . T h a t i s , firms make more profits i f they are able to o b t a i n " l o c a l m o n o p o l i e s " . F r o m the analyses of H o t e l l i n g a n d d ' A s p r e m o n t et a l , two forces seem to shape the l o c a t i o n a l e q u i l i b r i u m : a d e m a n d force (a desire to increase one's h inter land) w h i c h draws the firms together a n d a strategic force (a desire to reduce price compet i t i on ) w h i c h causes the firms to diflFerentiate. A n u m b e r of researchers have extended the h o r i z o n t a l d i f ferent iat ion m o d e l i n a n a t t e m p t to u n d e r s t a n d the nature of these forces. Economides (1986a) shows t h a t the results of b o t h H o t e l l i n g a n d d ' A s p r e m o n t et a l are sensit ive to the t r a n s p o r t a t i o n cost f u n c t i o n used. H e studies the HoteUing m o d e l w i t h a t r a n s p o r t a t i o n cost f u n c t i o n of cd'^ where d is the d istance f rom the consumer to the store l o ca t i on and a G [1,2]. H e finds that a pure -s trategy price e q u i l i b r i u m exists for a > 1.26 and that l o c a t i o n a l d i f f erent iat ion is not m a x i m a l for 1.26 < a < 1.67. d e P a l m a et a l (1985) show that the Principle of Minimum Differentiation is restored when " p r o d u c t s a n d consumers are suff ic iently heterogeneous". U n d e r Hote l l ing ' s o r i g i -n a l f o r m u l a t i o n , the c o m p e t i n g produc ts were i dent i ca l (i.e. they b o t h generate an equal consumer surp lus for a l l consumers) . However , d e P a l m a et a l assume that there are inher -ent character i s t i cs w i t h i n firms w h i c h cause d i f ferent iat ion ; that consumer preferences for these p roduc t s are not i d e n t i c a l ; a n d , that specific consumer tastes cannot be de termined a p r i o r i . T h e y m o d e l the consumer surplus der ived f rom c o n s u m i n g a g iven product as s + m c i where m is a parameter a n d is a c onsum er - and - f i rm specific r a n d o m v a r i a b l e w h i c h accounts for the lack of i n f o r m a t i o n regard ing the tastes of p a r t i c u l a r consumers. A s m becomes large , p roduc ts are di f ferentiated even t h o u g h they have the same l oca -t i o n . There fore , the strategic effect (the desire to soften price c o m p e t i t i o n ) is m i n i m i z e d a n d the d e m a n d effect dominates . T h e authors state that the i n c l u s i o n of heterogeneity i n b o t h firms a n d consumers amounts to a d d i n g a second n o n - s p a t i a l d i m e n s i o n . E c o n o m i d e s (1986b) extended Hote l l ing ' s m o d e l to two dimensions by h a v i n g the consumer 's u t i l i t y depend on the distance f r o m the produc t ' s l o c a t i o n to the consumer 's l o c a t i o n i n a c i r c u l a r market space. H e shows that a price e q u i l i b r i u m exists for a l l s y m m e t r i c a l l o cat ions whereas such an e q u i l i b r i u m does not i n the l inear m o d e l . H i s analys is restr i c ts products to s y m m e t r i c a l locat ions on the axis t h r o u g h the centre of the market a n d he does not a t t empt to find the produc t e q u i l i b r i u m . O t h e r i m p o r t a n t extensions to the one -d imens iona l h o r i z o n t a l d i f ferent iat ion m o d e l warrant m e n t i o n but do not d i re c t l y i m p a c t o n the issues s tud ied i n this thesis. Salop (1979) s t u d i e d a f o r m of monopohs t i c c o m p e t i t i o n by " c onnec t ing " the two ends of the linear city to f o r m the circular city. E c o n o m i d e s (1984) a n a l y z e d the H o t e l l i n g mode l i n an env i ronment where consumer d e m a n d was rec tangular i n n a t u r e (i.e. the consumer on ly purchases i f a c o m m o d i t y is avai lable at a dehvered pr i ce w h i c h is below an upper l i m i t ) . E a t o n a n d L i p s e y (1975) ex tend Hote l l ing ' s analys is to the case where there are more t h a n two f irms whi le Prescot t a n d Visscher (1977) ana lyze the p r o b l e m of sequent ia l en t ry of f i rms. For a more complete review of the o n e - d i m e n s i o n a l h o r i z o n t a l d i f ferent iat ion l i t e r a t u r e see G r a i t s o n (1982) a n d T i r o l e (1988, chapter 7). 2.2.2 V e r t i c a l Di f ferent iat ion V e r t i c a l d i f ferent iat ion models have o n l y recent ly begun to appear i n the l i t e ra ture ( M u s s a and Rosen 1978, Gabszewicz and T h i s s e 1979; Shaked a n d S u t t o n 1982). T h e basic a s s u m p t i o n b e h i n d the ver t i ca l d i f ferent iat ion m o d e l is that a l l consumers agree that more of a specif ic character is t i c is a lways better . T h u s , a l l consumers have the same idea l p o i n t : a n in f in i t e level of the character i s t i c . E c o n o m i s t s ca l l th is character is t i c " q u a l i t y " , but i t can refer to any a t t r i b u t e or p e r c e p t u a l d i m e n s i o n w h i c h can be v iewed i n a "more is be t te r " f ramework. In contrast w i t h the h o r i z o n t a l d i f ferent iat ion m o d e l , at equal pr ices , o n l y one produc t ( the one w i t h the highest q u a l i t y ) w i l l have a pos i t ive market share. C o n s u m e r s are heterogeneous w i t h respect to the i r wi l l ingness to pay for the p r o d u c t . Therefore , though a l l consumers can agree o n w h i c h p r o d u c t has more of the desired charac ter i s t i c , the a c t u a l p r o d u c t that the consumer w i l l b u y is dependent on the prices charged by the compet i t o rs . U s i n g T i r o l e ' s (1988) terminology , the general format of the o n e - d i m e n s i o n a l ve r t i ca l d i f ferent iat ion m o d e l is as fol lows. T w o f i rms , se l l ing a s u b s t i t u t a b l e p r o d u c t p roduced w i t h equa l (zero) costs, compete on q u a l i t y a n d pr ice . E a c h p r o d u c t ( indexed 1, a n d 2) has a p a r t i c u l a r qua l i ty , a, i n the range [a/, a''] a n d a price , p. A l l consumers b u y one unit per p e r i o d a n d they choose the product w h i c h m a x i m i z e s V = 9si - pi, for i = 1,2. T h e parameter 9 represents the consumer 's wilHngness to pay or taste and can have any d i s t r i b u t i o n a m o n g the p o p u l a t i o n . G a b s z e w i c z and Thisse (1979) a n d Shaked a n d S u t t o n (1982) assume that this parameter varies w i t h income w i t h consumers hav ing higher incomes preferr ing h igher q u a l i t y products . However , n o t h i n g is lost by consider ing a wi l l ingness to pay d i s t r i b u t i o n independent of income . T h i s environment leads to a d i v i s i o n of the market into two segments w i t h each segment purchas ing a different p r o d u c t . Consumers w i t h a taste parameter & > {p2 — Pi)/(-S2 — ^i) w i l l prefer to purchase the higher q u a l i t y p r o d u c t whereas the r e m a i n i n g consumers w i l l purchase the lower q u a l i t y p r o d u c t . Because of the desire to reduce price c o m p e t i t i o n (the strategic effect ment i oned above) , the resu l t ing produc t e q u i l i b r i u m has f i rms l ocated at the extreme ends of the q u a l i t y s p e c t r u m . T h e basic ver t i ca l d i f ferent iat ion m o d e l has been extended i n a n u m b e r of ways. S h a k e d and S u t t o n (1982) e x t e n d earl ier work by G a b s z e w i c z a n d Thisse (1979, 1980) by a n a l y z i n g a three stage game i n w h i c h the first stage was ent ry fol lowed by product a n d pr ice c o m p e t i t i o n . T h e y find that the o n l y perfect e q u i l i b r i u m i n the three stage game results when o n l y two firms enter the m a r k e t . S h a k e d and S u t t o n (1983) generalize this result by prov ing that i n any v e r t i c a l l y di f ferentiated m a r k e t , there can be at most a finite n u m b e r of c ompet i t o rs . T h i s "f initeness r e su l t " occurs because pr i ce c o m p e t i t i o n a m o n g h igh q u a l i t y firms drives pr ice d o w n to a level where lower q u a l i t y firms cannot enter a n d make a prof i t . M o o r t h y (1988) extends the basic m o d e l by i n c o r p o r a t i n g var iab le p r o d u c t i o n costs and a l l owing consumers the o p p o r t u n i t y not to buy. H i s e q u i h b r i u m analys is shows that firms choose produc ts w h i c h are di f ferentiated ( though not m a x i m a l l y ) . I n a d d i t i o n , the firms choose not to prov ide offerings w h i c h a p p e a l to the ent ire market (not a l l consumers purchase) . M o o r t h y also analyzes a sequent ia l entry p r o d u c t e q u i l i b r i u m . His results show that the first entrant chooses the lowest q u a l i t y possible wh i l e ensur ing that it remains the h i g h q u a l i t y p r o d u c t . In a d d i t i o n to s t u d y i n g market s t ruc ture prob lems , the ver t i ca l d i f ferent iat ion mode l has been used extens ive ly i n agency theory. Papers by M u s s a a n d Rosen (1978) and M a s k i n a n d R i l e y (1986) i l l u s t r a t e how a group of consumers di f ferentiated ver t i ca l ly on a character is t i c are used i n the analysis of adverse select ion (h idden character ist ics ) prob lems . So lut ions to these prob lems a l low monopohsts to exercise p a r t i a l price dis-c r i m i n a t i o n by offering a range of products at different qual i t ies as consumers self select the ir most preferred pr ice a n d q u a l i t y o p t i o n . 2.2.3 C o m b i n e d V e r t i c a l a n d H o r i z o n t a l Di f ferent iat ion Because of the recogni t ion t h a t produc ts often vary b o t h i n var ie ty a n d qual i ty , there have been a few models deve loped to s tudy the c o m b i n e d effects of these types of product d i f ferent iat ion. I re land (1987) s tud ied pr ice c o m p e t i t i o n i n a m o d e l i n w h i c h there are two groups of consumers who have different i dea l produc t variet ies . T h o u g h he allows for the poss ib i l i ty of f irms to set v a r y i n g quahty levels, he does not ana lyze the product e q u i l i b r i u m . G i n s b u r g h et a l (1987) analyze the s i t u a t i o n where f irms compete on prices and qua l i t y for g iven varieties of a p r o d u c t . Neven and T h i s s e (1988) a n a l y z e d a t w o - d i m e n s i o n a l ver t i ca l a n d h o r i z o n t a l differ-ent ia t i on m o d e l i n w h i c h f i rms compete on qua l i ty , var iety and pr i ce . F i r m s first choose their p r o d u c t , cons is t ing of two character ist i cs , a n d subsequent ly choose the i r price . T h e models descr ibed later i n th i s paper employ s i m i l a r analysis procedures to those used by Neven and Thisse . 2.2.4 C o m p e t i t i v e M o d e l s in M u l t i - d i m e n s i o n a l P r o d u c t Space K u e h n a n d D a y (1962) no ted t h a t if a firm differentiates i ts p r o d u c t f rom compet i tors , it w i l l o c cupy a separate p o s i t i o n a n d capture i ts o w n market segment rather t h a n share the market w i t h other firms. In the years since K u e h n a n d D a y ' s art i c le , a number of s oph is t i ca ted methodolog ies for measur ing consumer preferences a n d a n a l y z i n g produc t spaces have been developed. M e t h o d s i n c l u d i n g conjoint ana lys i s , m u l t i d i m e n s i o n a l sca l -i n g a n d other p e r c e p t u a l m a p p i n g techniques have l ed to a s ignif icant b o d y of research on p r o d u c t p o s i t i o n i n g issues (e. g. Hauser and U r b a n 1977, G r e e n and K r e i g e r 1985, Shocker a n d S r i n i v a s a n 1979, Day , Shocker a n d S r i v i s t a v a 1979, D e S a r b o and R a o 1986, U r b a n a n d H a u s e r 1980). T h e models w h i c h address produc t a n d price c o m p e t i t i o n i n m u l t i - d i m e n s i o n a l p r o d u c t markets w i l l be reviewed i n more de ta i l (note also the earl ier reviews of E c o n o m i d e s (1986b) a n d N e v e n a n d Th isse (1988)) . T h e models proposed by Hauser (1988) a n d L a n e (1980) represent variat ions of the h o r i z o n t a l d i f ferent iat ion m o d e l . Hauser analyzes p r i c i n g a n d p o s i t i o n i n g strategies us-i n g the D E F E N D E R consumer m o d e l (Hauser a n d S h u g a n 1983) i n w h i c h products are di f ferent iated i n a t w o - d i m e n s i o n a l per dollar pe r cep tua l m a p . A l t h o u g h the per dollar p e r c e p t u a l m a p p e r m i t s o n l y "more is be t ter " a t t r ibutes s i m i l a r to a ver t i ca l dif feren-t i a t i o n m o d e l , the l i m i t e d p r o d u c t p o s i t i o n i n g opt ions makes the resu l t ing p o s i t i o n i n g e q u i l i b r i u m behave i n m u c h the same way as the h o r i z o n t a l d i f ferent iat ion mode l . Hauser imposes the r es t r i c t i on that feasible products must l ie o n the c ircumference of a q u a r -ter c irc le i n s c r i b e d i n the pos i t ive q u a d r a n t . T h i s reduces the p o s i t i o n i n g decis ion to one d i m e n s i o n as each l o c a t i o n o n the quarter circle can be expressed i n terms of the angle w h i c h a Une f r o m the l o c a t i o n to the o r i g in makes w i t h the h o r i z o n t a l axis . L i k e Hote l l ing ' s m o d e l , each consumer has an i dea l produc t i n this d imens ion under equa l prices. T h e p r o d u c t e q u i l i b r i u m consists of m i n i m u m di f ferent iat ion at equal prices a n d m a x i m a l d i f ferent iat ion when b o t h prices a n d p r o d u c t pos i t ions are considered. L a n e represents brands i n t w o - d i m e n s i o n a l space on the basis of p roduc t character-ist ics where pr ice is considered separately. C o n s u m e r heterogeneity is modeled i n the parameters of a C o b b - D o u g l a s u t i l i t y f u n c t i o n of the two "more is be t te r " character is -t ics . Lane ' s a s s u m p t i o n of a single technology curve restr icts the produc t choice to a one -d imens iona l decis ion i n m u c h the same way as Hauser ' s "quar te r c i rc le " a s s u m p t i o n . T h e m a j o r focus of Lane ' s paper is the p r o d u c t entry a n d deterrence strategies. T h u s , he uses a sequential entry w i t h foresight p r o d u c t e q u i l i b r i u m concept w h i c h results i n an e q u i l i b r i u m so lut ion w h i c h tends towards m a x i m u m di f ferent iat ion . K u m a r and S u d h a r s h a n (1988) use Lane ' s m o d e l to discuss defensive p r i c i n g , adver-t i s i n g a n d d i s t r i b u t i o n (but not pos i t i on ing ) responses to an o p t i m a l a t tack by a new market entrant . T h e goa l of this research is to ex tend some of the results f o r w a r d e d by the D E F E N D E R m o d e l (Hauser a n d S h u g a n 1983) to s i tuat ions where there is one at tacker a n d n defenders. C a r p e n t e r (1989) analyzes a two b r a n d , t w o - d i m e n s i o n a l h o r i z o n t a l d i f ferent iat ion m o d e l i n w h i c h i n d i v i d u a l idea l po ints are u n i m o d a l l y d i s t r i b u t e d over the a l lowable p r o d u c t space. He makes the a s s u m p t i o n that a consumer o n l y considers purchas ing a produc t i f i t is w i t h i n a specified d istance , D^ax f r om that consumer 's i dea l po int . There fore , d r a m a t i c pr ice reduct ions i n a p a r t i c u l a r p r o d u c t ' s pr i ce w i l l not be effective i n a t t r a c t i n g consumers whose idea l po ints are fur ther t h a n D^ax f rom the produc t ' s l o c a t i o n . In this env i ronment , C a r p e n t e r out l ines the condi t ions w h i c h w o u l d cause firms to choose the same product l o ca t i on : the m i d p o i n t of the idea l po int d i s t r i b u t i o n . W h e n the rate of change i n d e m a n d is greater for a p r o d u c t movement towards the d i s t r i b u t i o n m i d p o i n t t h a n the rate of change i n d e m a n d for a movement away f rom the compet i t o r , b o t h firms choose to locate at the d i s t r i b u t i o n m i d p o i n t . If the reverse is true , C a r p e n t e r concludes that products w i l l locate at oppos i te corners of the al lowable produc t space. C h o i , D e S a r b o a n d H a r k e r (1990), s t u d y the p r o b l e m of o p t i m a l p r o d u c t pos i t i on ing i n the presence of pr ice c o m p e t i t i o n . A l t h o u g h C h o i et a l develop an a n a l y t i c a l mode l w h i c h exhib i ts ver t i ca l d i f ferent iat ion (the a s s u m p t i o n of a single i d ea l point at m a x i -m u m q u a l i t y ) , the i r n u m e r i c a l approach to the N a s h price e q u i h b r i u m so lut ion exhib i ts hor i zonta l d i f ferent iat ion . It is unc lear whether the comparat ive s ta t i c results for the a n a l y t i c a l mode l ho ld under the i r n u m e r i c a l approach . U s i n g a S t a c k e l b e r g - N a s h equi -l i b r i u m concept , these researchers develop a n u m e r i c a l procedure w h i c h enables t h e m to ca lculate the o p t i m a l produc t pos i t i on ( in m u l t i - d i m e n s i o n a l space) a n d price of a new entrant and o p t i m a l response prices of any n u m b e r of in cumbents . H o r s k y a n d Nelson (1989) also s tudy the o p t i m a l produc t p o s i t i o n i n g p r o b l e m us ing a vector m o d e l (vert i ca l d i f ferent iat ion) . L i k e C h o i et a l , the ir m a i n emphasis is the i n c o r p o r a t i o n of pr ice com-p e t i t i o n i n the search for an o p t i m a l p r o d u c t p o s i t i o n rather t h a n the charac ter i za t i on of the e q u i l i b r i u m so lu t i on . 2.2.5 S u m m a r y of L i t e r a t u r e R e v i e w T h e h o r i z o n t a l and ver t i ca l d i f ferent iat ion mode ls have generated a s igni f icant amount of research i n economics . T h e m a j o r i t y of th is research has been concerned w i t h a n a l y z i n g the e q u i h b r i u m i m p h c a t i o n s of var iat ions to the one d i m e n s i o n a l models w i t h k n o w n (and often un i f o rm) d i s t r i b u t i o n of consumers . T h e models of L a n e (1980), Economides (1986b) and N e v e n a n d Thisse (1988) represent the o n l y a t t empts e x t e n d the di f ferenti -a t i o n models to two d imens ions . Researchers i n m a r k e t i n g have v iewed the emphasis o n a one d i m e n s i o n a l product to be the most l i m i t i n g feature of th is s t ream of economics research. In response, most of the m a r k e t i n g models concerned w i t h p r o d u c t a n d pr ice c o m p e t i t i o n have inc luded m u l t i p l e p r o d u c t d imens ions . Because of the di f f i culty i n o b t a i n i n g closed form equi l ib -r i u m so lut ions i n these more complex env i ronments , researchers have rel ied on numer i ca l analys is (Hauser 1988; C h o i et a l 1990; H o r s k y and Nes lon 1989) or f unc t i ona l approx i -m a t i o n s ( C a r p e n t e r 1989) to augment the ir a n a l y t i c a l work. T h o u g h signif icant progress has been m a d e regard ing the i n c o r p o r a t i o n of c o m p e t i t i o n into p r i c i n g a n d product pos i -t i o n i n g models , research i n this area is s t i l l i n i ts ear ly stages. O f p a r t i c u l a r i m p o r t a n c e to current research is the fact t h a t , a l though models of m u l t i - d i m e n s i o n a l produc t markets have been developed, l i m i t i n g condit ions imposed by the authors have reduced the p r o d -uct dec is ion to a single d i m e n s i o n . T h u s , the i m p l i c a t i o n s of p r o d u c t ( rather t h a n price) c o m p e t i t i o n i n m u l t i - d i m e n s i o n a l produc t markets has not been adequate ly researched. 2.3 T h e M o d e l s T h r e e different models w i l l be ana lyzed , each i n c o r p o r a t i n g different p r o d u c t differen-t i a t i o n assumpt ions . T h o u g h there are s u b s t a n t i a l differences i n the m o d e l s tructures , there are s t rong s i m i l a r i t i e s i n the nature of the ir e q u i l i b r i u m so lut ions . 2.3.1 T w o - D i m e n s i o n a l V e r t i c a l Di f ferent iat ion M o d e l A s s u m p t i o n s T h e t w o - d i m e n s i o n a l v e r t i c a l d i f ferent iat ion m o d e l ana lyzed i n this paper is based on the f o l l owing assumpt ions : 1. T h e r e are 2 f i rms , i n d e x e d 1 and 2, who each choose one p r o d u c t to m a r k e t . P r o d -ucts are c o m p r i s e d of non-negat ive va luat ions on 2 character is t i cs , x a n d y. T h e character ist i cs are analogous to perceptua l d imensions or produc t a t t r ibutes and are assumed to be o r thogano l . T h u s , each f i rm's product is defined as a point {xi,yi), where Xi e [ x ^ m , x"^"''! and yi Ç [ y m m , 2 / " " " ' • 2. C o n s u m e r s are assumed to prefer more of each character is t i c to less. For e x a m -ple, persona l computers m a y be descr ibed on two d imensions l ike "power" and " p o r t a b i l i t y " i n w h i c h consumers always prefer more powerful a n d more por tab le computers h o l d i n g a l l other a t t r ibutes constant . It is assumed that price enters negat ive ly in to the consumer 's va luat i on equat i on . 3. C o n s u m e r s are able to observe product character ist i cs a n d prices before they make the ir purchase dec is ion . C o n s u m e r s ' reservat ion prices (R) for a p r o d u c t i n this market are h igh enough to ensure that a l l consumers buy. In a d d i t i o n each con-sumer is res t r i c ted to purchas ing one un i t — either f r o m f i r m 1 or f i r m 2. A t y p i c a l consumer 's v a l u a t i o n equat i on can be descr ibed by a s t a n d a r d i n d i v i d u a l level vec-tor m o d e l i n w h i c h u t i l i t y is expressed i n do l la r un i ts (Sr in ivasan 1982). C o n s u m e r heterogeneity is c a p t u r e d by two parameters 0 = (^1,^2)-U = R + e^Xi + Bzyi - Vi, for i = 1, 2. (2.1) where: p i is the pr ice of f i r m i ' s p roduc t T h e consumer w i l l choose the product f r o m the f i r m w h i c h m a x i m i z e s (2.1). 4. T h e parameters , 0 = {61,62), are assumed to be u n i f o r m l y d i s t r i b u t e d over the p o p u l a t i o n . S ince one character ist i c may, on average, be more i m p o r t a n t t h a n the other , the range of the parameter d i s t r i b u t i o n m a y be different for each char-acter is t i c . W i t h o u t loss of generality, b o t h of these ranges can be res tr i c ted to [0,1]. T h i s can be ac compl i shed by choosing the a p p r o p r i a t e scale for each of the character ist i cs {x,y). 5. P r o d u c t s are assumed to have a constant m a r g i n a l cost set, w i t h o u t loss of gen-eral i ty , to zero regardless of p r o d u c t p o s i t i o n . T h o u g h this s i t u a t i o n is obv ious ly u n r e a l i s t i c , the analys is is s ign i f i cant ly s impl i f i ed whi le r e t a i n i n g the strategic effects of p r o d u c t p o s i t i o n i n g . T h e pr i ce e q u i h b r i u m is unaffected by this a ssumpt i on . C o m p a r i s o n w i t h O t h e r M o d e l s T h e t w o - d i m e n s i o n a l ve r t i ca l d i f f erent iat ion m o d e l discussed i n this sect ion is designed to prov ide a direct extens ion of the o n e - d i m e n s i o n a l ve r t i ca l d i f ferent iat ion m o d e l . It is most s i m i l a r to the m o d e l presented by S h a k e d a n d S u t t o n (1982) because costs are assumed to be constant (equal) for a l l p r o d u c t pos i t i ons . Since the ma jor emphasis of this research is to assess the n a t u r e of c o m p e t i t i v e behav ior i n the presence of di f ferent d i f ferent iat ion assumpt ions , this r e d u c t i o n i n c o m p l e x i t y seems reasonable. A n obvious extens ion of the m o d e l w o u l d be to i n c o r p o r a t e pos i t ion-dependent var iable costs i n a m a n n e r s i m i l a r to M o o r t h y (1988). T h e m o d e l presented here is also qu i te s i m i l a r to Hauser (1988). B o t h models use two d imens ions to character ize the p r o d u c t space a n d assume that consumers have ho-mogeneous percept ions of the p r o d u c t s . Hauser assumes that percept ions can be ra t i o scaled a n d thus , s i m i l a r to the above m o d e l , h igher levels o n a per cep tua l a t t r i b u t e are always better . However , there are a n u m b e r of i m p o r t a n t differences. Hauser d iv ides the p r o d u c t s ' p e r c e p t u a l character is t i cs by pr i ce whereas pr ice enters i n a l inear fashion i n m y m o d e l . T h i s difference represents different methods of c o m p a r i n g prices between produc t s . Hauser ' s m o d e l assumes consumers compare re lat ive prices where m y m o d e l assumes consumers compare abso lute pr ice differences. E m p i r i c a l research by Hauser a n d U r b a n (1986) has shown that these two c r i t e r i a have per formed equal ly wel l i n assessing price response to durab les . C o n s u m e r s tastes i n Hauser ' s m o d e l are defined by one parameter , the angle between the consumer 's ( l inear) u t i l i t y curve a n d the h o r i z o n t a l axis i n per do l la r perceptua l space. In the t w o - d i m e n s i o n a l ver t i ca l d i f ferent iat ion m o d e l , two parameters , (^1,^2), are used to define consumer tastes. A n o t h e r notab le difference between Hauser ' s m o d e l and the one presented here has to do w i t h Hauser ' s quar ter c irc le a s s u m p t i o n i n w h i c h he imposes the r e s t r i c t i o n that feasible products must He o n the c ircumference of a quar ter circle i n s c r i b e d i n the pos i t ive q u a d r a n t . N o such p o s i t i o n i n g restr i c t ion is present i n the current m o d e l . M a n y of the same d i s t inc t i ons that are made between Hauser 's m o d e l a n d m y mode l can be extended to L a n e ' s m o d e l ( L a n e 1980). For a more complete descr ip t i on of the s imi lar i t i e s between L a n e (1980) and Hauser (1988), see K u m a r and S u d h a r s h a n (1988). D e f i n i n g the Indifference Surface for b o t h A s y m m e t r i c a n d D o m i n a t e d C h a r -acteristics C o m p e t i t i o n In the analys is of the v e r t i c a l d i f ferent iat ion m o d e l , there are two generic types of p r o d -uct p o s i t i o n i n g c o m p e t i t i o n : a s y m m e t r i c character is t i cs and d o m i n a t e d character is t i cs . Asymmetric characteristics competition is defined as c o m p e t i t i o n between firms when each firm has a re lat ive advantage o n one of the two characterist ics ( F i g u r e 2.1a). For example , i f the two character ist i cs w h i c h describe the personal computer m a r k e t are "ease of use" a n d " p o w e r " , A p p l e computers wou ld have a re lat ive advantage over I B M o n the "ease of use" d i m e n s i o n whi le I B M wou ld have the re lat ive advantage over A p p l e on the "power" d i m e n s i o n . Dominated characteristics competition is defined as c o m p e t i t i o n be-tween firms w h e n one firm has a relat ive advantage o n b o t h character ist ics ( F i g u r e 2.1b). T h i s s i t u a t i o n is typiccd of c o m p e t i t i o n between different "mode ls " of a s i m i l a r technol -ogy. C o m p e t i t i o n between X T , A T and 386 p e r s o n a l computers w o u l d be an example of a) Asymmetric Characteristics b) Dominated Characteristics F i g u r e 2.1: A l t e r n a t i v e P r o d u c t Pos i t i on ings d o m i n a t e d character ist ics c o m p e t i t i o n . For b o t h types of c o m p e t i t i o n , the re lat ive pos i t ions of the produc ts can be descr ibed by t a k i n g a ra t i o of the abso lute differences i n the charac ter i s t i c levels of the two products . T h e ra t i o (xi —X2)/{y2—yi) is equal to the tangent of the angle between the h o r i z o n t a l axis and a l ine f rom the o r i g i n p e r p e n d i c u l a r to a l ine j o i n i n g the two produc t s ( a i n F igures 2.1a, 2.1b). T h i s angle of competition i l lustrates the re lat ive p o s i t i o n i n g advantage of the firms a n d becomes i m p o r t a n t i n the d e t e r m i n a t i o n of the demands for each p r o d u c t . l t shou ld be noted that each angle represents the set of a l t e rnat ive p r o d u c t pos i t ionings that m a i n t a i n the same re lat ive separat ion . F i g u r e 2.2a provides a n example of a s y m m e t r i c character ist i cs c o m p e t i t i o n . W i t h o u t loss of general ity , i t is assumed that firm I 's p r o d u c t has the advantage on x and firm a) Characteristics Space b) Parameter Space (Pi = P2) Demand 2 Demand 1 1 0 . F i g u r e 2.2: R e l a t i o n s h i p Between C h a r a c t e r i s t i c s Space a n d P a r a m e t e r Space i n the T w o - d i m e n s i o n a l V e r t i c a l M o d e l w i t h A s y m m e t r i c C h a r a c t e r i s t i c s 2's p r o d u c t has the advantage o n y. C o n s u m e r s i n th i s market decide to purchase the p r o d u c t w h i c h m a x i m i z e s the i r u t i H t y as defined i n (2.1). T h i s c o m p a r i s o n leads to a set of consumers who are indi f ferent to choosing e i ther p r o d u c t . T h i s set is a l ine w h i c h intersects the set of consumer types . Consumers types above the indifference Une choose p r o d u c t 2 a n d consumers below the Une choose p r o d u c t 1. In x ^2 space, this indifference Une is defined as: ( y 2 - 2 / i ) ( y 2 - y i ) (2.2) T h e fact that th is indifference surface is a l ine is the po int of convergence for the ver-t i c a l d i f f erent iat ion , h o r i z o n t a l d i f ferent iat ion a n d m i x e d models . F i g u r e 2.2b i l lustrates this indifference l ine at equa l prices. T h e slope of this indifference l ine is the negative of the slope of the l ine connect ing the the two produc ts i n a; x y space. T h u s , the market share of each of the produc ts is dependent on the angle of c o m p e t i t i o n defined by the re l -ative produc t pos i t ions ( a i n F igures 2.2a and 2.2b). In a d d i t i o n , the terms [xi — X2) and (î/2 ^ Vi) p rov ide a measure of abso lute p r o d u c t d i f ferent iat ion . T h e difference between prices, P2—P1, shifts the indifference Hne up or down. F i r m s dev iate f rom equal prices to the extent that the ir respect ive p r o f i t a b i l i t y is increased. T h e d e m a n d for each product is defined by the area above (product 2) or below (product 1) the indifference l ine. Prof i ts are ca l cu la ted by m u l t i p l y i n g d e m a n d by pr ice a n d s u b t r a c t i n g by the (constant) var iable costs. T h e re la t i onsh ip between xxy space a n d 9i x 62 space ( v ia the angle of competition) c learly i l lus trates the advantage of a super ior produc t pos i t i on . In tu i t i ve ly , the des i rab i l -i t y of a f i rm's produc t is dependent on the re lat ive character ist i cs of the two products . If one produc t has more of x but b o t h p r o d u c t have v i r t u a l l y the same amount of y, i t would be expected t h a t , at equa l prices , this p r o d u c t w o u l d capture most of the market . Conversely , i f the each p r o d u c t h a d a p p r o x i m a t e l y equal abso lute p r o d u c t d i f ferent iat ion advantages o n the ir respect ive d o m i n a n t character is t i cs , at equal prices , they wou ld each o b t a i n a p p r o x i m a t e l y 5 0 % of the market . D o m i n a t e d character ist i cs c o m p e t i t i o n differs s l ight ly f r o m a s y m m e t r i c characterist ics c o m p e t i t i o n due to the presence of a super ior a n d an infer ior p r o d u c t ( F i g u r e 2.3a). W i t h o u t loss of general i ty , i t is assumed t h a t f i r m I 's p r o d u c t is the super ior produc t . A n a l y s i s proceeds i n the same manner as w i t h a s y m m e t r i c character is t i cs c o m p e t i t i o n . A s equat ion (2.2) ho lds , the slope of the indifference l ine is the negat ive of the slope of the Une connect ing the the two produc ts i n x x y space. T h e slope of the indifference hne a) Characteristics Space b) Parameter Space (Pi > P2) 0 . Demand 1 Demand 2 1 0 , F i g u r e 2.3: R e l a t i o n s h i p Between C h a r a c t e r i s t i c s Space a n d P a r a m e t e r Space i n the T w o - d i m e n s i o n a l V e r t i c a l M o d e l w i t h D o m i n a t e d Charac ter i s t i c s is negative, w i t h the angle of c o m p e t i t i o n be ing greater t h a n 90° ( F i g u r e 2.3b). A s w o u l d be expec ted , at equa l prices produc t 1 captures the entire m a r k e t . T h e r e must exist a lower price for the in fer ior p r o d u c t before any consumer w i l l purchase i t . T h i s is s i m i l a r to results o b t a i n e d us ing the one d i m e n s i o n a l v e r t i c a l d i f ferent iat ion m o d e l ( M o o r t h y 1988). 2.3.2 T w o - D i m e n s i o n a l H o r i z o n t a l Di f ferent iat ion M o d e l A s s u m p t i o n s T h e t w o - d i m e n s i o n a l h o r i z o n t a l d i f ferent iat ion m o d e l a n a l y z e d i n this paper is based on the f o l l owing assumpt i ons : 1. T h e r e are 2 f i rms , indexed 1 a n d 2, who each choose one p r o d u c t to market . P r o d -ucts are def ined b y the ir l o cat ions (non-negat ive va luat ions ) on 2 character ist ics , X and y. It is assumed that the ranges of b o t h character ist i cs is [0,1]. T h e char-acter ist ics are assumed to be o r t h o g a n o l a n d cont inuous w i t h i n the defined range. T h u s , each f i rm 's produc t is def ined as a po int (x, - ,yi ) , where Xi,yi G [0,1 . 2. C o n s u m e r s have idea l character i s t i c levels (x'jy'), where x'',y' G [0,1] and are. assumed to prefer products whose character is t i cs most closely m a t c h their idea l levels. F o r e x a m p l e , a f ood p r o d u c t can be defined by its level of sweetness. C o n -sumers have different op in ions o n the idea l level of sweetness such that two products w i t h different levels of sweetness w o u l d be preferred (at equal prices) by a non-zero group of consumers . It is assumed that pr ice enters negat ive ly in to the consumer 's v a l u a t i o n e q u a t i o n . 3. C o n s u m e r s are able to observe p r o d u c t character ist i cs a n d prices before they make the i r purchase dec is ion. C o n s u m e r s ' reservat ion prices {R) for a product i n this market are h i g h enough to ensure that a l l consumers buy. In a d d i t i o n each con-sumer is res t r i c ted to purchas ing one un i t — either f rom f i r m 1 or firm 2. A t y p i c a l consumer 's v a l u a t i o n equat i on can be descr ibed by a s t a n d a r d i n d i v i d u a l level i dea l po int m o d e l i n w h i c h u t i h t y is expressed i n do l lar un i ts ( S r i n i v a s a n 1982). C o n -sumer heterogeneity is c a p t u r e d the d i s t r i b u t i o n of i dea l po ints ( x ' , y " ) . U = R~{x' - Xi)' - {y' - yCf - P i for i = 1, 2. (2.3) where: p i is the pr i ce of f i r m i ' s p roduc t T h e consumer w i l l choose the product f r o m the f i r m w h i c h max imizes (2.3). 4. T h e consumer id e a l po ints , (x ' ,y " " ) , i d e a l po ints are assumed to be u n i f o r m l y dis-t r i b u t e d over b o t h character is t i cs . T h e u n i f o r m d i s t r i b u t i o n a s s u m p t i o n coupled w i t h the a s s u m p t i o n regard ing the range of the character ist i cs means that con-sumers value each charac ter i s t i c equal ly . T h o u g h this equa l v a l u a t i o n m a y be u n -real is t i c , the a n a l y t i c a l results der ived i n the analys is sect ion are not s t r u c t u r a l l y affected. 5. A s i n the ver t i ca l d i f ferent iat ion m o d e l descr ibed above, produc ts are assumed to have a constant m a r g i n a l cost regardless of p r o d u c t p o s i t i o n . C o m p a r i s o n w i t h O t h e r M o d e l s A s was o u t l i n e d i n the l i t e r a t u r e rev iew, the h o r i z o n t a l m o d e l is very sensit ive to the choice of the d istance f u n c t i o n (Economides 1986a). T h e t w o - d i m e n s i o n a l hor i zonta l d i f ferent iat ion m o d e l descr ibed here uses a q u a d r a t i c d is tance f u n c t i o n . T h i s funct ion is different t h a n the hnear f u n c t i o n used i n the t w o - d i m e n s i o n a l v e r t i c a l d i f ferent iat ion m o d e l a n d the l inear m o d e l proposed by H o t e l l i n g . T h e q u a d r a t i c d is tance funct ion was chosen to con form w i t h i dea l point models w h i c h are c o m m o n i n the m a r k e t i n g l i t e r a t u r e (e. g. G a v i s h , H o r s k y a n d S r i k a n t h 1983; C h o i , D e S a r b o a n d H a r k e r 1990, G r e e n a n d S r i n i v a s a n 1978). T h e m o d e l is a direct extens ion of the one -d imens iona l m o d e l a n a l y z e d by d ' A s p r e m o n t et a l (1979). These researchers used a q u a d r a t i c t e rm i n order to e l i m i n a t e a non-existence p r o b l e m w i t h the o r i g i n a l H o t e U i n g f o r m u l a t i o n . T h e extension of Hote l l ing ' s (1929) mode l to two d imensions is left for future research. T h e models by Economides (1986b) a n d C a r p e n t e r (1989) represent a l ternat ive two-d i m e n s i o n a l h o r i z o n t a l d i f ferent iat ion models . E c o n o m i d e s uses a c i r cu lar market to ana lyze the two -d imens iona l case. He assumes that a consumer whose idea l point is i d e n t i c a l to a product l o ca t i on w i l l be the last consumer to choose the a l ternat ive product as prices increase. T h e resu l t ing set of consumers who are indif ferent between the two produc t s is defined by a h y p e r b o l a . T h e m o d e l descr ibed here (defined by (2.3)) indicates that a consumer whose idea l po int is i d e n t i c a l to a p r o d u c t pos i t i on w i l l not choose his i dea l p roduc t i f the price is too h i g h re lat ive to the c o m p e t i t i o n . T h e indifference surface i n the current m o d e l is a l ine a n d the d istance f u n c t i o n meets E c o n o m i d e s ' c o n d i t i o n for-c o n t i n u i t y of the d e m a n d a n d profit funct ions . T h e purpose of C a r p e n t e r ' s m o d e l is s u b s t a n t i a l l y different t h a n the m o d e l ana lyzed here. Instead of seeking closed f o rm e q u i U b r i u m solut ions to b o t h produc t and p r i c i n g decisions, C a r p e n t e r analyzes a n u m b e r of scenarios to show how firms can repos i t ion to increase prof its . In a d d i t i o n , he analyzes the s i t u a t i o n where firms can compete w i t h the f u l l m a r k e t i n g m i x . T h e m a j o r s t r u c t u r a l difference between C a r p e n t e r ' s m o d e l a n d the one ana lyzed here is C a r p e n t e r ' s a s s u m p t i o n that a consumer w i l l o n l y consider purchas ing a product i f i t is w i t h i n a specified distance , D^ax f r o m that consumer 's i dea l po int Umits the strategic effect of pr ice . P r i c e w i l l enter i n t o the consumer 's decis ion process o n l y w h e n there are two products w i t h i n Dmax of the his i dea l po in t . I n a d d i t i o n . C a r p e n t e r uses a u n i m o d a l d i s t r i b u t i o n of idea l po ints i n the a l lowable p r o d u c t space whereas a u n i f o r m d i s t r i b u t i o n is assumed here. D e f i n i n g the Indifference Surface U s i n g the t e rmino logy i n t r o d u c e d w i t h the t w o - d i m e n s i o n a l ve r t i ca l d i f ferent iat ion mode l , a l l i n i t i a l conf igurat ions of p roduc ts can be represented by e i ther a s y m m e t r i c or d o m i -nated character is t i cs c o m p e t i t i o n . To fac ihtate compar isons between models , a s y m m e t r i c character ist ics c o m p e t i t i o n w i l l be mode led . Since it is ne i ther an advantage nor a d i sad -vantage to have " m o r e " of a specific charac ter i s t i c , the scales of the character is t i cs ' axes a n d f i r m indexes can be ad jus ted ( w i t h o u t loss of generahty) such that f i rm I's product has the greater l o c a t i o n a l value o n x a n d f i r m 2's p r o d u c t has the greater l o c a t i o n a l value on y. T h i s m a n n e r of represent ing produc ts i n j o in t ( p roduc t a n d consumer) space allows for easy c o m p a r i s o n of results w i t h the t w o - d i m e n s i o n a l v e r t i c a l m o d e l a n d the m i x e d m o d e l . F i g u r e 2.4 provides a n example of p roduc t s represented i n j o in t space. Consumers choose the p r o d u c t w h i c h m a x i m i z e s the i r u t i l i t y as def ined i n (2.3). T h i s compar ison leads to a set of consumers w h i c h are indif ferent to choos ing e i ther produc t . A s w i t h the ver t i ca l d i f ferent iat ion m o d e l , this set is defined by a Une w h i c h div ides the j o in t space. Consumers w i t h i d e a l po in ts above the indifference Une choose p r o d u c t 2 a n d consumers below the l ine choose p r o d u c t 1. T h e indifference l ine is defined as: _ {P2 - Pi) + jxl - xl) - {yl ~ yl) x'{x,-X2) F i g u r e 2.4 i l lus trates th i s indifference Une at equa l prices . T h e slope of this indifference Une is the negative of the slope of the Une connec t ing the the two produc t s i n j o in t space. T h u s , the market share of each of the p r o d u c t s is dependent on the angle of c o m p e t i t i o n (a ) defined by the re lat ive p r o d u c t pos i t i ons . However , u n l i k e the ver t i ca l diflPerentiation m o d e l , market share is dependent on absolute ra ther t h a n re lat ive produc t pos i t ions . y 1 1 X F i g u r e 2.4: J o i n t Space R e p r e s e n t a t i o n of the T w o - D i m e n s i o n a l H o r i z o n t a l Di f ferent ia -t i o n M o d e l T h i s is ev idenced by the express ion ( x j - X j ) - [yj - yl) i n (2.4). A s was the case w i t h the v e r t i c a l d i f ferent iat ion m o d e l , the difference between prices , p2 — Pi, shifts the indif ference l ine up or d o w n w i t h f irms d e v i a t i n g f rom equal prices to the extent that the ir respect ive p r o f i t a b i l i t y is increased. T h e d e m a n d for each p r o d u c t is defined by the area above (produc t 2) or below (product 1) the indifference l ine . Pro f i ts are ca l cu lated by m u l t i p l y i n g d e m a n d by price a n d s u b t r a c t i n g the (constant) var iab le costs. 2.3.3 M i x e d V e r t i c a l - H o r i z o n t a l Di f ferentiat ion M o d e l A s s u m p t i o n s T h e m i x e d m o d e l a n a l y z e d i n this paper is based on the fo l lowing assumpt ions : 1. A s i n the p r e v i o u s l y defined models , there are 2 firms, i n d e x e d 1 a n d 2, who each choose one p r o d u c t to m a r k e t . P r o d u c t s are defined by t h e i r non-negat ive va lua -t ions on 2 character i s t i cs , x a n d y. It is assumed that the character i s t i c x exhib i ts h o r i z o n t a l d i f ferent iat ion a n d thus (as above) has a range of [0,1]. T h e y character-ist ic is assumed to exh ib i t ve r t i ca l d i f ferent iat ion. T h e character is t i cs are assumed to be o r thogano l . T h u s , each firm's produc t is defined as a po int ( x i , y i ) , where Xi G [0,1] a n d yi £ [ y m m . Z / ' " " " ] . 2. C o n s u m e r s have an idea l level of character is t i c x, x' G [0,1], a n d are assumed are assumed to prefer more of character i s t i c y to less'. It is assumed that price enters negat ive ly i n t o the consumer 's v a l u a t i o n equat ion . 3. C o n s u m e r s are able to observe produc t character ist ics a n d prices before they make the ir purchase decis ion. C o n s u m e r s ' reservation prices (R) for a product i n this market are h i g h enough to ensure that a l l consumers buy. In a d d i t i o n each consumer is restr i c ted to purchas ing one un i t — e i ther f rom firm 1 or firm 2. W h e n u t i l i t y is expressed i n do l la r u n i t s , a t y p i c a l consumer ' s v a l u a t i o n equat i on can be described by: U = R - { x ' - XiY+ eyi-p,, f o r i = 1,2. (2.5) where: pi is the pr ice of firm i ' s p roduc t T h e consumer w i l l choose the product f r o m the firm w h i c h m a x i m i z e s (2.5). 4. T h e consumer id e a l levels of x, ( x " ) , are assumed to be u n i f o r m l y d i s t r i b u t e d over 0,1] . T h e parameter , 9, is assumed to be u n i f o r m l y d i s t r i b u t e d over the populat ion . -W i t h o u t loss of general i ty , the range of d c an be restr i c ted to [0,1]. T h i s can be' a c comphshed by choosing the appropr ia te scale for the character i s t i c y. 5. A s i n the models descr ibed above, products are assumed to have a constant m a r g i n a l cost regardless of p r o d u c t pos i t i on . C o m p a r i s o n w i t h O t h e r M o d e l s T h e m i x e d m o d e l defined here represents a c o m b i n a t i o n of the one -d imens iona l models of D ' A s p r e m o n t et a l (1979) a n d Shaked a n d S u t t o n (1982). A s i d e f rom differences i n terminology , the m o d e l is i d e n t i c a l to the m o d e l a n a l y z e d by N e v e n a n d Th isse (1988). T h e m o d e l is re -ana lyzed i n this research to d e m o n s t r a t e the general i ty of e q u i l i b r i u m results under different d i f ferent iat ion assumpt ions . D e f i n i n g the Indifference Surface S i m i l a r to the t w o - d i m e n s i o n a l h o r i z o n t a l d i f f erent iat ion m o d e l , a l l i n i t i a l conf igurations of p roduc ts can be represented by a s y m m e t r i c character is t i cs c o m p e t i t i o n . W i t h o u t loss of general i ty , the scales of the charac ter i s t i c s ' axes a n d firm indexes can be ad justed such t h a t firm I's p r o d u c t has the greater l o c a t i o n a l va lue o n x and firm 2's product has the p o s i t i o n i n g advantage o n y. T h i s representat ion of the products fac i l i tates compar i son of results between the three mode l s . O n e of the issues i n the ana lys i s of the m i x e d m o d e l concerns the cognit ive task requ i red by consumers to de te rmine the i r m a x i m u m u t i l i t y . Consumers must use two separate cognit ive strategies to evaluate the p r o d u c t s : d is tance f r o m idea l character is t i c level as wel l as p r o d u c t of the i r wi l l ingness to pay a n d ver t i ca l character is t i c levels. It is l i k e l y that consumers a n a l y z e b o t h character is t i cs us ing the same heur is t i c by t rans -f o r m i n g one of the charac ter i s t i c s . A n e x a m p l e i n the sp i r i t of Hauser and G a s k i n (1984) w o u l d be the t r a n s f o r m a t i o n of sweetness, a h o r i z o n t a l character i s t i c , to right amount of sweetness, a v e r t i c a l charac ter i s t i c . For the purposes of the current analys is , i t is as-s u m e d that the def ined c o m p e n s a t o r y m o d e l a c cura te ly represents the consumer decision m a k i n g process even i f the a c t u a l process is qu i te different ( G r e e n a n d Sr in ivasan 1978). In the m i x e d m o d e l descr ibed here, consumers choose the p r o d u c t w h i c h max imizes the i r u t i U t y as defined i n (2.5). F i g u r e 2.5 provides a representat ion of the indifference l ine w h i c h represents the set of consumers who are indif ferent to choosing either produc t . C o n s u m e r s types ( idea l l eve l of x, a n d taste parameter , 9) above the indifference Une choose produc t 2 and consumers be low the l ine choose p r o d u c t 1. T h e indifference hne is defined as: F i g u r e 2.5: R e p r e s e n t a t i o n of the Indifference L i n e i n the M i x e d V e r t i c a l - H o r i z o n t a l D i f f e rent ia t i on M o d e l U n l i k e the ver t i ca l a n d h o r i z o n t a l mode ls , the slope of this indif ference l ine for the m i x e d m o d e l represented i n F i g u r e 2.5 does not equa l the negative of the slope of the l ine connect ing the the two produc t s i n p r o d u c t space. However , the market share of each of the products is s t i l l dependent on the re lat ive p r o d u c t pos i t i ons . T h e angle of c o m p e t i t i o n , the angle created by v e r t i c a l axis and the l ine j o i n i n g the two products i n p r o d u c t space ( 7 i n F i g u r e 2 . 6 ) , is 1/2 the size of the angle between the indifference hne a n d the h o r i z o n t a l axis i n the space def ining consumer types ( a i n F i g u r e 2.5). T h i s different i n t e r p r e t a t i o n of the m i x e d m o d e l is the result of the presence of one rather t h a n two (or no) q u a d r a t i c expressions i n the consumers ' u t i l i t y funct ions . In a l l other respects, the m i x e d m o d e l behaves i n a s i m i l a r m a n n e r to the h o r i z o n t a l a n d ver t i ca l d i f ferent iat ion models . 2.3.4 G e n e r a l F o r m of the Indifference L i n e For the three models , equat ions (2.2), (2.4) , a n d (2 . 6 ) define the indif ference Unes i n the spaces w h i c h defines consumer types. Essent ia l ly , c o m p e t i t i o n between the two firms adjusts the l o c a t i o n of the indifference Une w i t h the r e s u l t i n g l o c a t i o n d e t e r m i n i n g the market share for each firm. A l l three indif ference l ines have the f o l l owing general f o rm: FiG) = iELUPpJ. + t^G (2.7) mo 0 where: firm i ' s p r o d u c t is (a i ,6 j ) a = ( a i - a j ) y F i g u r e 2.6: Charac ter i s t i c s Space Representa t i on of the M i x e d V e r t i c a l - H o r i z o n t a l D i f -f erent iat ion M o d e l k,m are parameters 0 for v e r t i c a l m o d e l 3 = {al — al) + (fcj — bl) for h o r i z o n t a l m o d e l (al — al) for m i x e d m o d e l T h e variables F a n d G are i n t r o d u c e d i n (2.7) for purposes of generality.^ D e p e n d i n g on the m o d e l under c ons idera t i on , these variables represent y', x', 0, 9i or 62 (see (2.2), (2.4), (2.6)). A s s u m i n g asymmetric characteristics competition, the indifference l ine is pos i t ive ly s loped w i t h angle a = tan~^{^). W h e n produc t pos i t ions are fixed, the indifference l ine is shi f ted u p or d o w n w i t h changes i n (p2 — P i ) These shifts alter the d e m a n d (and prof i ts ) for each firm. T h e d e m a n d effects of price changes w i l l be a n a l y z e d f r o m the perspect ive of firm 1. T h u s , p2 w i l l be t a k e n as g iven (denoted P2). Ana lys i s -under taken f rom the perspect ive of firm 2 w o u l d y i e l d p a r a l l e l results . G i v e n P 2 , four key pr ice levels for firm 1 can be defined. p[ is defined as the highest price at w h i c h a l l consumers purchase f r o m firm 1. T h i s occurs when the indifference hne passes t h r o u g h (0,1) i n F i g u r e 2.7. p " is defined as the lowest price at w h i c h no consumers are w i l l i n g to purchase f r o m firm 1. A t th is pr i ce , the indifference l ine passes t h r o u g h (1,0). T h e two r e m a i n i n g key pr ice levels , p " a n d p^*, occur w h e n the indifference l ine passes t h r o u g h (0,0) a n d (1,1) respect ively . A t each of these two prices, one of the most extreme consumer types is indif ferent between the two produc t s . These prices also define levels at w h i c h the shape of the d e m a n d funct ions change. A s firm 1 decreases its pr i ce f rom p " , two d i s t i n c t cases arise depending on the size of a. Characteristic x dominance occurs when a > 45°. T h i s occurs when ka > b. For b o t h ver t i ca l a n d h o r i z o n t a l d i f ferent iat ion , th is means that the absolute product ^Note the definitions of a and b. a is defined by subtracting firm 2's characteristic level from firm I's level whereas b is defined in the reverse fashion with firm I's characteristic level being subtracted from firm 2's level. Under asymmetric characteristics competition, both a and b are positive. F i g u r e 2.7: L o c a t i o n of the Indifference L i n e at B o u n d a r y Levels of p j (given P2) di f ferent iat ion on character i s t i c x, ( a i — 0 3 ) , is greater t h a n or equa l to the absolute p r o d u c t d i f ferent iat ion o n character i s t i c y, (62 — ^ i ) - For the m i x e d m o d e l , 2{a\ — 02) > (62 — bi). W h e n Characteristic x dominance ho lds , p[ < p " < PT* < P i - T h a t is , the indifference l ine passes t h r o u g h (1,1) i n the space de f in ing consumer types before it passes t h r o u g h (0,0) w h e n prices are decreased f r o m p" . W h e n a < 45°, Characteristic y dominance holds a n d p[ < P^ < Pi < p"- T h i s a l t e rnat ive order ing of key prices has a n i m p a c t on the pr ice e q u i l i b r i u m ca lcu lat ions . Therefore , the Characteristic x dominance a n d Characteristic y dominance cases are ana lyzed separately. Note that the case w h e n ne i ther character i s t i c dominates , a = 45°, can be represented by e i ther type of d o m i n a n c e . W h e n a = 0° or 90°, the produc t choice reduces to one d imens ion . 2.4 A G e n e r a l i z e d P r i c e E q u i l i b r i u m T h e r e are a number of approaches open to the analys is of p roduc t design and price c o m p e t i t i o n i n the env i ronment descr ibed i n the previous sect ion (see M o o r t h y 1985, T i r o l e 1988 for reviews) . T h i s paper w i l l a n a l y z e a sequent ia l game i n w h i c h firms first choose the ir p r o d u c t character ist i cs a n d subsequent ly choose the i r pr ice . In this approach , the subgame-perfectness c r i t e r i o n is used. A subgame perfect e q u i l i b r i u m consists of a produc t choice for each of f i r m 1 a n d 2 such that ne i ther f i r m w o u l d choose a different produc t un i la te ra l l y , recogniz ing t h a t the p r o f i t a b i l i t y of a l l p r o d u c t selections w i l l be de termined o n the basis of the pr i ce e q u i l i b r i u m that follows ( M o o r t h y 1985). T h e analysis procedure proceeds by backwards i n d u c t i o n . T h e pr i ce e q u i h b r i u m wiU be ana lyzed first fol lowed by the product choice e q u i l i b r i u m . ^ ^The following analysis describes the price equilibria. In some instances, second order conditions are calculated to show that they are satisfied. In all other instances, second order conditions have been analyzed by inspection. T h e pr ice e q u i l i b r i u m under Characteristic x dominance w i l l be a n a l y z e d before Char-acteristic y dominance. 2,4.1 C h a r a c t e r i s t i c x D o m i n a n c e D e m a n d A n a l y s i s In each of the models descr ibed above, the parameter space def ining the consumers consists of a uni t square of u n i f o r m density . To assess the d e m a n d of firm 1 as a func t i on of pi (g iven P 2 ) , the 4 key prices o u t h n e d i n the previous sect ion must be specif ied. A t p j , the lowest price at w h i c h no consumers are wi lUng to purchase f rom firm 1, the indifference Hne passes t h r o u g h (1 ,0 ) (see F i g u r e 2.7). T h e f u n c t i o n a l f orm of p " can b e found by s u b s t i t u t i n g 1 a n d 0 for G a n d F respect ive ly i n (2.7). T h i s yields Pi=P2+J + mka (2.8) S i m i l a r subs t i tu t i ons for p î " , p " a n d p[ result i n the fo l lowing equations : p ^ = P2 + j + mka - mb (2.9) Pi=P2+j (2.10) p[=p2+j-mb (2.11) A U of these prices are increas ing i n p 2 . W h e n the terms appear , the price equat ions are also increas ing i n a and decreasing i n 6. I n d i r e c t l y this impl i es that the prices are increas ing i n a. T h a t i s , the greater firm I 's re lat ive p o s i t i o n i n g advantage over firm 2, the h igher the pr ice firm 1 is able to charge to generate a s i m i l a r d e m a n d level . I n t u i t i o n suppor ts this f i n d i n g as one w o u l d expect that a p o s i t i o n i n g advantage shou ld lead to less rehance on p r i c i n g to generate d e m a n d . It is interest ing to note that the density f u n c t i o n of consumer types does not influence these price re lat ionships . p[ a n d p " can be considered to be the lower and upper bounds o n the prices that f i rm 1 w i l l charge for i ts p r o d u c t g iven p2 as i t wou ld not be o p t i m a l to charge a price outs ide of th i s range. A s f i r m 1 decreases its price f rom p " , the indifference Une shifts u p w a r d . T h r e e d i s t inc t d e m a n d regions can be defined on the basis the geometr ic s t ruc ture of the m o d e l . These regions correspond to the rate of change i n d e m a n d for a un i t shift i n price (see F i g u r e 2.8). I n region Rl, d e m a n d for firm 1 increases (as a f u n c t i o n of prices) at an increas ing rate . T h i s region is defined by the pr ice range < Pi < p"• In Rl, where Pi ^ Pi ^ P i * ' d e m a n d for firm 1 increases at a constant rate . F i n a l l y , i n Rl, where P i ^ P i ^ P i ) the d e m a n d for firm 1 increases at a decreasing rate.^ I n Rl, the possible prices that can be charged by firm 1 can be v iewed as a c o n t i n u u m f r o m p " to p ^ . Let Zi represent the p r o p o r t i o n of the distance p i is f r o m the p " end of the c o n t i n u u m . A t p i = p " , 2 i = 0 a n d at p i ~ PT>'^I — 1- the space def ining the consumer types , z i represents the d istance f rom the h o r i z o n t a l axis to the po int where the indifference l ine meets the r ight side of the " square" of consumer types (see F i g u r e 2.9). M a t h e m a t i c a U y Zi is defined as follows: Pi - Pi P2-P1+J + mka - - mb ^'-''^ T h e d e m a n d for firm 1 in Rl, Dl, is the t r iang le f o rmed by the indifference l ine and the edges of consumer types (see F i g u r e 2.9). In this t r iang le , the angle a is k n o w n as weU as the height of the t r iang le ( z i ) . T h e f o rmula for the area of a t r iang le , A = |:(base)(height), •'Firm 2's rate of change in demand in these regions is the compliment to firm 1 since Demand2 + Demandi = 1. Indifference Line F i g u r e 2.9: D e t e r m i n a t i o n o f D e m a n d i n R. is used to ca lcu late D } . Since c o t a = ^^^^i - ^ i c an be def ined as 1/ 2^ c o t a Pi - Pi + 3 + mka mb cot a I (2.13) F r o m (2.13), i t can be seen that d e m a n d depends on b o t h prices a n d p r o d u c t pos i t ions . In iî^, let Z2 represents the l o c a t i o n of p i on the pr i ce c o n t i n u u m f r o m -p^ to p " . In the space def ining the consumer types , 22 is the p r o p o r t i o n of the d i s tance f rom (1,1) to the point where the indifference l ine at p i =: p " meets the top edge of the consumer types (see F i g u r e 2.10). D e m a n d for firm 1 i n this region, D\, is the m a x i m u m area of R\ p lus the relevant p r o p o r t i o n of T h e equat ions for 22 a n d D\ are: 22 = PT* — PI P2 — PI + 3 — + mka PT-PI mka — mb (2.14) Z?J = - cot a + 1 + P2 - P i + j mka — mb (1 - c o t a ) (2.15) T h e procedures used to ca l cu late the d e m a n d i n the other regions a p p l y to Rl as wel l . Let Z3 represents the l o c a t i o n of p i o n the price c o n t i n u u m f r o m p " to p[. In the space def ining the consumer types , 23 is the p r o p o r t i o n of the d i s tance f r o m the po int where the indifference l i n e at p i = p " meets the left edge of the consumer types to (0,1) (see F i g u r e 2.11). D e m a n d for f i r m 1 i n this r eg i on ,D^ , the mcLximum area of R], a n d Rl p lus the relevant p r o p o r t i o n of Rl- T h e equat ions for 23 a n d Df are: F i g u r e 2.10: D e t e r m i n a t i o n of D e m a n d i n Rl Figure 2.11: Determination of Demand in Rl ^ PÎ -Pi ^ P2-P1+ J ^ Pi - P[ rnh (2.16) = l - - c o t a + -P2-P1+] mb cot a (2.17) P r i c e E q u i l i b r i a C o m b i n i n g equat ions (2.13) , (2.15) a n d (2.17), the d e m a n d for firm 1 as a funct i on of p i can be d e t e r m i n e d . Since i t is assumed t h a t a l l consumers buy, the d e m a n d for firm 2 is s i m p l y I — Di. B o t h of these curves are shown i n F i g u r e 2.12. E a c h d e m a n d curve is c ompr i sed of a convex, l inear a n d concave segment ( corresponding to the regions defined above) . There fore , one of three possible pr i ce e q u i U b r i a m a y result under character is t i c x d o m i n a n c e . These e q u i l i b r i a w i l l be denoted by the price regions i n w h i c h the e q u i l i b r i a l ie : ' ' s t r i c t l y convex segment of firm I 's d e m a n d c u r v e - s t r i c t l y concave segment of firm 2's d e m a n d curve [R].)] Hnear segments of firm I's a n d firm 2's d e m a n d curves [R].)] a n d , s t r i c t l y concave segment of firm I 's d e m a n d c u r v e - s t r i c t l y convex segment of firm 2's d e m a n d curve (i?^). S ince costs are assumed to be constant (and zero) regardless of p o s i t i o n , the profit f u n c t i o n for firm i [i — 1,2) is defined as 'U.i[pi,pj) = piDi{pi,pj) for i 7^  j. A noncoop-erat ive (or N a s h ) price e q u i l i b r i u m is a p a i r of prices ( p - , P j ) such t h a t : Uiiplp-) > Ui{pi,p;), V P i > 0; i,j = 1,2 ; a n d , i / j A n a l y s i s of the pr i ce e q u i l i b r i a w i l l proceed by cons ider ing each of the regions s t a r t i n g w i t h region 2. T h e m a t h e m a t i c a l proofs are conta ined i n A p p e n d i x A . In Rl, the d e m a n d ••An analysis from the perspective of firm 2 shows that the same regions apply for both firms. F i g u r e 2.12: D e m a n d as a F u n c t i o n of p i (given P2) U n d e r C h a r a c t e r i s t i c x D o m i n a n c e equat ions for the two firms are l inear i n prices. T h i s results i n profit funct ions for the two firms w h i c h are q u a d r a t i c i n prices a n d first order condit ions of the profit functions w h i c h are l inear i n prices . T h e first order condit ions of the profit funct ions have a single s o l u t i o n g iven by: . ^mka -mb + 2j Pi = â {^•^^) _ 2mka + mb- 2j ^ P2 - S (^-19) S ince the first order cond i t i ons are necessary, these prices are the price e q u i l i b r i u m prices prov ide they be long to the intervals def ining These intervals are: Pl^\Pl{P'2),PTiP'2) a n d p'2e\p^{pl),pT{pl) These restr i c t ions y i e l d two condit ions w h i c h must be satisf ied for equations (2.18) a n d (2.19) to represent the pr i ce e q u i h b r i u m i n Rl. F i r s t , pl > ^"(pâ) (^ •s g iven by e q u a t i o n 2.10) is satisf ied w h e n : mka — mb > j (A) Second, pl < p^{pl) (as g iven by equat ion 2.9) is satisf ied when : 2{mb~mka)<j (B) B y re f o rmula t ing the p r i c i n g equat ions , it can be shown that p^ G [P2{Pi)>P?iPl)] o n l y w h e n b o t h condi t ions ( A ) a n d ( B ) are satisf ied. In region R^, the d e m a n d equat ions for the two firms are q u a d r a t i c i n prices. T h i s results i n profit funct ions for the two firms w h i c h are cubic i n prices. T h e first order c o n d i t i o n for firm I's profit f u n c t i o n is a q u a d r a t i c i n pi. T h i s equat i on can be factored in to the fo l lowing two roots : Pi=P2+j + mka (2.20) a n d Pl = P2+ j + rnka (2.21) T h e root defined i n (2.20) is equa l to equat ion (2.8), the price at w h i c h d e m a n d equals zero. Therefore the second root is used i n the e q u i h b r i u m c a l c u l a t i o n . S u b s t i t u t i n g (2.21) into the first order c o n d i t i o n of firm 2 y ie lds : g + P 2 ( 5 i + ^mka) + [j + mkaf - -m'kab = 0 (2.22) T h e f u n c t i o n def ined i n (2.22) is q u a d r a t i c i n p2- T h e larger of the two roots max imizes 112 — 0 o i i l y for the larger root ) . S o l v i n g for this root a n d s u b s t i t u t i n g this value of p2 in to (2.21) y ie lds the fo l lowing pr ice e q u i l i b r i u m : j -f- mka + J{j + mkaY + Sm^kab PI = ^ (2.23) —5?' — 5mka + + mkaV + Sm^kab P2 = — (2.24) T h e pr ice e q u i l i b r i u m i n region R\ def ined by (2.23) and (2.24) is va l id prov ided > vTiPi) Pi ^ PTiVi)- These inequaht ies are satisfied when c o n d i t i o n ( B ) is v i o l a t e d or ho lds w i t h equahty. C o n d i t i o n ( A ) w i l l cont inue to ho ld as w i l l character is t i c X d o m i n a n c e . N o t i c e that w h e n c o n d i t i o n ( B ) holds w i t h equahty, pl = p\ and p^ = p^.^ T h i s ind i cates t h a t e q u i l i b r i u m prices move cont inuous ly when parameters change such that the e q u i h b r i u m moves f r o m region R?^ to R\. In region R^., the first order condi t ions o f the profit funct ions are quadrat i c i n prices. T h e pr ice e q u i l i b r i u m is not easi ly der ived i n this region as ne i ther of the first order condi t ions factor i n t o s imple f u n c t i o n a l forms. T h e exact so lut i on has not been ca l cu la ted as i t is not r e q u i r e d for the d e t e r m i n a t i o n of the p r o d u c t e q u i l i b r i u m solut ions. T h i s is due to the a r b i t r a r y choice of f i r m numbers . R e g i o n R]. f r o m the perspect ive of f i r m 2 is i d e n t i c a l to reg ion R]. f r o m the perspect ive of firm 1. ' ^Note the equilibrium price notation. In region R\, equilibrium prices are denoted by an asterisk (') whereas in region R)., equilibrium prices are denoted by a star (*). As defined below, the price equilibrium in region iZ^ is denoted by a double asterisk ("'). 2.4.2 C h a r a c t e r i s t i c y D o m i n a n c e D e m a n d A n a l y s i s T h e assessment of d e m a n d under character is t i c y d o m i n a n c e proceeds i n m u c h the same m a n n e r as the analysis for character i s t i c x dominance . U n d e r character i s t i c y dominance , the angle of c o m p e t i t i o n ( a ) is less t h a n 45° (see F i g u r e 2.13). T h i s impl i es that k{ai — <^2) ^ (^2 — ^ i ) - T h e same pr ice equations h o l d (equations 2.8-2.11) but now P l > P l > P l > P l since as f i r m 1 decreases its price f r o m p " (given P2), the indifference l ine passes t h r o u g h the o r i g i n before it passes t h r o u g h po int (1 , 1). U s i n g the same procedure as o u t l i n e d under character i s t i c x dominance , d e m a n d i n each of the regions can be defined as a f u n c t i o n of prices a n d a. I n Ry, the possible prices that can be charged by f i r m 1 can be v iewed as a c o n t i n u u m f rom Pl to p " . L e t 24 represent the p r o p o r t i o n of the d istance p i is f r o m the p " end of the c o n t i n u u m . A t p i = p " , z = 0 a n d at p i = p " , Z 4 = 1. In the space def ining the consumer types , 24 represents the distance f r o m the (1 , 0) to the po in t where the indif ference l ine meets the h o r i z o n t a l axis i n the " square " of consumer types (see F i g u r e 2.14). M a t h e m a t i c a l l y Z4 is defined as fol lows: P i - P i ^ ' T h e d e m a n d for f i r m \\n R}^, D\, is the t r iang le f ormed by the indi f ference hne a n d the edges of consumer types. U s i n g the fact that t a n a = ^ L ^ ^ ^ ^ a n d Z4 = base, D a s e F i g u r e 2.13: T h r e e D e m a n d Regions U n d e r C h a r a c t e r i s t i c y D o m i n a n c e ^ ( 2 4 ) ^ t a n a v mka t a n a (2.26) / In a s i m i l a r m a n n e r , the d e m a n d for f i r m 1 i n a n d can be ca l cu lated . T h e resu l t ing d e m a n d equat ions are: = - t a n a + ' P 2 - P l + ^mb — mka J (1 — t a n a) (2.27) Di = l--tana + -1 ( P2 — Pl + j + + mka ^ mka t a n a (2.28) P r i c e E q u i l i b r i a E q u a t i o n s (2.26), (2.27) a n d (2.28) define the d e m a n d for f i r m 1 as a func t i on of p i . T h e d e m a n d for f i r m 2 is s i m p l y 1 — Di. These d e m a n d curves have the same shape a n d properties of the d e m a n d curves defined under charac ter i s t i c x dominance (see F i g u r e 2.12). T h e d e t e r m i n a t i o n of the price e q u i h b r i u m proceeds i n the same manner as well . . T h e m a t h e m a t i c a l proofs are conta ined i n A p p e n d i x A . Since costs are assumed to be zero regardless of p o s i t i o n , the profit f u n c t i o n for f i r m i [i ~ 1,2) is defined as U.i[pi,pj) — PiDi{pi,pj) for z / j . A noncooperat ive price e q u i l i b r i u m is a p a i r of prices (p,-,p]) such that : n . ( p : , p * ) > n . ( p i , p ; ) , V p i > 0 ; i , j = l , 2 ; a n d , i ^ j In Ry, the d e m a n d equat ions for the two firms are l inear i n prices. T h e first order condi t ions of the profit funct ions have a single s o l u t i o n g iven by: p- = 4 m b - mka - 2j ^^.30) Since the first order condi t ions are necessary, these prices are the price e q u i h b r i u m prices prov ide they be long to the intervals def in ing Ry. These intervals are: Pi' e [pTip'2'),Pi{p'2') a n d PT e \p7ipnP2{pV) These restr i c t ions y i e l d two condi t ions w h i c h must be satisf ied for equations (2.29) and (2.30) to represent the pr ice e q u i U b r i u m i n Ry. F i r s t , p" > ^ ^ ' ( P i ' ) (^ ^ g iven by equat ion 2.9) is satisf ied w h e n : 2 ( m 6 - mka) > j ( C ) Second, p " < P i ( p 2 " ) (as g iven by equat i on 2.10) is satisf ied when : mka — mb < j ( D ) B y r e f o r m u l a t i n g the p r i c i n g equat ions , i t can be shown that pl' G [P2{P")iPT{PI') o n l y w h e n b o t h cond i t i ons ( C ) a n d ( D ) are satisf ied. N o t i c e that condi t ions ( C ) and (D) are the reverse of ( B ) a n d ( A ) respect ively . I n Ry, it can be shown that the d e m a n d equat ions for the two f irms are ident i ca l to the d e m a n d equat ions i n Rl ( (2 .26)=(2.13)) . There fore , the price e q u i l i b r i u m so lut ion i n th is region is i d e n t i c a l as we l l . T h i s pr i ce e q u i l i b r i u m is defined by (2.23) and (2.24) and is v a l i d p r o v i d e d > ^"(pg) a n d p j ^ P 2 ( P i ) - These inequal i t ies are satisf ied when, c o n d i t i o n ( D ) is v i o l a t e d or holds w i t h equal i ty . N o t i c e that c o n d i t i o n ( C ) w i l l c ont inue to h o l d as w i l l charac ter i s t i c y dominance . S i m i l a r to the analysis for character is t i c x d o m i n a n c e , w h e n c o n d i t i o n ( D ) holds w i t h equahty , = p j and P 2 " = P2- T h i s indicates that e q u i l i b r i u m prices move cont inuous ly w h e n parameters move between R^ and Ry. I n Ry, the f irst order cond i t i ons of the prof i t funct ions are quadrat i c i n prices. T h e price e q u i h b r i u m is not eas i ly der ived i n th is reg ion as nei ther of the first order condit ions factor i n t o s imple f u n c t i o n a l forms. T h e exact s o l u t i o n has not been c a l c u l a t e d as i t is not required for the d e t e r m i n a t i o n of the p r o d u c t e q u i h b r i u m so lut ions . 2.4.3 D o m i n a t e d C h a r a c t e r i s t i c s C o m p e t i t i o n A s was o u t l i n e d ear l ier , the t w o - d i m e n s i o n a l h o r i z o n t a l d i f ferent iat ion m o d e l and the m i x e d m o d e l can always be set up to con form w i t h a s y m m e t r i c character ist i cs c ompet i -t i o n . However , the two - d i m e n s i o n a l v e r t i c a l d i f f erent iat ion mode l allows for d o m i n a t e d character is t i cs c o m p e t i t i o n . A s the general ized price e q u i l i b r i u m analys is assumes a s y m -m e t r i c character is t i cs c o m p e t i t i o n , the d o m i n a t e d characterist ics case for the vert i ca l m o d e l must be a n a l y z e d separately. T h i s sect ion w i l l out l ine the d e m a n d analysis and price e q u i h b r i a for b o t h character i s t i c x d o m i n a n c e and character is t i c y dominance for the d o m i n a t e d character is t i cs case of the ver t i ca l m o d e l . C h a r a c t e r i s t i c x D o m i n a n c e T h e d o m i n a t e d character is t i cs case is a n a l y z e d i n m u c h the same way as the a s y m m e t r i c character ist i cs case. T h e general f orm of the indifference hne (defined i n (2.7)) applies as do the key pr i ce levels defined i n (2.8)-(2.11). Since the d o m i n a t e d character ist ics analys is is o n l y r equ i red for the ver t i ca l m o d e l , the parameters fc = 1, m = 1 and j = 0 are s u b s t i t u t e d in to these equat ions . T h e mod i f i ed versions of the indifference l ine a n d key prices are: FiG) = + (2.31) o o where: firm i ' s p r o d u c t is {ai,bi) a = ( o i - ai) 6 ^ ( 6 2 - 6 0 p';' = P2 + a - b (2.32) (2.33) Pi = P2 (2.34) P i =P2-b (2.35) W i t h o u t loss of generahty, it is assumed that f i r m 2's p r o d u c t is d o m i n a n t . T h a t i s , «2 > ^1 a n d 62 > ^1- T h i s imphes that a = ( o i - 0 2 ) < 0 a n d slope of the indifference curve is negative . U n d e r charac ter i s t i c x dominance , 90° < a < 135°. A l t e r n a t i v e l y , the angle of c o m p e t i t i o n can be descr ibed by a n angle /3 > 45° where /3 = 180° - a (see F i g u r e 2.15). T h i s imphes t h a t — ( a i — 02) ^ (^2 ~ ^ i ) - U n d e r these condi t ions , the o rder ing of the price equations is : P i < P i < P i < P i A s firm 1 decreases i ts price f r o m p " , the indifference l i n e shifts u p w a r d . L i k e the a s y m m e t r i c character ist i cs case, three d i s t inc t d e m a n d regions can be defined on the basis of the geometr ic s t ruc ture of the m o d e l (see F i g u r e 2.15). In reg ion j i ? ^ , d e m a n d for firm 1 increases at an increas ing rate . T h i s region is defined by the pr i ce range p[ < pi < p " . In dRl, where p " < P i < p[, d e m a n d for firm 1 increases at a constant rate. F i n a l l y , i n jRl, where pî" < P i < p " , the d e m a n d for firm 1 increases at a decreasing rate . U s i n g the same a n a l y t i c a l techniques as descr ibed i n the a s y m m e t r i c character ist ics case, the pr i ce e q u i h b r i u m solut ions i n ^Rl a n d ^Rl are d e t e r m i n e d . A p p e n d i x A contains the m a t h e m a t i c a l proofs. I n jRl, the price e q u i l i b r i u m is defined by : F i g u r e 2.15: T h r e e D e m a n d Regions U n d e r D o m i n a t e d C h a r a c t e r i s t i c s C o m p e t i t i o n P2 = - 4 a + b (2.37) T h i s e q u i h b r i u m is v a l i d p r o v i d e d Pl" e \piiP2'l,p[{p'2") a n d p r e k(pr")-P2(pr") These restr ic t ions y i e l d two cond i t i ons . F i r s t , pl"' > Pi{pl") is satisf ied when : -2a > b Second , pl" < p'lipl"') is satisf ied when : 26 < -a i n B y r e f o r m u l a t i n g the p r i c i n g equat ions , i t c a n be s h o w n that € P 2 ( p " ' ) , P2 (pr* ) o n l y w h e n b o t h condi t ions ( E ) a n d ( F ) are sat is f ied . In dRi, the price e q u i l i b r i u m is defined by: P l = (2.38) 3V-8âb Pr = (2.39) T h i s pr ice e q u i U b r i u m is va l id p r o v i d e d p p * > P i ( p 2 * * ) a n d pj** > P2(pî**)- These inequal i t ies are satisf ied w h e n c o n d i t i o n ( F ) is v i o l a t e d or holds w i t h equal i ty . C o n d i t i o n ( E ) w i l l cont inue to h o l d as w i l l charac ter i s t i c x dominance . A s was the true for the a s y m m e t r i c character ist i cs case, w h e n ( F ) holds w i t h equal i ty , pl" = p^** a n d p^" = P j * * . ^ T h i s ind i ca tes that e q u i l i b r i u m prices move cont inuous ly w h e n parameters change such that the e q u i l i b r i u m moves f r o m region ^Rl to region jRl-T h e pr ice e q u i l i b r i u m solut ions i n ^Rl a n d jR]. i l l us t ra te the fact t h a t the firm w i t h d o m i n a t e d p r o d u c t ( f i rm 1) must charge a lower price i n order to achieve pos i t ive sales. T h e pr i ce e q u i h b r i u m i n ^Rl has not been ca l cu lated as i t is not required for the d e t e r m i n a t i o n of the produc t e q u i h b r i u m so lut ions . C h a r a c t e r i s t i c y D o m i n a n c e C h a r a c t e r i s t i c y d o m i n a n c e i n the d o m i n a t e d characterist ics case follows the same p a t t e r n establ ished i n previous sections. T h e complete der ivat ion of the pr ice e q u i l i b r i a is g iven i n A p p e n d i x A . In th is case, /3 < 45°. T h i s imphes that - ( o i — 02) < (^2 — ^1) T h e price equations (2.32)-(2.35) h o l d but P i < P i < P i < P i In iR}y, the pr i ce e q u i l i b r i u m is defined by: ^Note the equilibrium price notation. Similar to the asymmetric characteristics case, In region dRl, equilibrium prices are denoted by a triple asterisk ("*') whereas in region dRl, equilibrium prices are denoted by a triple star ("**). As defined below, the price equilibrium in region dR^ is denoted by a quadruple asterisk ( " " ) • P l = P l = 26 + g 6 4 6 - g 6 (2.40) (2.41) T h i s e q u i l i b r i u m is v a h d prov ided p'r e [p[ipr)^Piipr) a n d PT' e f p 2 ( p r ' ) . P 2 ( P Ï " ) These restr i c t ions y i e l d two cond i t i ons . F i r s t , p " " > Pi(p2"'"') is satisf ied when : - 2 a < 6 Second, pl" < Pi{pl") is satisf ied when : 26 > - a These cond i t i ons are s i m p l y the reverse of condi t ions ( E ) and ( F ) . In jRy, the demands equations for each f i r m are i d e n t i c a l to those der ived i n jRl. There fore the pr ice e q u i l i b r i u m defined by equat ions (2.38) and (2.39) a p p l y i n this region as w e l l . T h i s price e q u i l i b r i u m is v a l i d prov ided c o n d i t i o n ( H ) is v i o la ted or holds w i t h equal -i ty . C o n d i t i o n ( G ) w i l l cont inue to ho ld as w i l l character i s t i c y dominance . In a d d i t i o n , w h e n ( H ) holds w i t h equahty , pl"' = pl** a n d p^'" = p^*'-I n b o t h jRy and ^Rl, because it controls the d o m i n a t e d p r o d u c t , the e q u i l i b r i u m pr ice for f i r m 1 is less t h a n t h a n the e q u i h b r i u m price for f i r m 2. T h e pr ice e q u i l i b r i u m i n dRy has not been ca l cu la ted as it is not requ i red for the d e t e r m i n a t i o n of the product e q u i l i b r i u m solut ions . 2.5 P r o d u c t E q u i l i b r i u m for the T w o - D i m e n s i o n a l V e r t i c a l M o d e l O n c e the e q u i h b r i u m prices have been estab l i shed , i t is possible to ana lyze the f i rms ' p o s i t i o n i n g choices. Since the parameters used i n the price e q u i h b r i u m analysis vary by m o d e l , the three d i f ferent iat ion models w i l l be a n a l y z e d separately. T h i s sect ion w i l l descr ibe the t w o - d i m e n s i o n a l v e r t i c a l m o d e l . Because the perfect N a s h e q u i h b r i u m so lu t i on is used, the f i rms ' choice of product pos i t ions is dependent o n the set of e q u i l i b r i u m prices . T h i s requires an analys is of the each of the possible pr ice e q u i l i b r i a . For the t w o - d i m e n s i o n a l ver t i ca l m o d e l , this includes b o t h the a s y m m e t r i c a n d d o m i n a t e d character ist ics cases. T o u n d e r s t a n d the nature of the p r o d u c t e q u i h b r i u m , i t is i m p o r t a n t to u n d e r s t a n d how changes i n p r o d u c t posit ions affect e q u i l i b r i u m prices. 2.5,1 A s y m m e t r i c C h a r a c t e r i s t i c s In the a s y m m e t r i c character ist i cs case, condi t ions ( A ) - ( D ) define the boundaries of the various price e q u i h b r i a (see sect ion 2.4). B y s u b s t i t u t i n g the parameter values per ta in ing to the ver t i ca l m o d e l {j = 0,m = I, k = 1), ( A ) - ( D ) can be restated as follows: (62 - fci) < ( f l i - ^2) i^v) ( 6 2 - i i ) < ( a i - 0 2 ) (Bv) (62 - 61) > ( a i - a2) {Cv) ( 6 2 - 6 1 ) > ( a i - a z ) (Dv) N o t e that ( A ^ ) a n d ( B y ) are equa l a n d that (Ci^) a n d ( D y ) are equa l a n d the reverse sign of ( A v ) and (Bv^). B y a l t e r ing the values of a i , 02, 61 a n d 62, i t is poss ible to determine the relevant price e q u i l i b r i u m regions for use i n the p r o d u c t p o s i t i o n i n g subgame. Cons ider the s i t u a t i o n where ai a n d 02 are g iven ( a i > 02) a n d 621^1 are var ied . 1. W h e n 62 = ^1, character i s t i c x d o m i n a n c e holds a n d condi t ions (Ay) and (By) are satisf ied. T h e pr ice e q u i h b r i u m is i n Rl. 2. A s (62 —bi) is increased (by e i ther ra i s ing 62 or l ower ing 61), (62 — ^i) w i l l eventual ly become larger t h a n ( a i — 0 2 ) so charac ter i s t i c y d o m i n a n c e w i l l h o l d . A and B are v io la ted a n d ( C v ) a n d {Dv) h o l d . T h e price e q u i h b r i u m is i n R^. N o w consider the s i t u a t i o n where 61, a n d 62 are g iven a n d ai,a2 are var i ed . 1. W h e n a i = 0 2 , character i s t i c y d o m i n a n c e holds a n d cond i t i ons (Cy) a n d ( D ^ ) are satisf ied. T h e pr ice e q u i h b r i u m is i n R^. 2. W h e n (a i — 03) is increased, (ai — 03) w i l l become larger t h a n (63 — 61) so char-acter ist ic X dominance w i l l h o l d . ( A K ) and (Bi^) become satis f ied a n d the price e q u i l i b r i u m w i l l be i n B}^. Several po ints are w o r t h n o t i n g . F i r s t , the sequences descr ibed above can be t e r m i -nated at any step depend ing of the range of poss ible produc t pos i t i ons . For example , the al lowable increase i n 63 (given 61, a i a n d 03) m a y be restr i c ted by the m a x i m u m level of 6, {y'^°''). Second, since ( A K ) = ( B I ^ ) ( a n d ( C v ) = ( D v ) ) , the relevant regions for the price e q u i l i b r i u m move d i r e c t l y f r o m R^. to R'^. I n this m o d e l , the o p t i m a l p o s i t i o n i n g equihb-r i u m w i l l not occur i n R\, R^, R^. or R^. F i n a l l y , since b o t h the d e m a n d functions and the e q u i l i b r i u m prices are cont inuous across regions, i t follows t h a t the profit functions are cont inuous as we l l . T h e above analys is indicates t h a t the prof it funct ions i n Rl a n d Ry must be considered i n the der iva t i on of the p r o d u c t e q u i h b r i u m . In Rl, the d e m a n d for f i r m 1 is given by ( 2 . 1 5 ) a n d the e q u i h b r i u m price is g iven by ( 2 . 1 8 ) . S u b s t i t u t i n g the ver t i ca l mode l parameters y ie lds For f i r m 2 , the d e m a n d is g iven hy D] = 1 — D^ a n d the e q u i l i b r i u m price is g iven by ( 2 . 1 9 ) . T h i s y ie lds a profit o f In Ry, the d e m a n d for firm 1 is g iven by (2.27) wh i l e the d e m a n d for firm 2 is 1 - D^. T h e e q u i l i b r i u m prices for the two firms are g iven by (2.29) a n d (2.30). C o m b i n i n g these equat ions y i e l d the firms' prof it funct ions i n R^: (26 + a ) ' n r = 4 ^ (2.44) n r = (2.45) 2.5.2 D o m i n a t e d C h a r a c t e r i s t i c s I n the d o m i n a t e d character is t i cs case, condit ions ( E ) - ( H ) define the boundar ies of the var ious pr ice e q u i h b r i a (see sect ion 2.4.3). B y a l ter ing the values of a i , a 2 , 6 i a n d 62, the relevant pr ice e q u i h b r i u m regions for use i n the p r o d u c t pos i t i on ing subgame can be d e t e r m i n e d . C o n s i d e r the s i t u a t i o n where Oi a n d 02 are g iven (02 > a i ) a n d 62,^1 are var ied . 1. W h e n 62 = 61, charac ter i s t i c x dominance holds a n d ( E ) a n d ( F ) are satisf ied. T h e pr ice e q u i l i b r i u m is i n j i ? ^ . 2. A s (62 — bi) is increased , c o n d i t i o n ( F ) is the first to f a i l , but character is t i c x d o m i n a n c e s t i l l ho lds . T h e pr ice e q u i h b r i u m is i n dRl-3. (62 — ^i) can be increased u n t i l character is t i c y d o m i n a n c e holds . Since ( E ) s t i l l ho lds , the price e q u i l i b r i u m is i n j i ?^ . 4. F i n a l l y , (63 - i i ) c a n be increased u n t i l ( E ) fai ls . N o w ( G ) and ( H ) h o l d a n d the pr ice e q u i l i b r i u m is i n j iZ^ . S i m i l a r to the a s y m m e t r i c character ist ics case, the reverse procedure of v a r y i n g (02 — tti) a n d h o l d i n g 61 a n d 62 constant yields the same relevant regions. A s w i t h the a s y m m e t r i c character is t i cs case, several po ints are w o r t h n o t i n g . F i r s t , the sequence descr ibed above can be t e r m i n a t e d at any step d e p e n d i n g of the range of possible p r o d u c t pos i t ions . Second , since (E)^^ ( F ) ( and (G)7^(H)) , there are 4 relevant regions for the pr ice e q u i h b r i u m w h i c h need to be cons idered : ^Rl, dRl> dR]j anàdR\. T h e p r o d u c t e q u i h b r i u m w i l l not occur i n dR^ or dR^- F i n a l l y , since b o t h the d e m a n d funct ions a n d the e q u i l i b r i u m prices are cont inuous across regions, i t follows that the profit funct ions are cont inuous as we l l . T h e profit funct ions for the relevant regions are as fo l lows (see A p p e n d i x A for detai ls ) . In dRl T h e same d e m a n d funct ions a n d e q u i l i b r i u m prices for the two firms a p p l y i n b o t h dRl a n d dRl- A t e q u i h b r i u m prices (defined by (2.38) a n d (2.39)), the d e m a n d for firm 1 is I a n d the d e m a n d for firm 2 is | (see A p p e n d i x A ) . T h e resu l t ing profit funct ions are: n r * = ^ (2.48) = 2 ^ (2.49) F i n a l l y , i n dRl, the relevant prof it funct ions are: 2.5.3 P r o d u c t E q u i l i b r i a T h e produc t e q u i l i b r i a that are possible i n the t w o - d i m e n s i o n a l v e r t i c a l m o d e l are deter-m i n e d by s i m u l t a n e o u s l y c o m p a r i n g a l l possible pr i ce e q u i h b r i u m regions. E q u i h b r i u m solutions occur w h e n ne i ther f i r m can i m p r o v e its profits by u n i l a t e r a l l y a l ter ing its chosen pos i t i on . In each of the regions, a two step procedure is used to ana lyze a f i rm's o p t i m a l po-s i t i on (subject to the compet i t o r ' s pos i t i on ) . F i r s t , the restr i c t ions w h i c h determine the range of p r o d u c t pos i t ions w h i c h are a l lowable i n each region are considered. These i n -c lude: (i) a s y m m e t r i c or d o m i n a t e d character is t i cs ; ( i i ) character i s t i c x or character ist i c y dominance ; a n d ( i i i ) condi t ions ( A K ) - ( D V ) a n d ( E ) - ( H ) descr ibed above. Second, the derivatives of the relevant profit funct ions are taken w i t h respect a f i rm 's o w n character-ist ics . T h e signs of these derivatives de termine whether a f i rm 's profits are improved by increas ing or decreasing a character is t i c ' s p o s i t i o n i n g value i n the range {xmin,x"^'"') or (î/mm,y'""'°) (subject to region res tr i c t ions ) . F o l l o w i n g this ana lys i s , the profits i n each of the relevant regions are d e t e r m i n e d . T h e signs of the prof it f u n c t i o n derivat ives i n the relevant regions are s u m m a r i z e d i n the fo l lowing table . F i r m 1 F i r m 2 R e g i o n Pro f i t F u n c t i o n E q u a t i o n N o . an, dai aui dbi Pro f i t F u n c t i o n E q u a t i o n N o . an , da2 db2 Rl 2.42 > 0 > 0 2.43 < 0 > 0 Rl 2.44 > 0 < 0 2.45 > 0 > 0 dRl 2.46 > 0 > 0 2.47 < 0 > 0 dRl or dRl 2.48 < 0 < 0 2.49 > 0 > 0 dRl 2.50 > 0 < 0 2.51 > 0 > 0 T h e r e are four poss ib le p r o d u c t e q u i h b r i u m solut ions i n the t w o - d i m e n s i o n a l vert i ca l m o d e l . These solutions are def ined a n d proven i n Propositions 1 to 4-Proposition I: If {x^"" - x^^) < ^ ( y " " * ' ' - ymin) , there exists a product equilibrium such that _max _ ™inax a\ = X a2 = X 1^ = 2/min h = y " Proof : I Cons ider F i r m 1 a n d assume 03 = x '^"'',62 = y"^°^-(i) In Rl, since ai — 0 3 , > 63 — i i , the o n l y response for f i r m 1 is a i = x'^^'^,bi yma.x rpj^jg results i n a zero prof i t . (h) In Ry, the best response is ai = x'^^,bi = j/min-T h i s results o n a profit of max _ , n r = (2.52) ( i i i ) In dRl, the best response is a j = x"^^,bi = ymin- T h i s results i n a zero prof it . ( iv) In dRi, a n d dR^, the best response is ai = x^n,bi = T/min To r e m a i n w i t h i n this region, th is response is o n l y v a l i d w h e n x™** — Xirùn ê [^(y"""' - ymin) , 2(y'^'" ' - y^in)] as condi t ions ( E ) a n d ( G ) must h o l d . T h i s results i n a profit of n r = ^ ' ^ ^ - - ^ ^ ( y ' - y j ^ (2.53) W h e n ( a ; ' " " —a;min) > "^{y"^"^ — Vnun), the best response for firm 1 i n this region is to choose 6a = y^ a n d = x'^^ - 2 (y™" ' ' - y^^). Chapter 2. Product and Price Competition in a Two-Dimensional Market 73 T h i s results i n a profit of max _ . = — (2.54) (v) In dRl, the best response is ai = x^^'^jbi = T/min- T h i s results i n a profit of TT'"' _ y y min - 7. T h i s is the same strategy as i n a n d yields the same prof i t . (vi ) C o m p a r e (2.52) and (2.53) F i r m 1 w i l l choose ai = a;™"'', hi — w h e n 9 - 32 w h i c h reduces to , 128 ( x — - x ^ „ ) < — ( y — - y ^ J (2.55) II N o w consider F i r m 2 a n d assume — x ™ " , bi = y, (i) I n Rl, the best response for firm 2 is «2 = ^minjh = y'^'"'^- T h i s response is v a h d as l ong as (a;"'"'' - Xmin) > iv"'^'' - Z/min)- If this c o n d i t i o n is not t rue , the best response for firm 2 is a2 = Xmin a n d 62 = y " " " - (x™^'' - x^in). T h e prof its assoc iated w i t h these responses are m a x i m i z e d when the above c o n d i t i o n holds w i t h equal i ty . T h i s results i n a profit of max _ . n ; = (2.56) ( i i ) I n Ry, the best response for firm 2 is 03 = x'^'',b2 = y™^*. T h i s results i n a prof it of ur = ^iy^^^ ^"^") (2.57) ( i i i ) I n dRl, since 02 > a j a n d (02 — a i ) > (62 — bi), the o n l y response i n this region is 02 = x'^^jbi = ymin- T h i s results i n a zero prof i t . ( iv ) In dRi a n d dR],, the best response is 02 = x"^"*,62 = j / ' " " . T h i s results i n a zero pro f i t . It is also the same strategy as Ry. (v) I n dRl, the best response is 02 = a;'""' ', 63 = y " " " T h i s results i n a prof it of 4(y"' '"^ - ymin) 9 T h i s is the same strategy a n d profits as i n R^. (v i ) C o m p a r e (2.56) and (2.57). (2.56) is m a x i m i z e d w l i en (x™^'' - x ^ n ) = [y'^^^ 2/min)- S u b b i n g t l ie equahty in to (2.57) y ie lds ^ „ 4 ( x - - - x ^ i „ ) T h i s profit is always greater t h a n (2.56). If (y'""' ' - y^^) > ( j ; " " " - x ^ i n ) , (2.57) becomes re lat ive ly larger when c o m p a r e d w i t h (2.56). I l l T h e o n l y c o n d i t i o n o n the product e q u i h b r i u m of 1^ = î/min ^2 = y is (2.55) w h i c h requires ( x ^ - - x ^ i n ) < ^ ( y ' " " - ymin) max Proposition 2 (a) / / ( x ' " ' " - x ^ n ) e [^(y"**"^ - ynùn),2{y""''' - y^^)], there exists as product equilibrium such that ai = Xn^n 0,2 = a^""" bi = ymin b2 = y'^^'' (b) / / ( x " * ' ' - Xmin) > 2{y"^^'^ - 2/tnin), ^^1656 exists o product equilibrium, such that bi = 2/min bi = 2 / - -Proo f : I C o n s i d e r f i r m 1 and assume a2 = x ™ " , 62 = 2/"'*'' (i) F r o m (2.55), f i r m I 's best response is ai — x ^ i m ^ i = 2/min w h e n 128 {X^""^ - a^min) > -^hT'^ - ymin) ( i i ) W h e n (x""*"^ - x^^) > 2(j/ '" '" ' - y ^ ^ ) , the best response for f i r m 1 i n dR\ is a i = x ' " - - 2 ( y - - - y ^ „ ) , 61 = y ^ , . T h i s results i n a profit defined i n (2.54). T h i s prof it is a lways the largest for f i r m 1 w h e n compared to the profits generated by other strategies. II N o w consider f i r m 2 a n d assume ax — X m i n j ^ i = J/min-(i) I n since ax > a^ a n d ax — ai > ^2 — ^ i , the o n l y response is ai = Xmin, ^2 = î/min- T h i s results i n a zero prof i t . ( i i ) I n the best response is ai = X m a x , i 2 = y^"^ s ince a r e s t r i c t i o n is that fli > ^2- T h i s results i n a prof it of n r = ^(^""'^ ^"^") (2.58) ( i i i ) In dRl, the best response is 62 = y " " " ' a n d 02 at t l ie m i n i m u m value possible w i t h i n the region. Since (02 — a i ) > (62 — ^ i ) , th is occurs when a2 = (y™*^ -2/min) + •»-rmn-T h i s results i n a profit of n r = ^ ° ' ^ ° ' ; - ^ - > (2,59) T h i s prof it is a lways greater t h a n (2.58). ( iv) In dRl a n d dR^, the best response is a2 = x " ' ^ ' ' , i 2 = 2/™"''- T h i s results i n prof it of 32 (2.60) is v a h d i f ( x - - - x ^ n ) € [ ^ ( y ' " " - y ^ i n ) , 2 ( y ™ ' ' - y ^ „ ) (v) I n dRl, the best response is 02 = x'^^'',b2 = y " ' " ' ' . T h i s is the same strategy a n d yields the same profits as i n Ry. vi ) C o m p a r e (2.59) a n d (2.60). (2.59) is m a x i m i z e d when (a2 — aimin) = ( y " ymin)- S u b b i n g this in to (2.60) y ie lds n ; * * = ^ ( y ' " ' " ' - y^in) > (2.59). T h i s proves P r o p o s i t i o n 2(a) . III C o n s i d e r f i rm 2. A s s u m e {x"'^'' - Xnain) > 2(y'"^=' - y^j^) and a j = x""^"" - 2{y"'^'' -ymin) , 1^ = ymin-(i) In Rl, t l ie best response for f i r m 2 is the m a x i m u m possible value of 03 a n d the m i n i m u m value of 63 w i t h the res t r i c t i on that (a j — a2) = (63 — ' ' i ) -T h i s results i n a profit of j j . = h _ I l ^ (2.61) ( i i ) I n dRl, the best response for f i rm 2 occurs w h e n (03 — Ui) = (63 - 61) where f i r m 2 chooses the m a x i m u m possible level of 63 and the m i n i m u m level of 03. T h i s results i n a profit of 25 = ^ ( 6 2 - ymin) (2.62) T h i s level of profit is always greater t h a n (2.61). ( i i i ) I n regions Ry,dRl,d Rl a n d dRl, the best response for f i r m 2 is 03 = x^^'^, 63 = y max Since the choice of Oi assures that dRl a n d dRl are feasible regions, firm 2's profit is m a x i m i z e d at n r = - î ' - i n ) (2.63) ( iv) C o m p a r e (2.62) a n d (2.63). In (2.62), the m a x i m u m value of 63 is T h u s (2.62) is a lways less t h a n (2.63). F i r m 2 w i l l choose = x^^'^j ia = y " ' ' " ' . Proposition 3: If {x^^ — Xmin) ^ thiy"^^^ ~ ymin)) then exists o product equilibrium such that a i = x'"^'^ a2 = Xmin fci = y ' " " ^ bi = y - - ' ^ Proo f : T h e d o m i n a t e d character ist i cs analys is was conducted w i t h 02 > ai a n d bi > bi. T h i s analysis resul ted i n P r o p o s i t i o n 1 be ing t rue . T h e d o m i n a n t character ist ics analysis w i t h a j > ai and 61 > 63, by s y m m e t r y , y ie lds P r o p o s i t i o n 3. N o t e that this produc t e q u i h b r i u m occurs w h e n the m a x i m u m profits are i n R^.. Proposition 4^ (a) If{x^-- - Xmin) G [ K y " " - y n u n ) , ^ ( y ' " ' ' " " ymin)] , there exists a product equilib-rium such that ax = X ' " " ' ' ai = Xmin hx = y - " bi = ymin (h) If [x"^^ — Xmin) < K y ' " " ^ — ymin), there exists a product equilibrium such that bi = y""'^ 62 = 2/"^ =^^  - 2 ( x - - - x„ ,n ) Proo f : T h e d o m i n a t e d character i s t i cs analysis was conducted w i t h a2 > ai and 62 > fci- T h i s analys is resul ted i n P r o p o s i t i o n 2 be ing true . T h e dominant character is t i cs analys is w i t h ai > a2 a n d bi > 62, by s y m m e t r y , yields propo-s i t i o n 4. 2.5.4 S u m m a r y a n d I m p l i c a t i o n s T h e produc t e q u i l i b r i a descr ibed i n Propositions 1-^ can be s u m m a r i z e d as follows (see F i g u r e 2.16): I If f i r m 2 is pos i t i oned at (x""**, y'""'^), there exists a n e q u i h b r i u m where f i r m 1 is pos i t i oned at : (i) ( X - - , 3/„i„) i f ( X - - - X ^ i „ ) < ^ ( y " * " ^ - ymin) ( i i ) [Xmin^Vmir.) if {x"^''' " ^ î ^ m ) G [ ^ ( y ' " " " " y^nin), 2(y '"»» - y^i„ ) ( ih) ( x - - - 2 ( y - - - y w ) , y „ i „ ) if ( x ™ - - x ^ ) > 2 ( r - - y^in) II If f i r m 1 is pos i t i oned at ( x ' " " * , y " " ' * ) , there exists an e q u i h b r i u m where f i r m 2 is pos i t i oned at : (i) ( X ^ i n . y ' " " ' ' ) i f {X^"' - Xrr^in) > Mv"""' ' Vmin) ( i i ) (Xr^ir,, ymin) i f {x""'' ' X^in) G [liv""'' ' Vmin), ^ ( y ' " " " - Vmin) ( i i i ) [xmin, y"""^ - 2 ( x ' " - - xmir.)) i f {x^'^'' - x „ . „ ) < K y " * " - y w ) F i r m 2 pos i t ioned at (x"""', y"'"") F i r m 1 pos i t ioned at: I {Xmin, ymin) 1 {x'"'''-2(y'"'''-ymin), ymin) 128 81 ~ Xmin) I I F i r m 1 pos i t ioned at [x"""", y"""^ F i r m 2 pos i t ioned at: {Xmin, y'"'''-2{y'^'''-ymin)) {Xmin, ymin) I {Xmin, 1 2 81 128 {X ~ Xmin) , max X {y - ymin) F i g u r e 2.16: S u m m a r y of P r o d u c t E q u i l i b r i a for the T w o - D i m e n s i o n a l V e r t i c a l M o d e l These results have a n u m b e r of in terest ing features. A s expected , one f i r m is always pos i t i oned at the m a x i m u m value on b o t h dimensions w h i c h is considered by consumers to be of the highest qua l i ty . L i k e Shaked a n d S u t t o n (1982), the f i r m pos i t ioned i n this l o c a t i o n has the highest prof i ts . Since b o t h f irms wou ld prefer this h igh profit pos i t i on , w i t h o u t i n c l u d i n g some other characterist ics i n the m ode l , it is imposs ib le to determine towards w h i c h e q u i l i b r i u m ( i f any) f irms w i l l t end . R e c a l l that prev ious research has suggested that two forces seem to shape the product e q u i l i b r i u m : a d e m a n d force (a desire to increase ones h in ter land ) w h i c h draw the firms together a n d a s trateg ic force (a desire to reduce price c o m p e t i t i o n ) w h i c h causes f irms to di f ferentiate . These effects o n the produc t e q u i l i b r i a der ived i n the two -d imens iona l v e r t i c a l m o d e l can be a n a l y z e d . U n d e r ce r ta in condi t ions , there exists a n e q u i l i b r i u m w h i c h exh ib i t s m a x i m u m di f ferent iat ion on one d imens ion a n d m i n i m u m di f ferent iat ion o n the other {MaxMin d i f ferent iat ion) . ' ' T h e MaxMin e q u i h b r i u m can be considered the n o r m a l case. T h i s is because this e q u i l i b r i u m spans the region i n w h i c h the range of the X charac ter i s t i c (x ' " "* — Xmin) equals the range of the y character is t i c {y"^'' — ymin)- T h e MaxMin result appears to be i n the spir i t o f d e P a l m a et a l (1985) who suggest that f irms w i l l l o cate next to one another prov ided that the products are di f ferentiated on other d imens ions . F o l l o w i n g this Hne of reasoning, b o t h firms want to have the highest qual i ty , but because of the s trateg ic force, o n l y one firm w i l l l ocate there. T h e firm w h i c h is unab le to choose the highest q u a h t y pos i t i on differentiates i ts produc t by choosing the m i n i m u m q u a h t y on o n l y one d imens ion because of the d e m a n d force. T h i s choice reduces price c o m p e t i t i o n whi l e at the same t i m e m a i n t a i n s a suff ic iently h igh q u a l i t y level for the d i f ferent iat ing firm's produc t to appea l to a n u m b e r of consumers . ^MaxMin differentiation was found in the mixed horizontal-vertical model analyzed by Neven and Thisse (1988). For details, see the analysis of the mixed model product equilibrium. T h e second type of p r o d u c t e q u i h b r i u m possible i n the ver t i ca l mode l exh ib i t s m a x -i m u m di f ferent iat ion . T h a t is , one firm chooses the m a x i m u m level on b o t h dimensions whi le the other firm chooses the m i n i m u m level on b o t h d imensions . T h e decision to change f r o m MaxMin d i f ferent iat ion to f u l l d i f ferent iat ion is a u n i l a t e r a l decis ion made be the firm not l ocated at the highest q u a h t y level . However , the profits for b o t h firms increase (as c ompared to the MaxMin e q u i l i b r i u m ) when th is e q u i l i b r i u m holds . T h i s suggests that the strategic effect is quite s trong . In choosing MaxMin, the d i f ferent iat ing firm t r a d e d off increased d e m a n d for a lower pr i ce (because of increased price compe-t i t i o n ) . T h i s choice affects the p r o f i t a b i l i t y of the firm l o ca ted at m a x i m u m q u a l i t y as b o t h d e m a n d and price are lowered. W h e n the d i f ferent iat ing firm moves to m a x i m u m di f ferent iat ion , i ts d e m a n d decreases ( f rom | to ^) but i ts pr i ce increases to the extent that prof i ts increase. Since b o t h d e m a n d a n d pr ice increase for the h igh q u a l i t y firm, it appears t h a t the strategic effect is reduced. T h e final type of p r o d u c t e q u i h b r i u m has the two firms m a x i m a l l y di f ferentiated on one character is t i c a n d p a r t i a l l y di f ferentiated on the other . T h i s e q u i l i b r i u m shows that the strategic effect does not always dominate . T h a t is , w i t h sufficient product d i f ferent iat ion , the d e m a n d effect becomes more i m p o r t a n t t h a n the strategic effect. T h e firm w i t h the lower q u a l i t y p r o d u c t chooses the p o s i t i o n at w h i c h these two oppos ing forces are offset. T h e re lat ive prices a n d demands r e m a i n constant w i t h p2 = 3p i a n d D 2 = 3Z ) i . T h i s result adds an i m p o r t a n t d imens ion to the m a x i m u m versus m i n i m u m di f ferent iat ion debate. It suggests that t r a d i t i o n a l one- d i m e n s i o n a l p o s i t i o n i n g models m a y not be adequate to u n d e r s t a n d the oppos ing d e m a n d a n d strategic effects. T h e p r o d u c t e q u i h b r i u m results f r o m the t w o - d i m e n s i o n a l ver t i ca l m o d e l prov ide some i m p o r t a n t insights in to the compet i t i ve behavior of firms c o m p e t i n g on more t h a n one d i m e n s i o n . T h e results are consistent w i t h past research findings w h i c h suggest dif-f e rent ia t ion . In a d d i t i o n , new ins ights i n the analysis of c o m p e t i t i v e produc t p o s i t i o n i n g are advanced . T h o u g h the results po int to specific pat terns of d i f f erent iat ion , it is i m -por tant to note that the f indings of this m o d e l are affected by the N a s h pr ice game in the second stage. T h i s non-cooperat ive a s s u m p t i o n gives f irms a s t rong m o t i v a t i o n to dif ferentiate. A c o m p a r i s o n w i t h an a l t e rnat ive t w o - d i m e n s i o n a l m o d e l , whi ch lessens the price c o m p e t i t i o n aspect , w o u l d be of value i n this area. 2.6 P r o d u c t E q u i l i b r i u m for the T w o - D i m e n s i o n a l H o r i z o n t a l M o d e l A s was the case i n the t w o - d i m e n s i o n a l v e r t i c a l m o d e l , the choice of p r o d u c t posit ions is dependent on the set of e q u i l i b r i u m prices . For the t w o - d i m e n s i o n a l h o r i z o n t a l mode l , the order ing of p roduc ts a long a charac ter i s t i c ( f rom 0 to 1) is a r b i t r a r y . Therefore , an analysis of on ly the a s y m m e t r i c character is t i cs case is required . In a d d i t i o n , there is no need to consider character is t i c y d o m i n a n c e since this case can be converted to character is t i c x dominance by reverse sca l ing one d i m e n s i o n . A n i m p o r t a n t feature of the h o r i z o n t a l m o d e l is the fact that produc ts l o cated i n any pos i t i on are of equal qua l i ty . Since cost is independent of l o c a t i o n , this feature results i n the product subgame be ing p layed between 2 s y m m e t r i c compet i to rs w h o each choose a pos i t i on (xi,yi) i n the a l lowable p r o d u c t space. Because of this s y m m e t r y a n d the fact that there are no f ixed costs, there exists a p r o d u c t e q u i h b r i u m where the competi tors w i l l have equal d e m a n d , equa l prices a n d equa l profits (since there are no f ixed costs). A s y m m e t r i c e q u i l i b r i u m is descr ibed below. T h o u g h it is be l ieved that th is e q u i l i b r i u m is un ique , the existence of other e q u i l i b r i a cannot be ru l ed out . In a s y m m e t r i c e q u i l i b r i u m , the demands for the two f irms are equa l . Therefore , an analys is of Rl is requ ired since equa l demands are not possible i n e i ther Rl or Rl- In Rl, the d e m a n d for f i r m 1 is g iven by (2.15) a n d the e q u i h b r i u m price is g iven by (2.18). S u b s t i t u t i n g the h o r i z o n t a l m o d e l parameters ( j = [al — a^) + (fcj — b\),m = 2,k = I) yields : n, - ~ (2.64) For firm 2, the d e m a n d is g iven hy Dl = 1 - Df a n d the e q u i l i b r i u m price is g iven by (2.19). T h i s y ie lds a profit o f {2a + b-{al-al)-{bl-bl))' 18a (2-^^) Proposition 5: For the two-dimensional horizontal model, there exists a product equi-librium such that a\ = \ a2 = 0 h ^ h ^ fti = 2 b2 = -Proo f : (i) C o n s i d e r firm 1 and assume that b2 = \ and a2 = 0. T h e der ivat ive of firm I 's prof it func t i on (2.64) w i t h respect to a i is : dai ~ [ 18a2 {2a-{A-2a,)-4a+b-{al-al)-{bl~bl)) (2.66) T h e f rac t i on i n (2.66) is pos i t ive , the second t e r m reduces to a ( 4 - 3 a i + az) + b + {bl - b^) Since a l l o f these t e rms are pos i t ive , -g^ > 0. Therefore , the best response for f i rm 1 is ûi = 1. T h e der ivat ive of (2.64) w i t h respect to bi i s : = 7 ^ ( 4 " - b + {al- al) + (6^ - 6?))(1 - 2 6 0 (2-67) dbi 9a Hi is o p t i m i z e d w h e n bi = ^ (note that (2 .67)=0 and < 0). Therefore , the best response for f i r m 1 is 6i = | . ( i i ) N o w consider F i r m 2 a n d assume that 6i = | a n d Oi = 1. T h e der ivat ive of f i rm 2's profit f u n c t i o n (2.65) w i t h respect to 62 is : IP ± ( 2 a + 6 - (a^ - al) - {bj - 6?))(1 - 262) (2.68) II j is o p t i m i z e d when ^2 = 2 (Note that (2.68) = 0 a n d < 0). Therefore , the best response for f i rm 2 is 62 = |. A t 61 = 62 = | , n: = {2{ai - aj) + {al - al)y 18(ai - ai) ( a i - a2 ) (2 + ai + aif _ I I j is m a x i m i z e d when «2 = 0. There fore , the p r o d u c t e q u i l i b r i u m defined i n Proposition 5 holds . T h e r e are a number of po ints w o r t h n o t i n g about the p r o d u c t e q u i l i b r i u m descr ibed above. F i r s t , profits for the f irms are equal (II j = I I j = | ) as are demands ( D i = D 2 = | ) a n d prices ( p i = p2 = 1). Second, since the o rder ing of character is t i cs is a r b i t r a r y , a p a r a l l e l e q u i l i b r i u m w i t h a i = 02 = | , 6 2 = 1 a n d bi = 0 also exists . Therefore , w i t h o u t i n c l u d i n g some other character ist i cs i n the m o d e l , i t is imposs ib le to de termine w h i c h e q u i h b r i u m w i l l emerge. T h i r d , the produc t e q u i h b r i u m descr ibed above exh ib i t s MaxMin d i f ferent iat ion . T h i s is s i m i l a r to Propositions 1 a n d 3 as we l l as the results of d e P a l m a et a l (1985). F i n a l l y , the e q u i h b r i u m c a n be a n a l y z e d i n terms of the two forces ( d e m a n d a n d strategic ) discussed i n the analys is of the v e r t i c a l m o d e l . T h e strategic force (the desire to reduce price c ompet i t i on ) ensures that there does not exist a n e q u i h b r i u m at a i = a2 = 61 = 62 = |: the point w h i c h w o u l d be chosen i f prices were f ixed a n d equal . T h e d e m a n d force (the desire to increase one's h i n t e r l a n d ) , though d o m i n a t e d by the strategic force, pushes the f irms towards equal i ty on one d i m e n s i o n . 2.7 P r o d u c t E q u i l i b r i u m for the M i x e d V e r t i c a l - H o r i z o n t a l Dif ferentiat ion M o d e l T h e p r o d u c t e q u i l i b r i u m for the m i x e d m o d e l is s i m i l a r to the analysis comple ted by N e v e n a n d Thisse (1988).* It is i n c l u d e d here to a l low for comparisons between the three models . R e c a l l that character i s t i c x is the h o r i z o n t a l character i s t i c (thus ( a i — 02) has a range of 1) and character i s t i c y is the ver t i ca l character i s t i c (thus (62 — 61) has a range of (^max _ y^.^)). Since the o r d e r i n g of p roduc ts a long the h o r i z o n t a l character is t i c ( from 0 to 1) is a rb i t rary , o n l y an analys is of the a s y m m e t r i c character is t i cs case is necessary. However , since a ve r t i ca l character i s t i c is present, b o t h character i s t i c x dominance and character is t i c y d o m i n a n c e need to be considered. In the a s y m m e t r i c character is t i cs case, condi t ions ( A ) - ( D ) define the boundar ies of the various price e q u i h b r i a (see sect ion 2.4). B y s u b s t i t u t i n g the parameter values per ta in ing to the m i x e d m o d e l (j ~ {al — al),m = l,k — 2) , ( A ) - ( D ) can be restated as follows: (62 - bi) < ( a i - a2 ) (2 + {a] - al)) {AM) (62 - b,) < {ax - a2){i - {al - al)) {BM) (62 - br) > {ai - a2){A - {al - al)) {CM) (62 - i l ) > ( a i - a2 ) (2 + {al - al)) {DM) ^Although similar results are obtained, the procedure used to determine the product and price equi-libria is different. N o t e that (Ajv/) a n d (B^f) are equa l a n d that ( C M ) and (D^,/) are equal a n d the reverse s ign of (AM) and ( B M ) - B y a l t e r ing the values of a j , 02,61 a n d 62, it is possible to determine the relevant price e q u i l i b r i u m regions for use i n the p r o d u c t pos i t i on ing subgame. C o n s i d e r the s i t u a t i o n where a i a n d 02 are g iven ( a i > 02) a n d 62,61 are var ied . 1. W h e n 62 = 61, charac ter i s t i c x dominance holds and ( A M ) a n d ( B M ) are satisf ied. T h e pr ice e q u i U b r i u m is i n Rl-2. A s (62 — 61) is increased (e i ther by increas ing 62 or decreasing 61), c o n d i t i o n (BM) is the first to f a i l , b u t character i s t i c x dominance s t i l l ho lds . T h e price e q u i l i b r i u m is i n Rl. 3. (62 — 61) c an be increased u n t i l character is t i c y dominance ho lds . Since ( A M ) s t i l l ho lds , the pr ice e q u i l i b r i u m is i n R^. 4. F i n a U y , (62 — 6 i ) can be increased u n t i l ( A M ) fai ls . N o w ( C M ) a n d ( D M ) ho ld and the price e q u i l i b r i u m is i n R^. N o w consider the s i t u a t i o n where 61 a n d 62 are g iven (62 > 61) a n d 02, a i are var ied . 1. W h e n a2 = ffli, charac ter i s t i c y dominance holds and ( C M ) a n d ( D M ) are satisf ied. T h e price e q u i l i b r i u m is i n R^. 2. A s (02 — fli) is increased , c o n d i t i o n ( D M ) is the first to f a i l , but character ist i c y dominance st iU holds . T h e pr ice e q u i U b r i u m is i n R^. 3. (02 — a i ) can be increased u n t i l character is t i c x dominance holds . Since ( C M ) s t i l l holds , the pr ice e q u i U b r i u m is i n Rl. 4. F i n a l l y , (63 - ^i) can be increased u n t i l (CM) fa i ls . N o w ( A ^ ) a n d ( B ^ ) h o l d and the price e q u i l i b r i u m is i n R^. Several points are w o r t h no t ing . F i r s t , the sequence descr ibed above can be t e r m i -nated at any step depend ing of the range of possible p r o d u c t pos i t ions . Second, since (AM)^ ( B M ) (and ( C M ) / ( E ) M ) ) , there are 4 relevant regions for the price e q u i l i b r i u m w h i c h need to be considered: Rl, R]., R^ andR^. T h e produc t e q u i l i b r i u m w i l l not occur i n dRl or dRl- F i n a l l y , since b o t h the d e m a n d funct ions a n d the e q u i h b r i u m prices are cont inuous across regions, i t follows that the profit funct ions are cont inuous as wel l . Before the produc t e q u i l i b r i u m can be ca l cu la ted , i t is necessary to determine the prof it funct ions i n each of the relevant regions. In Rl, the d e m a n d for f i r m 1 is g iven by (2.15) a n d the e q u i l i b r i u m price is g iven by (2.18). S u b s t i t u t i n g the m i x e d mode l parameters [j = {al — al),m. = l , f c = 2) y ie lds : 72a For f i r m 2, the d e m a n d is g iven hy Dl — 1 — D^ a n d the e q u i l i b r i u m price is g iven by (2.19). T h i s yields a profit o f (4a + b-2(al-al)Y n; = ^ — ^ ^ ^ (2.70) In Rl, the d e m a n d for f i r m 1 is g iven by (2.27) w h i l e the d e m a n d for f i r m 2 is 1 — Dl-T h e e q u i h b r i u m prices for the two f irms are g iven by (2.29) a n d (2.30). C o m b i n i n g these equations y i e l d the f i rms ' profit funct ions i n Rl: nr {a + b + {al~al)y 96 {2b-a-{al-al)Y 96 (2.71) (2.72) Since the same pr ice e q u i h b r i u m applies i n b o t h Rl and R^, profits for the f irms i n these regions are equa l as weU. These profit funct ions are not presented here as they are not required i n the d e t e r m i n a t i o n of the p r o d u c t e q u i l i b r i u m . T h i s is discussed i n more d e t a i l below. 2.7.1 P r o d u c t E q u i l i b r i a T h e product e q u i l i b r i a t h a t are possible i n the m i x e d m o d e l are de termined by s i m u l -taneously c o m p a r i n g the relevant price e q u i l i b r i u m regions. E q u i l i b r i u m solut ions occur w h e n neither f i r m can i m p r o v e i ts profits by u n i l a t e r a l l y a l t e r ing its chosen pos i t i on . T h e first step i n the p r o d u c t e q u i l i b r i u m analys is is d e t e r m i n a t i o n that there does not exist a produc t e q u i l i b r i u m i n the in ter i o r o f Rl or R^. B y the l e m m a proved i n A p p e n d i x B , i t is i l l u s t r a t e d that the first order c o n d i t i o n of the profit f u n c t i o n for f i r m 1 ( f i rm 2) evaluated at pl,pl, w i t h respect to bi (62) c an never be satisf ied i n the inter ior of Rl or R^. Therefore , o n l y Rl or Ry need to be considered i n the p r o d u c t e q u i h b r i u m analys is . In each of the regions, a two step procedure is used to ana lyze a f i rm 's o p t i m a l pos i t i on (subject to the compet i tor ' s pos i t i on ) . F i r s t , the restr ic t ions w h i c h determine the range of p r o d u c t pos i t ions w h i c h are a l lowable i n each region are considered. These inc lude b o t h character i s t i c x or character is t i c y d o m i n a n c e a n d cond i t i ons {AM)-{T)M) described above. Second, the derivatives of the relevant profit funct ions are taken w i t h respect a firm's o w n character is t i cs to de te rmine the profit m a x i m i z i n g l o c a t i o n on a charac ter i s t i c (subject to region res t r i c t i ons ) . T l i e r e are two possible p r o d u c t e q u i l i b r i u m solut ions i n the m i x e d mode l . These solut ions are def ined a n d proven i n Propositions 6 a n d 7. Proposition 6: For the mixed model, if [y'^^'^ — j/min) > ( H ) ^ ; there exists a product equilibrium given by 1 1 = 2 = 2 bi = ymin 62 = y^""" Proo f : I. C o n s i d e r F i r m 1 a n d assume a2 — \ a n d 62 = y^'^^-(i) I n Rl, profits for firm 1 are g iven by (2.69). F r o m this equat i on , i t is apparent t h a t the best response for firm 1 w i t h respect to the ver t i ca l character is t i c is fei = y"""". S u b s t i t u t i n g 6 i = 63 = y""** in to (2.69) reduces the profit func t i on to : _ - ffl2)(4 - a2 - aif Di f f e rent ia t ing this f u n c t i o n w i t h respect to Oi y ie lds : 5 n * 1 ^ = T ^ ( 4 - « 2 - « i ) ( 4 - 3 a i + a 2 ) > 0 (2.73) oai i o S ince = > 0, t i i e best response for f i r m 1 w i t h respect to the h o r i z o n t a l character i s t i c is ai = 1. W i t h ai = 1 a n d = è, Hî becomes: n ; = ( 2 7 4 ) ( i i ) In Ry, prof its for f i r m 1 are g iven by (2.71). D i f f e rent ia t ing w i t h respect to y ie lds : ^ = ^ ( 2 ( a + b + { a l - a ' - 1))(1 - 2a,)) (2.75) is o p t i m i z e d w h e n a, = ^ (note that (2.75)=0 and < 0). Since i t is assumed that 03 = |, i n s e r t i n g a i = 03 = | in to the profit func t i on yie lds : n r = ^ F a c i n g this e q u a t i o n , the o p t i m a l response for f i r m 1 w i t h respect to the v e r t i c a l character i s t i c is 61 = ymin- There fore the profit for f i r m 1 w i l l be: ..max _ . . n r = (2.76) ( i i i ) C o m p a r i n g (2.74) a n d (2.76), firm 1 w i l l prefer to choose a j = ^,bi = j/min when: y ' " ^ ' ' - y m i „ > (2.77) I I . N o w consider F i r m 2 a n d assume 6 i = y^rùn a n d a i = |. (i) In Rl, the prof i t for firm 2 is defined i n (2.70). Faced w i t h this equat i on , the best choice of 62 for firm 2 is the highest level of 62 such that the so lut ion remains i n i ?^ .Th i s means that c o n d i t i o n ( B ) w i l l be satisf ied w i t h equal i ty : {b2 - h) = {a^ - a2){4 - {al - al)) S u b b i n g the equa l i ty in to the prof it f u n c t i o n y ie lds : ( a i - a 2 ) ( 4 + ^ ^ ^ + 2 ( a , + a 2 ) ) ^ • F r o m (2.78), i t is obvious that the best response for firm 2 is 02 = 0. S u b b i n g ai = ^ a n d 02 = 0 in to (2.78) y ie lds n ; = (^)' (2.79) ( i i ) In Ry, the profit for firm 2 is defined by (2.72). D i f f e rent ia t ing this funct ion w i t h respect to = ^ ( 2 ( 2 6 - a - { a l - a ' - 1))(1 - 2a,)) (2.80) da2 9b' f l j " is o p t i m i z e d when 03 = |. Insert ing a, = a, = ^ y ie lds : ~ 9 T h e o p t i m a l response for firm 2 is 63 = y™"''. G i v e n 6i = ymin, the profit for firm 2 i n this region is: n r = y-^n) 2^.81) ( i i i ) C o m p a r i n g (2.79) a n d (2.81), firm 2 w o u l d prefer to choose a, = ^ 63 = y w h e n 4 ( y ' " " - y m m ) ^ f9\' max 9 - V 1 6 / [32) {21\' y-^^^-Vr^r. > - (2.82) Chapter 2. Product and Price Competition in a Two-Dimensional Market I I I . Since (2.82) is more restr i c t ive t h a n (2.77), the propos i t i on is proven . Proposition 7: For the mixed model, if {y^^^ — î/min) < 2 + there exists a product equilibrium given by: ai = 1 a2 = 0 L ^.max L ..max bi = y 02 = y Proo f : I. C o n s i d e r f i r m 1 a n d assume 03 = 0, 62 = y^^. ( i ) In Rl, the analys is i n the proof of Proposition 6 (part I.(i)) i n d i c a t e d that faced w i t h the profit f u n c t i o n defined i n (2.69), the best response for firm 1 w o u l d be tti = 1,61 = y " * " . S u b s t i t u t i n g these values, as wel l as the assumed values for firm 2, in to (2.69) y ie lds : ^\ = \ (2.83) (h) I n iZy, the profit for firm 1 is defined by (2.70). A s shown i n (75), the best response for firm 1 w i t h respect to the h o r i z o n t a l character i s t i c is a i = |. S e t t i n g ax = J and a, = 0, (70) reduces to : ^ 96 Di f f erent ia t ing w i t h respect to bi y ie lds : Ô6i 1^  9fc2 ^ ( i - (2.84) T h e first t e r m of the der ivat ive is a lways pos i t ive . T h e second t e r m is negative i f 62 — 6 i < ^. However , for a so lu t i on to be i n th is reg ion , c o n d i t i o n D must h o l d . Insert ing 62 = y " ' " * , ^ ! = | , a 2 = 0 in to c o n d i t i o n D y ie lds : y -ax _ fc^ > _ a2 ) (2 + (ax + 0 2 ) ) G i v e n this result , < 0 and the best response for firm 1 is 61 = y„ prov ided that y"^'^ — y^^ > |. T h i s y ie lds a profit of 1 - 9 ( 2 / — - y ^ n ) Note that i f y ™ " — y^in < |, the admiss ib le charac ter i s t i c values w h i c h can be chosen by firm 1 ( a i , ftj) is the proper subset of the admiss ib le values considered above. Therefore , (2.85) represents the m a x i m u m profit poss ib le for f i rm 1 i n this region. ( i i i ) C o m p a r e (2.83) a n d (2.85). For f i r m 1 to choose a, = l,bi = y""^"", it must be true t h a t : U s i n g the q u a d r a t i c f o r m u l a a n d select ing the largest root , - ymin < 2 + ^ (2.86) II . N o w consider F i r m 2 and assume that aj = 1 a n d = y"^'^^. (i) In Rl, the profit for f i r m 2 is defined by (70). B y observat ion , the best response for f i rm 2 w i t h respect to the v e r t i c a l charac ter i s t i c is b, = y"*"*. T h i s reduces (2.70) to : G i v e n (2.87), the best response for firm 2 w i t h respect to the h o r i z o n t a l charac-ter is t i c is 02 = 0. S u b s t i t u t i n g firm 2's best response (given firm I's posit ion) into (2.87) y ie lds : (2.88) (i i) In since bi = y"^'^^ is g iven a n d (62 — bi) > 0, the o n l y response for firm 2 i n this region w i t h respect to the v e r t i c a l character i s t i c is 62 = J / " " * * - Since character i s t i c y d o m i n a n c e holds i n th is region ((62 — 61) > ( o i — 1 2 ) ) , f i r m 2's on ly response w i t h respect to the h o r i z o n t a l character i s t i c is 02 = Oj = 1. T h e choice of these character i s t i c levels w o u l d result i n a zero prof i t . ( i i i ) G i v e n O i = 1 a n d bi = y""^^, firm 2 w o u l d always prefer 02 — 0 and 62 = 2/™*''-III . Since the o n l y res t r i c t i on to the p r o d u c t e q u i l i b r i u m is (2.86), the propos i t i on is proven. 2.7.2 S u m m a r y a n d Impl icat ions T h e product e q u i h b r i a descr ibed i n Propositions 6 and 7 can be s u m m a r i z e d as follows (see F i g u r e 2.17): I. If J / ™ " — ymin < (H) , the p r o d u c t e q u i h b r i u m is tti = 1 02 = 0 6 _.max J _ ...max 1 = 2/ 02 = 2/ II . If y""^"" - 2/min > 2 + the product e q u i h b r i u m is bi = yn b2 = y'^ I I I . If y - - - ymin e %/63 4 , e i ther product e q u i l i b r i u m is possible. Firm 1 = ( 1, y"*"^,^ Firm 2 = (0, y"""^ 132 Finn 1 = (i.ym.,.), Fimi 2 = (!->''"'''') 2 + 1 ^ 4 (>' '" ' ' ' - :ym.n) F i g u r e 2.17: S u m m a r y of P r o d u c t E q u i h b r i a for the M i x e d V e r t i c a l - H o r i z o n t a l M o d e l These results have a n u m b e r o f interest ing features. F i r s t , an analysis of the equi -l i b r i u m profits ind icates t h a t , regardless of e q u i l i b r i u m , f i r m 2 ( w h i c h always chooses y^'^ on the v e r t i c a l charac ter i s t i c ) has profits w h i c h are. at least as h i g h as f i r m 1. Since the choice of f i r m was a r b i t r a r y i n the def in i t ion of the a s y m m e t r i c character ist ics case, b o t h f i rms w o u l d want to choose the p r o d u c t w h i c h is a lways l o ca ted at y " " " * . Therefore , w i t h o u t i n c l u d i n g some other character is t i cs i n the m o d e l , it is imposs ib le to determine e q u i l i b r i u m w i l l emerge. Second, b o t h of the ident i f ied p r o d u c t e q u i h b r i a exh ib i t m a x i -m u m d i f ferent iat ion on one d i m e n s i o n a n d m i n i m u m di f ferent iat ion on the other {MaxMin di f ferent iat ion) . A s was ment i oned i n t l ie sections d e a l i n g w i t h the v e r t i c a l and hor izon-t a l models , this result appears to be i n the sp ir i t of d e P a l m a et a l (1985) who suggest that f irms w i l l agg lomerate prov ided that the produc ts are d i f ferent iated on some other d imens ion . F i n a l l y , a n analysis of the two e q u i l i b r i a ind icates that w h e n the firms dif-fer on ly on the h o r i z o n t a l character is t i c , the two f irms have equa l prices , demands and prof its . Pro f i ts for the firms are equal ( f l^ = 112 = ^) as are demands {Di = D2 = \) and prices (p i = P2 = 1). T h i s is s i m i l a r to the h o r i z o n t a l m o d e l i n w h i c h a l l locat ions on the h o r i z o n t a l character is t i cs are v iewed as h a v i n g equal q u a l i t y by consumers . W h e n the firms differ o n the v e r t i c a l character i s t i c , the firm w i t h the h i g h q u a l i t y product has higher profits t h a n the firm w i t h the lower q u a l i t y p r o d u c t . T h i s is s i m i l a r to the s i t u a t i o n descr ibed i n the ver t i ca l m o d e l . 2.8 S u m m a r y In this chapter , three models were developed to s t u d y the c o m p e t i t i v e i m p h c a t i o n s of var-ious product d i f ferent iat ion assumptions i n markets charac ter i zed by m u l t i p l e d imensions . T h e one -d imens iona l h o r i z o n t a l a n d ver t i ca l models were extended to two d imensions . In a d d i t i o n , a t w o - d i m e n s i o n a l m i x e d v e r t i c a l - h o r i z o n t a l m o d e l was developed. E a c h m o d e l was ana lyzed us ing a two-stage game theoret ic analys is i n w h i c h two firms compete first o n product pos i t ions a n d t h e n on price . C l o s e d f o r m e q u i l i b r i u m solut ions were ob ta ined for each stage i n w h i c h compet i tors are u n r e s t r i c t e d i n their choices of pr i ce or product pos i t ions . T h e research y i e lded a n u m b e r of in teres t ing findings. P e r h a p s the most signif icant finding was t h a t , i n e q u i l i b r i u m , there is a prevalence of MaxMin p r o d u c t d i f ferent iat ion. T h a t is , the two firms t e n d to choose pos i t ions w h i c h w i l l represent m a x i m u m differ-ent ia t i on on one d i m e n s i o n and m i n i m u m di f ferent iat ion o n the other d imens ion . T h i s so lut ion i m p l i e s that the m a x i m u m di f ferent iat ion so lut ions f ound i n one -d imens iona l models ( d ' A s p r e m o n t et a l 1979, S h a k e d a n d S u t t o n 1982) do not ex tend to two d i m e n -sions. A l t h o u g h there was a prevalence for MaxMin p r o d u c t d i f ferent iat ion , i t was found that i n the t w o - d i m e n s i o n a l ver t i ca l d i f ferent iat ion m o d e l , under ce r ta in condit ions , m a x -i m u m produc t d i f ferent iat ion does occur . F u r t h e r m o r e , there are condit ions i n w h i c h the f irms di f ferentiate on b o t h d imens ions , but not ful ly . T h i s l a t t e r f ind ing appears to i l l u s -trate that there are l i m i t s to the strategic effect ( the desire to reduce price compet i t i on ) w h i c h leads to m a x i m u m di f ferent iat ion i n the o n e - d i m e n s i o n a l case. F i n a l l y , the pr ice e q u i l i b r i a for the three models share a general ized f o r m w i t h some parameter values de-pend ing on the product d i f ferent iat ion assumpt ions used. T h i s f ind ing accentuates the s imi lar i t i es between the three models . In recent years , there has been a g rowing l i t e r a t u r e o n p r o d u c t a n d price c o m p e t i t i o n i n markets character ized by m u l t i p l e produc t d imens ions (e.g. Hauser 1988; K u m a r and S u d h a r s h a n 1988; C a r p e n t e r 1989; C h o i , D e S a r b o a n d H a r k e r 1990, H o r s k y a n d Ne lson 1989). A s was o u t l i n e d earher , none of the current models character ize a product e q u i h b r i u m where f irms are aUowed to choose freely i n the al lowable product space. Consequent ly , the t w o - d i m e n s i o n a l p r o d u c t e q u i h b r i u m so lut ions o b t a i n e d i n this chapter l ead to a be t ter u n d e r s t a n d i n g of c o m p e t i t i v e markets .^ ^Chapter 5 includes a discussion of model limitations and future research. C h a p t e r 3 S e t t i n g the Strategic D i r e c t i o n in a P r o d u c t - S e r v i c e F i r m 3.1 I n t r o d u c t i o n C o m p a n i e s c o m p e t i n g o n a g l oba l basis increas ing ly need to decide whether c ompet i t i ve success requires t h e m to emphas ize p r o d u c t features or service. A n increased emphasis on e i ther of these components requires the development of unique ski l ls a n d capabi l i t ies . W h i l e ne i ther the p r o d u c t nor services can be neglected, sett ing resource a l l o ca t i on p r i -orit ies often necessitates some trade-offs. To ensure the m a x i m u m i m p a c t of p o t e n t i a l investments , a s t rateg ic d i r e c t i o n needs to be set. T h e purpose of this research is to develop a m o d e l to help a f i rm determine the strate-gic d i r e c t i o n it s h o u l d pursue . A strategic direction is defined as the company ' s overr id ing focus for i m p r o v e m e n t s r e l a t i n g to i ts p r o d u c t / s e r v i c e offering(s).^ For example , a com-pany m a y choose a service or iented strategic d i re c t i on . T h i s imphes t h a t , i n the m e d i u m t e r m , the m a j o r i t y of offering improvements w i l l be re lated to service. T h e development of a t e c h n i c a l service d e p a r t m e n t , an improvement i n the parts dehvery system a n d / o r an increase the n u m b e r of dealerships m a y a l l be part of this "service" emphasis . T h e need for a strategic d i r e c t i o n stems f r o m the a s s u m p t i o n t h a t companies must cont inuous ly i m p r o v e the i r offerings i n order to r e m a i n compet i t i ve . In a w o r l d of increas ing g loba l c o m p e t i t i o n , th i s a s s u m p t i o n appears to be reasonable . M a j o r corporat ions are recog-n i z i n g th is need to i m p r o v e as wel l ; for example , D u P o n t recent ly created the pos i t i on of ^The term offering is used to describe what the customer is purchasing. Since both product and service features are often important in the customer's purchase decision, it was felt that the terms product or product offering placed undo emphasis on the product component. V i c e Pres ident for C o n t i n u o u s Improvement ( W a l l Street J o u r n a l 1990). Besides sat is fy ing the need to i m p r o v e a firm's offering, a s trateg ic d i rec t i on can have other benefits. T o p management suppor t for a p a r t i c u l a r s trategic d i rec t ion should a l low for the c oo rd ina t i on of the sometimes diverse f unc t i ona l areas of p r o d u c t i o n , R & D , m a r k e t i n g . In a d d i t i o n , i f i m p l e m e n t a t i o n managers have h a d i n p u t into the selection of the strategic d i r e c t i o n , a stronger c o m m i t m e n t to i ts success s h o u l d resu l t . B o t h of these features should have a pos i t ive i m p a c t on the c ompany ' s corporate c u l t u r e . D e t e r m i n i n g the o p t i m a l strategic d i r e c t i o n for a c ompany is d i f f i cu l t . P r a g m a t i c a l l y , the goal is to choose the strategic d i r e c t i o n (either p r o d u c t or service) w h i c h w i l l l ead to the m a x i m u m r e t u r n on investment . However , assessing the i m p a c t of a p a r t i c u l a r strategic d i rec t ion is c o m p l i c a t e d by the fact that cost a n d techno log i ca l requirements often d e m a n d g loba l sourc ing whi le cus tomer needs a n d c o m p e t i t i v e in tens i ty vary on a reg ional market basis . These features lead to a di f ferential i m p a c t of changes i n the c o m -pany ' s product -serv ice offering. O f t en , p r o d u c t improvements affect aU markets (a lbeit w i t h various degrees of effectiveness) whi le service improvements o n l y affect the markets i n w h i c h they are i m p l e m e n t e d . There fore , to enable the a p p r o p r i a t e comparisons , the l o c a l effects of proposed improvements must be aggregated o n a g l o b a l basis. It is at this g l oba l level that the strategic d i r e c t i o n dec is ion is made . T h e strategic d i r e c t i o n m o d e l ( S D M mode l ) developed i n th is chapter , h m i t s the strategic d i rec t i on dec is ion to the choice between a produc t o r i e n t a t i o n a n d a service o r i en ta t i on . T h e m o d e l is based on a cons iderat i on of market by market compet i t i ve analyses , but concentrates on the more strategic issues. T h e m o d e l is relevant to c o m -panies who are responsible for p r o v i d i n g b o t h the phys i ca l p r o d u c t a n d the associated services. T h i s s i t u a t i o n is t y p i c a l of m a n y companies m a n u f a c t u r i n g i n d u s t r i a l and c o m -m e r c i a l products . For example , the e m p i r i c a l s t u d y descr ibed i n the next chapter focuses on a single offering, combine harvesters , i n the f a r m equipment i n d u s t r y . M a n u f a c t u r e r s of combines , l ike J o h n Deere, m a n u f a c t u r e combines i n centra l i zed p r o d u c t i o n faci l it ies and m a r k e t t h e m t h r o u g h a p r o p r i e t a r y dealer network. T h e scope of this chapter is l i m i t e d to the development a n d descr ip t i on of the S D M m o d e l s t r u c t u r e . In order for the S D M mode l to be i m p l e m e n t e d , a d d i t i o n a l research is necessary. P a r t of this a d d i t i o n a l research is addressed by the e m p i r i c a l s tudy descr ibed i n the next chapter . O t h e r areas r e q u i r i n g a d d i t i o n a l research are beyond the scope of this d i s ser ta t i on . These areas are h i g h l i g h t e d d u r i n g the m o d e l development a n d s u m m a r i z e d at the end of the chapter . T h i s chapter is o rganized as follows. F i r s t , the relevant l i t e r a t u r e is reviewed. T h i s is fo l lowed by the development of the mode l s t ruc ture . T h e chapter concludes w i t h a s u m m a r y of the m o d e l and its c ont r ibut i ons . In a d d i t i o n , the next steps i n the overa l l development of an i m p l e m e n t a b l e S D M mode l are discussed. 3.2 L i t e r a t u r e R e v i e w T h e h t e r a t u r e review is o rganized as follows. F i r s t , a short rev iew of the g loba l m a r k e t i n g and the services m a r k e t i n g Hteratures w i l l be presented to i l l u s t r a t e the na ture of the g loba l - l o c a l a n d product - serv i ce t rade offs w h i c h represent i m p o r t a n t features of the m o d e l . T h i s w i l l be fol lowed by a review of the o p t i m a l produc t p o s i t i o n i n g l i t e ra ture . 3.2.1 G l o b a l M a r k e t i n g O v e r the last several years, academic interest i n the s t u d y o f g l o b a l a n d i n t e r n a t i o n a l m a r k e t i n g issues has grown d r a m a t i c a l l y . Several i m p o r t a n t research streams have been developed. These inc lude the s t u d y of c u l t u r a l effects (Tse , Lee , V e r t i n s k y a n d W e h r u n g 1988), country of o r i g i n effects ( H o n g a n d W y e r 1989), i n t e r n a t i o n a l negot iat ions ( C a m p -be l l , G r a h a m , J o l i b e r t a n d Meissner 1988) a n d market e n t r y strategies ( R y a n s 1988). One of the most w ide ly debated g l o b a l i z a t i o n issues is that of i n t e r n a t i o n a l s t a n d a r d i z a t i o n of m a r k e t i n g strategies. W i t h i n m a r k e t i n g , the iner i ts of g l oba l s t a n d a r d i z a t i o n versus marke t - specific strategies has been discussed extensively . It is this aspect of the g loba l m a r k e t i n g l i t e ra ture w h i c h is most re lated to the current research. P r i o r to d iscussing s t a n d a r d i z a t i o n issues, it is necessary to the define w h a t is meant by g l oba l and l o ca l strategies. A g l oba l l y s t a n d a r d i z e d m a r k e t i n g strategy can be defined as a strategy w h i c h uses a c o m m o n offering, pr ice , d i s t r i b u t i o n and p r o m o t i o n strategy w o r l d w i d e ( J a i n 1989). S ta ted i n these terms , most researchers have argued against " t o t a l " s t a n d a r d i z a t i o n (e.g., O h m a e 1989, J a i n 1989). A l o ca l m a r k e t i n g strategy has been referred to as a m u l t i d o m e s t i c s trategy ( Y i p 1989). In this strategy, the products offered i n a p a r t i c u l a r c o u n t r y are ta i l o red to the l o c a l needs. In a d d i t i o n , a l l m a r k e t i n g ac t iv i t i es , i n c l u d i n g p r i c i n g , p r o m o t i o n a n d d i s t r i b u t i o n are gu ided by the l o c a l (or coun-t r y ) s i t u a t i o n . P a r t i c i p a t i o n i n a market is d e t e r m i n e d by that country ' s s tand-alone p o t e n t i a l for revenues a n d profits ( Y i p 1989, p.31) T h e recent debate over the need for s t a n d a r d i z e d m a r k e t i n g strategies was i n i t i a t e d by L e v i t t ' s (1983) ar t i c le , " T h e G l o b a l i z a t i o n of M a r k e t s " . In this ar t i c l e , L e v i t t argues that i n t e r n a t i o n a l markets were homogen iz ing into w o r l d w i d e market segments. He cal led for the s t a n d a r d i z e d p r o d u c t i o n of p r o d u c t s to serve the g loba l m a r k e t . T h r o u g h this strategy, higher q u a h t y products c o u l d be produced at lower costs. L e v i t t argues that the consumer a t t r a c t i o n to these affordable, h i g h q u a l i t y produc ts w i l l d o m i n a t e products w h i c h are designed to meet the needs of i n d i v i d u a l markets . L e v i t t ' s ar t i c le was met w i t h m i x e d react ion . O n the one h a n d , the economies of scale w h i c h cou ld be achieved t h r o u g h s t a n d a r d i z a t i o n was general ly accepted as i t had a lready been recognized i n m a n y industr ies (e.g. the a u t o m o b i l e indus t ry , lead by Japanese companies ) . O n the other h a n d , the ca l l for the deve lopment of a s t a n d a r d i z e d strategy ( i n c l u d i n g services, p r i c i n g a n d p r o m o t i o n ) , g iven the s t r u c t u r a l a n d c u l t u r a l differences between markets was quest ioned . Douglas and W i n d (1987) argue that i m p l e m e n t i n g a s tandard i zed g loba l strategy w o u l d be i n a p p r o p r i a t e i n most s i tuat ions . These authors note that p r o d u c t strategies can range anywhere f r o m g l oba l l y s t a n d a r d i z e d to l o c a l l y cus tomized a n d that the choice of extreme strategies is rare ly the most appropr ia te . A n ob ject ive assessment of the appropriateness of a g l oba l or l o c a l s trategy has been h a m p e r e d by the i n a b i l i t y to generate e m p i r i c a l ev idence (other t h a n anecdotal ) i n sup-port of e i ther p o s i t i o n . A s such , researchers have proposed cont ingency frameworks w h i c h enable managers to decide what type of s trategy is most a p p r o p r i a t e for the i r own orga-n izat i ons . Y i p (1989) presents a f ramework w h i c h c o u l d be used to assess the meri ts of g l oba l a n d l o c a l strategies i n various s i tuat ions . Q u e l c h a n d Hoff (1986), t h o u g h suppor t -ive of a more g lobahzed product strategy, recognize the existence of s t r u c t u r a l a n d / o r o r g a n i z a t i o n a l barr iers w h i c h i n h i b i t the ac compl i shment of this goal . These authors present a f ramework to a i d companies i n the t r a n s i t i o n f r o m a m u l t i n a t i o n a l o r i entat i on to a more g loba l o r i enta t i on . Since l i t t l e e m p i r i c a l evidence has been generated, the g loba l s t a n d a r d i z a t i o n versus market -spec i f i c strategies debate has been large ly descr ipt ive i n nature . T h e S D M mode l presented here takes a somewhat different approach . Instead of a r g u i n g for or against g l oba l s t a n d a r d i z a t i o n , a n a n a l y t i c a l m o d e l is developed to s t u d y the strategic p r i c ing a n d pos i t i on ing i m p h c a t i o n s of c o m p e t i n g i n markets i n w h i c h some variables are chosen g loba l ly and others on a market by market basis. T h e research conceives of strategies as be ing m u l t i - d i m e n s i o n a l i n nature as they inc lude b o t h g l o b a l a n d l o c a l d imens ions . T h i s approach does not lessen the i m p o r t a n c e of c o n t i n u i n g the g l oba l - l o ca l debate . R a t h e r , the research addresses a specific issue (i.e., the choice of s trategic d i rec t i on ) w h i c h is relevant to a signif icant subset of i n t e r n a t i o n a l c ompet i t o rs . 3.2.2 Services M a r k e t i n g L i k e g l o b a l m a r k e t i n g , the h t e r a t u r e on services m a r k e t i n g has g r o w n d r a m a t i c a l l y i n re-cent years . M u c h of this research has dealt w i t h the opera t i on and management of service o r g a n i z a t i o n s . Specif ic emphasis has been p laced on the c lass i f i cat ion of services (Love-lock 1983), the service encounter ( Z e i t h a m l , B e r r y and P a r a s u r a m a n 1988), c ompla int h a n d l i n g ( S i n g h 1988) a n d service b u n d l i n g ( G u i l t i n a n 1987). T h e r e has been re la t ive ly l i t t l e research concerned w i t h c o m b i n e d produc t and ser-vice o r g a n i z a t i o n s despite the fact that such research has been considered a M a r k e t i n g Science I n s t i t u t e p r i o r i t y ( M S I 1988). T h i s m a y be due to the fact the services m a r k e t i n g researchers have tended to concentrate o n consumer rather t h a n i n d u s t r i a l markets . In consumer m a r k e t s , where the d i s t r i b u t i o n channels tend to be l ong , the produc t m a n u -fac turer has l i m i t e d contro l over the services prov ided to the end user. I n a d d i t i o n , there are a s igni f icant n u m b e r of o rganizat ions w h i c h offer on ly services. In i n d u s t r i a l markets , where d i s t r i b u t i o n channels t end to be shorter , the manufac turer of the produc t m a y also be responsib le for offering m a n y of the associated services. A t a recent M a r k e t i n g Science I n s t i t u t e conference, the i m p o r t a n c e of b o t h the p r o d u c t a n d service components was recognized by m a n y of the i n d u s t r y par t i c ipants ( G u i r y 1989). T h e i m p o r t a n c e of services i n t r a d i t i o n a l m a n u f a c t u r i n g organizat ions has not gone u n n o t i c e d by academic researchers. Chase and G a r v i n (1989) i n t r o d u c e d the service fac-t o ry concept w h i c h por t rays the m a n u f a c t u r i n g fac ihty as a center for the development of services w h i c h a i d i n the m a r k e t i n g of the company ' s p r o d u c t s . These services inc lude us ing fac tory personnel as a resource i n a i d i n g customers w i t h i n s t a l l a t i o n , maintenance a n d t r o u b l e s h o o t i n g . In a d d i t i o n to these service o p p o r t u n i t i e s . C h a s e a n d G a r v i n i l -l u s t r a t e how the fac tory can be used as a l a b o r a t o r y to test new produc t designs and m a n u f a c t u r i n g processes; as a s h o w r o o m to demonstrate the q u a l i t y of the products ; a n d . as an i n f o r m a t i o n source i n p r o v i d i n g after sales service support to customers . In order to imp lement the service fac tory concept , Chase a n d G a r v i n argue that signif icant changes must be m a d e i n the s k i l l s , capab i l i t i es and a t t i tudes of employees and managers . T h i s impl ies that the corporate c u l t u r e is an i m p o r t a n t ingredient i n the successful i m p l e m e n t a t i o n of this increased service o r i e n t a t i o n . C o r p o r a t e cu l ture is also i m p o r t a n t i n the development of a strategic d i r e c t i o n . A t b o t h the top management and i m p l e m e n t a t i o n levels, managers and employees must work together to evaluate current ski l ls and capabi l i t ies as wel l as ident i f y p r o m i s i n g avenues for i m p r o v e m e n t . T h i s requires teamwork across different func t i ona l areas ( p r o d u c t i o n , R &:D, m a r k e t i n g ) . L i k e C h a s e a n d G a r v i n (1989), Q u i n n , D o o r l e y a n d Raquet te (1990) also comment on the i m p o r t a n c e of services i n t r a d i t i o n a l m a n u f a c t u r i n g o rgan izat i ons . These researchers state that 6 5 % to 7 5 % of employees i n m a n u f a c t u r i n g industr i es " p e r f o r m service tasks rang ing f rom c r i t i c a l p r o d u c t i o n - r e l a t e d ac t iv i t i es hke research, log is t i cs , maintenance , and produc t a n d process design to ind irec t staff services hke a c c o u n t i n g , law, financ-i n g and p e r s o n n e l " . Q u i n n et a l argue that because most m a n u f a c t u r i n g industr ies are p r i m a r i l y service o rgan iza t i ons , companies s h o u l d focus o n the tasks that gives t h e m a compet i t i ve edge a n d outsource the rest. In b o t h of the art ic les reviewed here, the authors beheve that the i m p r o v e d m a n -agement of services can lead to success i n m a n u f a c t u r i n g o rgan i za t i ons . However , i t is i m p o r t a n t to note that b o t h papers have defined services to i n c l u d e ac t iv i t i es w h i c h serve other departments w i t h i n the c o m p a n y as we l l as ac t iv i t i es w h i c h serve the cus-tomer direct ly . Despi te this expanded de f in i t i on of services, i t appears t h a t b o t h papers are a d v o c a t i n g a n increased emphasis on the service component of the customer offering. A s these papers are p r i m a r i l y descr ipt ive , they prov ide ne i ther an ana lys i s of the re lat ive i m p o r t a n c e of product a n d service components of the customer offerings nor a d iscuss ion of the f inanc ia l a n d o r g a n i z a t i o n a l tradeoffs w h i c h must be m a d e i n developing the p r o d -uct and service strategies . T h e a n a l y t i c a l m o d e l presented here assumes the existence of these tradeoffs i n the c h a r a c t e r i z a t i o n of the strategic d i r e c t i o n dec is ion a n d suggests an increased emphasis on services o n l y w h e n a s igni f icant increase i n r e t u r n can be expected. 3.2.3 O p t i m a l P r o d u c t P o s i t i o n i n g Over the past two decades, m a r k e t i n g researchers have developed a n u m b e r of models w h i c h have the p o t e n t i a l to a i d managers i n the o p t i m a l design of new products . T h e research s t ream has t ended to concentrate p r i m a r i l y o n the development of c o m p u t a -t i o n a l a lgor i thms w h i c h search for o p t i m a l p r o d u c t pos i t ions . T h i s review w i l l trace the development of o p t i m a l produc t p o s i t i o n i n g models a n d discuss the l i m i t a t i o n s of this research s t ream. Spec ia l emphasis w i l l be p laced on d iscuss ing those models w h i c h are most closely re la ted to the current research. E a r l y O p t i m a l P r o d u c t P o s i t i o n i n g M o d e l s M a n y of the ear ly o p t i m a l p r o d u c t p o s i t i o n i n g mode ls were concerned w i t h developing a lgor i thms w h i c h o p t i m i z e d a new p r o d u c t l o c a t i o n i n j o in t p e r c e p t u a l space. A jo int space per cep tua l m a p i l lus t rates the l o c a t i o n of b o t h produc ts a n d consumer idea l points i n the same space (see F i g u r e 3.1). T h i s representat ion is u s u a l l y accomphshed us ing m u l t i - d i m e n s i o n a l sca l ing techniques ( M D S ) ( C a r r o l l 1972; S r i n i v a s a n a n d Shocker 1973, D e S a r b o a n d R a o 1986). E m p i r i c a l a p p h c a t i o n s l ike G r e e n a n d C a r m o n e (1970) and models hke P E R C E P T O R ( U r b a n 1975) i l l u s t r a t e how this approach can be used to describe a p a r t i c u l a r p r o d u c t m a r k e t . T h e basic o p t i m a l p r o d u c t p o s i t i o n i n g p r o b l e m i n j o in t space is as fol lows. G i v e n a Dimension 2 X X ^ X , X X X X * ^ X X X • A X X X X X X X X X X X X X X 1 " . 1 X B ^ X ^ ^ X C ^ X * X X D X Dimens ion 1 • = Locat ion o f a Brand X = A n Individual 's Ideal Po int F i g u r e 3.1: A J o i n t Space P e r c e p t u a l M a p I l l u s t r a t i n g P r o d u c t L o c a t i o n s a n d C o n s u m e r Ideal Po ints representat ion of b rands a n d consumer idea l points a n d a consumer choice rule , what new p r o d u c t l o c a t i o n i n the j o in t space m a p would y i e l d the highest share of demand? T h e s implest vers ion of th is p r o b l e m is the de termin is t i c choice p r o b l e m where the choice ru le is s i m p l y that the consumer w i l l choose the produc t w h i c h is closest to h i s / h e r idea l po in t . T o solve th is p r o b l e m , the p o t e n t i a l d e m a n d of each produc t l o c a t i o n can be eva luated w i t h the o p t i m a l l o c a t i o n of a new produc t be ing the one w i t h the highest expec ted d e m a n d . T h o u g h the procedure for l o c a t i n g the o p t i m a l produc t pos i t i on seems straightfor-w a r d , searching every poss ib le l o c a t i o n , even i n re la t ive ly s m a l l prob lems, is imposs ib le . N o t o n l y is there a n i n f i n i t e n u m b e r of possible l ocat ions , a unique so lut i on is un l ike ly as there w o u l d o r d i n a r i l y be a n o p t i m a l region rather t h a n an o p t i m a l point ( G a v i s h , H o r s k y a n d S r i k a n t h 1983). T h u s , the thrust of ear ly research was the development of efficient c o m p u t a t i o n a l a l g o r i t h m s to solve the j o in t space prob l em descr ibed above. Papers b y A l b e r s (1979), A l b e r s a n d Brockho f f (1977), G a v i s h , H o r s k y a n d S r i k a n t h (1983), a n d Z u f r y d e n (1979) a l l present solutions to the basic p r o b l e m by employ ing various s i m p l i f y i n g heurist ics to reach a so lu t i on w h i c h can be considered " o p t i m a l " . T h e basic j o i n t space o p t i m a l product pos i t i on ing m o d e l has been extended i n a n u m b e r of ways. T h e basic m o d e l assumes that a l l consumers perceive the current brands s i m i l a r l y but have i d i o s y n c r a t i c i d e a l po ints . In a d d i t i o n , distance is va lued equa l ly i n a l l d imens ions for a l l consumers . A l b e r s (1979) extended the assumpt ion of equa l d imens ion weights by a l l o w i n g these weights to vary at the i n d i v i d u a l level . T h i s a d d i t i o n a l v a r i a t i o n be t ter captures the n a t u r e of differences i n consumer preferences. M o s t models w h i c h were developed after A l b e r s ' a r t i c l e in co rpora ted this feature. A n o t h e r m a j o r enhancement to the basic m o d e l was the i n c o r p o r a t i o n of a probab ihs -t i c choice ru le . S u c h a choice rule posits that the p r o b a b i h t y that a consumer chooses a specific b r a n d f r o m a set of b rands is a decreasing f u n c t i o n of the d istance of the b r a n d f r o m the consumer 's idea l po in t . Research i n number of areas i n c l u d i n g var iety seeking behav ior ( M c A l i s t e r and Pessemier 1982) and cons iderat ion sets (S i lk a n d U r b a n 1978) has i n d i c a t e d that for f requently purchased goods (and poss ib ly other p r o d u c t categories) a p r o b a b i h s t i c choice rule is more reasonable. A p r obab i l i s t i c choice rule has been i m -p l emented i n a number of o p t i m a l p r o d u c t pos i t i on ing a lgor i thms i n c l u d i n g P R O P O P P ( A l b e r s 1982) a n d P R O D S R C H ( S u d h a r s h a n , M a y and Shocker 1987). T h o u g h the probab i l i s t i c choice rule appears more rea l is t i c for the analysis of fre-q u e n t l y purchased goods, the de te rmin i s t i c choice rule m a y be more app l i cab le in cer ta in s i tua t i ons . G a v i s h , H o r s k y a n d S r i k a n t h (1983) proposed a de termin i s t i c choice mode l spec i f i ca l ly designed for in f requent ly purchased goods or durab les . T h e y argue t h a t i n these s i t u a t i o n s , consumers evaluate a l l a l ternat ives and choose the most preferred alter-nat ive w i t h certa inty . Interest ingly , i n S u d h a r s h a n , M a y a n d Shocker 's (1987) s i m u l a t i o n c o m p a r i s o n of o p t i m a l produc t p o s i t i o n i n g a lgor i thms , G a v i s h , H o r s k y and Sr ikanth ' s a l -g o r i t h m per f o rmed weU regardless of whether s imula ted consumers u t i h z e d a p r obab i l i s t i c or d e t e r m i n i s t i c choice ru le . O p t i m a l P r o d u c t P o s i t i o n i n g a n d S p a t i a l E c o n o m i c s A n u m b e r of researchers have recognized the s imi lar i t i es between the o p t i m a l product p o s i t i o n i n g p r o b l e m a n d problems i n s p a t i a l economics a n d have developed models w h i c h a t t e m p t to integrate the two l i t e ra tures . In order to do th i s , some of the shortcomings of the basic m o d e l require m o d i f i c a t i o n . T h e basic j o int space m o d e l uses the s imple ob jec t ive f u n c t i o n of m a x i m i z i n g share of d e m a n d . T h i s ob jec t ive has been c r i t i c i zed because f i rms w o u l d t y p i c a l l y consider pro f i tab ihty , rather t h a n d e m a n d , when designing new p r o d u c t s . In a d d i t i o n , the j o i n t space m o d e l relies on character is t i cs w i t h f inite i dea l po ints ( t e rmed " h o r i z o n t a l " character is t i cs i n economics) . E q u a l l y as relevant are models w h i c h consider character is t i cs w i t h in f in i te idea l po ints (ver t i ca l character ist ics ) . T h e models w h i c h address these issues i n a more economics or iented f ramework w i l l be reviewed i n more d e t a i l . H a u s e r a n d S i m m i e (1981) propose a profit m a x i m i z i n g p r o d u c t pos i t i on ing mode l based o n a t t r i b u t e s w i t h in f in i t e idea l po ints . T h e i r mode l provides an operat i onaUzat ion of L a n c a s t e r ' s goods -character is t i cs economic theory (Lancas ter 1971, 1979). A s s u m i n g homogeneous p r o d u c t percept ions , Hauser a n d S i m m i e m o d e l p r o d u c t perceptions i n a ra t i o scaled, per- do l la r p e r c e p t u a l m a p . Increasing (decreasing) a p roduc t ' s price moves the p e r c e p t u a l p o s i t i o n of that p r o d u c t t oward (away from) the o r i g i n of the per -do l lar p e r c e p t u a l m a p . C o n s u m e r s are assumed to have l inear u t i l i t y funct ions whose arguments are the p e r - d o l l a r per cep tua l d imens ions . Heterogeneous preferences are incorporated by a s s u m i n g a (or measur ing the) d i s t r i b u t i o n of the u t i l i t y f u n c t i o n d imens ion weights. Costs are assumed to be a f u n c t i o n of the locat ions i n per -do l lar per cep tua l space w i t h increased d i s tance f r o m the o r i g i n representing higher product costs. Hauser a n d S i m -mie o u t h n e a procedure by w h i c h this i n f o r m a t i o n , w h i c h inc ludes prices , costs a n d a consumer choice ru le , can be used to find the profit m a x i m i z i n g per cep tua l pos i t i on . Hauser a n d S i m m i e ' s a p p r o a c h , t h o u g h theoret i ca l ly appeahng , exposes a number of di f f icult p r o b l e m s . A l t h o u g h they discuss how the ir m o d e l can incorpora te heteroge-neous percept ions and preferences, the profit m a x i m i z i n g procedure w h i c h they suggest incorporates homogeneous preferences a n d percept ions . S o l v i n g for the o p t i m a l so lut ion w h e n heterogenei ty is a l lowed appears to be very di f f icult . In a d d i t i o n , Hauser and S i m -mie note that a n u m b e r of measurement issues must be addressed before the mode l can be successful ly i m p l e m e n t e d . T h e most signif icant of these is the ident i f i ca t i on of the re la t i onsh ip between p r o d u c t costs a n d perceptua l l o ca t i on . Schmalensee a n d Th isse (1988) integrate the o p t i m a l product p o s i t i o n i n g hterature i n m a r k e t i n g w i t h p r o d u c t d i f ferent iat ion hterature i n economics a n d l o c a t i o n theory l i t e r a t u r e i n operat i ons research. T h e i r basic ob jec t ive is to develop an analysis pro-g r a m w h i c h can l ead to the i dent i f i ca t i on of p r o m i s i n g new produc t designs. As such, no specific a l g o r i t h m s or approaches are presented. Instead , the authors argue that op-t i m a l p r o d u c t p o s i t i o n i n g models s h o u l d c o n t a i n a n u m b e r of key features. T h e n , the authors prov ide a n u m b e r of suggestions as to how these features might be incorpora ted . Schmalensee a n d T h i s s e suggest t h a t o p t i m a l new p r o d u c t design models shou ld have the a b i l i t y to h a n d l e charac ter i s t i c s w i t h e i ther finite and in f in i te idea l points ; have a profit m a x i m i z i n g ob jec t ive f u n c t i o n i n w h i c h costs are i n c o r p o r a t e d ; a n d , have the a b i l i t y to i n c o r p o r a t e c o m p e t i t i v e react ions . In a d d i t i o n , they discuss many of the issues re lat ing to o p t i m i z a t i o n . T h e m a i n c o n t r i b u t i o n of this paper comes f rom its development of p r a g m a t i c approaches to the generat ion of new p r o d u c t designs whi le adher ing to the theore t i ca l arguments presented i n the m a r k e t i n g , economics a n d operat ions research hteratures . T w o recent models by C h o i , D e S a r b o and H a r k e r (1990) and H o r s k y and Ne lson (1989) present what can be referred to as the state of the art i n o p t i m a l product pos i -t i o n i n g models . B o t h mode ls i n c o r p o r a t e c o m p e t i t i v e reactions a n d m a n y other feature w h i c h address the c r i t i c i s m s of ear l ier models . In a d d i t i o n , there appears to be a more concerted effort i n these art ic les to a p p l y the o p t i m a l produc t pos i t i on ing approaches to a c t u a l prob lems . T h i s is espec ia l ly true of H o r s k y a n d Nelson 's paper . C h o i , D e S a r b o a n d H a r k e r (1990) develop a n o p t i m a l produc t pos i t i on ing mode l w h i c h incorporates pr i ce c o m p e t i t i o n . T h e m o d e l they, ana lyze is closely re lated to the theore t i ca l m o d e l suggested by Schmalensee a n d T h i s s e (1988). C h o i et a l measure a j o in t b r a n d - i d e a l p o i n t p e r c e p t u a l space us ing an M D S un fo ld ing a l g o r i t h m (DeSarbo and R a o 1986) a n d i n c o r p o r a t e a p robab ihs t i c choice rule based o n the m u l t i n o m i a l logit m o d e l . U s i n g a S t a c k e l b e r g - N a s h e q u i h b r i u m concept , these researchers develop a n u m e r i c a l procedure w h i c h enables t h e m to ca l cu late the o p t i m a l product pos i t ion ( in m u l t i - d i m e n s i o n a l space) a n d price of a new entrant a n d o p t i m a l response prices of any number of i n c u m b e n t s . T h e authors provide a l i m i t e d a p p l i c a t i o n of the methodo logy to the analgesics market to demonstrate the power of the i r a l g o r i t h m . I n the a p p h c a t i o n , an o p t i m a l p r o d u c t p o s i t i o n and pr ice e q u i h b r i u m s o l u t i o n for a new analgesic is f ound i n a market w i t h 4 per cep tua l d imensions a n d 15 compet i tors . T h o u g h the mode l uses a profit m a x i m i z a t i o n ob ject ive func t i on , costs are assumed to be equa l for a l l c ompet i t o rs . Therefore , C h o i et a l avo id the diff icult p r o b l e m of e s t i m a t i n g the cost of per cep tua l pos i t ions . H o r s k y a n d N e l s o n (1989) develop an o p t i m a l produc t p o s i t i o n i n g m o d e l w h i c h i n -corporates a n u m b e r of features not present i n earl ier research. U s i n g automob i l e market survey d a t a ( w h i c h i n c l u d e d choice i n f o r m a t i o n ) , several f u n c t i o n a l forms of a preference m o d e l w i t h in f in i te i d e a l po ints are es t imated (vector models ) . T h e authors select a func-t i o n a l f o r m w h i c h incorporates consumer u n c e r t a i n t y a n d recognizes a t t r i b u t e s a t i a t i o n . F r o m th is preference m o d e l , a consumer 's expected u t i l i t y is u p d a t e d us ing the m u l t i n o -m i a l logit m o d e l to account for the observat ion that s tated preferences do not per fect ly reflect choice. T h e resu l t ing choice probabi l i t i es are used to f o r m d e m a n d funct ions for each b r a n d . T h e ob jec t ive f u n c t i o n of the firm cons ider ing the development of the new automob i l e is the net present value of earnings s t ream (less investment ) over the life of the b r a n d . In order to ca l cu late this value , the start up costs a n d year ly overhead are assumed to be at i n d u s t r y s tandards . T h e var iable costs associated w i t h different p e r c e p t u a l pos i t ions are e s t i m a t e d u s i n g R o s e n (1974). Rosen proved that by a s s u m i n g t h a t there is a pr ice e q u i l i b r i u m i n the current market and that firms have the same var iab le cost f u n c t i o n , var iab le costs as a f u n c t i o n of a t t r ibutes can be measured . Sen (1982) c ommented o n the theore t i ca l a p p e a l of th is procedure for o p t i m a l p r o d u c t p o s i t i o n i n g mode ls , but H o r s k y a n d Nelson 's paper represents the first a p p h c a t i o n of th is procedure . T h e o p t i m a l produc t l o c a t i o n is der ived v i a a m a t h e m a t i c a l p r o g r a m w h i c h calculates the p r o f i t a b i h t y of a l l poss ible a t t r i b u t e bundles (defined as unit values f r o m 3 to 7 o n s ix a t t r ibutes ) whi le a l l owing for pr ice c o m p e t i t i o n . A number of theoret i ca l a n d measurement issues are ra ised by H o r s k y a n d Nelson 's paper . T h e most i m p o r t a n t of these is the a p p l i c a b i l i t y of Rosen 's m o d e l i n an a c t u a l market s i t u a t i o n . T h e a s s u m p t i o n that the current market (of 14 brands ) is at a price e q u i l i b r i u m is quest ionable . In a d d i t i o n , the a t t r i b u t e p o s i t i o n assigned to a b r a n d (and subsequent ly a cost) is based o n the mode of the sample of consumer percept ions rather t h a n on more ob ject ive measures. Desp i te these concerns , H o r s k y a n d Nelson ' s paper provides a theoret i ca l ly appeahng approach to the o p t i m a l p r o d u c t p o s i t i o n i n g p r o b l e m . L i m i t a t i o n s of the O p t i m a l P r o d u c t P o s i t i o n i n g M o d e l s A s was ment ioned at the outset of this sect ion, o p t i m a l p r o d u c t p o s i t i o n i n g models have not been frequently apphed i n a c t u a l s i tuat i ons . T h i s lack of i n d u s t r y acceptance appears to s tem f rom two i m p o r t a n t shortcomings of o p t i m a l p r o d u c t p o s i t i o n models : the lack of a one to one re la t ionship between p e r c e p t u a l a n d p h y s i c a l space a n d the i n a b i l i t y to accurate ly es t imate the cost of a per cep tua l p o s i t i o n . These issues w i l l be discussed i n more detai l .^ Perhaps the most severe c r i t i c i s m of o p t i m a l p r o d u c t p o s i t i o n i n g mode ls is the i n -a b i l i t y of these models to de termine the p h y s i c a l p r o d u c t assoc iated w i t h an o p t i m a l p r o d u c t pos i t i on . For example , the o p t i m a l new a u t o m o b i l e l o c a t i o n i n H o r s k y a n d N e l -son's (1989) paper is defined as (on a 7 po int scale) : per formance = 7; d e p e n d a b i l i t y = 7; comfort = 3; exter ior style = 3; prestige = 4; a n d , f a m i l i a r i t y = 4. Eng ineers faced ^Other issues, like the limited consideration of time dynamics or "product" competition, also represent shortcomings of optimal product positioning models. Discussion of these issues is beyond the scope of this dissertation. w i t h the task of des igning this a u t o m o b i l e are given few prac t i ca l guidel ines . Devel -opment of the o p t i m a l product must proceed by d e t e r m i n i n g the re la t i onsh ip between the perceptua l d i m e n s i o n w h i c h descr ibe the o p t i m a l produc t a n d phys i ca l at tr ibutes w h i c h can be a l tered . Hauser and C l a u s i n g (1988) describe a procedure ( Q u a h t y Func -t i on D e p l o y m e n t ) d e t e r m i n i n g these re lat ionships and measur ing the impac t of quahty improvements . However , it is dif f icult to de termine what phys i ca l change w i l l lead to the desired per cep tua l l o c a t i o n . A l l o p t i m a l p r o d u c t pos i t i on ing mode ls re ly on the o p t i m i z a t i o n of new product loca-tions i n reduced per cep tua l space.^ W h e t h e r the per cep tua l space is developed through M D S , d i s c r i m i n a n t analysis (Pessemier 1975) or factor analys is (Hauser a n d U r b a n 1977), the ob jec t ive is the same: the representat ion of p roduc ts w h i c h are comprised of m a n y at t r ibutes i n a space bounded by a s m a l l n u m b e r of d imensions . T h e result of this com-p a c t i n g of d a t a is that each po int i n p e r c e p t u a l space relates to m a n y (possibly very different) p roduc t s i n phys i ca l space. F o r example , a hne i n two dimensions is repre-sented by a po in t i n one d imens ion . A cub i c region i n three d imensions is represented by a hne i n two d imens ions , a n d so o n . T h e p r o b l e m for o p t i m a l p r o d u c t pos i t i on ing models is that the preciseness of the search a l g o r i t h m is lost i n the descr ip t i on of the o p t i m a l phys i ca l p r o d u c t . T h e i n a b i l i t y of o p t i m a l p r o d u c t p o s i t i o n i n g models to adequate ly incorporate costs is also a severe l i m i t a t i o n . M o s t f i rms interested i n the development of new products ut ihze a profit ob ject ive . Therefore , the i n c o r p o r a t i o n of p roduc t costs i n t o the o p t i m a l p r o d u c t p o s i t i o n i n g m o d e l is essential . T h o u g h a n u m b e r of authors have emphas ized the i m p o r t a n c e of cost i n f o r m a t i o n , the e x i s t i n g l i t e r a t u r e provides h t t l e d i rec t i on as to how that i n f o r m a t i o n might be gathered or used. A s i l l u s t r a t e d above, even H o r s k y a n d •'Green, Carroll and Goldberg (1981) can be considered an exception. These researchers attempt to identify an optimal new product concepts via conjoint analysis. Nelson 's a p p l i c a t i o n of Rosen 's m o d e l , t h o u g h theoret i ca l ly correct , requires a number of quest ionable assumpt ions . T h e p r i m a r y reason for the i n a b i l i t y to accurate ly est imate costs is re lated to the first c r i t i c i s m of o p t i m a l produc t p o s i t i o n i n g models . T h a t is , each point i n per cep tua l space relates to m a n y produc ts i n p h y s i c a l space. These phys i ca l products m a y have very different costs. E v e n i f costs cou ld be defined as a funct ion of perceptua l l o ca t i on . T h e p r o b l e m of i n c o r p o r a t i n g costs in to the models does not d isappear . P e r c e p t u a l pos i t ions of the brands are d e t e r m i n e d by consumer perceptions rather t h a n by ob jec t ive measures. S ince consumers differ i n the i r perceptions of a b r a n d , it is di f f icult to de termine w h i c h specif ic per cep tua l l o c a t i o n on w h i c h to base the cost est imate . T h e two l i m i t a t i o n s descr ibed i n this sect ion a p p l y to the o p t i m a l produc t pos i t i on ing h tera ture i n general . A s l ong as o p t i m a l produc t p o s i t i o n i n g models ana lyze some type of reduced space, a reso lut ion to these prob lems does not appear to be possible. Therefore , the a n a l y t i c a l procedures need to be a l tered i f o p t i m a l p r o d u c t p o s i t i o n i n g models are to become more accepted i n indus t ry . S u m m a r y T h i s review of the o p t i m a l p r o d u c t p o s i t i o n i n g l i t e r a t u r e has not been exhaust ive . T h e goal was to prov ide a n overview of the h tera ture a n d a d iscuss ion of the models w h i c h i m p a c t on the current research. There fore , a n u m b e r of o ther i m p o r t a n t models have not been discussed because e i ther the i r focus was different t h a n the current research (e.g. U r b a n (1975) a n d G r e e n C a r r o l l a n d Goldberg (1981) ) or the models were s i m i l a r to those reviewed (e.g. Pessemier (1982) a n d B a c h e m and S i m o n (1981)) . M o r e i n f o r m a t i o n on models not rev iewed here can be f ound i n the h t e r a t u r e review sections of Schmalensee and Th isse (1988) a n d S u d h a r s h a n , M a y and Shocker (1987). 3.3 S t r u c t u r e of the S D M M o d e l T h e S D M m o d e l deve loped t h r o u g h this research is re la ted to research on o p t i m a l product p o s i t i o n i n g . L i k e o p t i m a l p r o d u c t p o s i t i o n i n g models , the m o d e l S D M uti l izes consumer preference a n d per cep t i on d a t a to e s t imate the d e s i r a b i l i t y of different locat ions i n per-c e p t u a l space. However , where o p t i m a l product p o s i t i o n i n g models seek to o p t i m i z e a p roduc t ' s p o s i t i o n , the goa l of our research is to o p t i m i z e a more fundamenta l decis ion: the choice of s trategic d i r e c t i o n . A l t h o u g h i t appears t h a t the strategic d i rec t ion decis ion is mere ly a choice between two types of improvement strategies , it is beheved that this choice is c r u c i a l . T h e change f r o m , say, a product o r i ented company to a more service or iented c o m p a n y requires the deve lopment of new ski l l s a n d capabi l i t ies . In a d d i t i o n , a l l f u n c t i o n a l areas must adjust the i r focus i n order ensure t h a t the effects of the strategic shift are successfully i m p l e m e n t e d i n the c ompany ' s offerings. T h e offering pos i t i on ing decis ion is v iewed as t a k i n g p lace w i t h i n the bounds def ined by the company 's strategic d i r e c t i on . A n i m p o r t a n t component of the S D M m o d e l is the recogn i t i on that there are three d is t inc t levels at w h i c h analys is can take place (see F i g u r e 3.2). T h e mode l conducts analys is at each of these levels. A t the strategic l eve l , senior managers prov ide strategic d i r e c t i o n to the managers i n m a r k e t i n g , research a n d deve lopment and p r o d u c t i o n . T h e choice of s trategic d i rec t ion based o n a n es t imate of the i n c r e m e n t a l p ro f i tab i l i t y and r e t u r n associated w i t h prospect ive p r o d u c t or service improvements . A t the i m p l e m e n -t a t i o n leve l , managers i n the f u n c t i o n a l areas develop the p r o d u c t and the components of the m a r k e t i n g m i x assoc iated w i t h the customer of fering. Pr i ces a n d costs for b o t h current a n d i m p r o v e d offerings are e s t i m a t e d at th is l eve l . F i n a l l y , at the customer or market leve l , p o t e n t i a l customers ana lyze the var ious offerings o n the basis of pr ice and the relevant p r o d u c t a n d service features. A t th i s l eve l , a n es t imate of d e m a n d for the current and i m p r o v e d offerings can be o b t a i n e d . A t the current stage of deve lopment , the S D M m o d e l is designed to analyze a single offering. T h a t i s , the c o m p a n y must de te rmine its s trategic d i r e c t i o n as i t relates to a single product offering. T h e m o d e l is descr ibed as i t relates to a s ingle market . A second order a l g o r i t h m w o u l d be needed to i n c o r p o r a t e m u l t i p l e markets or regions. In p r i n c i p a l , this extension is s t r a i g h t f o r w a r d . In fact , t h r o u g h o u t the chapter , the procedure for ex tend ing the m o d e l to m u l t i p l e markets is d iscussed. For m a n y companies , the s i t u a t i o n a n a l y z e d by the S D M m o d e l represents a s i m -p l i f i ca t i on of the prob lems they face because they market a range of products i n many markets . T h o u g h a m u l t i p l e p r o d u c t - m u l t i p l e markets m o d e l w o u l d be more reahstic , it is be l ieved that S D M m o d e l concentrates o n the core of the s trateg ic d i rec t ion prob-l e m . T h i s provides ins ights for m a n a g e r i a l use. T h e extens ion of the current mode l to a c o m p a n y m a r k e t i n g an ent ire p r o d u c t l i n e w i l l be left to future research. F i g u r e 3.3 provides an overview of the S D M m o d e l . T h e first phase of the S D M m o d e l is c onduc ted at the customer level . Here i n f o r m a t i o n on customer perceptions and preferences are co l lected on a l l b rands i n the market (s ) under cons iderat ion . F r o m this i n f o r m a t i o n , a cus tomer decis ion m o d e l is developed (Shocker a n d S r i n i v a s a n 1979). T h e customer dec is ion m o d e l is a s u b - m o d e l w i t h i n the S D M m o d e l . T h e customer decision m o d e l est imates b r a n d preferences as a f u n c t i o n of b r a n d s ' p e r c e p t u a l locat ions and prices. T h e customer i n f o r m a t i o n (as wel l as o ther R & D a n d p r o d u c t i o n in format ion) is used by managers at the i m p l e m e n t a t i o n level i n the next phase of the S D M mode l . In this phase, managers develop a l ist of p r o m i s i n g p r o d u c t a n d service improvements along w i t h the assoc iated cost es t imates . T h e n , us ing procedures w h i c h hnk phys i ca l characterist ics to percept ions (see e.g., Hauser a n d C l a u s i n g 1988, N a r a s i m h a n and Sen 1990), each of the proposed improvements is m a p p e d back in to the customer decision mode l . A re -analys is of the customer dec is ion mode l , i n c o r p o r a t i n g a specific p r i c ing Slrategic Level Senior Management Strategic Direction y Product ^Service Iinpienientation Level Marketing Research & Development Production Implementation _ Translate Direction mto Marketing Mix Advertising Product Services Price & Distrib. Sales Force Customer (Market) Level Customer Offering Perceptions of Product, Service and Price Customers F i g u r e 3.2: Levels of A n a l y s i s i n the S D M M o d e l a s s u m p t i o n (e.g., N a s h e q u i l i b r i u m p r i c i n g ) , al lows for the e s t i m a t i o n of the demand effects re lated to each of the proposed offering improvements . F i n a l l y , us ing price and d e m a n d i n f o r m a t i o n d e t e r m i n e d i n the previous step and cost i n f o r m a t i o n es t imated by the i m p l e m e n t a t i o n managers , the expected pro f i tab ih ty a n d R O l of the produc t and service improvements can be assessed. T h i s i n f o r m a t i o n guides the strategic d i rec t ion dec is ion . E a c h of the components of the S D M m o d e l w i l l be discussed i n more d e t a i l . 3 . 3 . 1 P r o d u c t - S e r v i c e S e t t i n g A s was o u t l i n e d i n the i n t r o d u c t i o n , the S D M is most relevant to companies who are responsib le for p r o v i d i n g b o t h the phys i ca l p roduc t a n d the associated services. In this t y p e of se t t ing , the c o m p a n y is d i re c t l y responsible for b o t h product a n d service features of the offering. ' ' In a d d i t i o n , i t is possible to improve a company ' s market pos i t i on by e m p h a s i z i n g e i ther p r o d u c t or service features. A signif icant number of manufacturers of i n d u s t r i a l a n d c o m m e r c i a l p roduc t s f a l l in to this category. For example , i n the em-p i r i c a l s t u d y o u t l i n e d chapter 4, the customer decis ion m o d e l is app l i ed i n the combine harvester market of the f a r m equ ipment indust ry . T h i s market is provides a good ex-a m p l e of a product - serv i ce se t t ing . E a c h of the compet i tors i n the m a r k e t , hke J o h n Deere , m a n u f a c t u r e a l ine of combine harvesters a n d market t h e m t h r o u g h a network of exc lus ive dealerships . C u s t o m e r s ( farmers) consider b o t h p r o d u c t re lated at t r ibutes (e.g., durability) a n d service re la ted a t t r ibutes (e.g., parts availability) w h e n m a k i n g a purchase dec is ion . There fore , it is i m p o r t a n t to consider the entire offering ( consist ing of b o t h p r o d u c t a n d service features) . •'Contrast this with a shoe manufacturer. To the customer, service may be an important feature when purchasing shoes. When poor service is delivered, it is the responsibility of the retailer, not the manufacturer. The customer may choose to buy the same shoes from a different retailer. Data Collection Attribute Ratings Preference Data (with Price) Data Analysis Perceptual Map Parameterize Model Offering Improvement Product or Service Cost Estimates Mapping into Perceptual Space Positional Shift Error Estimates Share of Demand Probability of selecting improved offering Incremental ROI & Profitability Strategic Direction Decision Customer Level Implementation Level Customer Level Strategic Level 3.3.2 D e v e l o p m e n t of a C u s t o m e r D e c i s i o n M o d e l T h e first phase of the S D M m o d e l requires the co l lect ion of customer percept ion and preference d a t a . T h i s i n f o r m a t i o n is used to develop a customer decis ion mode l (Shocker and S r i n i v a s a n 1979). T h e m a j o r components of the customer decision mode l are the p e r c e p t u a l m a p of the produc t market a n d the customer value func t i on which defines customer preferences for various locat ions i n per cep tua l space. These two components w i U be discussed i n more d e t a i l . T h e perceptua l s t ruc ture for the customer decision m o d e l is developed through the use of c o n f i r m a t o r y factor analys is : a specific f o rm of factor analys is . E m p i r i c a l research conduc ted by Hauser a n d K o p p e l m a n (1979) i n d i c a t e d that p e r c e p t u a l maps der ived v i a factor analysis are superior to those developed v i a M D S a n d d i s c r i m i n a n t analysis i n terms of i n t e r p r e t a b i l i t y a n d pred i c tab i l i t y . T h e con f i rmatory factor m o d e l differs f rom c o m m o n factor analys is (and p r i n c i p a l components factor analys is ) i n that i t allows for the spec i f i cat ion of constructs or d i -mensions . In the context of the S D M m o d e l , two constructs , product a n d service, are defined.^ These constructs are assumed to be s u m m a r y d imensions w h i c h measure a cus-tomer 's overa l l percept ion of product q u a h t y a n d service qua l i ty . T h e compos i t i on of the product a n d service constructs is based o n a categor izat ion of the i m p o r t a n t a t t r ibutes of the offering. T h e l is t of a t t r ibutes is categor ized i n t o groups of a t t r ibutes w h i c h are affected by e i ther a produc t or a service i m p r o v e m e n t . For e x a m p l e , durability w i l l o n l y be affected by a change i n the produc t w h i l e parts availability w i U o n l y be affected by a change i n the company ' s service capabiht ies . It is possible for a t t r ibutes to be categorized i n b o t h the p r o d u c t a n d service groups. For example , an a t t r i b u t e l ike speed of repairs m a y be affected by b o t h a produc t improvement (e.g. a design change to make repair ^The modeling approach here easily extends to more dimensions. This would accommodate several dimensions of product quality and service quality (see Garvin 1987). F i g u r e 3.4: A n I n d i v i d u a l ' s P e r c e p t u a l M a p easier) a n d a service improvement (e.g. better t r a i n e d technic ians) . T h e group of a t t r i b u t e s w h i c h are affected by a p r o d u c t (service) change are combined us ing a c o n f i r m a t o r y factor m o d e l to develop the p r o d u c t (service) construct . Fac tor scores are used to de termine the offering l ocat ions . F i g u r e (3.4) provides a n d example of a p e r c e p t u a l m a p developed us ing this procedure . N o t i c e that the product a n d service dimensions m a y be corre la ted . T h i s impl ies that higher levels of p r o d u c t q u a l i t y are perceived to be assoc iated w i t h higher levels of service quahty . T h i s co r re la t i on (r ) is e s t i m a t e d d u r i n g the c o n f i r m a t o r y factor analysis and is reflected i n the angle {6) between the p r o d u c t a n d service d imens ions i n the perceptua l m a p [6 — cos~^ r ) . T h e second m a j o r component of the customer dec is ion m o d e l is a value f u n c t i o n w h i c h defines customer preferences for various locat ions i n perceptua l space. T h e value funct ion also incorporates price w h i c h is assumed to be ob jec t ive (i.e., k n o w n w i t h cer ta inty and perceived accurate ly by a l l customers) . Since the product a n d service constructs are measured as quaht ies , a vector mode l ( i n c o r p o r a t i n g price) is assumed to be the form of the value f u n c t i o n (Shocker and S r i n i v a s a n 1979). T h e vector m o d e l al lows on ly "more is be t te r " a t t r ibutes . T h e o p t i m a l produc t p o s i t i o n i n g models of Hauser a n d S i m m i e (1981) and H o r s k y a n d Ne lson (1989) use s i m i l a r models to describe customer percept ions and preferences. T h e value, U, that customer i places on k's offering is defined as follows (the customer subscr ip t , i is exc luded) : Uk = wi^pk + W2i,k - wm (3.1) where: ipk,iak = offering A:'s l o c a t i o n on the p r o d u c t and service d imens ions respect ively . Pk = price of offering k. Wi,W2,W3 = parameters to be e s t i m a t e d ( > 0). T h e r e are a n u m b e r of po ints w o r t h n o t i n g about the value f u n c t i o n descr ibed i n (3.1). F i r s t , income effects are not i n c l u d e d . M o d e l s based o n the L a n c a s t e r t r a d i t i o n incorporate pr i ce by subt rac t ing i t f r o m income. T h i s y ie lds a t e r m , Y — pk, w h i c h represents the amount of funds avai lable for e x p e n d i t u r e on a l l o ther goods. A s i m i l a r f o rmula t i on w o u l d also app ly i n the current m o d e l . However , since (3.1) is e s t imated at the i n d i v i d u a l leve l , income becomes redundant (see R a t c h f o r d 1979, p.80) . Second, no i n t e r a c t i o n t e r m is i n c l u d e d i n the value f u n c t i o n . T h o u g h it is c o m m o n i n models of this type not to inc lude i n t e r a c t i o n terms (e.g., H a u s e r a n d S h u g a n 1983, H o r s k y a n d N e l s o n 1989), the i m p o r t a n c e of interact ions remains an open quest ion (see G r e e n a n d S r i n i v a s a n 1990, p.5) . T h e most relevant in te rac t i on t e r m to inc lude would be between the product a n d service factors . However , this in te rac t i on t e r m is not i n c l u d e d i n m o d e l because the cor re la t i on between these factors (as d e t e r m i n e d by the con f i rmatory factor analys is ) a l ready captures some of the interact ive effect.® Nevertheless , a test of whether the product-service i n t e r a c t i o n t e r m adds to the pred i c t ive v a l i d i t y of the m o d e l is i n c l u d e d i n the e m p i r i c a l s t u d y discussed i n chapter 4.^ F i n a l l y , a de te rmin i s t i c choice rule is incorporated into the customer decis ion m o d e l . It is assumed that when the customers purchase, they w i l l choose the offering for which (3.1) is m a x i m i z e d . A s discussed i n the l i t erature review, G a v i s h , H o r s k y a n d S r i k a n t h (1983) suggest that a d e t e r m i n i s t i c m o d e l is appropr ia te for durab le goods. M o s t offerings p r o v i d e d by product - serv i ce f i rms , i n c l u d i n g the example presented i n the e m p i r i c a l study, f a l l i n t o this category. T h e mode ls proposed by G a v i s h , H o r s k y a n d S r i k a n t h (1983) and Hauser a n d Shugan (1983) also incorporate a de termin is t i c choice ru le . T h e value func t i on is p a r a m e t e r i z e d v i a conjoint measurement . C o n j o i n t measure-ment techniques have received widespread acceptance i n b o t h a c a d e m i a a n d i n d u s t r y as a set of methods for m e a s u r i n g customer 's tradeoffs between m u l t i - a t t r i b u t e offer-ings ( W i t t i n k a n d C a t t i n 1989). G r e e n a n d S r i n i v a s a n (1978, 1990) review the m a j o r deve lopments i n conjoint analys is a n d discuss i m p l e m e n t a t i o n procedures . T h e m a j o r advantage of us ing conjoint measurement is the parameters are measured on the basis of a customer ' s response to a range of levels on each of the d imens ions {product, service and price). T h i s al lows for a more rehable est imate of say, pr ice sens i t iv i ty , t h a n a m e t h o d w h i c h est imates the pr ice p a r a m e t e r based o n customer preferences at a single price level . ^This is particularly true when improved offerings are being assessed. ^Chapter 4 outlines an empirical study which was undertaken in the combine harvester market. Using the procedure developed by Hagerty and Srinivasan (1991), it was found that the model described in (3.1) had a higher predictive validity than a model incorporating the product-service interaction. M o r e detai ls of the measurement procedure are g iven i n C h a p t e r 4. T h e customer dec is ion m o d e l is a n a l y z e d at the i n d i v i d u a l level . T h a t is, i n d i v i d -u a l differences i n b o t h perceptions a n d preferences are p e r m i t t e d . M o s t models of this type al low for e i ther heterogeneous percept ions or heterogeneous preferences, but rarely b o t h s imul taneous ly (Shocker and S r i n i v a s a n 1979). In a product - serv i ce set t ing , it is expected that there w i l l be s ignif icant differences i n preference. It appears reasonable to expect v a r i a t i o n i n the i m p o r t a n c e that customers place on the p r o d u c t , service and price components of an offering. In a d d i t i o n , it is expected that there w i l l be consider-able differences i n the customer perceptions of the offerings. T h i s p r e d i c t i o n is p r i m a r i l y due to the fact that there is a service component . T h e r e are two causes w h i c h can lead to differences i n the customer percept ions . F i r s t , un l ike " p r o d u c t s " , the offerings vary across customers due to i n d i v i d u a l experiences w i t h service prov iders . In a d d i t i o n , i n m a n y s i tuat ions ( i n c l u d i n g the one ana lyzed i n the e m p i r i c a l s t u d y ) , there are m u l t i p l e service centers (of v a r y i n g quahty ) for each of the manufac turers . T h i s impl i es that there are true differences i n the offerings across customers . Second , i n d i v i d u a l differences i n customers ' evaluat ions of the offerings lead to p e r c e p t u a l heterogeneity even when the of-ferings are i d e n t i c a l . These two causes i m p l y that i t is i m p o r t a n t to a l l ow for di f ferential perceptions ( i n c l u d i n g a l ternat ive rankings ) between customers . In a d d i t i o n to i n c o r p o r a t i n g i n d i v i d u a l differences, the customer dec is ion m o d e l can be extended to incorpora te differences across regions or countr ies . A n a s s u m p t i o n of the factor a n a l y t i c technique descr ibed above is that a l l respondents share the same perceptua l space, but vary i n their percept ions of i n d i v i d u a l brands . B y segmenting the g loba l market into d i s t inc t regions a n d c o n d u c t i n g a separate analys is i n each region, a new layer of heterogeneity is i n c l u d e d . F o r example , the set of a t t r i b u t e s considered i m p o r t a n t i n f o r m i n g the product d imens ion m a y differ across regions. In the combine harvester m a r k e t , differences i n crops and g r o w i n g cond i t i ons i n the prairies versus the midwest i m p l y that customers place s ign i f i cant ly different emphasis on at tr ibutes l ike power a n d threshing technology. B y a l l o w i n g these differences to enter into the factor m o d e l , reg ional cond i t i ons can be i n c o r p o r a t e d in to the S D M mode l . 3.3.3 Of fer ing I m p r o v e m e n t It is at th is stage that the S D M m o d e l descr ibed here departs most s igni f i cant ly from the s t a n d a r d o p t i m a l p r o d u c t p o s i t i o n i n g h tera ture . O p t i m a l p r o d u c t pos i t i on ing models search for an o p t i m a l p r o d u c t pos i t i on i n p e r c e p t u a l space a n d a t tempt to relate this p e r c e p t u a l p o s i t i o n to a p h y s i c a l p r o d u c t . T h i s a p p r o a c h has been cr i t i c i zed because of the lack of a one to one r e l a t i o n s h i p between p e r c e p t u a l (reduced) space and phys i ca l p r o d u c t a t t r ibutes (see the l i t e r a t u r e rev iew, sect ion 3.2.3). T y p i c a l l y , a l o c a t i o n i n p e r c e p t u a l space can be o b t a i n e d by m a n y different p h y s i c a l products . T h i s p r o b l e m , coupled w i t h the heterogeneity of consumer percept ions , makes i t dif f icult to define the o p t i m a l product let alone es t imate i ts costs. T h e S D M m o d e l descr ibed here reverses the d i r e c t i o n of the r e l a t i o n s h i p between p e r c e p t u a l a n d phys i ca l space. Speci f ical ly , the p h y s i c a l character is t i cs of i m p r o v e d offerings are defined i n de ta i l . F o l l o w i n g this spec i f i cat ion , the ir l o c a t i o n is e s t i m a t e d i n p e r c e p t u a l space. T h i s procedure allows for more precise cost e s t i m a t i o n of a n i m p r o v e d offering w h i l e sacr i f ic ing the a b i l i t y to search for a n o p t i m a l p e r c e p t u a l p o s i t i o n . Since the ob jec t ive of the m o d e l is the o p t i m i z a t i o n of s trategic d i re c t i on ra ther t h a n produc t p o s i t i o n , th is trade-off is acceptable . T h e offering i m p r o v e m e n t phase of the S D M m o d e l occurs at the i m p l e m e n t a t i o n level of the company. M a n a g e r s at this level are g iven the ob ject ive of developing a l ist of the most p r o m i s i n g p r o d u c t a n d service i m p r o v e m e n t s w h i c h cou ld be made to the company ' s offering. T h i s l i s t i n g is d i v i d e d in to a p r o d u c t improvement p r o g r a m and a service improvement p r o g r a m . For example , a service improvement p r o g r a m may inc lude the development of a t e chn i ca l service d e p a r t m e n t , an improvement i n the parts del ivery sys tem a n d / o r a n increase the n u m b e r of dealerships i n a p a r t i c u l a r c o u n t r y / r e g i o n . E a c h of these programs can be considered as a m e d i u m - t e r m agenda of improvements to the offering should a p r o d u c t or service or iented strategic d i rec t i on be chosen. E a c h i t e m i n the p r o d u c t (service) i m p r o v e m e n t p r o g r a m s h o u l d inc lude three character ist ics : an out l ine of the exact produc t (service) ad justments w h i c h need to be made; an es t imate of the f ixed a n d var iab le costs assoc iated w i t h the i m p r o v e m e n t ; a n d , an est imate of the improvement ' s effect o n perce ived p r o d u c t (service) qua l i ty . T h e g l oba l nature of the produc t - serv i ce f i r m can be i l l u s t r a t e d by the compos i t i on of the improvement programs . P r o d u c t improvements t end to be changes to the manufac -t u r e d produc t a n d wou ld a p p l y i n a l l regions w h i l e service improvements can be ta i l ored to specific markets . T h i s al lows for more flexibihty i n the choice of service improvements as service improvements can be targeted to markets i n w h i c h they w i l l have the greatest i m p a c t . T h e development of the p r o d u c t a n d service i m p r o v e m e n t programs represents a sig-ni f icant task for the managers at the i m p l e m e n t a t i o n leve l . However , this step of the m o d e l is not res tr i c t ive as a n u m b e r of firms are a l ready i m p l e m e n t i n g s i m i l a r proce-dures (Hauser a n d C l a u s i n g 1988). A key component i n the successful development of improvement programs is a n u n d e r s t a n d i n g of the re la t i onsh ip between engineering a t t r ibutes* a n d p e r c e p t u a l character i s t i cs . A s igni f icant amount of research has been u n -der taken to u n d e r s t a n d this r e l a t i o n s h i p (e.g. H o l b r o o k 1981, H u b e r 1975, Hauser and ^The term "engineering" is used to designate both product and service attributes. Engineering attributes are attributes which are under the product and service designer's control. S i m m i e 1981, N e s l i n 1983). T w o approaches w h i c h can be i n c o r p o r a t e d into the S D M m o d e l are br ie f ly ou thned below. Q u a h t y F u n c t i o n D e p l o y m e n t ( Q F D ) has received considerable a t t ent i on at a number of m a j o r manufac turers i n c l u d i n g T o y o t a , F o r d , H e w l e t t - P a c k a r d a n d A T & T (Hauser a n d C l a u s i n g 1988, S u l l i v a n 1986, O r s i n i 1991). Q F D is a set of p l a n n i n g a n d c o m m u n i c a -t i o n rout ines w h i c h prov ide a means of t r a n s l a t i n g customer desires i n t o the appropr ia te t echn ica l requirements at each stage of the p l a n n i n g a n d p r o d u c t i o n processes. Q F D begins by def ining a deta i led l i s t i n g of what the customer wants i n the offering. These wants or desires are a set of a t t r i b u t e s w h i c h are usua l ly expressed i n the customer 's own words . U s i n g the example f r o m Hauser a n d C l a u s i n g (1988), two desirable a t t r ibutes of a car door m a y be easy to close from the outside a n d stays open on a hill. N e x t , the re lat ive i m p o r t a n c e of these a t t r i b u t e s is de termined e i ther t h r o u g h m a n a g e r i a l exper i -ence or customer s u r v e y s / e x p e r i m e n t s . W i t h this set of perce ived needs, the company can ana lyze the changes i n engineer ing character ist ics w h i c h wiU l ead to improvements i n sat i s fy ing these perceived needs. For example , a car door a t t r i b u t e hke easy to close from the outside can be re lated to engineering character ist i cs l ike energy to close door and door seal resistance.^ A d d i t i o n a l surveys a n d / o r e x p e r i m e n t a t i o n is necessary to de termine the amount of change i n engineer ing character ist ics needed per u n i t change i n a customer a t t r i b u t e . T h e process of r e la t ing customer a t t r ibutes to engineer ing char-acter ist ics is under taken for a l l aspects of the p r o d u c t . T h r o u g h a series of re lat ionship matr i ces , the customers "vo ice" can l i n k e d to other areas of the m a n u f a c t u r i n g process i n c l u d i n g parts dep loyment , process p l a n n i n g and p r o d u c t i o n p l a n n i n g . Because of these s t rong hnkages , the cost of the i m p r o v e d product can be es t imated w i t h a considerable ^The relationship between physical features and engineering characteristics is known to the engineers. . degree of accuracy.^" A n o t h e r approach to h n k i n g engineering at t r ibutes to customer percept ions is outhned by N a r a s i m h a n and Sen (1990). T l iese researcliers develop a n e m p i r i c a l procedure to o b t a i n the qua l i t y percept ions f rom users of office copiers, however, the methodo logy can be app l i ed to a wide var iety of s i tuat ions . U s i n g a m u l t i p l e regression approach , N a r a s i m h a n a n d Sen relate q u a h t y perceptions to à series of engineering a t t r ibutes . T h e resu l t ing a t t r i b u t e - t o - perceptions m o d e l can be used to design copiers w h i c h w i l l be perce ived to have higher copy quahty . Since the costs of chang ing the phys i ca l feature is k n o w n , a good est imate of the cost of the i m p r o v e d produc t can be ob ta ined . T h e spec i f i cat ion of a procedure to develop the produc t a n d service improvement programs is beyond the scope of this d i sser tat ion a n d wiU be left for future research. However , the i m p l e m e n t a t i o n of e ither Q F D or the N a r a s i m h a n a n d Sen approach ap-pears to have the p o t e n t i a l of deve loping feasible improvement programs . B o t h of these procedures a l low for the development of programs w h i c h meet the three essential c r i t e r ia of improvement programs : (i) the precise spec i f i cat ion produc t (service) ad justments ; ( i i ) a n es t imate of the fixed and var iab le costs assoc iated w i t h the improvement ; a n d , (hi) an es t imate of the improvement ' s effect on perce ived produc t (service) qual i ty . 3.3.4 M a p p i n g P o t e n t i a l I m p r o v e m e n t s into P e r c e p t u a l Space T h i s stage of the S D M m o d e l merges the i m p l e m e n t a t i o n level w i t h the customer level . E a c h of the p o t e n t i a l improvements l i s ted i n the produc t and service improvement pro-grams are to be m a p p e d ( in t u r n ) into the per cep tua l spaces def ined by the customer i n p u t . ^°For an application of Q F D to services see Orsini (1990). For purposes of e x p o s i t i o n , consider a service improvement p r o g r a m i n a single m a r k e t . L e t the subscr ipt / represent an i t e m i n the service improvement program. For each i t e m , the i m p l e m e n t a t i o n managers provide three pieces of i n f o r m a t i o n : (i) d', an es t imate of the average amount that service q u a h t y is increased i n an i n d i -v idua l ' s per cep tua l m a p as a result of the i m p r o v e m e n t . T h e a c t u a l amount wou ld vary by i n d i v i d u a l , df focuses on the i m p a c t of a p r o d u c t improvement on customer percept ions . For example , i f the customer is concerned about parts ava i lab ihty , df would define the degree to w h i c h the customer percept ions of service increase when the ava i lab i l i t y of parts is reduced f rom 3 days to 24 hours . ( i i ) cf, an est imate of the var iable cost of the i m p r o v e m e n t . ( i i i ) F', an es t imate of the f ixed costs associated w i t h the i m p r o v e m e n t . W h e n m a p p i n g p o t e n t i a l improvements into p e r c e p t u a l space, the d' est imates are required . T h e est imates of var iable a n d f ixed costs are used i n the c a l c u l a t i o n of es t imated profits a n d investment r e t u r n (see below) . T h e per cep tua l p o s i t i o n of an offering is defined as = (6pfc)6»fc), where rep-resents offering k's l o c a t i o n on d i m e n s i o n j (e ither p r o d u c t , " p " , or service, "s" ) i n . customer i 's p e r c e p t u a l space. A s s u m i n g that the analys is is be ing u n d e r t a k e n for f i rm 1, the pred ic ted p e r c e p t u a l pos i t i on of f i r m I's offering ( ^ i j for customer i fo l lowing a service improvement is defined as fol lows: L = + dtO' + e' (3.2) '^Multiple markets can be considered by analyzing the improvement program effects in each market. Global demand effects from improvements are obtained by summing over all markets •^^ The same analysis can be undertaken for a product improvement. where: ^ i i = p o s i t i o n of target offering (as measured by customer data) i n customer i ' s per cep tua l space, = {^ipi,^iai)-9' = (r-p,, 1), where Tp, is the corre la t ion between the product a n d service d imens ions . e' = error , er' = ie'p^e',) T h e t e r m e' has been added to account for the errors associated w i t h the m a p p i n g of an improvement in to p e r c e p t u a l space. T h e r e are two types of error w h i c h can result f rom the analys is of a p o t e n t i a l service i m p r o v e m e n t . F i r s t , the degree of improvement m a y be perce ived to be bet ter (worse) t h a n expected . T h i s is essential ly a n error i n the es t imate of the a m o u n t of offering i m p r o v e m e n t . Second, the d i rec t ion of the perceptua l improvement m a y not be prec ise ly i n the same d i re c t i on as the service d imens ion . In order to account for these errors the p e r c e p t u a l pos i t i on of a service improvement is defined by a p r o b a b i h t y d i s t r i b u t i o n w i t h a m e a n of = $,ir+d'iO' and a variance m a t r i x , Ti'. It is assumed that E ' is the same for a l l customers . T h e na ture of the errors descr ibed above does i m p l y a p a r t i c u l a r error d i s t r i b u t i o n . For the S D M m o d e l , i t is assumed that the errors have a b i v a r i a t e n o r m a l distr ibution.^ '* M a n a g e r i a l judgement can be used to es t imate the parameters of the error d i s t r i b u t i o n . E s s e n t i a l l y this requires a n e s t i m a t i o n o f cTp a n d cr^ w h i c h are the variances along the product a n d service d imens ions ^•'A third source of error results from individual differences in perception. This source of error has not been specifically addressed as it is assumed that d\ and the distribution of errors are constant across individuals. ^''To account for the fact the larger improvements are more uncertain, it is assumed that the variance of the error distribution increases with the magnitude of the expected movement in perceptual position, F i g u r e 3.5: A n I n d i v i d u a l ' s P e r c e p t u a l M a p F o l l o w i n g a Service Improvement respectively.^^ I m p l e m e n t a t i o n managers m a y be best qual i f ied to make these judgements as they have considered the extent of offering improvement i n the development of the improvement programs. F i g u r e 3.5 i l lus t rates a perceptua l m a p fo l l owing a service i m p r o v e m e n t . T h e ehpses a r o u n d f i r m I 's new pos i t i on represent different p r o b a b i l i t y levels of the i m p r o v e d offer-ing 's l o c a t i o n . ^^The covariation is calculated using estimate of the correlation between the product and service dimensions (r-p,). 3.3.5 E s t i m a t i n g P r i c e a n d S h a r e of D e m a n d for an I m p r o v e d Offering T h e p r o f i t a b i l i t y of a produc t or service improvement is often dependent bo th on an increased d e m a n d for the offering and a higher price. N o t i c e that d e m a n d is also a f u n c t i o n of price (see the i n d i v i d u a l value func t i on (3.1)). Therefore , the assessment of the value of an improvement must consider the expected pr ice of the i m p r o v e d offering. T h e specific price charged for a n offering is a l o c a l dec is ion . T h a t is , the price i n a p a r t i c u l a r market is de termined b y a cons iderat ion of the customers , the compet i tors a n d the company ' s offering i n that market.^® T h e S D M m o d e l is flexible enough to incorpora te a n u m b e r of p r i c i n g assumptions i n -c l u d i n g o p t i m a l p r i c i n g a n d c o m p e t i t i v e ( N a s h e q u i l i b r i u m ) p r i c i n g . Hauser a n d S i m m i e (1981) used an o p t i m a l p r i c i n g s trategy whi le more recently , H o r s k y a n d Ne lson (1989) a n d C h o i , D e S a r b o and H a r k e r (1990) have i n c o r p o r a t e d c o m p e t i t i v e p r i c i n g into the i r o p t i m a l p r o d u c t pos i t i on ing f rameworks . T h e i m p l e m e n t a t i o n of c o m p e t i t i v e pr i c ing w i l l be descr ibed here. However , an e m p i r i c a l a p p l i c a t i o n of this p r i c i n g f ramework is beyond the scope of the d issertat ion . T h e compet i t i ve p r i c i n g a s s u m p t i o n models how firms might " reac t " to p o t e n t i a l i m -provements by the target firm. It also assures that the price the target firm charges for its improvements is i n l ine w i t h market cond i t i ons . T h e c o m p e t i t i v e p r i c i n g frame-work assumes t h a t , g iven the current pos i t i on of the offerings, a l l firms o p t i m i z e their price levels s imultaneous ly . It is a short t e r m decis ion w h i c h does not incorporate fixed investments . T h e profit for the kth firm is def ined as: life = (pfe - Ck)mkD It is assumed that there are sufficient barriers between markets to prevent arbitrage. (3.3) where: Cfc = the var iable cost of offering k. TTifc = the market share of f i r m k (dependent on pr ices ) . D = the market d e m a n d over the p l a n n i n g h o r i z o n ( u s u a l l y 1 year) . A s s u m e d to be independent of pr ice . A N a s h price e q u i h b r i u m so lu t i on occurs w h e n no f i r m can i m p r o v e its profits by u n i l a t e r a l l y a l ter ing its pr ice . In a specific m a r k e t , this requires the se lect ion of k prices w h i c h solve each f irm's first order c o n d i t i o n . T h e first order c o n d i t i o n of the the A:th f i rm is : ^ = ( m . + ( . . - c O ^ D = 0 (3.4) T h e so lut i on to the set of equat ions descr ibed by (3.4) can be d e t e r m i n e d through a n u m e r i c a l analys is . Readers interested i n the development of a n u m e r i c a l procedure are d i rec ted to Hauser (1988, p. 27). T h e d e t e r m i n a t i o n of pr i ce a n d d e m a n d est imates for a n i m p r o v e d offering follows a n u m b e r of steps: 1. Determine the price e q u i h b r i u m re lat ing to current posit ions of a l l offerings i n the market . Since the f i r m is able to adjust prices independent of the strategic direct ion decis ion, the price e q u i h b r i u m so lut ion to the current offering posit ions becomes the base case against w h i c h improvements are compared . 2. Re -eva luate the i n d i v i d u a l customer value funct ions cons ider ing the est imated po-s i t i on of the target f i rm's i m p r o v e d offering. 3. Develop the pr ice e q u i l i b r i u m fo l lowing the offering i m p r o v e m e n t . 4. D e t e r m i n a t i o n of the f ina l d e m a n d es t imate for the i m p r o v e d offering us ing the e q u i l i b r i u m prices. E v a l u a t e d iagnost i c i n f o r m a t i o n . E a c h of these steps w i l l be discussed i n more de ta i l . T h e first step i n the price a n d d e m a n d assessment of a n i m p r o v e d offering is the development of the pr i ce e q u i l i b r i u m re la t ing to the current market s i t u a t i o n . In order to complete this ana lys i s , a var iab le cost es t imate is required for each of the compet i t o r s ' offerings. A n engineer ing analys is shou ld be able to prov ide a reasonable est imate . T h e price e q u i l i b r i u m re la t ing to the current pos i t ions o f the offerings w i l l be used as a base case against w h i c h p o t e n t i a l improvements w i l l be compared . T h i s assures that the profit results of p o t e n t i a l improvements are not affected by inefficiencies i n the current p r i c i n g s t ruc ture . In the second step, the d e m a n d for i m p r o v e d offerings is es t imated . T h i s requires a re -analys is of the i n d i v i d u a l value funct ions (as g iven by (3.1)) w i t h the pos i t i on for the target f i rm be ing the e s t i m a t e d pos i t i on of the new offering (as discussed above) . W i t h o u t loss of general i ty , assume once aga in that the target f i r m is f i rm 1 a n d that a service improvement is c u r r e n t l y under cons iderat i on . A l l o ther f irms are assumed to r e m a i n i n the same l o c a t i o n i n per cep tua l space. T h e value that i n d i v i d u a l place o n these offerings is ca l cu la ted at the e q u i h b r i u m prices d e t e r m i n e d i n the previous step. T h e target f i r m , f o l l owing the service i m p r o v e m e n t , has a n expected perceptua l po-s i t i on i n customer i ' s p e r c e p t u a l m a p defined by a p r o b a b i h t y d i s t r i b u t i o n w i t h a mean of {(ipi,^i,i) a n d a var iance of S* . W h e n a p p l y i n g the value f u n c t i o n to this e s t imated l o c a t i o n , the r e s u l t i n g value for the target f i rm w i l l be a n o r m a l l y d i s t r i b u t e d r a n d o m var iab le w i t h a mean and variance of (G lass a n d S tan ley 1970, p. 127): Un = WiJij^i + W2^i,i - W3PI (3-5) V a r = w^ap + wla] + 2wxW2crpCr,pp, (3.6) where p\ = the e q u i l i b r i u m price for firm I's offering. Pp, = the corre lat ion between product a n d service d imens ions . F i g u r e 3.6a i l lus t ra tes an i n d i v i d u a l ' s v a l u a t i o n of the offerings p r i o r to an offering improvement by firm 1. In this scenario , each offering has a specific value: the value Uk as d e t e r m i n e d i n (3.1). U s i n g a first preference choice ru le , an i n d i v i d u a l wiU choose the offering w h i c h has the highest value ( f i rm 4's offering i n F i g u r e 3.6a). F i g u r e 3.6b i l lus t rates an i n d i v i d u a l ' s v a l u a t i o n of the offerings fo l l owing a n improvement i n firm I's offering. T h e l o c a t i o n of a l l c o m p e t i n g oflferings remains unchanged . T h e mean v a l u a t i o n of firm I 's offering has shifted to a higher value a n d the p r o b a b i l i t y d i s t r i b u t i o n of the i m p r o v e d l o c a t i o n is g iven by a n o r m a l distribution.^ '^ Because of the inc lus i on of an e s t i m a t e d offering l o c a t i o n , the first preference choice ru le becomes a p r o b a b i h t y of choice between two offerings. T h e i n d i v i d u a l w i l l e i ther choose the target offering or the offering w i t h the highest value a m o n g the comp.etitors. T h e p r o b a b i l i t y that an i n d i v i d u a l w i l l choose the target firm is the area under the n o r m a l d i s t r i b u t i o n to the r ight of the highest va lued compet i t o r . In F i g u r e 3.6b, this is the area to the r ight of firm 4. Since the m e a n a n d variance of the value d i s t r i b u t i o n of firm I's offering has been '^^ Since firm I's offering is being improved, it is assumed that the probability that the new offering will have a lower value than before the improvement is arbitrarily small. es t imated , the p r o b a b i h t y that the i n d i v i d u a l w i l l choose firm 1 can be de termined . T h e probab ih ty that the i n d i v i d u a l w i l l choose the c o m p e t i t i v e offering is s i m p l y l - P r [ F i r m I's Offering]. A n est imate of aggregate d e m a n d for the offerings i n a p a r t i c u l a r region can be ob ta ined by s u m m i n g the p r o b a b i l i t y levels across i n d i v i d u a l s . T h e t h i r d step i n the pr ice a n d d e m a n d e s t i m a t i o n for an i m p r o v e d offering is the re-establ ishment of the pr ice e q u i l i b r i u m . N o t i c e that the d e m a n d est imates i n the above analys is d i d not consider the effects of chang ing prices. A s prices for the firms change, the re lat ive value that an i n d i v i d u a l places of the offering changes as we l l . For firm 1, the mean of the p r o b a b i l i t y d i s t r i b u t i o n increases (decreases) w i t h a pr ice increase (decrease). T h e variance of the d i s t r i b u t i o n is unaffected. A n u m e r i c a l procedure w h i c h adjusts for these changing probabi l i t i es can be used to de termine the new price e q u i l i b r i u m . T h e final step i n the analys is s i m p l y inserts the e q u i h b r i u m prices in to the value funct ions to determine the final es t imate of d e m a n d for the i m p r o v e d offering. Fo l l ow ing the analys i s , it is i m p o r t a n t to ana lyze the shifts that o c curred i n the market as the result of offering improvement . D i a g n o s t i c i n f o r m a t i o n such as an analys is of the sources of increased d e m a n d a n d the movement i n e q u i l i b r i u m prices shou ld i n d i c a t e w h i c h firms wiU be most affected by the p o t e n t i a l improvement . T h i s i n f o r m a t i o n m a y a id i n the m a r k e t i n g of the i m p r o v e d offering. In the previous d iscuss ion , emphasis was p laced on how a single p o t e n t i a l improve -ment c o u l d be ana lyzed w i t h the customer d a t a . Before adequate i n f o r m a t i o n is avai lable to make the strategic d i re c t i on dec is ion , each of the i tems i n the p r o d u c t a n d service improvement programs s h o u l d be assessed i n a s i m i l a r m a n n e r . T h i s "one - improvement -a t - a - t i m e " analysis allows management to assess the re lat ive p o t e n t i a l of an emphasis on p r o d u c t or service improvements . However , the analysis does not consider the interac -t ive effects of s imul taneous ly i m p l e m e n t i n g several offering improvements . Because the a) Before an Offering Improvement H • Value b) Following an Offering Improvement 3 1* 4 Value F i g u r e 3.6: A n I n d i v i d u a l ' s V a l u a t i o n of the Offerings e s t i m a t i o n of these effects is e x t r e m e l y di f f icult , they are not i n c l u d e d i n the analysis . 3 . 3 . 6 A s s e s s i n g R e t u r n o n I n v e s t m e n t In the previous sect ion , the S D M m o d e l assessed the share of d e m a n d under c ompet i t i ve prices for the each i t e m i n the p r o d u c t and service improvement programs. These ca l -cu la t ions were based o n the n o t i o n of profit m a x i m i z a t i o n . However , i n order to assess the mer i t s of an i m p r o v e m e n t , fixed costs have to be incorpora ted . Therefore , r e t u r n on investment is used as a basis of c o m p a r i s o n for each improvement . T h e R O l measure as-sumes that c ompet i t o r s w i l l not react w i t h offering improvements a n d customers are fu l l y aware of the target firm's i m p r o v e m e n t . T h i s s i t u a t i o n is un l ike ly i n reahty. However , R O I does prov ide a n effective means of c o m p a r i n g product and service improvements w h i c h m a y differ i n terms of p r i ce , fixed and var iable costs, and share of d e m a n d . A two stage procedure is used to determine the R O I for a p a r t i c u l a r improvement p r o g r a m . F i r s t , a n es t imate of the i n c r e m e n t a l p ro f i tab i l i t y of each improvement is d e t e r m i n e d . Second , a weighted average R O I c a l c u l a t i o n for the entire improvement p r o g r a m is c a l c u l a t e d . T h i s procedure wiU be descr ibed i n more detai l .^* F o l l o w i n g the service i m p r o v e m e n t /, the profit for firm 1, H ' (the firm subscr ipt is o m i t t e d ) , can be expressed as fo l lows: H? = if - c\)m\D (3.7) ^^Note again that this discussion relates to a single market. A second order algorithm is required to capture the multiple market effects. where: = the e q u i l i b r i u m price d e t e r m i n e d i n the e s t i m a t i o n of d e m a n d stage. c' — the var iable costs of the i m p r o v e d offering (/) as e s t imated d u r i n g the offering improvement stage. m\ — the expected share of d e m a n d of the i m p r o v e d offering {Ï) determined i n the e s t i m a t i o n of d e m a n d stage. T o de termine the i n c r e m e n t a l prof it r esu l t ing f r o m the service improvement , the base case profits must be s u b t r a c t e d f r o m (3.7). B a s e case profits are de termined by inser t ing the e q u i h b r i u m prices associated w i t h the current pos i t i on ing of the offerings (as ca l cu -l a t e d i n step 1 of the analys is i n the previous section) into the customer value funct ions . Base case prof its for f i r m 1, II" (the f i r m subscr ipt is o m i t t e d ) , can be defined as: n- = [f - c)mD (3.8) where : p^ = the e q u i h b r i u m pr ice . c = the var iable costs of the current offering. m = the share of d e m a n d d e t e r m i n e d i n the e s t i m a t i o n of N a s h e q u i h b r i u m prices . I n c r e m e n t a l profit der ived f r o m the service improvement / is A l l f = I l f — II" . S u m m i n g over a l l i t ems , the t o t a l i n c r e m e n t a l profit der ived f r o m the service improvement p r o g r a m ( A H " ) is defined as: AW = X! n? - n" I B y i n c o r p o r a t i n g the fixed cost est imates (F;* 's) , an R O l value for each i t e m i n the service improvement p r o g r a m [ROI') can be ca l cu la ted : ROIl = {^^') X 100% (3.9) O n c e the R O I ca l cu lat ions have been conducted for each i t e m of b o t h the product a n d service i m p r o v e m e n t programs , the strategic d i r e c t i o n dec is ion can be made . T h e analysis descr ibed i n th is section considers o n l y one market or region. If the S D M m o d e l is i m p l e m e n t e d over a number of markets , the e q u i l i b r i u m prices, market share, d e m a n d a n d poss ib ly costs need to be subscr ip ted by market . T h e i n c r e m e n t a l improve-ment i n prof its for each region w o u l d be s u m m e d to assess the p o t e n t i a l prof it impact of a n i m p r o v e m e n t . It is at th i s stage that (3.9) is evaluated . A s above, th is procedure w o u l d be u n d e r t a k e n for b o t h the product and the service improvement programs . 3.3.7 Strategic D i r e c t i o n D e c i s i o n T h e strategic d i r e c t i o n dec is ion follows a compar i son of R O I levels across improvement programs . In the process of u n d e r t a k i n g this c o m p a r i s o n , there are two issues that need to be taken i n t o cons idera t i on : 1. W h e n i m p l e m e n t a t i o n managers suggest i tems for the improvement programs, they are o p t i m i z i n g the best they can. However , they m a y not be fu l ly aware of the c o m p e t i t i v e s i t u a t i o n . A s a result , the market outcome of these projects may not be favorable . There fore , the inc lus ion of a l l improvement p r o g r a m items i n an R O l c o m p a r i s o n is not appropr ia te . A n a l ternat ive w o u l d be compare the n best product improvements to the n best service improvements . T h e choice of ri is subject ive . It s h o u l d be s m a l l enough so that on ly p r o m i s i n g improvements are considered and large enough to ensure that the set of product or service improvements represents a m e d i u m t e r m improvement program. 2. In every company , there is a h m i t as to the amount of money that can be invested i n offering i m p r o v e m e n t s . Therefore , i t is necessary to ensure the improvement programs w h i c h are considered can be feasibly f inanced by the company. A budget constra int can be used to l i m i t the improvements w h i c h are to be considered i n the R O I c o m p a r i s o n . If i tems i n the product a n d service improvement programs are ordered f r o m highest to lowest R O I , i tems can be sequent ia l ly added into the c o m p a r i s o n such that the fo l lowing constra ints are satisf ied: J:FI'<F and ZF^'<F N o t e that these constra ints m a y result i n different numbers of i t ems i n the R O I compar i son . However , each p r o g r a m w o u l d require an equa l inves tment . In a d d i -t i o n , the budget constra ints give d i re c t i on to the i m p l e m e n t a t i o n managers i n the offering i m p r o v e m e n t stage. T h e issues discussed above forward two approaches to e q u a l i z i n g the R O I compar i son across improvement programs . C h o o s i n g the best n projects ensures that o n l y promis ing improvements are cons idered . However , a f fordabi l i ty of the p r o g r a m is not considered. I n c l u d i n g the highest R O I i tems such that the budget constra ints are satisfied ensures that the chosen p r o g r a m can be feasibly financed. However , w i t h a sufficiently h igh budget , F, th is approach cou ld inc lude low R O I i m p r o v e m e n t s . G i v e n the counterba l -anc ing strengths a n d weakness of these e q u a l i z a t i o n rules , i t is suggested that b o t h rules be i m p l e m e n t e d s imul taneous ly . T h a t is, i f improvements are renumbered i n terms of R O I (/ = 1 has the highest R O l ) , e i ther the budget constra int or the best n constraint can h m i t the n u m b e r of improvements w h i c h are cons idered i n the product and service improvement c o m p a r i s o n . Once the a p p r o p r i a t e p r o d u c t a n d service improvements have been selected for c o m -par i son , an overa l l R O I c a l c u l a t i o n can be made for the p r o d u c t improvements and the service improvements . T h i s can be accompl i shed by s u m m i n g the i n c r e m e n t a l profits for the selected i tems of a n improvement p r o g r a m a n d d i v i d e d by the s u m of the fixed costs associated w i t h those improvements . T h e i m p r o v e m e n t p r o g r a m (product or ser-vice) w h i c h yields the highest R O I i n this c o m p a r i s o n s h o u l d govern the firm's choice of strategic d i r e c t i on . A g a i n , i t is i m p o r t a n t to note t h a t the interac t ive effects of s i m u l t a -neously i m p l e m e n t i n g several offering improvements is not considered. T h o u g h this is a weakness, it is be l ieved that the suggested c o m p a r i s o n w i l l a l low management to assess the re lat ive p o t e n t i a l of an emphasis on p r o d u c t or service improvements . ' ^ A s s u m i n g that i tems i n a n improvement p r o g r a m are ranked by R O I (/ = 1 has the highest R O I ) , the strategic d i r e c t i o n decis ion can be s u m m a r i z e d by the fo l lowing m a t h p r o g r a m . '^Subjective judgements made by implementation managers can provide an estimate of interactive effects. M a . , m i z e (^jP) + ( 1 ^ ) (3.10) subject to (as appropr ia te ) : FPxP + F'x' < F L < n xP + x' < 1 (Budge t C o n s t r a i n t ) (Best n Improvements ) (Strategic D i r e c t i o n Choice ) where : xP = 1 i f p r o d u c t strategic d i rec t i on chosen, 0 otherwise . x' = 1 i f service strategic d i re c t i on chosen, 0 otherwise . pp, F' = F i x e d costs for the p r o d u c t and service improvement programs. FP = EiF!', F' = EiFi' (3.10) cal ls for a c o m p a r i s o n of the expected R O I levels for the product and service improvement p r o g r a m s . T h e budget constra int and the best n improvements constraint de termine w h i c h i m p r o v e m e n t i tems enter in to the compar ison . F i n a l l y , the strategic d i re c t i on choice cons t ra in t ensures that on ly one of the two strategic d irect ions can be chosen. T h e r e are several features of the strategic d i rec t i on decis ion that are w o r t h no t ing . F i r s t , the dec i s ion is based o n a n analys is of expected outcomes. T h i s market or iented approach considers the p o s i t i o n of the p a r t i c u l a r firm i n the markets i n w h i c h it c om-petes ra ther t h a n i n d u s t r y trends alone. N o t i c e that the strategic d i r e c t i o n decision for two compet i t o r s m a y be different. Second, u p o n selection of the a p p r o p r i a t e strategic d i r e c t i o n , a r e l a t i v e l y de ta i l ed p l a n of a c t i on is i m m e d i a t e l y avai lable for i m p l e m e n t a t i o n . T h e r e s h o u l d be re lat ive ly h t t l e " d o w n " t ime between dec is ion a n d a c t i o n . F i n a l l y , the fact that i m p l e m e n t i n g managers , w h o develop the improvement p r o g r a m s , are invo lved i n the strategy f o rm ula t i o n of the c o m p a n y shou ld have a pos i t ive inf luence on the cor-porate c u l t u r e of the f i r m . T h i s effect can be enhanced i f senior management emphasizes this p a r t i c i p a t i v e role. 3.4 C o n t r i b u t i o n s , F u t u r e R e s e a r c h a n d S u m m a r y C o n t r i b u t i o n s T h e S D M m o d e l is designed to a i d combined product - serv i ce f i rms i n m a k i n g offering p o s i t i o n i n g a n d p r i c i n g decisions. D r a w i n g on the o p t i m a l produc t p o s i t i o n i n g l i t e r a t u r e , the m o d e l uses an a n a l y t i c a l approach to the reso lu t i on of the strategic quest ion of whether to invest i n p r o d u c t or service improvements . A c o m p a r i s o n of the m o d e l w i t h more t r a d i t i o n a l o p t i m a l p r o d u c t pos i t i on ing mode ls i l lus trates the c o n t r i b u t i o n s of this research. A s u m m a r y of this c o m p a r i s o n is shown i n T a b l e 3.1. T h e m o d e l presented i n th i s research is f u n d a m e n t a l l y different f r o m o p t i m a l product p o s i t i o n i n g models as i t opt imizes a f i rm's s trategic d i r e c t i o n ra ther t h a n searches for the o p t i m a l new product l o c a t i o n . T h i s strategic focus adds a n u m b e r of d imens ions to the m o d e l i n g p r o b l e m i n c l u d i n g : 1. T h e inc lus i on of several " leve ls " of ana lys i s . T h e p o s i t i o n i n g p r o b l e m is ana lyzed f r o m the perspect ive of the customer a n d the company. W i t h i n the company, managers at b o t h the i m p l e m e n t a t i o n a n d senior management levels combine to assess the appropr ia te strategic d i rec t i on for the f i r m . 2. T h e cons iderat ion of services. Services are v iewed as a c r i t i c a l c omponent i n the S t r a t e g i c D i r e c t i o n M o d e l O p t i m a l P r o d u c t P o s i t i o n i n g Strategic D i r e c t i o n O p t i m a l N e w P r o d u c t L o c a t i o n P h y s i c a l -> Perceptua l Perceptua l -> P h y s i c a l • K n o w n O f f e r i n g • O p t i m a l Perceptual P o s i t i o n • A c c u r a t e C o s t E s t i m a t e s • L a c k o f 1 to 1 r e la t i onsh ip between perceptua l /phys i ca l I m p r o v e m e n t P r o g r a m " B e s t P r o d u c t " R O I O v e r E n t i r e P r o g r a m Share o f D e m a n d , P r o f i t E s t i m a t e d N e w O f f e r i n g L o c a t i o n R e g i o n a l Di f f e rences Serv i ces T a b l e 3.1: C o m p a r i s o n of the S D M m o d e l w i t h O p t i m a l P r o d u c t P o s i t i o n i n g M o d e l s company ' s offering. 3. T h e cons iderat ion of m u l t i p l e markets . E a c h market m a y differ i n terms of size, n u m b e r of compet i tors a n d the s t ruc ture of customer perceptions and preferences. In a d d i t i o n , the ab i l i t y to m o d i f y services at the regional level adds f l ex ib i l i ty to the c ompany ' s p o s i t i o n i n g opt ions . O n e of the p r i m a r y cont r ibut i ons of the S D M m o d e l is the nature of i ts speci f icat ion of the l i n k between p h y s i c a l a n d percep tua l spaces. In the offering improvement phase, the m o d e l develops a number of p r o m i s i n g offering improvements a n d subsequent ly est i -mates the i r l o c a t i o n i n per cep tua l space. T h i s approach is the reverse of o p t i m a l product p o s i t i o n i n g models w h i c h t y p i c a l l y search for an o p t i m a l product l o ca t i on i n per cep tua l space and a t t e m p t to relate this to a p h y s i c a l p r o d u c t . A l t h o u g h the S D M m o d e l does not f ind the o p t i m a l p e r c e p t u a l l o c a t i o n , it does address the m a j o r c r i t i c i sms of o p t i -m a l produc t p o s i t i o n i n g models i n c l u d i n g the ident i f i ca t i on of the character ist ics of the phys i ca l offering and an accurate es t imate of p r o d u c t i o n costs. F i n a l l y , the S D M m o d e l contr ibutes to the research on g loba l m a r k e t i n g by p r o v i d -i n g an a n a l y t i c a l , f irm-speci f ic approach to the development of a g l oba l product - serv i ce strategy. T h e m o d e l takes the v iew that an offering, espec ia l ly i ts service component , need not be s t a n d a r d i z e d across regions. M o r e i m p o r t a n t l y , the mode l determines a com-pany 's s trategy by cons ider ing the pos i t i on of the firm's offering re lat ive to c ompet i t i ve offerings as wel l as other reg ional market cond i t i ons . F u t u r e Research In this chapter , the components of the S D M m o d e l have been descr ibed i n deta i l . How-ever, a d d i t i o n a l research is requ ired i n a n u m b e r of areas before the m o d e l can be i m -plemented i n an a c t u a l c o m p a n y se t t ing . F i r s t , an approach to the development of an i n d i v i d u a l - l e v e l customer dec is ion m o d e l needs to be developed. T h i s research require-ment is addressed i n the next chapter of this d i sser ta t i on . Second, the development of improvement programs requires a d d i t i o n a l e m p i r i c a l re-search. T h e improvement programs are c r i t i c a l to the success of the m o d e l . To be of value, the produc t a n d service improvement programs must be specif ic enough to ident i fy the most p r o m i s i n g a l ternat ives , but s imple enough to be of value i n a modeUng proce-dure . In a c o m p a n y w h i c h is not c u r r e n t l y invo lved i n a q u a h t y f u n c t i o n deployment sys tem, a procedure s i m i l a r to the one developed by N a r a s i m h a n a n d Sen (1990) appears to be the most p r o m i s i n g . T h i r d , a n u m e r i c a l procedure for the development of a pr ice e q u i l i b r i u m has not been developed. T h e c r i t i c a l component of this research step is the deve lopment of accurate cost assessments for the c o m p e t i t i v e offerings. T h e customer m o d e l deve loped i n the next chapter can be used as synthet i c d a t a to i l l u s t r a t e how the pr i ce e q u i l i b r i u m analysis w o u l d operate . F i n a l l y , a d d i t i o n a l research is necessary to ex tend the current m o d e l to the analysis of m u l t i p l e regions. C o n c e p t u a l l y , this extens ion i n s t r a i g h t f o r w a r d as an a d d i t i o n a l level of analysis can be a c c o m m o d a t e d by a l l phases of the m o d e l . T h e development of improvement programs w o u l d p r o b a b l y present the most d i f f i cu l ty i n this extension as m u l t i p l e markets w o u l d c o m p o u n d the n u m b e r of projects w h i c h w a r r a n t considerat ion . S u m m a r y T h i s research addresses a s ignif icant management p r o b l e m : the choice of strategic direc-t i o n . A s the i m p o r t a n c e of services i n t r a d i t i o n a l m a n u f a c t u r i n g organ izat i ons increases, research is necessary to a i d managers fac ing new s trateg ic trade-offs. Moreover , the issues facing these organizat ions are made more c omplex w h e n g l o b a l m a n u f a c t u r i n g require-ments are to be ba lanced against l o c a l c o m p e t i t i v e needs. N o s ingle research project can expect to resolve such complex i t i es , b u t i t is be l ieved that the research presented here is a step i n that d i r e c t i o n . C h a p t e r 4 A n I n d i v i d u a l L e v e l C u s t o m e r D e c i s i o n M o d e l 4.1 I n t r o d u c t i o n M a r k e t i n g researchers have developed a n u m b e r of m u l t i - a t t r i b u t e customer decision models designed to a i d i n the f o r m u l a t i o n of m a r k e t i n g strategy or the generat ion new or o p t i m a l produc t concepts (e.g., Shocker a n d S r i n i v a s a n 1974, Hauser and S i m m i e 1981, Hauser a n d S h u g a n 1983, H o r s k y a n d Ne l son 1989). A customer dec is ion mode l est imates b r a n d preferences as a f u n c t i o n of b r a n d s ' per cep tua l locat ions a n d prices. T h e m o d e l is p r i m a r i l y used to es t imate the effects of changes i n the current market condi t ions . For example , the customer dec is ion m o d e l i n c o r p o r a t e d i n D E F E N D E R (Hauser a n d Shugan 1983) est imates the change i n d e m a n d w h i c h results f rom the entry of a new product . In this chapter , the research on customer dec is ion models is ex tended by the develop-ment a n d i m p l e m e n t a t i o n of a n i n d i v i d u a l level m o d e l . T h e m o d e l combines a perceptua l m a p p i n g technique ( con f i rmatory factor analys is ) w i t h conjoint analys is to a l low for i n d i -v i d u a l differences i n b o t h percept i on a n d preference. T h e m o d e l is speci f ical ly designed for s i tuat ions where the relevant a t t r i b u t e s are character ized by in f in i te idea l po ints . T h a t i s , customers always prefer more of an a t t r i b u t e . C u s t o m e r dec is ion models devel-oped by Hauser a n d S i m m i e (1981), Hauser a n d Shugan (1983) a n d H o r s k y a n d Nelson (1989) also consider more is i e f f e r a t t r i b u t e s . T h e m o d e l is un ique i n a number of respects. F i r s t , c o n f i r m a t o r y factor analysis is used to define the p e r c e p t u a l space. L i k e o ther factor a n a l y t i c techniques , c on f i rmatory factor analys is al lows for heterogeneous perceptions t h r o u g h the e s t i m a t i o n of i n d i v i d u a l factor scores. In a d d i t i o n , con f i rmatory factor analys is allows for a p r i o r i speci f icat ion of n u m b e r of p e r c e p t u a l d imensions and the measurement of their in te r - co r re la t i on . Second, the m o d e l uses conjo int measurement to es t imate customers ' preference weightings for each of the p e r c e p t u a l d imensions a n d price . Parameters are e s t i m a t e d at the i n d i v i d -u a l level a n d a p p l i e d to an i n d i v i d u a l ' s b r a n d percept ions to de termine the i n d i v i d u a l ' s re lat ive preference for each of the brands i n the m a r k e t . F i n a U y , the m o d e l allows for the i n c o r p o r a t i o n of price c o m p e t i t i o n between brands . Because the price parameter is e s t imated over a range of price levels, the customer decis ion mode l is s t i l l vahd as current prices are ad justed to N a s h e q u i h b r i u m prices. B u i l d i n g on the S D M mode l developed i n chapter 3, the customer decision mode l is speci f ical ly designed for markets w h i c h are character ized by the presence of p roduc t -service f i rms. However , i ts general f o r m u l a t i o n al lows it to be a p p l i e d i n any sett ing . A product - serv i ce f i r m is defined as a c o m p a n y w h i c h is responsible for p r o v i d i n g b o t h the m a n u f a c t u r e d produc t a n d the associated services. A signif icant number of m a n u -facturers of i n d u s t r i a l a n d c o m m e r c i a l products f a l l in to this category. In the e m p i r i c a l s t u d y o u t l i n e d la te r i n this chapter , the customer decision m o d e l is a p p l i e d i n the com-bine harvester market of the f a r m equipment indus t ry . T h i s market < provides a good example of a product - serv i ce sett ing. E a c h of the compet i tors i n the m a r k e t , hke J o h n Deere, m a n u f a c t u r e a l ine of combine harvesters a n d market t h e m t h r o u g h a network of exc lusive dealerships . C u s t o m e r s ( farmers) consider b o t h p r o d u c t re lated at t r ibutes (e.g., durability) a n d service re lated a t t r ibutes (e.g., parts availability) when m a k i n g a purchase dec is ion . There fore , it is i m p o r t a n t to consider the ent ire offering ( consist ing of product a n d service features) i n the development of the customer dec is ion mode l . I n a product - serv i ce se t t ing , it is expected that there wiU be s igni f icant differences i n the customer percept ions of t l ie offerings. T h i s p r e d i c t i o n is p r i m a r i l y due to the fact that there is a service component . T h e r e are two p r i m a r y causes for s ignif icant differences in the customer percept ions . F i r s t , unhke " p r o d u c t s " , the offerings vary across customers due to i n d i v i d u a l experiences w i t h service prov iders . I n a d d i t i o n , i n m a n y s i tuat ions ( i n c l u d i n g the one a n a l y z e d i n the e m p i r i c a l s t u d y ) , there are m u l t i p l e service centers (of v a r y i n g qua l i ty ) for each of the manufac turers . T h i s imphes that there are true differences i n the offerings across customers . Second , i n d i v i d u a l differences i n peoples ' eva luat ions of the offerings l ead to perceptua l heterogeneity even when the offerings are i d e n t i c a l . These two causes i m p l y that it is i m p o r t a n t to a l low for d i f ferent ia l perceptions ( i n c l u d i n g a l ternat ive rank ings ) between customers . T h e i n c l u s i o n of heterogeneous preferences is t y p i c a l of most customer decision m o d -els. I n a product - serv i ce se t t ing , where the offerings are often compr i sed of complex produc t s w h i c h require spec ia l ized service, the measurement of preferences at the i n d i -v i d u a l level is reasonable . T h e remainder of this chapter is organized as fol lows. F i r s t , the customer decision m o d e l is developed. T h i s is fol lowed by a descr ip t i on of the features of the e m p i r i c a l s t u d y a n d a r e p o r t i n g of i ts results . T h e chapter concludes w i t h a d iscuss ion of mode l c o n t r i b u t i o n s . 4.2 M o d e l D e v e l o p m e n t 4 .2 .1 A F r a m e w o r k for M u l t i - a t t r i b u t e C u s t o m e r D e c i s i o n M o d e l D e v e l o p -ment A signif icant amount of research has been conducted into the development of m u l t i -a t t r i b u t e customer dec is ion models . Shocker a n d S r i n i v a s a n (1979) o u t l i n e d the ma jor components of customer dec is ion m o d e l i n g approaches : 1. Determination of relevant product-market(s): A set of procedure used to define the bounds of relevant sub -markets a n d compet i t o rs . These bounds are often defined on usage s i tuat ions . 2. Identification of determinant attributes: Ident i f i ca t ion of the set of a t t r ibutes which are probab le de terminants of choice. 3. Creation of an abstract representation of the product-market(s): E x i s t i n g brands ( and poss ib ly i d ea l po ints ) are represented as locat ions i n a n abstract perceptual space. 4. Development of models of individual behavior towards existing (and potential) brands: A m o d e l is developed to predic t the preferences (choice) for each i n d i v i d u a l among a l ternat ives i n the relevant sub -marke ts . T h e m o d e l determines how locat ions i n per cep tua l spaces are va lued by i n d i v i d u a l s . M o r e recent mode ls have incorporated pr ice into the preference (choice) m o d e l . 5. Evaluation of new product concepts and/or search of the perceptual space for "op-timal" new product concepts: N e w concepts are p o s i t i o n e d i n the perceptua l space a n d sub jec ted to the mode l of i n d i v i d u a l behavior developed above. Recent m o d -els (e.g., H o r s k y and Ne lson 1989, C h o i , D e S a r b o a n d H a r k e r 1990) have al lowed c o m p e t i t i v e react ion to the new p r o d u c t concepts i n the form of price c o m p e t i t i o n . T h e customer dec is ion m o d e l developed here follows general f ramework (Shocker a n d S r i n i v a s a n 1979). However , the suggested approach for the creat ion of the perceptua l space a n d the p a r a m e t e r i z a t i o n of the i n d i v i d u a l decis ion m o d e l differs s igni f i cant ly f r o m research to date . It is on these topics that m u c h of the fo l lowing d iscuss ion concentrates. 4.2.2 P e r c e p t u a l S t r u c t u r e T h e p e r c e p t u a l s t r u c t u r e for the i n d i v i d u a l level customer decis ion m o d e l is developed t h r o u g h the use of c on f i rmatory factor analys is : a specific f o r m of factor analysis . E m -p i r i c a l research conducted by Hauser a n d K o p p e l m a n (1979) i n d i c a t e d that perceptual maps der ived v i a factor analys is are super ior to those developed v i a M D S and d i s c r i m i -nant analys is i n terms of i n t e r p r e t a b i l i t y a n d pred i c tab i l i ty . W h e n factor analys is is used i n the development of a p e r c e p t u a l space, a t t r i b u t e r a t i n g d a t a is r equ i red f rom a sample of customers . U r b a n a n d Hauser (1980) out l ine the most c o m m o n procedures for the co l lect ion of this d a t a a n d the development of per cep tua l maps . A s i m i l a r procedure is adopted i n the current m o d e l . A s s u m e that N i n d i v i d u a l s evaluate (an average of) J ex i s t ing brands o n K a t t r i b u t e s . E a c h set of b r a n d a t t r i b u t e rat ings is considered as a single case. Therefore an NJ x K m a t r i x of person-b r a n d a t t r i b u t e rat ings is factor ana lyzed . T h e use of a d a t a m a t r i x i n w h i c h i n d i v i d u a l responses on different brands are " s t a c k e d " on top of each other is referred to as a Total Analysis s ince b o t h the v a r i a b i h t y between i n d i v i d u a l s a n d between s t i m u h (brands) is b e i n g factor ana lyzed . S r i n i v a s a n , V a n d e n Abee le a n d B u t a y e (1989) discuss the s i tuat i ons where this type of approach is most app l i cab le a n d compare Total Analysis w i t h Within Analysis (between i n d i v i d u a l s ) and Among Analysis (between s t i m u l i or brands ) . In most per cep tua l m a p p i n g s i tuat ions , a Total Analysis is used as i t is i m p o r t a n t to c a p t u r e differences between i n d i v i d u a l s as wel l as between brands . T h i s al lows for the spec i f i cat ion of i n d i v i d u a l differences i n percept ion . F a c t o r analys is searches for a s m a l l n u m b e r of latent variables or factors w h i c h can e x p l a i n the variance i n the observed set of a t t r i b u t e rat ings . These factors become the d imens ions of a perceptua l m a p . It is assumed that customers use these latent factors i n f o r m u l a t i n g judgements about the brands i n the market . T h e r e are several types of factor analys is . C o m m o n factor analysis a n d p r i n c i p a l components analys is ( P C A ) are the types most often used to develop p e r c e p t u a l maps ( U r b a n a n d Hauser 1980). These approaches w i l l be compared to the c on f i rmatory factor analysis approach used for the i n d i v i d u a l level customer dec is ion m o d e l . Readers interested i n a more deta i led d e s c r i p t i o n of factor analysis are d i rec ted to M u l a i k (1972) a n d R u m m e l (1970). C o n f i r m a t o r y F a c t o r A n a l y s i s T h e basic d i s t i n c t i o n between con f i rmatory factor analys is and other forms of factor analys is is s i m i l a r to the d i s t i n c t i o n between con f i rmatory a n d e x p l o r a t o r y research. In a c o n f i r m a t o r y factor analys is , it is assumed t h a t the researcher has o b t a i n e d a ce r ta in a m o u n t of knowledge about the customers i n the market a n d is , therefore, i n a pos i t i on to speci fy the latent factors a n d the re la t i onsh ip between these factors and the a t t r ibutes o n w h i c h they depend. T h i s s i t u a t i o n is t y p i c a l of m a n y markets i n w h i c h p e r c e p t u a l maps are developed. Essent ia l l y , the researcher is c on f i rming a s t ruc ture w h i c h has been recognized i n previous analyses. S t a t i s t i c a l procedures are used to test the signif icance of the hypothes i zed re lat ionships . T h i s approach differs f rom c o m m o n factor analysis and P C A . These methods of factor analys is are e x p l o r a t o r y i n nature . T h e m a i n object ive of an e x p l o r a t o r y analysis is to find a s imple but m e a n i n g f u l i n t e r p r e t a t i o n of survey results. T w o steps are required i n an e x p l o r a t o r y analys is . F i r s t , the researcher must decide how m a n y factors to re ta in to e x p l a i n the variance i n the d a t a . Second the es t imated factors are s u b m i t t e d to a l inear t r a n s f o r m a t i o n or r o t a t i o n . T h i s procedure yields new factors w h i c h can be g iven a more mean ing fu l i n t e r p r e t a t i o n . E x p l o r a t o r y factor analysis does not use pr ior knowledge about the market under cons iderat ion and the re lat ionships between factors and at t r ibutes cannot be tested s ta t i s t i ca l ly . T h e con f i rmatory factor m o d e l , l ike c o m m o n factor ana lys i s , postulates that the at -t r ibutes are hnear funct ions of latent factors plus a res idua l t e r m : x = A^ + 6 (4.1) where: X = a. vector of K observable a t t r ibutes . ^ = a vector of F latent factors. F < K A = a m a t r i x of factor loadings w h i c h specifies the re la t i onsh ip between the a t t r ibutes a n d the latent factors . 6 - measurement error. N o t e E(^5 ' )=0 a n d E{5(')=0. T h e con f i rmatory factor mode l a t t e m p t s to e x p l a i n the variance i n the observed at -t r i b u t e rat ings w i t h a s m a l l number of factors . F r o m (4.1), the variance i n the a t t r i b u t e rat ings , S, can be defined as: (4.2) where: &s = 66'. A s descr ibed thus far, the c o n f i r m a t o r y m o d e l is v i r t u a l l y i d e n t i c a l to the common factor m o d e l (pr ior to a r o t a t i o n ) . T h e difference between the two approaches is i n the spec i f i cat ion of A a n d ^ . In the c o m m o n factor m o d e l , once the n u m b e r of factors has been selected, a l l e lements of A a n d ^ are e s t i m a t e d . In the c o n f i r m a t o r y mode l , the number of factors (F) is set a p r i o r i as is the p a t t e r n of re la t i onsh ips between the F factors a n d the K a t t r i b u t e s . These re la t i onsh ips c a l l for the e s t i m a t i o n of on ly certain parameters i n A. For e x a m p l e , a researcher m i g h t propose a two factor m o d e l for a set of s ix variables w i t h the f o l l owing p a t t e r n : / X 0 X 0 X X 0 X 0 X \ 0 X / T h e co lumns of the above m a t r i x re late to the la tent factors w h i l e the rows relate to the observed a t t r i b u t e s . T h e X ' s represent free parameters w h i c h are to be est imated . A l l r e m a i n i n g elements are f ixed w i t h a value of zero. T h e s t a t i s t i c a l signif icance of the free parameter est imates a n d the overa l l goodness of fit of the m o d e l can be assessed v i a M a x i m u m L i k e h h o o d . In a s i m i l a r manner , the p a t t e r n of elements of ^ can be specif ied. T h i s al lows for the e s t i m a t i o n of corre lated factors. T h e es t imated b r a n d l o ca t i ons i n the perceptua l space are d e t e r m i n e d by the factor scores r e l a t i n g to an i n d i v i d u a l a t t r ibutes rat ings of the brands . T h e factor scores are e s t i m a t e d as a l inear f u n c t i o n of the o r i g i n a l rat ings . T h e parameters of this equat ion are ca l led " factor score coeff ic ients" . T h e con f i rmatory m o d e l incorporates measurement error a n d the factor score coefficients can be es t imated v i a O L S regression. These coef-ficients are s t a n d a r d o u t p u t i n c omputer packages l ike L I S R E L (Joreskog a n d S o r b o m 1985). A s descr ibed above, the m a j o r d i s t i n c t i o n between con f i rmatory factor analys is , c o m -m o n factor analysis a n d P C A is the fact that b o t h the l a t t e r two factor a n a l y t i c tech-niques are e x p l o r a t o r y i n n a t u r e . O t h e r differences, ou thned i n the development of the con f i rmatory factor m o d e l , are the measurement of corre lated factors a n d the inc lus i on of measurement error. These two issues w i l l be discussed i n more d e t a i l . O n e of the m a j o r advantages of the con f i rmatory factor m o d e l is the a b i l i t y to mea-sure ( and test s t a t i s t i c a l l y ) the cor re la t i on between perceptua l d imens ions . V i r t u a l l y a l l per cep tua l maps created v i a e x p l o r a t o r y factor analysis (as we l l as M D S and d i s c r i m -inant analys is ) restr ict the latent factors to be ing o r thogona l w h e n , i n fact , i t is qu i te l i k e l y that the " t r u e " la tent factors are correlated.^ T h e factors ex t rac ted us ing an ex-p l o r a t o r y approach are r o t a t i o n a l l y inde terminate . T h a t is , the factor m a t r i x can be ^Although an oblique rotation of factors is possible, it is rarely, if ever, used. One of the possible explanations for this fact is the ambiguity in interpreting the output of an oblique rotation as two factor matrices, a factor pattern matrix and a factor structure matrix, are given as output along with an estimate of the correlation between factors. See Green (1978) for a discussion of oblique rotations. ro ta ted i n an i n f i n i t e n u m b e r of ways w h i c h m a y lead to different in terpretat ions of the d a t a . T h e o r t h o g o n a l r o t a t i o n most often suggested, V A R I M A X , m a x i m i z e s the co lumns of the squared factor m a t r i x . T y p i c a l l y , this leads to a factor m a t r i x i n w h i c h only a few a t t r i b u t e s l oad h i g h l y on each d imens ion . A l t h o u g h the o r t h o g o n a h t y constraints ahows for a n easy p i c t o r i a l representat ion of the produc t m a r k e t , i t is unc lear whether it offers a better u n d e r s t a n d i n g of the u n d e r l y i n g p e r c e p t u a l s t ruc ture . T h i s can be iUust ra ted by means of a n example . C o n s i d e r a h y p o t h e t i c a l p r o d u c t - m a r k e t i n w h i c h a factor analys is y ie lded two per-c e p t u a l d imensions (say, ease of use and power). F i g u r e 4.1a i l lus t rates an i n d i v i d u a l ' s perce ived l o c a t i o n of 3 brands i n this per cep tua l space. T h i s p e r c e p t u a l m a p impl ies that i f b r a n d A was successful i n increas ing its perce ived ease of use, it wou ld have no effect on its perce ived power. N o w assume that the two latent constructs [ease of use a n d power) have an in ter - corre la t i on of 0.5. T h i s impl ies that h igher levels of power are perce ived to be associated w i t h higher levels of ease of use. F i g u r e 4.1b i l lustrates a the p e r c e p t u a l m a p w i t h these corre lated constructs . T h e axes are separated by a 60° angle rather be ing o r t h o g o n a l (cos(60°) = 0.5). In this revised m o d e l of per cep tua l s t ruc ture , an improvement of a; uni ts i n b r a n d A ' s perceived ease of use w o u l d result i n an increase of x c o s ^ = .5x uni ts i n b r a n d A ' s perceived power. T h i s secondary effect on perceived power is not c a p t u r e d i n an analysis us ing an o r t h o g a n o l factor r o t a t i o n . If the goal of the development of a perceptua l space is to ga in ins ight into consumer 's perceptions of the various brands , the res t r i c t i on of o r thogano l constructs m a y h ide some i m p o r t a n t i n f o r m a t i o n . It is not h a r d to i m a g i n e that a h i g h inter - factor co r re la t i on c o u l d have a s ignif icant i m p a c t i n any repos i t i on ing strategy. T h e t reatment of measurement error ( t e rmed a t t r i b u t e uniqueness i n the c o m m o n factor model ) is another feature on w h i c h the factor a n a l y t i c techniques differ. B o t h a) Orthoganol Power A 0 B 0 b) Correlated Power xcos(60°) .9 Ease of Use Ease of Use F i g u r e 4.1: P e r c e p t u a l M a p s I l l u s t r a t i n g O r t h o g o n a l Versus C o r r e l a t e d Facte c o n f i r m a t o r y a n d c o m m o n factor analysis inc lude measurement error whereas p r i n c i p a l components analysis does not . T h e o r e t i c a l l y the i n c l u s i o n of measurement error is de-s irable as i t is imposs ib le to measure a latent factor w i t h o u t error . However , there are i m p l i c a t i o n s to its i n c l u s i o n . In con f i rmatory a n d c o m m o n factor ana lys i s , the objec-t ive is to repl i cate the covar ia t i on between a t t r ibutes (off- d iagonals i n the corre lat ion m a t r i x ) w i t h a reduced n u m b e r of factors. Differences i n the variances (the d iagonal of the corre la t i on m a t r i x ) between the observed d a t a a n d the pred i c ted m o d e l are assumed to be measurement error. T h i s leads to the factor i n d e t e r m i n a c y p r o b l e m . T h a t is , it is poss ible to derive different sets of factor scores a n d measurement errors w h i c h fit the d a t a equa l ly as wel l but have very different in terpre ta t i ons . Steiger (1979) discusses the h i s t o r y of the factor i n d e t e r m i n a c y p r o b l e m . In short , proponents of the c o m m o n and con f i rmatory factor models suggest that factor i n d e t e r m i n a c y is not a serious p r o b l e m as it rare ly affects in terpre ta t i ons (e.g. M c D o n a l d (1974), G r e e n 1976). These researchers prefer the more theore t i ca l ly sound m o d e l f o rmal i za t i ons . O t h e r researchers prefer to c i rcumvent the i n d e t e r m i n a c y p r o b l e m t h r o u g h the use of p r i n c i p a l components analys is . P C A assumes no a t t r i b u t e uniquenesses or measurement error ( U r b a n a n d Hauser 1980). Since the results f rom b o t h of these methods tend to have h t t l e or no difference i n i n t e r p r e t a t i o n , the use of P C A seems a p p r o p r i a t e . However , i t is i m p o r t a n t to note t h a t there exists no c on f i rmatory factor procedure w h i c h assumes no measurement error . T h e use of p r i n c i p a l components analysis for the c o n s t r u c t i o n of a p e r c e p t u a l space has been discussed extensive ly by H u b e r a n d H o l b r o o k (1979) and D i l l o n , Freder ick a n d Tangpanichdee (1985). C o n f i r m a t o r y factor ana lys i s , when used i n s i tuat ions where a base of p r i o r k n o w l -edge about the produc t market is avai lable , has a n u m b e r of advantages over c o m m o n factor analysis a n d p r i n c i p a l components analys is . F i r s t , the mode l defines a n d tests the s ta t i s t i ca l s ignif icance of the re la t ionships between offering a t t r ibutes a n d latent factors. Essent ia l ly , the researcher is test ing a theory about the s tructure of customer prefer-ences. T h i s gives the researcher a better unders tand ing of the compos i t i on of the latent factors a n d should a id i n the development of offering improvements w h i c h w i l l have a posi t ive i m p a c t on customer perceptions. Second, the conf i rmatory factor mode l does not suffer f rom the r o ta t i ona l indeterminacy w h i c h results f rom an exploratory factor mode l . D i l l o n , Frederick a n d Tangpanichdee (1985) suggest that the effects of ro tat ion-al ly i n d e t e r m i n a c y as i t relates to perceptual space construct ion has not been adequately s tudied . F i n a l l y , the conf i rmatory m o d e l allows for the speci f ication of correlated factors. A s discussed above, this m a y y i e l d i m p o r t a n t i n f o r mat i on about the re lat ionship between latent factors. I n a d d i t i o n , w h e n conf i rmatory factor analysis is used (as opposed to an obhque ro ta t i on ) , the s tat i s t i ca l signif icance of the factor correlations can be assessed. In s u m , con f i rmatory factor analysis for use i n the development of perceptual maps provides an a t t rac t ive a l ternat ive to exp loratory factor analys is . 4.2.3 Preference M e a s u r e m e n t Once the per cep tua l s t r u c t u r e is deve loped , the next task i n the development of a cus-tomer dec is ion m o d e l is the measurement of i n d i v i d u a l preferences. A s was stated earl ier , the customer dec is ion m o d e l deve loped here is speci f ical ly designed for s i tuat ions where the relevant a t t r ibutes a n d latent constructs are charac ter i zed by in f in i t e idea l points . Therefore , the vector m o d e l , w h i c h models u t i h t y as a we ighted s u m of factor or d i m e n -sion levels of each a l t e rnat ive , is a n a t u r a l choice for a m o d e l of preference. T h e vector m o d e l postulates that the value , t / , that customer i places o n k's offering is defined as follows (the customer subscr ip t , i is exc luded ) : J Uk = J2 ^J^ii' ~ ^J+iPk (4.3) j=i where: ^jk — offering k\ l o c a t i o n on the factor j. Pk = pr ice of offering k. Wi,...,wj+i = parameters to be es t imated . T h e r e two points w o r t h n o t i n g about the vector m o d e l descr ibed i n (4.3). F i r s t , income effects are not i n c l u d e d . M o d e l s based on the L a n c a s t e r t r a d i t i o n incorporate pr ice by s u b t r a c t i n g i t f r o m income. T h i s yields a t e r m , Y' — pk, w h i c h represents the amount of funds avai lab le for e x p e n d i t u r e on a l l other goods. A s i m i l a r f o rmula t i on wou ld also a p p l y i n the current m o d e l . However , since (4.3) is e s t imated at the i n d i v i d u a l leve l , income becomes r e d u n d a n t (see R a t c h f o r d 1979, p.80).^ Second , no i n t e r a c t i o n t e r m is i n c l u d e d i n the value func t i on . T h o u g h i t is c o m m o n i n models of this type not to inc lude in terac t i on terms (e.g., Hauser and S h u g a n 1983, H o r s k y a n d Ne l son 1989), the i m p o r t a n c e of interact ions remains an open quest ion (see G r e e n a n d S r i n i v a s a n 1990, p.5). In terac t i on terms are not i n c l u d e d i n (4.3) because the corre la t i on between the latent factors (as d e t e r m i n e d by the con f i rmatory factor analys is ) a lready captures some of the interact ive effect when p r o d u c t improvements are be ing eva luated . Nevertheless , the e m p i r i c a l s tudy descr ibed later i n this chapter includes a test of whether i n t e r a c t i o n terms a d d to the pred i c t ive a b i l i t y of the m o d e l . ^Because a combine is a major purchase, income probably has some explanatory value. For example, income may be a good predictor of whether a farmer purchases a combine in the new or used market. The inclusion of this type of income effect is beyond the scope of this dissertation. Issues S u r r o u n d i n g Preference M e a s u r e m e n t P r o c e d u r e s in C u s t o m e r D e c i -sion M o d e l s In most cus tomer decis ion models , the p a r a m e t e r i z a t i o n of the m o d e l of i n d i v i d u a l pref-erence has proceeded by c o m p a r i n g customer preferences of the brands i n the produc t -market to the ir l o c a t i o n i n the per cep tua l produc t space. B r a n d preferences are t y p i c a l l y d e t e r m i n e d by e i ther a r a n k i n g or r a t i n g procedure . T h e r a n k i n g of brands yields o r d i n a l preferences whereas a r a t i n g of brands y ie lds rat io - sca led preferences when an intens i ty measure l ike constant s u m p a i r e d compar isons is employed (Hauser a n d Shugan 1980). W h e n price is i n c l u d e d i n the customer dec is ion m o d e l , b r a n d preferences are determined at a specific " s t i cker p r i c e " . These prices usua l ly correspond to the preva i l ing market prices.^ T h e r e are several issues w h i c h are raised by this type of parameter e s t i m a t i o n pro-cedure. F i r s t , the re l i ab i l i t y of the est imates is affected by the n u m b e r of brands i n the p r o d u c t - m a r k e t . E a c h preference r a n k i n g (or ra t ing ) of a b r a n d represents an observa-t i o n to be used i n the mode l e s t i m a t i o n . In markets where there is a low rat io between the n u m b e r of observations (brands) a n d the n u m b e r of parameters to be es t imated , the re l iab ih ty of the parameter est imates is reduced. For example , H o r s k y a n d Nelson (1989) use 12 observat ions to est imate i n d i v i d u a l preference models w i t h 7 to 9 parameters . T h e good fit of m o d e l to the d a t a must be t empered against the low r e l i a b i l i t y of the parameter est imates . To improve this s i t u a t i o n , the m o d e l can be e s t i m a t e d on segments of respondents ra ther t h a n at the i n d i v i d u a l level . •'Actual brand choice information can be used if this information is available and can be assumed to represent the current preferences of the respondents. Hauser and Gaskin (1984) use choice information to assess the relative importance of price scaled dimensions. Rather than estimate individual preferences, the distribution of customer tastes is estimated. Second , parameter est imates are affected by t l ie range of brands i n the produc t -m a r k e t . In markets where there are few brands or markets where brands tend to be c lustered i n a few perceptua l l o ca t i ons , the customer decis ion m o d e l m a y place too much emphas is on the d i f ferent iat ing features of the re lat ive ly homogeneous brands . For ex-a m p l e , assume that three features are i m p o r t a n t i n the m a r k e t , but a l l brands are equal on the most i m p o r t a n t feature (say Power). W h e n b r a n d preferences are compared to p r o d u c t l o cat i ons . Power w i l l not be v iewed as an i m p o r t a n t i n d i c a t o r of choice. T h i s f i n d i n g is t rue of the current m a r k e t , but i f the ob ject ive of the customer decis ion mode l is to develop new p r o d u c t concepts , the Poi£;er feature may be ignored . In a re lated issue, i f b rands tend to be c lustered i n a few p e r c e p t u a l l o cat ions , the customer decis ion mode l is e s t i m a t e d o n observations w h i c h s p a n on ly a f rac t i on of the p e r c e p t u a l produc t space. It is unc lear whether the parameter est imates wou ld a p p l y to new concepts w h i c h are l o ca ted i n an " u n e x p l o r e d " area of the per cep tua l produc t space. A f ina l measurement issue arises when price is i n c l u d e d as a var iab le i n the customer dec is ion m o d e l . T h e ob jec t ive is to es t imate a price parameter w h i c h w i l l correct ly assess the pr ice sens i t iv i ty of p o t e n t i a l customers . In a t y p i c a l procedure , a l l brands i n the market are l i s ted at a st icker pr ice a n d respondents are asked to rank (or rate) the brands . T h e r e appears to be two m a j o r problems w i t h this d a t a co l lect ion m e t h o d . F i r s t , the preference d a t a co l lected i n th is m a n n e r is used to est imate a m u l t i - f a c t o r m o d e l w i t h pr ice . W h e n the i n f o r m a t i o n is co l lected , the b r a n d is supposed to act as a p r o x y for the m u l t i p l e factors or per cep tua l d imens ions whereas the price component is separated. It w o u l d appear that respondents to this quest ion w o u l d al locate too m u c h i m p o r t a n c e to the pr ice of b r a n d . Second , recent o p t i m a l product p o s i t i o n i n g models ( C h o i , D e S a r b o a n d H a r k e r 1990, H o r s k y a n d N e l s o n 1989) as wel l as the m o d e l developed here, al low for the i n c o r p o r a t i o n of pr ice c o m p e t i t i o n . T h e resu l t ing N a s h e q u i l i b r i u m m a y y i e l d a b r a n d - p r i c e profile w h i c h is s u b s t a n t i a l l y different to the one for w h i c h the preference d a t a was col lected. T h i s raises questions about the appropr iateness of the es t imated m o d e l . A C o n j o i n t M e a s u r e m e n t A p p r o a c h to the P a r a m e t e r i z a t i o n of the M o d e l of I n d i v i d u a l B e h a v i o r In order to address the issues o u t l i n e d above, the customer decis ion m o d e l developed i n this research uses conjoint measurement to parameter ize the m o d e l of i n d i v i d u a l behavior . C o n j o i n t measurement techniques have received widespread acceptance i n b o t h academia and i n d u s t r y as a set of methods for measur ing customer 's tradeoffs between m u l t i -a t t r i b u t e products a n d services ( W i t t i n k a n d C a t t i n 1989). G r e e n a n d Sr in ivasan (1978, 1990) review the m a j o r developments i n conjoint analys is a n d discuss i m p l e m e n t a t i o n procedures . C o n j o i n t measurement is used to es t imate the weights of the i n d i v i d u a l preference models ( the Wj's i n (4.3)). To do th i s , a series of profiles i n c o r p o r a t i n g price and the the latent factors der ived t h r o u g h the con f i rmatory factor analysis are developed. These pro-files are, i n t u r n , eva luated by p o t e n t i a l customers a n d the r e s u l t i n g preference weights are e s t i m a t e d . In a d d i t i o n to design issues l ike the selection of e x p e r i m e n t a l profiles a n d the profi le presentat ion f ormat , there are two issues w h i c h have a signif icant impact on the a p p h c a t i o n of conjoint measurement discussed here. F i r s t , i n order for the prefer-ences developed t h r o u g h the conjoint measurement procedure to be v a h d , the customers must be cons ider ing the latent factors when eva luat ing the various profiles. If the l a -be lhng of the factors i n the conjoint measurement task does not i m p l y the construct developed t h r o u g h the con f i rmatory factor analysis ( in the m i n d s of the customer) , it is i n a p p r o p r i a t e to use the resu l t ing preference est imates i n equat i on (4.3). Second, it is i m p o r t a n t that the range of levels on each of the factors used i n the conjoint measurement task covers the possible range of p o t e n t i a l per cep tua l l ocat ions . S a t i s f y i n g this c ond i t i on ensures that the parameter est imates are v a l i d for a l l l ocat ions i n the perceptua l space. Approaches to address ing these issues are discussed below. Labelling of Factors T h e customer decision m o d e l developed i n this chapter is designed to be apphed i n markets where the researcher has some a pr ior i in f o rmat i on about the structure of per-ceptions. In these s i tuat ions , the latent factors or dimensions of the perceptual space (and thus , the factors i n the conjoint measurement exper iment) are hypothesized pr ior to d a t a col lect ion. A l t h o u g h there m a y be a h i g h degree of confidence that the chosen attr ibute- to - factor associations are relevant i n the market under cons iderat ion , the n a m -i n g or labe lhng of these factors is arb i trary . Since it is these factor labels that are to be used i n the conjoint measurement task, i t is i m p o r t a n t that the selected labels cap-ture the essence of the u n d e r l y i n g construct . Speci f ical ly , do customers make the same attr ibute- to - factor associations as hypothes ized i n the conf i rmatory factor analysis when they are presented w i t h the factor labels? One approach to assessing this issue would be to coUect da ta from an independent sample of po tent ia l customers i n the product -market . Respondents can be asked w h i c h of the determinant attr ibutes (used i n the conf irmatory factor analysis) are associated w i t h the factors as label led i n the conjoint measurement task. To be confident that the appropr iate factor labels are be ing used, the results of these questions should ident i fy a factor pat tern ident i ca l to that w h i c h was used i n the conf irmatory factor analys is . Selection of Factor Levels N o t on ly is i t i m p o r t a n t to have a m a t c h between the factors used i n the con f i rmatory factor analysis a n d the conjoint measurement task, the levels used i n b o t h analyses must m a t c h as wel l . T h i s m a t c h i n g is is necessary because the researcher must ensure that the range of levels used i n the conjoint analys is covers the possible range of po tent ia l per cep tua l locat ions o n each of the factors . N o t e that m a t c h i n g is not necessary for the price factor as it is assumed to be ob jec t ive rather t h a n per cep tua l i n nature . However , l ike the perceptua l factors , the range of price levels used i n the analys is s h o u l d cover the range of possible p r i c i n g opt ions . In the e m p i r i c a l s t u d y w h i c h fol lows, the levels for the latent factors used i n each of the analyses are s e m a n t i c a l l y l i n k e d . Respondents were asked to evaluate the various brands o n the de terminant a t t r ibutes us ing the fo l lowing 7 po int scale: P o o r - 1 2 F a i r - 3 4 G o o d - 5 6 Exce l l en t - 7 In the subsequent conjoint measurement task , the levels Poor, Fair, Good a n d Excel-lent were used i n the design. T h e vector preference m o d e l was es t imated ( v ia regression) us ing a cod ing scheme w h i c h m a t c h e d the a t t r i b u t e scale. In order to have an equal number of levels for each factor , the pr ice factor was also specified at 4 levels. 4.2.4 C u s t o m e r C h o i c e R u l e T h e customer dec is ion m o d e l combines the c o n f i r m a t o r y factor m o d e l and results of the conjoint measurement task w i t h a specific choice rule . A n i n d i v i d u a l ' s u t i h t y or value for a p a r t i c u l a r b r a n d is ca l cu la ted by us ing the brand ' s p e r c e p t u a l l o c a t i o n (factor scores) a n d its price as the var iab le levels of the vector m o d e l defined i n (4.3). T h e weights used to parameter ize this m o d e l are ca l cu la ted at for each i n d i v i d u a l f rom the conjoint d a t a . These u t i l i t y or value levels f o r m the basis of the customer choice r ide . It is re la t ive ly s t ra ight f o rward to a p p l y e i ther a d e t e r m i n i s t i c or p r o b a b i l i s t i c choice rule to the value funct i on defined i n (4.3). T h e select ion of a choice rule depends on the p r o d u c t market under inves t i ga t i on . S ince the customer decision m o d e l developed here is designed for markets w h i c h are character ized by product - serv i ce firms, a de te rmin i s t i c , first choice ru le is i m p l e m e n t e d . T h i s choice rule assumes that the b r a n d of choice is the b r a n d w h i c h receives the highest value i n equat i on (4.3). G a v i s h , H o r s k y a n d S r i n k a n t h (1983) suggest that a d e t e r m i n i s t i c choice rule is a p p r o p r i a t e for in frequent ly purchased goods or durables . T h i s descr ip t i on appl ies i n most product - serv i ce markets , such as the combine harvester market used i n the e m p i r i c a l study. G a v i s h , H o r s k y a n d S r i n k a n t h argue that i n these s i tuat i ons , customers choose w i t h cer ta in ty after a n eva lua t i on of a l l a l ternat ives . A s part of the e m p i r i c a l s tudy , discussions w i t h farmers c lear ly ident i f ied a conscious (and ongoing) e v a l u a t i o n of a l ternat ives i n the combine harvester market . 4.2.5 W h y N o t U s e C o n j o i n t A l o n e C o n j o i n t analysis continues to grow i n p o p u l a r i t y a m o n g academic ians a n d p r a c t i t i o n -ers ( W i t t i n k and C a t t i n 1989). In i n d u s t r y , i t is c o m m o n pract i ce to use the e l ic i ted a t t r ibutes i n a conjoint exper iment a n d t h e n use the resu l t ing preferences used as input i n a choice s i m u l a t o r ( G r e e n a n d S r i n i v a s a n 1990). T h i s procedure ehminates the need for the deve lopment of a p e r c e p t u a l p r o d u c t space as the customer decision m o d e l is based on the u n d e r l y i n g a t t r i b u t e s . However , the choice s imulator uses the researcher's subject ive j u d g e m e n t to es t imate a brand ' s character is t i c levels. In a d d i t i o n , perceptua l heterogeneity is i gnored . These issues w i l l be discussed i n more deta i l . G r e e n a n d S r i n i v a s a n (1990) suggest that one of the m a i n reasons for the p o p u l a r i t y of conjoint analys is i n i n d u s t r y is the a v a i l a b i l i t y of choice s imulators . Cho i ce s imulators use the i n d i v i d u a l preference est imates o b t a i n e d through the conjoint s tudy to answer various " w h a t i f " quest ions about the market under cons iderat ion . T h e i n p u t to a choice s i m u l a t o r is the m a t r i x o f cus tomers ' p a r t - w o r t h s (customers ' preference intens i ty for each level of each a t t r i b u t e ) . To assess the current market s i t u a t i o n , each of brands i n the market is descr ibed by i t s levels o n the i m p o r t a n t a t t r ibutes . These descriptions are used as i n p u t i n the choice m o d e l . F o l l o w i n g the selection of a choice rule ( m a x u t i h t y , logit ru l e , etc.,) the m a r k e t shares of the brands are es t imated based on analysis of the customers ' p a r t - w o r t h s . T h e sub jec t ive ass ignment of a t t r i b u t e or character is t i c levels to describe a c t u a l brands a n d new p r o d u c t concepts m a y be l i m i t i n g . In m a n y s i tuat ions , at least some of the e l i c i ted a t t r i b u t e s are latent (e.g., durability, ease of use). It is very diff icult to l i n k the levels of these a t t r i b u t e s w i t h the a c t u a l brands w i t h o u t an independent measure-ment of customer perceptions. '* In a d d i t i o n , these percept ions w i l l vary at the i n d i v i d u a l level whi le the choice s i m u l a t o r assumes homogeneous percept ions . T h e i m p a c t of us ing subject ive j u d g e m e n t to descr ibe the character ist i cs of brands and new product concepts * A n alternative may be to consider only objective, physical attributes. Agarwal and Ratchford (1980), use physical attributes in a model of car preference. They selected objective characteristics which correlated with a set of independently determined perceptual dimensions (e.g. engine displacement and passing time are related to performance). However, these researchers note that not all perceptual dimensions could be associated with objective attributes. depends on the market under cons iderat i on . In markets where there is very ht t le per-c e p t u a l heterogeneity a n d / o r the i m p o r t a n t a t t r ibutes are ob ject ive , the use of a choice s i m u l a t o r can be very effective. However , w h e n signif icant perceptua l heterogeneity ex-ists , the homogeneous percept ions a s s u m p t i o n of the choice s i m u l a t o r m a y y ie ld results w h i c h are s ign i f i cant ly different f r o m the " t r u e " market response. T h i s is due to the fact that customers m a y have very different op in ions about the character is t i c levels of the brands . In markets whicl\ are ci iafactertzed by product -service f i rms, the signif icant differences i n i n d i v i d u a l perceptions ehminate the opt ion of using of a conjoint choice s imulator as a customer decision mode l unless homogeneous segments can be f ound . T h e methodology outhned above, w i i i c h combines a perceptual m a p p i n g technique w i t h conjoint measure-ment , w o u l d be more appropr iate i n these s i tuat ions . A n a l ternat ive to a conjoint choice s imulator w o u l d be the development of an a l ternat ive f o rm of choice s imulator w h i c h i n -cludes b o t h percept ion a n d preference in fo rmat ion . T h i s s imula tor , w h i c h could operate i n m u c h the same way as conjoint choice s imulators , w o u l d have the added benefit of in corpora t ing customer perceptions when " w h a t i f " analyses are undertaken . Because the customer decision mode l outhned above is analyzed at the i n d i v i d u a l level , the de-velopment of this type of s imulator w o u l d be relat ively s t ra ight forward . 4.2.6 S u m m a r y of the C u s t o m e r D e c i s i o n M o d e l T h i s sect ion out l ines a procedure for the development of a cus tomer decision m o d e l i n s i tuat ions where relevant a t t r i b u t e s are character ized by in f in i te i d e a l points . T h e proce-dure addresses a n u m b e r of the issues raised by previous m o d e h n g efforts. B y c o m b i n i n g con f i rmatory factor analys is w i t h conjoint measurement , a i n d i v i d u a l level mode l w h i c h incorporates b o t h heterogeneous percept ions a n d preferences is developed. M o d e l ad -vantages i n c l u d e the a b i l i t y to s t a t i s t i c a l l y test the a t t r i b u t e - t o - f a c t o r re lat ionships , the measurement of corre lated p e r c e p t u a l d imens ions , an i m p r o v e d m e t h o d for preference es-t i m a t i o n a n d the i n c o r p o r a t i o n of pr i ce i n a more mean ing fu l way. T h o u g h an e m p i r i c a l a p p l i c a t i o n of the m o d e l w i l l f o l low, extensive e m p i r i c a l test ing is required to fu l ly assess the i m p o r t a n c e of these m o d e l i n g i m p r o v e m e n t s . 4 .3 A n E m p i r i c a l A p p l i c a t i o n of the I n d i v i d u a l L e v e l C u s t o m e r Decis ion M o d e l T h e i n d i v i d u a l level customer dec is ion m o d e l w i l l be i U u s t r a t e d w i t h an apphcat i on to combine harvesters w i t h i n the f a r m equ ipment i n d u s t r y . T h i s sect ion w i l l provide some b a c k g r o u n d o n the selected p r o d u c t - m a r k e t as wel l as de ta i l ed descr ipt ion of the s tudy w h i c h was u n d e r t a k e n . 4.3.1 T h e N o r t h A m e r i c a n C o m b i n e I n d u s t r y C o m b i n e s are soph is t i ca ted machines ( cost ing up to US$200,000) w h i c h are used to har -vest a wide var iety of crops. T h e combine harvester market provides a good example of a market cons is t ing of a set of p roduc t - serv i ce firms. B o t h product related and ser-vice re lated a t t r ibutes as wel l as pr ice have s ignif icant i m p a c t o n the customer 's purchase decis ion. Farmers interested i n p u r c h a s i n g a combine consider p r o d u c t features hke d u r a -b i l i ty , thresh ing technology a n d ease of m o n i t o r i n g the combine ' s opera t i on . In a d d i t i o n , they consider service features l ike parts a v a i l a b i l i t y a n d the l o c a t i o n of the loca l dealer. T h e N o r t h A m e r i c a n combine marlset is d o m i n a t e d by four manufacturers : Case-I n t e r n a t i o n a l , D u e t z - A l h s (G leaner ) , J o h n Deere a n d N e w H o l l a n d . ^ E a c h of the m a -j o r combine manufac turers ut i l izes centra l ized p r o d u c t i o n facihties p r o d u c i n g combines w h i c h incorpora te a s t a n d a r d g loba l technology. In a d d i t i o n , a l l manufacturers operate a dealer network w h i c h markets a n d services that f i rm's entire l ine of f a r m machinery . D e p e n d i n g on the crop g r o w i n g region, dealers t y p i c a l l y operate i n a 30-70 mi le radius . T h e combine m a r k e t , as well as the f a r m equipment i n d u s t r y i n general , has under-gone s u b s t a n t i a l change i n recent years. T h e change has been brought o n by a severely depressed f a r m economy. In the last five years, two m a j o r combine manufac turers . W h i t e F a r m E q u i p m e n t a n d M a s s e y Ferguson , have ceased p r o d u c t i o n . Together , these m a n u -facturers represented 2 5 % - 3 0 % of the inventory of combines i n N o r t h A m e r i c a . T h o u g h independent manufac turers are a t t e m p t i n g to revive the p r o d u c t i o n of these combines (apparent ly because of the i r super ior technology) , the lack of an establ ished dealer net-work has l i m i t e d the i r m a r k e t penetrat i on . T h e depressed f a r m economy has also led to a d r a m a t i c r e d u c t i o n i n the n u m b e r of new combines purchased i n recent years. However , forecasts for the 1990 year were encouraging as sales were expected to improve i n a l l regions ( A g r i - M a r k e t i n g 1990). T h e N o r t h A m e r i c a n market for combines can be d i v i d e d in to a n u m b e r of d is t inct regions o n the basis of crops grown. F r o m a d e m a n d perspect ive , the two most i m p o r t a n t regions are the p r a i r i e s / p l a i n s ( p r i m a r i l y wheat and bar ley ) a n d the midwes tern states ( p r i m a r i l y corn a n d soybeans) . T h o u g h m a n y of the i m p o r t a n t p r o d u c t and service a t t r ibutes are s i m i l a r for these two regions, there are some i m p o r t a n t differences. In a d d i t i o n , a d i s t i n c t i o n c a n be made between markets i n C a n a d a a n d the U n i t e d States. ^There are also a number of minor manufacturers (Klaas, Belarus, Coop Implements) who together account for less than 5% of combine inventory. T h e current s t u d y concentrates on the C a n a d i a n pra ir ies . Therefore , the m u l t i p l e re-gions component of the strategic d i rec t i on m o d e l w i l l not be tested at this t i m e . However, i t is s t r a i g h t f o r w a r d to see how the mode l extends to m u l t i p l e regions. 4.3.2 D a t a C o l l e c t i o n P r o c e d u r e s T h e e m p i r i c a l s t u d y consisted of two separate surveys of combine owners. T h e m a i n survey co l lected the farmers ' percept ion a n d preference i n f o r m a t i o n that was used i n the m o d e l p a r a m e t e r i z a t i o n . T h e secondary survey was used to test whether farmers associated the d e t e r m i n a n t a t t r ibutes w i t h the la tent factors as discussed i n the previous chapter . T h e m a j o r features of the d a t a co l lect ion phase of the research are as foUows: 1. Interviews were c o n d u c t e d at the C a n a d a W e s t e r n A g r i b i t i o n i n R e g i n a , Saskatchewan. T h i s t rade show, w h i c h ran f rom November 24 -30, 1990, is a t t e n d e d by an est i -m a t e d 30,000 farmers annual ly . T h e m a j o r i t y of these farmers o w n a combine . 2. W i t h the c o o p e r a t i o n of the A g r i b i t i o n , a b o o t h was set up to conduct the inter -v i ewing . T h i s b o o t h was set up i n a h i g h traffic area where the m a j o r i t y of exhibi ts were ded icated to g r a i n and oilseed p r o d u c t i o n . In a d d i t i o n , interv iewers were granted permiss i on to approach trade show v is i tors who passed the b o o t h . U s i n g a r a n d o m intercept procedure , farmers were asked to complete one of the two ques-t ionnaires . N o farmer was asked to complete b o t h quest ionnaires . C o m p l e t i o n of b o t h interv iews o c curred concurrent ly o n a l l days of the show. T h i s i n t e r v i e w i n g approach represented an economica l means of o b t a i n i n g the necessary d a t a to test and demonstra te the proposed f ramework. 3. M a r k V a n d e i i b o s c h superv ised t l ie in terv iew process. T h e p r i m a r y in terv iew was computer d r i v e n a n d col lected o n one of 4 computer systems set up at the booth . T h e survey was c o m p l e t e d independent ly by the respondents , however, each of the m a j o r ques t i on ing sections was exp la ined by the supervisor . T h i s was i n a d d i t i o n to t y p e d ins t ruc t i ons p r o v i d e d throughout the computer quest ionnaire . T h e su-perv isor also answered any questions the respondents m a y have h a d concerning the quest ionnaire a n d the s t u d y itself. T h e secondary quest ionnaire was collected v i a a personal in te rv i ew w i t h one of two h i red interviewers . These interviewers , h i red l o c a l l y f r o m a m a r k e t i n g research f i r m , also recru i ted the respondents for the c omputer i n t e r v i e w . 4 . 3 . 3 Q u e s t i o n n a i r e D e s i g n T h e c o m p u t e r quest ionnaire was developed us ing S a w t o o t h Software's C i 2 software pack-age. A p p e n d i x C contains a copy of the quest ionnaire a n d Tab le 4.1 outhnes its ma jor sections. E a c h of these sections w i l l be discussed i n more d e t a i l . L e v e l of A n a l y s i s W i t h i n the combine m a r k e t , each of the m a j o r manufac turers markets a range of com-b ine models to a p p e a l to different f a r m sizes a n d cond i t i ons . T h o u g h there may be specif ic except ions , the manufac turers are wel l m a t c h e d at the m o d e l leve l . For example , there are three models i n J o h n Deere's M a x i m i z e r l ine of combines a n d four models i n Case - In te rnat i ona l ' s 1600 Series ( J o h n Deere 1990, J . I. Case C a n a d a 1990). T h e m a i n d i f ferent iat ing feature between the models is the capac i ty of the combine . T h e basic 1 Crops Information and Combine Inventory 2 Combine Attribute Ratings 3 Ranking of Manufacturer Preferences 4 Conjoint Measurement 5 Demographics Tab le 4.1: Ques t i onna i re O u t l i n e technology used i n the combine is the same for a l l models of each manufac turer . T h u s , the n u m b e r of acres to be harvested determines what m o d e l size t h a t farmers compare across manufac turers . A n i m p o r t a n t quest ion is whether to consider each m o d e l of each manufac turer as compet i tors or to consider manufac turers as compet i tors . A l t h o u g h i n c o r p o r a t i n g a l l models as compet i tors m a y y i e l d some i m p o r t a n t insights into c a n n i b a h z a t i o n , there are not sufficient differences between models to warrant the e x t r a d e t a i l . N o n e of the service a t t r ibutes a n d o n l y some of the p r o d u c t a t t r ibutes w o u l d vary between different models of the same manufac turer . In a d d i t i o n , the manufac turers do not m a r k e t the i n d i v i d u a l models separately. Therefore , analys is was conducted at the m a n u f a c t u r e r level . In order to ensure that respondents considered the m a n u f a c t u r e r c ompar i son , each respondent was asked to "consider a combine of a size w h i c h w o u l d be su i t ed to [his] f a r m o p e r a t i o n " w h e n m a k i n g i n t e r - b r a n d comparisons . To c o m p h m e n t th is approach , size or capac i ty features were not i n c l u d e d i n the hst of i m p o r t a n t a t t r i b u t e s . T h i s assumes that aU manufac turers were able to offer choices i n aU desired capac i ty ranges. T h i s a s s u m p t i o n does not a p p e a r to be restr ic t ive . C r o p s I n f o r m a t i o n a n d C o m b i n e Inventory T h e first sect ion of the quest i onna ire was used to f a m i l i a r i z e respondents w i t h the com-puter quest ionnaire f o r m a t . Several m u l t i p l e choice questions explored the type of farm type , crops grown i n 1990 a n d the brand(s ) of combines owned. In a representative survey, these quest ions w o u l d ident i fy key b a c k g r o u n d variables w h i c h may affect the purchase dec is ion. V a r i a b l e s l ike brand of combine owned and number of acres seeded can be used to weight respondents i n order to m a t c h k n o w n d i s t r i b u t i o n s . A t t r i b u t e R a t i n g s T h e next sect ion cons is ted of a r a t i n g of the 4 m a j o r brands on i m p o r t a n t product and service a t t r ibutes . M a n y farmers were very f a m i h a r w i t h a l l manufac turers ' combines. T h i s is p r o b a b l y due to the fact that the combine is the largest single mach inery invest-ment of the f a r m . B e c a u s e of this h igh level o f awareness, respondents were asked to rate a l l 4 of the m a j o r manufac turers on a l l relevant a t t r ibutes rather t h a n on ly those i n their i n d i v i d u a l choice set. Respondents who s tated they were u n f a m i l i a r w i t h par t i cu lar brands were p e r m i t t e d to w i t h h o l d the ir r a t i n g of those features and brands w i t h which they were u n f a m i h a r . A t o t a l of eight a t t r i b u t e s were i n c l u d e d i n the r a t i n g task. These at t r ibutes were selected p r i m a r i l y t h r o u g h a review of previous m a r k e t i n g research studies . T h e m a i n source was a s t u d y i n w h i c h 10 focus groups were conducted w i t h farmers i n the prair ies ( b o t h C a n a d a and U . S . A . ) a n d the m i d w e s t e r n states ( D e l o i t t e , Hask ins a n d Sells 1985). U s i n g the N o m i n a l G r o u p Technique ( C l a x t o n , R i t c h i e a n d Za i chkowsky 1980), the focus groups de termined w h i c h a t t r ibutes were i m p o r t a n t to farmers when e v a l u a t i n g a n d choosing combines. E a c h group devised its o w n hst of i m p o r t a n t a t t r ibutes and the l ists were subsequently c o m p i l e d across groups. A t t r i b u t e s w h i c h were considered i m p o r t a n t at each of the pra i r i e groups m a d e up the p r e l i m i n a r y a t t r i b u t e hst for the present study. T h e p r e l i m i n a r y a t t r i b u t e list was mod i f i ed t h r o u g h discussions w i t h m a r k e t i n g researchers who have recent ly c onduc ted combine studies i n western C a n a d a . T h e goal was to ensure that the a t t r ibutes were relevant to the specif ic region i n w h i c h the e m p i r i c a l s t u d y was to take place. T h e revised l ist of a t t r ibutes went t h r o u g h four more mod i f i ca t i ons before the f ina l a t t r i b u t e hst was selected. F i r s t , a n a t t r i b u t e re la t ing to the harves t ing capac i ty of the combine was removed to be consistent w i t h the level of ana lys i s to be addressed i n the e m p i r i c a l study. Second, combine adver t i s ing l i t e r a t u r e was surveyed to see how well the p r e h m i n a r y a t t r i b u t e hst m a t c h e d the a t t r ibutes stressed by the manufac turers . T h i r d , seven dealers i n Saskatchewan were contacted and asked for the i r input o n what a t t r ibutes they thought farmers used i n the i r combine e v a l u a t i o n processes. T h i s exercise resul ted i n o n l y m i n o r semant ic changes to the a t t r ibutes . F i n a l l y , farmers p a r t i c i p a t i n g i n the quest ionnaire pretest were asked how wel l the p r e l i m i n a r y a t t r i b u t e l ist c a p t u r e d the essence of the combine eva luat i on task . T h e f ina l a t t r i b u t e hst consisted of eight a t t r ibutes . Durability, Ease of Maintenance, Ease of Controlling Operation a n d Threshing Technology were hypothes i zed to be asso-c iated w i t h Combine Quality. Parts Availability, Dealer Location a n d Dealer-Farmer Relations were hypothes ized to be assoc iated w i t h Service Quality ( t e rmed Dealer Ser-vice f o l lowing discussions w i t h farmers) . T h e f ina l a t t r i b u t e . Combine Warranty, was hypothes ized to consist of two components . F i r s t , a review of ear l ier studies seemed to ind i ca te that a "good" w a r r a n t y was associated w i t h higher Combine Quality. Sec-o n d , the wilhngness of dealers to honor the warrant y a n d per form w a r r a n t y repairs was considered a service feature (see F i g u r e 4.2). Farmers c o m p l e t i n g the quest ionnaire were asked to rate C a s e - I n t e r n a t i o n a l , G leaner , J o h n Deere and N e w H o l l a n d combines on each of the 8 a t t r ibutes us ing the fo l lowing 7 po int scale: P o o r - 1 2 F a i r - 3 4 G o o d - 5 6 E x c e l l e n t - 7 Respondents rated each b r a n d o n a p a r t i c u l a r a t t r i b u t e before c o n t i n u i n g . T h e order i n w h i c h the a t t r ibutes appeared was r a n d o m i z e d for each respondent , but the b r a n d order was not. M a n u f a c t u r e r Preferences A n i m p o r t a n t component of the strategic d i r e c t i o n m o d e l is the i n c l u s i o n of price . T h e assessment of farmer preferences for the various m a n u f a c t u r e r brands i n c o r p o r a t e d this feature. B o t h a r a n k i n g of brands "at a st icker pr i ce " a n d a r a n k i n g of brands at or-thogona l l y var ied prices were used to assess farmer preferences for c ombine brands at ) " Durability Ô3 Threshing ; ^ Technology Ease of X 3 1 7 Maintenance e 44 Ease of Controlling Operation Combine ) *• Warranty 677 Parts ) ^ Availability 088 Dealer-Farmer Relations Dealer Location ^62 ^ F i g u r e 4.2: C o n f i r m a t o r y F a c t o r A n a l y s i s P a t h D i a g r a m different prices. S ince the level of analys is was set at the m a n u f a c t u r e r rather t h a n the m o d e l level , c ombine prices could not be i n c l u d e d as an a c t u a l do l la r a m o u n t . T h i s is due to the fact t h a t there is a s u b s t a n t i a l price difference between h i g h a n d low capac i ty combine models . Therefore , prices were expressed as re lat ive to the average pr ice for a combine of the desired capacity . F o r example . B r a n d A p r i c e d at 5% A b o v e Average or B r a n d C pr i ced at 5% Be low Average . B o t h the dealers a n d pretest farmers were comfortable w i t h this p r i c i n g m e t h o d . It is unc lear whether the use of re lat ive pr ice levels is res tr i c t ive . O n the one h a n d , a c t u a l prices are more salient to the respondent , espec ia l ly w h e n a 10% difference cou ld m e a n as m u c h as $20,000. However , a do l lar f igure m a y lead to a "s t i cker shock" effect w h i c h w o u l d over emphas ize the i m p o r t a n c e of pr ice . In a d d i t i o n , the extensive negot ia-t ions w h i c h take place between dealer and farmer o n the purchase of the combine raises questions about the m e a n i n g of l ist prices i n a b r a n d - p r i c e c ompar i son . O n the other h a n d , the re lat ive prices a l lowed for a c ompar i son based o n pr ice percept ions even though the levels of re lat ive pr ice were chosen object ive ly . A d d i t i o n a l e m p i r i c a l research is nec-essary to determine w h i c h approach w o u l d be super ior i n the context of the strategic d i r e c t i o n m o d e l . In the b r a n d "at a st icker pr i ce " quest ion , respondents were asked to rank their preference for the various manufacturers at specific re lat ive prices. T h e re lat ive prices were d e t e r m i n e d t h r o u g h discussions w i t h 7 f a r m equipment dealers i n Saskatchewan. T w o dealers for J o h n Deere, C a s e - I n t e r n a t i o n a l a n d N e w H o l l a n d were contacted as wel l as a Gleaner dealer. T h e dealers were first asked whether the various manufacturers were m a t c h e d on m o d e l size. A U were i n agreement that th i s was generaUy the case. Second, the dealers were asked what the re lat ive prices of the m a n u f a c t u r e r combines for models of equa l size. T h e m a j o r i t y of dealers rep l ied that the l ist prices were very close together . W h e n p r o b e d about a c t u a l selHng prices , most dealers felt that J o h n Deere combines " h e l d t h e i r p r i c e " wh i l e D e u t z - A l h s combines "d iscounted more t h a n the o t h e r s " . F i n a n c i n g packages a n d t rade - ins m a d e exact p r i c i n g comparisons diff icult for the dealers. T h e f inal prices selected for the analys is were Case In ternat i ona l pr iced at Average ; D u e t z - A l h s pr i ced at 5% below average; J o h n Deere pr i ced at 10% Above Average ; a n d . N e w H o U a n d p r i c e d at A v e r a g e . These exact re la t ive prices were offered by two of the dealers. T h e order i n w h i c h the b r a n d "at a st icker pr i c e " combinat ions were shown was r a n d o m i z e d for each respondent . T h e second measure of m a n u f a c t u r e r preferences i n c o r p o r a t i n g price was der ived t h r o u g h a r a n k i n g of 8 b r a n d - p r i c e pa i rs . T h e b r a n d - p r i c e combinat ions selected for e v a l u a t i o n were chosen f r o m a b r a n d - p r i c e trade-of f tab le c o n t a i n i n g the four manufac -turers a n d four pr ice levels : 1 5 % B e l o w Average , 5% B e l o w Average , 5% A b o v e Average , a n d 1 5 % A b o v e A v e r a g e . T a b l e 4.2 i l lus t rates the selected combinat i ons . E a c h b r a n d and each price leve l a p p e a r e d twice i n the analys is . T h e order i n w h i c h the brand-pr i ce combinat i ons were s h o w n was r a n d o m i z e d for each respondent . C o n j o i n t M e a s u r e m e n t F o l l o w i n g the questions r e l a t i n g to m a n u f a c t u r e r preferences, the respondents completed a conjoint task c o n t a i n i n g three factors : Combine Quality, Dealer Service a n d Price. T h e r e were four levels for each factor . T h e levels for Combine Quality a n d Dealer Service were E x c e l l e n t , G o o d , F a i r a n d P o o r . These levels were d i re c t l y re lated to the scale used i n the a t t r i b u t e r a t i n g task . T h e levels for pr ice were 1 5 % B e l o w Average , 5% 1 Case International Priced at 5% Below Average 2 Gleaner Priced at 15% Below Average 3 John Deere Priced at 5% Below Average 4 New Holland Priced at 15% Below Average 5 Case International Priced at 15% Above Average 6 Gleaner Priced at 5% Above Average 7 John Deere Priced at 5% Above Average 8 New Holland Priced at 15% Above Average Tab le 4.2: B r a n d - P r i c e Pa i r s B e l o w A v e r a g e , 5% A b o v e A v e r a g e , a n d 1 5 % A b o v e Average . These levels m a t c h e d the b r a n d - p r i c e r a t i n g task. T w e l v e profiles were developed for the task (see T a b l e 4.3). T h e profiles a l lowed for the measurement of the m a i n effects as wel l as a Combine Quality a n d Dealer Service i n t e r a c t i o n p r o v i d e d that a vec tor - type preference m o d e l was es t imated . T h e hypothe -sized preference m o d e l ca l led for the e s t i m a t i o n of 4 parameters ( i n c l u d i n g the constant) us ing the 12 d a t a po ints . A l t h o u g h the low rat i o of d a t a po ints to e s t i m a t e d parameters (^ = 3.0) raises some concern over the re l i ab i l i t y of the parameters , the ra t i o improves on previous studies w h i c h measured b o t h heterogeneous perceptions a n d preferences. For example , H o r s k y a n d N e l s o n (1989) es t imate a m o d e l w i t h 9 parameters (plus a constant) us ing 12 d a t a po ints . F u t u r e e m p i r i c a l research shou ld consider this parameter r ehab ih ty issue. T h e so lut i on is not mere ly co l l ec t ing more d a t a as the d a t a requirements have to be ba lanced against the real i t ies of the d a t a co l lect ion s i t u a t i o n . Respondents were asked to r a n k the 12 profiles w h i c h were shown s imul taneous ly on the computer screen. T h e order i n w h i c h the profiles were d isp layed on the screen was r a n d o m i z e d for respondent . D e m o g r a p h i c s T h e final questions i n the c o m p u t e r quest ionnaire col lected general f a r m i n f o r m a t i o n i n c l u d i n g the na ture of hvestock on the f a r m , number of years the respondent has been f a r m i n g a n d l o ca t i on of the f a r m opera t i on . Combine Quality Dealer Service Price 1 Excellent Good 15% Above 2 Excellent Fair 5% Above 3 Excellent Poor 5% Below 4 Good Excellent 5% Below 5 Good Good 5% Above 6 Good Poor 15% Below 7 Fair Excellent 15% Below 8 Fair Fair 15% Above 9 Fair Poor 5% Above 10 Poor Excellent 15% Above 11 Poor Good 15% Below 12 Poor Fair 5% Below T a b l e 4.3: C o m b i n e Profi les Used i n C o n j o i n t A n a l y s i s 4.3.4 C o m p u t e r Interview Pretest Since t i iere are few combine owners near Vancouver , pretes t ing t l i e quest ionnaire on a large sample of farmers was not possible . However , a l i m i t e d pretest was undertaken d u r i n g a t r ip to southwestern O n t a r i o . U s i n g a l ap top c o m p u t e r , personal interviews were comple ted w i t h seven farmers . T h e farmers , who used the ir combines to harvest wheat , corn a n d soybeans, co l lect ive ly represented ownership of the four combine manufacturers . T h e farmers also var ied i n age a n d f a r m size. W h i l e being observed, the farmers independent ly c o m p l e t e d the c o m p u t e r quest ion-naire . F o l l o w i n g th is , an i n - d e p t h discuss ion of the quest ionnaire a n d the eva luat ion of combine harvesters was u n d e r t a k e n . M i n o r changes were made to the quest ionnaire as a result of the pretest in terv iews . 4.3.5 S e c o n d a r y Q u e s t i o n n a i r e I n a d d i t i o n to the computer quest ionnaire , a short persona l in terv iew was conducted w i t h a separate sample of farmers at the C a n a d a W e s t e r n A g r i b i t i o n . A copy of the quest ionnaire is i n A p p e n d i x D . T h e m a i n purpose of this quest ionnaire was to conf i rm the re la t i onsh ip between the factor labels used i n the conjo int analys is section a n d the a t t r ibutes used i n the a t t r i b u t e r a t i n g task. F o l l o w i n g a series of demograph i c questions ( w h i c h were i d e n t i c a l for b o t h quest ion-naires) , combine owners were asked whether a p a r t i c u l a r a t t r i b u t e represented Combine Quality or represented Dealer Service. Speci f i cal ly , respondents were shown the list o f combine a t t r ibutes a n d asked: "P lease read the f o l l owing l ist of combine features. In your o p i n i o n , w h i c h features represent C o m b i n e Q u a l i t y a n d w h i c h features represent Dea ler S e r v i c e ? " . A s s u m i n g that the secondary in terv iew sample is s i m i l a r to the com-puter i n t e r v i e w sample , it is hypothes ized that the s u m m a r y tabu la t i ons i n the secondary ques t i onna i re w o u l d y i e l d a p a t t e r n of a t t r ibute - fa c to r associat ions equal to the factor p a t t e r n r e s u l t i n g f r o m a factor analysis of the a t t r i b u t e rat ings i n the computer interv iew. 4.4 R e s u l t s of the E m p i r i c a l S t u d y 4.4.1 S a m p l e D u r i n g 7 days of i n t e r v i e w i n g at the C a n a d a Western A g r i b i t i o n , a t o ta l of 322 combine owners c o m p l e t e d the c o m p u t e r quest ionnaire . O f this n u m b e r , 4 interv iews were i n c o m -plete . O n l y eleven percent of the combine owners who were asked to par t i c ipa te i n the s t u d y refused. T h e h i g h response rate was p r o b a b l y due to farmer interest i n the topic ( combine harvesters ) a n d the fact that the quest ionnaire was c o m p u t e r dr iven . For m a n y respondents , th i s was the ir first i n t e r a c t i o n w i t h personal computers . A n average of 17 minutes was requ i red to complete the quest ionnaire . T h e 318 useable interv iews were fur ther screened to de termine the u l t i m a t e sample size to be used i n m o d e l e s t i m a t i o n . T h r e e screens were used i n this process. F i r s t , 6 interv iews were d r o p p e d f r o m the sample because they were comple ted by farmers who l i ved outs ide of the C a n a d i a n prair ies ( M a n i t o b a , Saskatchewan, A l b e r t a ) . Second, 32 respondents were removed f rom the sample because they gave don ' t know responses for some of the b r a n d a t t r i b u t e rat ings . Since i t was dec ided at the outset to inc lude the four m a j o r brands as the evoked set, i t was felt that the results w o u l d be skewed by u n i n f o r m e d respondents . T h e f ina l screening procedure considered the consistency i n w h i c h the respondents answered the quest ionnaire . T w o sections of the quest ionnaire , the ranlc ing of t l ie 8 brand-pr i ce combinat ions a n d the conjoint taslf, c on ta ined combinat i ons or profiles which were log ica l ly d o m i n a t e d by other choices. For e x a m p l e , in the r a n k i n g of brand-pr i ce combinat i ons , two of the combinat ions were: John Deere Priced at 5% Below Average and John Deere Priced at 5% Above Average. S ince a l l respondents were i n f o r m e d that the same combine was represented at two different prices , the lower pr i ced c o m b i n a t i o n should be preferred by everyone. T h e logic screen counted the n u m b e r of inconsistencies for each respondent w i t h the goal of e l i m i n a t i n g those respondents who e x h i b i t e d a re la t ive ly h igh n u m b e r of logic errors. It was assumed that these respondents d i d not c omprehend the tasks or were s i m p l y answer ing at r a n d o m . A m a x i m u m of four logic errors were possible i n the b rand -pr i ce r a n k i n g task a n d 18 errors i n the conjo int task. Respondents w i t h a h igh n u m b e r of errors t ended to make errors i n b o t h task. Respondents w h o made 4 or more logic errors i n the conjo int task were removed f r o m the sample . T h i s dec is ion rule also e l i m i n a t e d a l l respondents who made more t h a n one logic error i n the b r a n d - price r a n k i n g task. T h e 14 respondents affected by this screen represented less t h a n 5 percent of the t o t a l sample . T h e three screens reduced the 318 completed interv iews to a final sample size of 266 respondents. S a m p l e D e m o g r a p h i c s T h e demographics of the sample are s u m m a r i z e d i n T a b l e 4.4. For ty -e ight percent of the respondents operated farms w i t h b o t h crops a n d l ivestock . A wide v a r i a t i o n i n f a r m size was exh ib i t ed across respondents . T w e n t y - s i x percent of the farmers seeded over 1600 acres wh i l e the size ranges 320-640 acres, 641-960 acres, 961-1280 a n d 1281-1600 each accounted for about 17% of the sample . W h e a t was grown by 9 6 % of the sample respondents . B a r l e y was grown by 5 1 % of the farmers surveyed whi le 3 6 % grew cano la and 16% grew flax. T h e d o m i n a n c e of the wheat crop was a funct i on of the reg ional l o c a t i o n of the farmers in te rv i ewed . T h i s , i n t u r n , was the due to the fact that the A g r i b i t i o n was he ld i n R e g i n a i n southern Saskatchewan: a p r e d o m i n a n t l y wheat g r o w i n g region. N i n e t y percent of the respondents were f rom Saskatchewan whi le 5 8 % had farms l o ca ted i n southern h a l f of the prov ince . C o m p a r e d w i t h 1986 census i n f o r m a t i o n , the respondents tended to operated larger farms. T h i s result was expected as larger farmers t end to a t t e n d t rade shows. In a d d i t i o n , these farmers are more l i k e l y to purchase a combine . F a r m e r s seeded an average of 777 acres of wheat i n 1990 c o m p a r e d to a f a r m average of 350 acres repor ted i n the census. Respondents who repor ted growing the specific crops seeded a n average of 264 acres of bar ley (census - 162 acres) , 216 acres of cano la (census - 178 acres) , a n d 233 acres of flax (census - 133 acres). Farmers who comple ted the survey h a d a wide range of experience . T w e n t y - t h r e e percent of the farmers h a d been f a r m i n g for 10 years or less. A t o t a l of 4 4 % of the farmers h a d been f a r m i n g for between 11 a n d 20 years w h i l e 2 2 % h a d f a r m e d between 21 and 30 years and 1 1 % h a d over 30 years of experience . C o m b i n e Inventory T w e n t y - s i x percent of the sample owned more t h a n one combine . T a b l e 4.5 out l ines the inventory of combines a m o n g the farmers in terv iewed . C a s e - I n t e r n a t i o n a l (26%) , J o h n Deere (25%) a n d Massey Ferguson (22%) were the d o m i n a n t combine brands . Gleaner (9%) , N e w H o U a n d (8%) a n d W h i t e (6%) r o u n d e d out the i n v e n t o r y shares of the ma jor l*rimary Secondary Sample Sample (pet) (pet) Kegiun: Manitoba 5.6 7.3 Northeast Saskatchewan 14.3 12.7 Northwest Saskatchewan 16.2 11.5 Southeast Saskatchewan 44.7 43.7 Southwest Saskatchewan 14.7 20.5 Alberta 4.5 3.4 Other — 0.9 Farm Type: Crops Only 51.9 44.3 Both Crops and Livestock 48.1 55.7 Acres Seeded in 1990: 320 acres or less 4.9 11.2 321 -640 acres 15.8 24.4 641 -960 acres 17.3 18.0 961 - 1280 acres 18.4 17.8 1281 - 1600 acres 17.3 11.2 Over 1600 acres 26.3 17.3 Crops Grown in 1990: Wheat 96.2 95.9 Barley 51.5 55.6 Canola 35.7 29.5 Flax 16.2 18.5 Farming Expérience: 5 years or less 7.5 6.6 6-10 years 15.4 13.7 11 - 20 years 43.6 36.1 21-30 years 22.2 24.1 31 - 40 years 8.6 13.7 Over 40 years 2.6 5.9 Base: 266 410 Tab le 4.4: Demograph i c s of P r i m a r y a n d Secondary Samples Manufacturer Share of Combines Share of Farmers (pet) (pet) Case-International 25.5 28.9 John Deere 24.9 27.1 Massey Ferguson 22.0 24.1 Gleaner 8.5 9.8 New Ilulland 8.2 9.0 White 6.2 7.1 Other 4.7 5.3 Base: 341 266 Tab le 4.5: C o m b i n e Inventory combine manufac turers . These inventory percentages were con f i rmed to be close to recent m a r k e t i n g research est imates . 4.4.2 Results of the S e c o n d a r y S u r v e y T h e secondary survey was completed by 500 farmers a t t e n d i n g the C a n a d a Western A g r i b i t i o n . E i g h t y - t w o percent of these farmers owned a combine (410) and completed the sect ion w h i c h re lated the t h e b r a n d a t t r ibutes to the latent factors . T h e demographics of this sample was s i m i l a r to the farmers who comple ted the c o m p u t e r survey. Table 4.4 provides a demographic compar i son . N o farmers c o m p l e t e d b o t h in terv iews . Combine Quality Dealer Service (pet of resp.) (pet of resp.) Durability 94.9 5.1 Threshing Technology 93.7 6.3 Ease of Maintenance 87.3 12.7 Ease of Controlling Operation 92.7 7.3 Combine Waranty 38.3 6 L 7 Dealer Location 4.4 95.6 Parts Availability 7.6 92.4 Dealer-Farmer Relations 12.2 87.8 Tab le 4.6: A t t r i b u t e - F a c t o r A s s o c i a t i o n s i n the Secondary Survey T h e a t t r ibute - fa c t o r associat ions p r o v i d e d by the farmers was s i m i l a r to the h y p o t h -esized factor p a t t e r n (see Tab le 4.6). A n o v e r w h e l m i n g m a j o r i t y of farmers associated Durability (95% of respondents ) , Ease of Maintenance (87%) , Ease of Controlling Op-eration (93%) a n d Threshing Technology (94%) w i t h Combine Quality. In a d d i t i o n . Parts Availability (93%) , Dealer Location (96%) a n d Dealer-Farmer Relations (88%) were strongly associated w i t h Dealer Service. T h e C o m b i n e W a r r a n t y a t t r i b u t e was not as s t rong ly assoc iated w i t h one of the two factors. S i x t y - two percent of the respondents assoc iated the Combine Warranty w i t h Dealer Service whi le 3 8 % re lated the a t t r i b u t e to Combine Quality. It is apparent that the d u a l assoc iat ion w h i c h was discussed i n the previous chapter does apply . Perhaps a better u n d e r s t a n d i n g of the nature of the Combine Warranty a t t r i b u t e would have been o b t a i n e d i f respondents were aslced w h y they made their chosen factor assoc iat ion. F r o m these results , i t is apparent that the factor labels Combine Quality a n d Dealer Service are good choices for the conjo int measurement task. 4.4.3 C r e a t i o n of P e r c e p t u a l Space T h e p e r c e p t u a l space for the combine harvesters i n the C a n a d i a n prair ies was developed v i a c o n f i r m a t o r y factor analys is . U s i n g the termino logy forwarded by S r i n i v a s a n , V a n d e n Abee le a n d B u t a y e (1989), a Total Analysis was per formed. T h i s type of analysis factor analyzes an NJ x K m a t r i x where each row is person ri 's r a t i n g of the j ' t h b r a n d on the K a t t r ibutes .^ As a basis of c o m p a r i s o n , the d a t a were also s u b m i t t e d to a c o m m o n ( m a x i m u m l ike l ihood ) factor analys is a n d a p r i n c i p a l components analys is . P r e p r o c e s s i n g T r a n s f o r m a t i o n s Several researchers have r e c o m m e n d e d preprocessing t rans format ions of the raw a t t r i b u t e rat ings d a t a to e h m i n a t e response tendency effects (Hauser a n d K o p p e l m a n 1979, H u b e r a n d H o l b r o o k 1979, S r i n i v a s a n , V a n d e n Abee le and B u t a y e 1989). D i l l o n , Freder ick and Tangpani chdee (1985) review the effects of various preprocess ing t rans format ions . T h e m a i n argument for r e t a i n i n g the raw d a t a is that no assumpt ions are made as to the m a n n e r i n w h i c h respondents comple ted the questions. However , because of the °Note that this type of matrix contains rows which are not independent (4 brand evaluations per re-spondent). This issue has been recognized by many researchers (see Dillon, Frederick and Tangpanichdee 1985), but the methodology has remained the "standard" in the development of perceptual maps. A preprocessing transformation (see below) can partially address this issue. three mode nature of the d a t a ( a t t r i b u t e x b r a n d x respondent ) , analysis of the raw d a t a is i n a p p r o p r i a t e because the the variance i n the a t t r i b u t e rat ings for respondents is confounded w i t h the var iance of each b r a n d on an a t t r i b u t e for each respondent ( D i l l o n et a l 1985, p. 57). To correct this p r o b l e m , D i l l o n et a l suggest a t rans fo rmat ion i n w h i c h each a t t r i b u t e is s t a n d a r d i z e d across brands for each respondent. T h a t is , the first a t t r i b u t e for the first respondent is s t a n d a r d i z e d over the K b rands . T h e n , the second a t t r i b u t e for the first respondent is s t a n d a r d i z e d over the K b rands , a n d so on for a l l a t t r i b u t e s a n d for a l l respondents . T h e ob jec t ive of this t r a n s f o r m a t i o n approach is to b r i n g out the wi th in - respondent var iance o n the a t t r ibutes over b rands for each respondent a n d to al low for compar -isons across brands . T h e s t a n d a r d i z a t i o n s w i t h i n each respondent remove the var iance on a t t r ibutes due to i n d i v i d u a l level effects. T h e r e m a i n i n g var iance i l lustrates the i n -terre lat ionships between changes i n a t t r ibutes over the brands general ized across the respondents ( D i l l o n et a l 1985, p. 58). D i l l o n et a l suggest that this is a reasonable approach to coUapsing three m o d e d a t a in to a two-way m a t r i x . T h e results presented be low are c o m p u t e d fo l lowing the preprocess ing s t a n d a r d i z a t i o n suggested by D i l l o n et a l (1985). A paraUel analysis us ing the raw d a t a showed o n l y m i n o r differences between the two d a t a sets. Tab le 4.7a a n d 4.7b conta in the corre lat ion matr ices for the eight a t t r ibutes p r i o r to a n d fo l lowing the preprocess ing t rans fo rmat ion respectively. a. Correlation Matrix Using Raw Data Dur. T.T. E .O .M. E.C.O. C.W. D.L. P.A. D.F.R. Durability 1.00 Threshing Technology 0.50 1.00 Ease of Maintenance 0.57 0.50 1.00 Ease of Controlling Operation 0.57 0.50 0.56 1.00 Combine Waranty 0.51 0.43 0.47 0.49 1.00 Dealer Location 0.41 0.27 0.34 0.36 0.33 1.00 Parts Availability 0.52 0.35 0.47 0.47 0.44 0.54 1.00 Dealer-Farmer Relations 0.49 0.34 0.46 0.45 0.47 0.49 0.59 1.00 b. Correlation Matrix Following the Preprocessing Transformation Dur. T .T . E . O . M . E.C.O. C.W. D.L. P.A. D.F.R. Durability 1.00 Threshing Technology 0.41 1.00 Ease of Maintenance 0.56 0.47 1.00 Ease of Controlling Operation 0.54 0.47 0.51 1.00 Combine Waranty 0.44 0.37 0.40 0.41 1.00 Dealer Location 0.38 0.21 0.33 0.37 0.31 1.00 Farts Availabihty 0.50 0.31 0.45 0.47 0.44 0.58 l.OO Dealer-Farmer Relations 0.48 0.32 0.46 0.45 0.46 0.54 0.58 1.00 T a b l e 4.7: C o m b i n e A t t r i b u t e C o r r e l a t i o n M a t r i x P e r c e p t u a l S t r u c t u r e For c ompar i son purposes , three different approaches were use to develop the perceptual s t ruc ture : c o n f i r m a t o r y factor ana lys i s , c o m m o n factor analysis a n d p r i n c i p a l compo-nents analys is . W i t h i n each of these m e t h o d s , a n u m b e r of var iat ions were analyzed to check the appropr iateness of various models . T h e c o n f i r m a t o r y factor analys is was per f o rmed us ing L I S R E L V I (Joreskog a n d S o r b o m 1985). T h r e e different models were e s t i m a t e d . T h e first m o d e l , C F A l describes the hypothes ized factor s t ruc ture . In C F A l , the Combine Warranty a t t r i b u t e was associ-ated w i t h b o t h Combine Quality a n d Dealer Service. T h e p a t h d i a g r a m for this mode l is shown i n F i g u r e 4.2. T h e second m o d e l , C F A 2 , removes the Combine Warranty - Dealer Service assoc iat ion . T h i s m o d e l was a n a l y z e d to m a t c h the results of the c o m m o n factor m o d e l (see d iscuss ion be low) . T h e f ina l m o d e l , C F A 3 , was a single factor mode l i n w h i c h a l l a t t r ibutes were assoc iated w i t h a single latent var iab le . T h e C F A l m o d e l fit the d a t a ex t reme ly wel l . T h e chi -square s tat i s t i c was significant {Xis = 90.85, p < 0.001). However , th is can be p a r t i a l l y a t t r i b u t e d to the large sample size. T h e ad jus ted goodness of fit i n d e x ( A G F I ) was 0.959 a n d the root mean square res idua l ( R M R ) was 0.027. T y p i c a l l y , an A G F I of greater t h a n 0.9 and a n d R M R of less t h a n 0.05 i n d i c a t e a good m o d e l f it . See B o U e n (1989, p.257-281) for a discussion of procedures for the assessment of m o d e l f it . In a d d i t i o n a l l parameter values were signif icant at the p < 0.01 level . W h a t th is i n d i c a t e d was that the C F A l m o d e l d i d a very good j ob at m e a s u r i n g the covar ia t i on between a t t r i b u t e s (off d iagona l elements of the corre la t i on m a t r i x ) . T h e squared m u l t i p l e corre lat ions of the a t t r ibutes show how wel l the w i t h i n a t t r i b u t e v a r i a t i o n is c a p t u r e d . T h e average squared m u l t i p l e corre lat ion is 0.505 i n d i c a t i n g a reasonable fit . T h e C F A l m o d e l e s t i m a t e d a signif icant corre lat ion of .77 between the Combine Quahty a n d Dealer Service factors. Tab le 4.8 summarizes these results . T h e C F A 2 m o d e l , w h i c h on ly removed one p a t h , also fit the d a t a very wel l . T h i s m o d e l also had a signif icant chi -square s tat i s t i c (Xig = 109.05, p < 0.001). T h e reduced m o d e l h a d a n A G F I of 0.950 and an R M R of 0.031. T h e parameter est imates a n d squared m u l t i p l e corre lat ions for the a t t r ibutes are also found i n Tab le 4.8. S ince the C F A l a n d C F A 2 models are nested, a sequent ia l chi -square test can be used to assess w h i c h m o d e l provides a better fit. T h i s test i n d i c a t e d that the C F A l mode l p r o v i d e d a s ign i f i cant ly bet ter fit of the d a t a (x? = 18.2, p < 0.001). Therefore , the C F A l m o d e l w i l l be used i n further analyses. T h e t h i r d c on f i rmatory factor analysis mode l , C F A 3 , e s t imated a single factor mode l . T h i s m o d e l d i d not fit as wel l as the f u l l m o d e l . T h e results of the m a i n tests of fit were: Xlo = 308.7, p < 0.001; A G F I = . 8 1 7 ; R M R = . 0 5 6 . These results suggest that the C F A l m o d e l provides a better descr ip t i on of the u n d e r l y i n g factor s t ruc ture . T h e results of the c on f i rmatory factor analysis were c ompared w i t h c o m m o n factor analys is a n d p r i n c i p a l components analys is . U s i n g the eigenvalue > 1 ru le , the p r i n c i p a l components a n d c o m m o n factor analyses y ie lded a two factor so lut ion . T h e first two eigenvalues were 4.08 a n d 1.00 respect ive ly e x p l a i n i n g 6 4 % of the c o m m o n variance . A scree plot ( F i g u r e 4.3) also suggested a two factor so lu t i on . T h e average c o m m u n a l i t y in the c o m m o n factor analys is was 0.503. T h i s is very close the average squared m u l t i p l e corre lat ions i n the C F A l m o d e l (0.505). T h e two factor s o l u t i o n , us ing a v a r i m a x r o t a t i o n y ie lded a factor p a t t e r n i n w h i c h Durability, Ease of Maintenance, Ease of Controlling Operation, Threshing Technology, a n d Combine Warranty h a d h igh loadings o n the first factor ( n a m e d Combine Quality) a n d Dealer Location, Parts Availability a n d Dealer-Farmer Relations h a d h i g h loadings C F A l C F A 2 Parameter Value T-Value Squared Mult. R* Parameter Value T-Value Squared Mult. R* Combine Quality Indicators Durability 0.72 26.81 0.57 0.72 26.82 0.57 Threshing Technology 0.56 19.58 0.35 0.56 19.44 0.34 Ease of Maintenance 0.69 25.62 0.53 0.69 25.42 0.52 Ease of Controlling Operation 0.67 25.46 0.53 0.67 25.38 0.52 Combine Warranty 0.32 6.80 0.36 0.51 20.07 0.36 Dealer Service Indicators Combine Warranty 0.21 4.40 0.36 — — — Dealer Location 0.63 23.55 0.47 0.63 23.65 0.48 Parts Availability 0.77 28.74 0.64 0.77 28.77 0.65 Dealer Farmer Relations 0.72 27.03 0.59 0.72 26.82 0.58 Errors 6(1 .1) 0.39 17.13 0.40 17.54 6(2, 2) 0.59 17.98 0.59 20.88 6(3, 3) 0.42 20.71 0.43 18.43 6(4, 4) 0.40 21.36 0.41 18.45 6(5, 5) 0.46 18.09 0.45 20.69 6(6, 6) 0.44 18.93 0.43 18.81 6(7, 7) 0.33 14.64 0.33 14.46 8(8, 8) 0.37 16.43 0.37 16.51 Factor Correlations Combine Qual. - Dealer Serv. 0.77 36.46 0.79 40.02 Analysis of Model Fit chi-square statistic chi-square(18) = 90.85 chi-square(19) = 109.05 P< 0.001 P< 0.001 Adjusted Goodness of Fit Index 0.959 0.95 Root Mean Square Residual 0.027 0.031 Model Comparison C F A l vs. CFA2 chi-square(l) = 18.2, p< 0.001 •"Squared Mult R = Squared Multiple Correlation Note: All parameters significant at the p=0.001 level Table 4.8: C o n f i r m a t o r y Fac tor A n a l y s i s Resu l t s F i g u r e 4.3: Scree P l o t of the V a r i a n c e E x p l a i n e d by C o m m o n Factors a n d P r i n c i p a l C o m p o n e n t s Common Fad tor Analysis Principal Components Combine Quality Dealer Service Combine Quality Dealer Service Durability 0.65 0.42 0.63 0.39 Threshing Technology 0.82 0.01 0.64 0.13 Ease of Maintenance 0.73 0.29 0.67 0.30 Ease of Controlling Operation 0.70 0.34 0.63 0.35 Combine Waranty 0.54 0.39 0.47 0.37 Dealer Location 0.10 0.85 0.18 0.72 Parts Availability 0.32 0.78 0.35 0.72 Dealer-Farmer Relations 0.35 0.74 0.38 0.64 T a b l e 4.9: L o a d i n g s for C o m m o n Factor a n d P r i n c i p a l C o m p o n e n t s Ana lyses on the second factor (named Dealer Service) (See T a b l e 4.9). T h e h igh l oad ing of the Combine Warranty a t t r i b u t e o n Combine Quality is c o n t r a r y to what was expected given the results of the secondary in te rv i ew . B o t h the p r i n c i p a l components and con f i rmatory factor analyses suggest the two factor m o d e l provides a reasonable fit the the d a t a . T h e three factor a n d the one factor so lut ions for b o t h analyses were also computed . These analyses d i d not improve the i n t e r p r e t a b i h t y of the d a t a . In general , the results of the three types of factor analys is were s i m i l a r . A U three methods suggested a two factor so lu t i on w i t h agreement o n v i r t u a l l y a l l a t t r i b u t e factor associat ions . For reasons descr ibed i n sect ion 4.2.2, t l ie best c o n f i r m a t o r y factor mode l , C F A l , w i l l be used i n the development of the customer dec is ion m o d e l . T h e s ta t i s t i ca l results for this m o d e l suggested a s trong corre la t i on between Combine Quality and Dealer Service as wel l as a n assoc iat ion between Combine Warranty a n d b o t h latent factors. P e r c e p t u a l M a p a n d Offering Posi t ions T h e C F A l m o d e l es t imated that the corre lat ion between the two latent factors {Combine Quality a n d Dealer Service) is 0.77. T h i s translates to a 39° angle between the axes of the per cep tua l m a p . Of fer ing locat ions are d e t e r m i n e d by m u l t i p l y i n g the o r i g i n a l a t t r i b u t e rat ings ( fo l lowing the preprocessing t rans format ion ) by the factor score coefficients (given as o u t p u t i n L I S R E L ) . T h e factor score coefficients are for the C F A l m o d e l are shown i n T a b l e 4.10. F i g u r e 4.4a shows the p e r c e p t u a l m a p for one respondent whi le F igure 4.4b shows the average per cep tua l map . T h e two axes are j o i n e d at -4. T h i s is done for iUust ra t ive purposes as i t shows a l l manufacturers pos i t i oned between the two axes. T h e posit ions of the manufacturers var ied s u b s t a n t i a l l y between respondents (see Tab le 4.11). T h e s t a n d a r d d e v i a t i o n of the manufac turer pos i t ions were re la t ive ly large (.64 to .84) i n compar i son to the range of factor scores used to develop the perceptual maps (4.34). T h i s large v a r i a t i o n i n respondent percept ions was expected given the na ture of the p r o d u c t - m a r k e t (see section 4.1). S u m m a r y In s u m m a r y , there are several points w o r t h n o t i n g . F i r s t , the hypothes i zed m o d e l C F A l , p rov ided a good fit o f the survey data . A l l a t t r i bute - fa c t o r re lat ionships were significant Attribute Combine Quality Dealer Service Durability 0.290 0.076 Threshing Technology 0.151 0.040 Fflse of Maintenance 0.259 0.068 Ease of Controlling Operation 0.263 0.069 Combine Warranty 0.130 0.103 Dealer Location 0.056 0.231 Parts Availability 0.096 0.376 Dealer Farmer Relations 0.081 0.315 T a b l e 4.10: Fac tor Score Coeff icients F r o m C F A l Combine Quality a) An Individual 's Perceptual Map 1 0 Case-Intenialional Dealer Service b) Average Perceptual Map -4 Combine Quality 1 Dealer Service F i g u r e 4.4: P e r c e p t u a l M a p s Case- John New International Gleaner Deere Holland CO DS CQ DS CO DS CQ DS Mean Location 0.26 0.41 -0.52 -0.78 0.67 0.74 -0.41 -0.37 Standard Deviation 0.73 0.64 0.84 0.73 0.79 0.66 0.75 0.73 Highest Score 2.10 1.89 1.89 1.75 ( ^ 2 . I 5 J 2.01 2.09 1.78 lowest Score -1.70 -1.95 (^.19) -2.15 -1.31 -1.09 -2.01 -1.85 Range 3.80 3.84 4.08 3.90 3.46 3.10 4.10 3.63 Tab le 4.11: M e a n a n d S t a n d a r d D e v i a t i o n of M a n u f a c t u r e r Pos i t i ons at the p < 0.01 level . Secondly, a s ignif icant corre la t i on between latent factors was found i n d i c a t i n g that the i n c o r p o r a t i o n of corre lated d imensions i n p e r c e p t u a l space is i m p o r t a n t . F i n a l l y , respondents var ied s ign i f i cant ly i n the i r p e r c e p t u a l locat ions of the manufacturers . T h i s suggests that the i n d i v i d u a l level approach to the development of the customer decis ion m o d e l is w a r r a n t e d . 4 .4 .4 Preference M e a s u r e m e n t A conjoint measurement task was u n d e r t a k e n to assess i n d i v i d u a l preferences for various combine profiles. Respondents were asked to r a n k 12 combine profiles (see Tab le 4.3). E a c h profile p r o v i d e d a Combine Quality r a t i n g , a Dealer Service r a t i n g , a n d a price. A vector mode l of preference was assumed (see (4.3)) : U = (3o + 0iCQ+f32DS + (33Price (4.4) T h e conjoint m o d e l was e s t i m a t e d us ing O L S regression w i t h the dependent var iable be ing the reverse r a n k i n g of profi les. T h a t is , the most preferred profile was given a value of " 1 2 " whi le the least preferred prof i le was g iven a value of " 1 " . W i t t i n k a n d C a t t i n (1981) report that there is very l i t t l e difference i n the pred i c t ive va l id i ty of e s t i m a t i o n techniques a n d that m e t r i c procedures , l ike O L S , c ompare favorably w i t h n o n m e t r i c approaches w h e n a t t r i b u t e weights do not e x h i b i t a l ex i cographic s t ructure . T h e levels for Combine Quality a n d Dealer Service were E x c e l l e n t , G o o d , F a i r a n d P o o r . These levels were d i r e c t l y re la ted to the scale used i n the a t t r i b u t e r a t i n g task. T h e levels for price were 1 5 % B e l o w A v e r a g e , 5% B e l o w A v e r a g e , 5% A b o v e Average , and 1 5 % A b o v e Average . In e s t i m a t i n g (4.4), the prices can be coded i n any form (percentages, levels, etc.) w h i c h incorporates the differences between levels. M o r e care must be taken i n the c o d i n g of the latent factors . T h e conjoint measurement task allows for a n e s t i m a t i o n of the relat ive i m p o r t a n c e of the factors w h i c h f o r m a n i n d i v i d u a l ' s preference for a set of ob jects . However , i n the context of the customer dec is ion m o d e l , these i m p o r t a n c e parameters are o n l y useful when they are e s t i m a t e d i n the same uni ts as the produc t pos i t ions i n p e r c e p t u a l space. Because the customer dec is ion m o d e l incorporates b o t h preferences a n d percept ions o n the latent factors , the same uni ts must be used in the measurement of each. If this m a t c h i n g of un i ts is achieved , the relat ive i m p o r t a n c e of price i n a n i n d i v i d u a l ' s preference f u n c t i o n is adequate ly represented.'^ ^For example, the relative importance of the factors in a conjoint analysis would be unchanged if the the latent factors were coded with a range of (10,10) or (-100,100). The only difference would be the scaling of the parameters. Now assume that the product positions (estimated through the confirmatory For the current ana lys i s , the d a t a w h i c h were used i n the c o n s t r u c t i o n of the per-ceptua l space was s t a n d a r d i z e d i n a m a n n e r i n w h i c h each of the a t t r ibutes h a d a mean of zero and a s t a n d a r d d e v i a t i o n of one at the i n d i v i d u a l level . Since factor scores are s i m p l y a l inear t r a n s f o r m a t i o n of the a t t r i b u t e levels, the manufac turer posit ions derived f rom this analysis also have fi = 0 a n d cr = 1 at the i n d i v i d u a l level.® To m a t c h the units used i n the p e r c e p t u a l space c o n s t r u c t i o n , the levels of the latent factors i n the conjoint analys is were coded w i t h /x = 0 a n d cr = 1. Assessment of the I m p o r t a n c e of a Combine Quality-Dealer Service Interact ion A s was o u t l i n e d i n sect ion 4.4.3, there was a signif icant corre la t i on between Combine Quality a n d Dealer Service. A n i m p o r t a n t issue i n the development of the preference m o d e l is the assessment of whether or not this corre la t ion yields an i m p o r t a n t in terac t i on t e r m i n the preference f u n c t i o n . In order to test this issue, the pred ic t ive v a l i d i t y of the preference m o d e l defined i n (4.3) w i t h a Combine Quality-Dealer Service in terac t i on t e r m (shown as (4.4)) was c o m p a r e d to (4.3). P r e d i c t i v e vahdi ty , o p e r a t i o n a l i z e d by the es t imated mean squared error of p r e d i c t i o n , is an appropr ia te c o m p a r i s o n cr i ter ion as the m a i n purpose of the customer decis ion m o d e l is to predict the effect of p roduc t or service improvements to the target offering. T w o conjoint mode ls were es t imated at the i n d i v i d u a l level . T h e general mode l i n -c luded the Combine Quality-Dealer Service i n te rac t i on whi le the reduced m o d e l d id not . factor analysis) had a possible range of (-10,10). When the preference parameters are combined with the perceptual positions of the products (to estimate value for a particular product), the importance of the price in model estimates would be dramatically different for the two codings of the latent factors in the conjoint analysis. ^The manufacturer positions for all respondents will have = 0, but not all positions have a = I. This is because respondents sometimes rated all brands equally on a particular attribute. Therefore, for these attributes the across brand variation (within a respondent) will have / i = 0 and cr = 0. T h e two models were compared i n terms of their predic t ive v a l i d i t y using the procedure developed by Hager ty and Sr in ivasan (1991). T h e procedure est imates the mean squared error of p r e d i c t i o n for each m o d e l w i t h the fo l lowing e q u a t i o n . ESAIEPa = {Rl - Rl) + (1 - Rl){l - ^) (4.5) where: ESMEPR = e s t imated mean squared error of p r e d i c t i o n for the reduced m o d e l . R^ = adjusted R' for the general m o d e l . Rl = ad justed R' for the reduced m o d e l . k — the n u m b e r of parameters e s t i m a t e d i n the reduced mode l . n = the number of profiles used i n e s t i m a t i o n . T h e m o d e l w h i c h has the lowest ESMEP shou ld have the highest pred ic t ive v a h d i t y ( G r e e n a n d S r i n i v a s a n 1990). T h e results of the m o d e l c ompar i son i n d i c a t e d that on average, the reduced m o d e l , w i t h no i n t e r a c t i o n t e r m , h a d the lowest ESMEP. A t the i n d i v i d u a l leve l , 6 4 % of respondents h a d a lower ESMEP w i t h the reduced m o d e l . For the current e m p i r i c a l s tudy , the m o d e l w h i c h h a d the lowest , p o p u l a t i o n - w i d e ESMEP was selected. There -fore, the reduced m o d e l was selected as the preference m o d e l . T h i s m o d e l is the same as the vector mode l descr ibed i n (4.3).^ A s has been discussed by other researchers (e.g. S r i n i v a s a n and Shocker 1973), the e s t i m a t i o n of preference models v i a O L S regression m a y y i e l d i n a p p r o p r i a t e parameter est imates , hke a pos i t ive pr ice parameter , w h i c h are di f f icult to interpret . To e l iminate this p r o b l e m , i n e q u a l i t y c ons t ra ined hnear regression was per formed. U s i n g the procedure descr ibed by Geweke (1986), the models for i n d i v i d u a l s w i t h i n a p p r o p r i a t e parameter values were re -est imated whi le c o n s t r a i n i n g Combine Quality a n d Dealer Service to be greater t h a n or equa l to zero and Price to be less t h a n or equa l to zero. T h i s e s t imat i on is r e la t ive ly s t r a i g h t f o r w a r d i n S H A Z A M ( W h i t e , H a u n , H o r s m a n a n d W o n g 1988). '° T h e average R' for the preference m o d e l , (4.3), was 0.79. T h e Combine Quality factor was, o n average, about twice as i m p o r t a n t as Dealer Service i n the customer 's value funct ions . T h e m e a n value of the p r o d u c t p a r a m e t e r was 2.90 as compared to 1.36 for the service parameter . W h e n Price is scaled to the same uni ts as the latent factors, the mean value of the price parameter was 0.93. T h e re la t ive sizes of these parameter values co inc ided w i t h i n f o r m a l discussions w i t h farmers f o l l owing the in terv iews . However , the low value of the pr ice parameter m a y have been a f u n c t i o n of the f o rm i n w h i c h price was i n c o r p o r a t e d in to the analys is a n d the range of pr i ce levels i n c l u d e d . F igures 4.5-4.7 show the d i s t r i b u t i o n s for the three parameters . It is i m p o r t a n t to note that a l though averages give some ins ight in to the re lat ive i m p o r t a n c e of the various factors , a l l analysis was u n d e r t a k e n at the i n d i v i d u a l level . ^An alternative option would be to individualize the preference model on the basis of the ESMEP results. That is 64% of the respondents would use the reduced model as a model of preference and 36% would use the general model. If it is assumed that the sample represents the population of farmers, then this approach would be reasonable as it can be assumed that a different segments of the population have different preference models. ' " A total of 35 parameters (4% of the estimated parameters excluding the constant) from 26 respon-dents had the inappropriate sign and were re-estimated using the constrained regression procedure. 1 6, Service Parameter Mean: Std. Dev.: Std. Error: Variance: Coef. Var.: Count: 1.355 .787 .048 .619 58.063 266 30 25 20 Price Parameter Mean: Std. Dev.: Std. Error: Variance: Coef. Var.: Count: - .083 .056 .003 .003 -67.476 266 4 . 4 . 5 E s t i m a t i o n of Preferences for B r a n d s T h e customer dec is ion m o d e l is developed by c o m b i n i n g i n d i v i d u a l va lue funct ions est i -m a t e d i n the conjo int measurement task w i t h manufac turer l ocat ions i n the perceptua l space a n d re lat ive price . A de termin i s t i c choice rule is used. Therefore , the mode l pre-dicts that a respondent w i l l choose the b r a n d w h i c h max imizes (4.3). T h e best measure of the predic t ive v a l i d i t y of the mode l w o u l d be a c ompar i son of a c t u a l choice d a t a to m o d e l pred ic t ions . However , g iven the na ture of the p r o d u c t - m a r k e t a n d the avai lable sample , this was not possible i n the context of the current study. A test of how well the customer decis ion m o d e l pred i c ted choice can be o b t a i n e d by c o m p a r i n g the farmers ' b r a n d "at a st icker pr i ce " rankings and r a n k i n g of b r a n d - p r i c e pairs to the m o d e l pred i c t i ons . T h e i n d i v i d u a l perceptions and preferences used i n the customer dec is ion m o d e l were co l lected independent of these r a n k i n g tasks . M o d e l vs. B r a n d " a t a St icker P r i c e " R a n k i n g s In the survey, respondents were asked to rank their preference for the four brands at a specific pr ice . T h e respondents ' first choices were compared to the m o d e l p r e d i c t i o n us ing the k a p p a s ta t i s t i c ( C o h e n 1960). T h e k a p p a s ta t i s t i c is an overa l l measure of agreement between two tests a n d is useful for measur ing agreement i n the absence of a s t a n d a r d . It compares the observed p r o p o r t i o n of respondents i n w h i c h the first choice a n d m o d e l p r e d i c t i o n agree w i t h the p r o p o r t i o n w h i c h w o u l d be expected to agree by chance. It is n o r m a l i z e d to have values between 1 a n d — p / ( l — p ) , where p i s the p r o p o r t i o n of respondents that w o u l d be expected to agree by chance. U s i n g the n o t a t i o n i n Tab le 4.12, the k a p p a s ta t i s t i c is defined as K = {a + d-p)/{l-p), where p = {a + b){a + c) + {c + d){b + d). L a n d i s a n d K o c h (1977) First Choice Preferences Brand A Brand B 2 Brand A a b Brand B c d Tab le 4.12: A T w o - W a y Tab le that Serves as a Bas is for D e f i n i n g Agreement Measures prov ide the fo l lowing benchmarks for i n t e r p r e t i n g k a p p a : « < 0 corresponds to "poor " agreement; 0 < K < 0.20 is " s l i g h t " agreement; 0.20 < K < 0.40 is fa i r agreement; 0.40 < K < 0.60 is "moderate " agreement; 0.60 < K < 0.80 is " s u b s t a n t i a l " agreement; and 0.80 < K < 1.00 is "a lmost perfect" agreement. C a l c u l a t i o n s of confidence intervals are based on s t a n d a r d errors der ived f r o m a p p r o x i m a t i o n s to its var iance ( B i s h o p , Fe inberg a n d H o U a n d 1975). Table 4.13 presents the two -way tab le c o m p a r i n g the respondents ' first choices w i t h the m o d e l pred ic t ions . O v e r a l l , the m o d e l y i e lded good pred i c t i ons . T h e r e was 7 1 % agreement between first choices a n d m o d e l pred ic t ions . T h e k a p p a s ta t i s t i c of 0.57 i n d i -cated a moderate to s u b s t a n t i a l agreement between first choices a n d m o d e l pred ic t ions . A s t a n d a r d d e v i a t i o n of .041 y i e lded a 9 5 % confidence i n t e r v a l o n k a p p a of (.494, .654). T h e m o d e l pred ic ted the preferences of the smal ler share brands ( G l e a n e r , N e w H o l l a n d ) quite wel l . T h e largest source of " e r r o r " i n m o d e l pred ic t ions was between C a s e - I n t e r n a t i o n a l and J o h n Deere. Speci f i cal ly , the m o d e l pred i c ted a J o h n Deere preference for 26 respon-dents (9.8%) who stated a preference for Case - I n t e r n a t i o n a l . T h e m o d e l also per formed wel l i n p r e d i c t i n g the b r a n d "at a s icker pr i ce " rankings for a l l 4 brands . T h e m o d e l pred ic t ions exac t ly m a t c h e d the respondents rankings 3 6 % of the t i m e whi le a further 3 9 % of the respondents h a d the reversed order o n 1 pa i r of brands (Tab le 4.14). T h e fact that later choices i n the r a n k i n g task are dependent on earl ier choices e h m i n a t e d the o p t i o n of us ing a nested k a p p a s ta t i s t i c as a measure of agreement. P r o b a b l y of more i m p o r t a n c e to managers is a c ompar i son of first choice preferences to m o d e l predict ions at the aggregate level . T h e m o d e l pred i c ted J o h n Deere to have the highest share of preference (43%, first choice preference=34%) w h i l e more respondents s tated that they preferred C a s e - I n t e r n a t i o n a l (40%, m o d e l = 3 4 % ) . T h e average dev ia t i on between the pred i c ted shares a n d the stated first choice shares was 5.7%. In an a t t e m p t to get a better u n d e r s t a n d i n g of the re la t i onsh ip between mode l pre-d i c t i ons , s tated preferences a n d a c t u a l choice, an analys is was u n d e r t a k e n w i t h the 187 respondents who owned at least one of the 4 brands i n the s tudy . Inventory is used as a p r o x y for choice. However , i t is recognized that the use of inventory d a t a concen-trates on past choices a n d is an imperfect s u b s t i t u t e for recent choice d a t a . Tables 4.15 -4.17 conta in the two-way tables c o m p a r i n g first choice preferences to m o d e l predic t ions , inventory to first choice preferences, and inventory to m o d e l pred i c t i ons respectively. T h e k a p p a stat is t i cs for these comparisons i n d i c a t e d s u b s t a n t i a l agreement between first choice preferences, m o d e l pred ic t ions a n d inventory {K ranged f r o m 0.62 to 0.66). T h e k a p p a s tat i s t i c for the first choice preference vs. m o d e l pred ic t ions ( K = 0.62) was on ly a shght improvement over the k a p p a s tat i s t i c for the entire sample . T h i s indicates that ownership of one of the four brands d i d not have a signif icant i m p a c t o n the model 's First Choice Preferences Case-In temational Gleaner John Deere New Holland Total Case-International 70 26.3% 2.t 9 3.4% 3 1.1% 89 33.5% C o Gleaner 5 1.9% 26 9.8% 2 0.8% 33 12.4% John Deere 26 9.8% 8 3.0% 76 28.6% 4 1.5% 114 42.9% New Holland 2.2 4 1.5% 4 1.5% 16 26.3% 30 11.3% Total 107 40.2% 45 16.9% 91 34.2% 23 8.7% 266 100% Percentage Agreement = 70.7% kappa statistic = 0.57 95% CI on kappa statistic = (0.494,0.654) Brand Prices: Case-International » Avewge; Gleaner » 5% Below Average; John Deere » 10% Above Average; New Holland » Average. Table 4.13: T w o - W a y Tab le C o m p a r i n g F i r s t C h o i c e Preferences w i t h M o d e l Pred i c t i ons Number of Agreements Percent Cumulative Percent Four (Complete Agreement) 36.1 36.1 Two 39.1 75.2 One 14.7 89.9 Zero (No Agreement) 10.2 100.0 * Note: It is impossible to agree on 3 of 4 rankings. Agreement on 2 of 4 rankings implies that Rank Order Preferences and Model Predictions disagreed on the order of 2 brands. Table 4.14: E x t e n t of Agreement Between R a n k O r d e r Preferences a n d M o d e l P r e d i c t ' a b i l i t y to m a t c h respondents ' preferences.^^ O n an aggregate leve l , the shares of first preference, mode l predict ions a n d inventory were very s i m i l a r (Tab le 4.18). T h e average d e v i a t i o n between these inventory shares and the stated first choice preferences was 3.2%. T h e average d e v i a t i o n between the inventory shares a n d the shares pred ic ted by the m o d e l was 2 .1%. U n f o r t u n a t e l y , the age of the inventory was not asked so a separate analysis w i t h recent purchasers could not be u n d e r t a k e n . Nevertheless , it appears that there is some consistency between the m o d e l pred ic t ions , s tated preference a n d a c t u a l choice. M o d e l vs . B r a n d - P r i c e P a i r s R a n k i n g s T h e respondents were asked to rank 8 b r a n d - p a i r s compr i sed of each manufac turer l i s ted at 2 separate prices . T h e farmers were i n s t r u c t e d to consider a combine of a size suited to the ir f a r m o p e r a t i o n a n d that this same size was l i s t ed at two different prices. T h i s quest ion was more dif f icult to complete t h a n the b r a n d " a t a sticker pr i ce " r a n k i n g and resul ted i n 6% of the respondents c o m m i t t i n g a n " e r r o r " by choosing the higher pr iced b r a n d over the lower pr i ced one. To s imp l i f y the task , respondents may have resorted to p a t t e r n i z e d responses s i m i l a r to those encountered i n tradeoff analysis ( Johnson 1974). These p o t e n t i a l d a t a prob lems should reduce the pred ic t ive v a l i d i t y of the customer decis ion m o d e l . T h e customer dec is ion m o d e l was compared to the respondents ' s tated first choice i n the b r a n d - price r a n k i n g . A l l respondents chose a low pr i ced b r a n d as the i r first choice. ^^The kappa statistics for the inventory to first choice preferences {K = 0.66) and inventory to model predictions {n = 0.65) illustrate that first choice preferences and model predictions do equally as well in predicting inventory (choice). The lower than expected levels of agreement (76%-77%) are probably the result of changes in product offerings and/or changes in offering perceptions since the inventory was purchased. First Choice Preferences Case-In temational Gleaner John Deere New Holland Total Case-Intematiunal 47 25.1% 5 2.7% 9 4.8% 2 1.1% 63 33.7% Gleaner 4 2.1% 20 10.7% 0 0 24 12.8% . 0 y ••5 John Deere 17 9.1% 4 2.1% 58 31.0% 1 0.5% 80 42.8% .s 0 New Holland 3 1.6% 3 1.6% 1 0.5% 13 7.0% 20 10.7% Total 71 38.0% 45 16.9% 68 36.4% 16 8.6% 187 100% Percentage Agreement = 73. S kappa statistic = 0.62 95% CI on kappa statistic = (0.540, 0.695) Brand Prices: Case-International » Average; Gleaner » 5% Below Average; John Deere » 10% Above Average; New HoUand » Average. Table 4.15: T w o - W a y Tab le C o m p a r i n g F i r s t C h o i c e Preferences w i t h M o d e l Pred i c t i ons U s i n g Respondents W h o O w n O n e of the F o u r Survey B r a n d s Combine Inventory Case-International Gleaner John Deere New Holland Total Case-In temational 57 30.5% 3 1.6% 9 4.8% 2 1.1% 71 38.0% C Gleaner 5 2.7% 20 10.7% 5 2.7% 3 1.6% 33 17.7% _o 0 '•B 1 John Deere 10 5.4% 1 0.5% 53 28.3% 3 1.6% 67 35.8% o New Holland 2 1.1% 1 0.5% I 0.5% 12 6.4% 16 8.6% Total 74 39.6% 25 13.4% 68 36.4% 20 10.7% 187 100% Percentage Agreement = 75.9% kappa statistic = 0.65 95% CI on kappa statistic = (0.574, 0.725) Brand Prices: Case-bitemational » Average; Gleaner » 5% Below Average; John Deere » 10% Above Average; New Holland » Average. Note: 12 respondents (6.4%) owned combines of 2 different brands. Agreement occurs when the model predicts one of these brands. T a b l e 4.16: T w o - W a y T a b l e C o m p a r i n g C o m b i n e Inventory w i t h M o d e l Pred i c t i ons U s i n g Respondents W h o O w n O n e of the F o u r Survey B r a n d s C o m b i n e Inventory Case-International Gleaner John Deere New Holland Total </> (U 0 c 1 <u o o u » ' £ Case-Inteniational 52 27.8% 3 1.6% 6 3.2% 3 1.6% 64 34.2% Gleaner 3 1.6% 19 10.2% 0 1 0.5% 23 12.3% John Deere 14 7.5% 2 1.1% 59 31.6% 5 2.7% 80 42.8% New Holland 3 1.6% 1 0.5% 3 1.6% 13 7.0% 20 10.7% Total 72 38.5% 25 13.4% 68 36.4% 22 U.8% 187 100% Percentage Agreement = 76.5% kappa statistic = 0.66 95% CI on kappa statistic = (0.581, 0.731) Brand Prices: Case-International » Average; Gleaner » 5% Below Average; John Deere » 10% Above Average; New Holland » Average. Note: 12 respondents (6.4%) owned combines of 2 different brands. Agreement occurs when the model predicts one of these brands. Table 4.17: T w o - W a y Tab le C o m p a r i n g C o m b i n e Inventory w i t h F i r s t C h o i c e Preferences U s i n g Respondents W h o O w n O n e of the F o u r Survey B r a n d s Manufacturer Model Predictions First Choice Preferences Sample Inventory* (pet) (pet) (pet) Case-International 33.7 38.0 38.0 Gleaner 12.8 16.9 12.7 John Deere 42.8 36.4 37.1 New Holland 10.7 8.6 12.2 *Note: Inventory shares reflect ownership of multiple combines. T a b l e 4.18: A g g r e g a t e L e v e l M o d e l P r e d i c t i o n s Versus F i r s t Cho ice Preferences a n d S a m p l e Inventory U s i n g Respondents W h o O w n One of the F o u r Survey B r a n d s B y des ign, the m o d e l also p r e d i c t e d a l ow pr i ced b r a n d for a l l respondents. T h e mode l p red i c t ed 6 6 % of the respondents ' first choices (Tab le 4.19). T h e k a p p a s tat i s t i c of 0.50 i n d i c a t e d a m o d e r a t e leve l of agreement between first choices and m o d e l predict ions . A s t a n d a r d d e v i a t i o n of .044 y i e l d e d a 9 5 % confidence in te rva l o n k a p p a of (.414, 584). A s was the case i n the b r a n d "a t a st icker pr i ce " analys is , the m o d e l predicts choice at a reasonable level . I n a d d i t i o n , the aggregate level pred ic ted shares were w i t h i n 6% of the s tated first choice shares. T h e average d e v i a t i o n was 4 .2%. T h e lower k a p p a s tat i s t i c can be a t t r i b u t e d to a more d i f f i cul t r a t i n g task a n d a different d i s t r i b u t i o n of prices between the brands . P r i c e Responsiveness of the C u s t o m e r D e c i s i o n M o d e l A n interest ing aspect o f the b r a n d - p r i c e rankings is that i t is possible to see how re-sponsive the m o d e l was to pr i ce changes. A m o n g the 8 b rand -pr i ce pairs , each of the 4 First Choice Preferences Case-International Gleaner John Deere New Holland Total Case-Intemational 44 16.5% 9 3.4% 10 3.8% 6 2.3% 69 25.9% c Gleaner 2 0.75% 25 9.4% 4 1.5% 2 0.75% 33 12.4% i John Deere 26 9.8% 5 1.9% 92 34.6% 6 2.3% 129 48.5% •§ New Holland 8 3.0% 7 2.6% 6 2.3% 14 5.3% 35 13.2% Total 80 30.1% 46 17.3% 112 42.1% 28 10.5% 266 100% Percentage Agreement = 65.S kappa statistic = 0.50 95% CI on kappa statistic = (0.414, 0.584) Brand Prices: Case-International » 5% Below Average; Gleaner » 1-5% Below Average; John Deere » 5% Below Average; New Holland » 15% Below Average. Note: O f the 8 brand-price pairs, one of the 4 low-priced pairs was always selected by respondents and predicted by the model. Tab le 4.19: T w o - W a y T a b l e C o m p a r i n g F i r s t C h o i c e Preferences w i t h M o d e l Pred i c t i ons U s i n g the B r a n d - P r i c e P a i r s I n f o r m a t i o n brands was l i s ted at two different prices. A t o t a l of 16 b r a n d - p r i c e combinat ions of the 4 brands can be der ived f rom this l i s t . For each of the 16 c o m b i n a t i o n s , the percentage of agreement between first choice preferences a n d m o d e l pred ic t ions a n d the kappa s tat i s t i c were ca l cu la ted . These results are i l l u s t r a t e d i n F i g u r e 4.8. T h e m e a n level of agreement for 16 combinat i ons was 62 .7%. T h e average k a p p a s ta t i s t i c was 0.41. O v e r a l l , the mode l per formed wel l despite large var iat ions i n pr ice . T h e m o d e l was not as responsive to pr ice changes as were respondents when m a k i n g r a n k i n g decisions. T h i s can be i l l u s t r a t e d t h r o u g h an analys is of the two ma jor brands : C a s e - I n t e r n a t i o n a l and J o h n Deere. U s i n g the i n f o r m a t i o n f r o m the b r a n d "at a sticker pr i ce " rankings a n d the r a n k i n g of b r a n d - p r i c e pa irs , first choice preferences were com-pared to m o d e l predic t ions at different price levels. F i g u r e 4.9 iUustrates the results of these comparisons . W h e n J o h n Deere was pr i ced equa l to or above C a s e - I n t e r n a t i o n a l , a greater p r o p o r t i o n of respondents preferred C a s e - I n t e r n a t i o n a l t h a n predic ted by the m o d e l . W h e n J o h n Deere was pr i ced less t h a n Case - I n t e r n a t i o n a l , th is t r e n d was re-versed a n d a greater p r o p o r t i o n of respondents preferred J o h n Deere t h a n predicted by the m o d e l . U s i n g the C o c h r a n Q test (Seigel 1956), the net change i n J o h n Deere pref-erences between stated preferences a n d m o d e l pred ic t ions was f ound to be significant {xl = 192.87, p < 0.0001).^^ G i v e n the nature of the e m p i r i c a l s tudy , it is imposs ib le to determine whether the m o d e l was less pr i ce - responsive t h a n necessary or that the wide v a r i a t i o n i n preference levels was due to respondents over - emphas i z ing the pr ice ^^The kappa statistic deteriorated more than the percentage agreement because of the dominance of John Deere in many of the combinations. This increased the likelihood of "chance" agreements. In 4 of the 16 combinations, John Deere was priced at 20% below Case- International, its largest competitor. This is a 30% price change as compared to the brand "at a sticker price" ranking. ^•'The data used in CochraniQ was calculated as follows. At each price level, the model prediction of the number of respondents preferring John Deere was subtracted from the number of respondents who stated that they preferred John Deere. To eliminate negative values, a constant was added to each of the subtraction results. a) Case-International @ 5% Below John @ 5% Above Avg. Deere Avg. Lpii = Percent of Agreement K = Kappa Statistic b) Case-International ® 5% Below .John @ 5% Above Avg. Deere Avg. F i g u r e 4.8: L e v e l o f Agreement Between F i r s t C h o i c e Preferences a n d M o d e l P r e d i c t i o n s for A l t e r n a t i v e P r i c i n g s of C o m b i n e B r a n d s 0.9 T 0.8 •• 0.7 •• 0.6 •• Share of ^— Preference 0.5 • 0.4 •• 0.3 •• 0.2 •• 0.1 • 0.0 — -10 F i g u r e 4 . 9 : J o h n Deere's Share of Preference at V a r i o u s Pr i ces . Share of Preference Specif ic to the J o h n Deere Versus C a s e - I H C o m p a r i s o n . component of the combines. M o r e research is necessary to bet ter u n d e r s t a n d this issue. S u m m a r y of M o d e l P e r f o r m a n c e T h e d a t a co l lected i n the s t u d y al lowed for a n u m b e r of tests of m o d e l per formance . A t the i n d i v i d u a l leve l , the m o d e l h a d re la t ive ly h i g h levels of agreement w i t h the respon-dents ' s tated choices. These levels of agreement were s ign i f i cant ly h igher t h a n what would be expected by chance. A t the aggregate leve l , the m o d e l p r o v i d e d very good predic t ions even when the price differences between manufacturers var ied subs tant ia l l y . In a d d i t i o n John Deere -Model Predictions John Deere - Stated Preferences 0 10 Price of Case-IH - Price of John Deere (%) 20 the m o d e l pred ic t ions c ompared favorab ly w i t h the w i t h i n sample share of inventory . It is evident that the proposed customer decis ion mode l does capture the essence of u n d e r l y i n g percept ions and preferences i n the western C a n a d a combine harvester m a r k e t . 4 .5 C o n t r i b u t i o n s a n d C o n c l u s i o n s T h i s chapter develops a n d tests an i n d i v i d u a l level customer decision m o d e l . M e t h o d -o logical ly , the m o d e l extends the research on customer decis ion models i n a n u m b e r of ways. F i r s t , the analys is is c onducted at the i n d i v i d u a l level . A l t h o u g h the perceptua l space is shared by a l l respondents ( in a p a r t i c u l a r region) , the specific p e r c e p t u a l l o ca -t ions of the offerings and the preference func t i on are unique to the i n d i v i d u a l . T h i s level of analys is is a p p r o p r i a t e i n s i tuat ions where there is a large degree of heterogeneity i n b o t h percept ions a n d preferences. M a r k e t s character ized by product - serv i ce f irms fa l l in to th is category. T h e i n d i v i d u a l level modeUing approach also allows for the develop-ment of a customer decis ion m o d e l s i m u l a t o r s i m i l a r to choice s imulators avai lable on c o m m e r c i a l conjo int packages. G r e e n and S r i n i v a s a n (1990) suggest that the a v a i l a b i h t y of choice s imula to r s is one of the m a i n reasons for the p o p u l a r i t y of conjoint analysis i n i n d u s t r y . Second , the use of a c on f i rmatory analys is i n the development of the p e r c e p t u a l space represents a n advance i n p e r c e p t u a l m a p p i n g research. In most p e r c e p t u a l m a p p i n g s i tuat i ons , a s ignif icant amount of i n f o r m a t i o n is k n o w n about the market under con-s iderat ion pr ior to d a t a co l lec t ion . C o n f i r m a t o r y factor analysis takes advantage of this k n o w n i n f o r m a t i o n to develop a m o d e l w h i c h can be tested s tat i s t i ca l ly . In a d d i t i o n , the s t ruc ture allows for the e s t i m a t i o n of corre lated p e r c e p t u a l d imensions wh i l e e l i m i n a t -i n g the r o t a t i o n a l i n d e t e r m i n a c y of c o m m o n factor analys is a n d p r i n c i p a l components analys is . In the e m p i r i c a l s tudy , the use of conf i rmatory factor analys is s ta t i s t i ca l l y con-f i rmed hypothes ized factor p a t t e r n as wel l as the i m p o r t a n c e of the corre la t ion between per cep tua l d imens ions . T h i r d , the m o d e l uses conjo int measurement to est imate customers ' preference weight-ings for each of the p e r c e p t u a l d imensions and price. Despi te the fact that the use of conjoint measurement i n the development of customer dec is ion models was suggested over a decade ago by Shocker a n d S r i n i v a s a n (1979), it is bel ieved the customer dec is ion mode l presented here is the first to incorporate this f o rm of preference measurement . A vec-tor preference m o d e l , ra ther t h a n the t r a d i t i o n a l p a r t - w o r t h m o d e l , is used. T h e vector m o d e l s impli f ies the d a t a co l lec t ion procedure and increases the r e l i a b i l i t y of parameter est imates . F i n a l l y , the customer decis ion m o d e l improves on past procedures i n the way it i n -corporates pr ice . T h e price parameter is e s t imated i n the conjoint measurement task in w h i c h price and other p e r c e p t u a l d imens ions are factors. T h i s improves o n earl ier prefer-ence measurement approaches , l ike the b r a n d "at a st icker pr i ce " r a n k i n g or r a t i n g tasks, w h i c h tend to place more i m p o r t a n c e on the price factor re lat ive to o ther dimensions of the offering. In a d d i t i o n , because the price parameter is e s t imated over a range of pr ice levels, the customer decis ion m o d e l is s t i l l va l id as current prices are adjusted to incorporate price c o m p e t i t i o n between brands . T h e customer dec is ion m o d e l developed i n this research should be of interest to mar -ke t ing researchers a n d prac t i t i oners . T h e mode l provides an i n t u i t i v e , easy to unders tand i n t e r p r e t a t i o n of the preference decisions made by customers i n the market . A l t h o u g h , d a t a analysis procedures are "s tate of the a r t " , the m o d e l bui lds on wel l k n o w n research tools hke p e r c e p t u a l m a p p i n g a n d conjoint analys is . F u r t h e r m o r e , the p o t e n t i a l for the development of a choice s i m u l a t o r is appea l ing . A p p h c a t i o n of the m o d e l s h o u l d not pose any s u b s t a n t i a l d i f f i cult ies . T h e m e t h o d o l o g y uses s t a n d a r d d a t a co l lec t ion techniques. In a d d i t i o n , g iven that p o p u l a r s tat i s t i cs packages are m a k i n g con f i rmatory factor anal -ysis packages avai lable (e.g. S P S S w i t h L I S R E L , S Y S T A T w i t h E Z P A T H ) , the da ta analysis procedures are r e la t i ve l y s t r a i g h t f o r w a r d . C u s t o m e r dec is ion models e s t imate b r a n d preferences as a funct i on of b rands ' per-cep tua l pos i t ions a n d prices . A s was i l l u s t r a t e d by the e m p i r i c a l study, the customer decis ion m o d e l developed i n this research does a good j o b i n p r e d i c t i n g the respondents ' first choice preferences i n the western C a n a d a combine harvester m a r k e t . A l t h o u g h this represents on ly one implementation,^** the model ' s general s t r u c t u r e shou ld al low for its a p p l i c a t i o n i n a wide range of sett ings . Chapter 5 includes a discussion of model limitations and future research. C h a p t e r 5 C o n c l u s i o n s a n d C o n t r i b u t i o n s , L i m i t a t i o n s a n d F u t u r e Research In this d i s ser ta t i on , three essays concerned w i t h p o s i t i o n i n g issues i n product - serv i ce f irms were developed. T h o u g h l i n k e d w i t h the c o m m o n theme, the essays differ i n terms of the specific issues that are addressed. A s such , no overr id ing conclusions or s u m m a r y is offered. Instead , the purpose of this chapter is to s u m m a r i z e each of the essays i n t u r n . For each essays, three aspects are discussed. F i r s t , the conclusions a n d contr ibut ions of the research are h i g h h g h t e d . T h i s is fol lowed by a d iscuss ion of l i m i t a t i o n s and of relevant future research. 5.1 P r i c e a n d P o s i t i o n i n g C o m p e t i t i o n in a T w o - D i m e n s i o n a l M a r k e t 5.1.1 C o n c l u s i o n s a n d C o n t r i b u t i o n s In chapter 2, three models were developed to s t u d y the c o m p e t i t i v e i m p h c a t i o n s of various product d i f ferent iat ion assumpt ions i n markets character ized by m u l t i p l e d imensions . T h e one -d imens iona l h o r i z o n t a l a n d ver t i ca l models were extended to two dimensions . In a d d i t i o n , a t w o - d i m e n s i o n a l m i x e d v e r t i c a l - h o r i z o n t a l m o d e l was developed. E a c h m o d e l was ana lyzed us ing a two-stage game theoret ic analys is i n w h i c h two firms compete first on product pos i t ions a n d t h e n on pr ice . C losed f o rm e q u i l i b r i u m solutions were ob ta ined for each stage i n w h i c h compet i t o rs are unres t r i c ted i n the i r choices of price or product posit ions i n the defined m a r k e t . T h e research y ie lded a n u m b e r of interest ing findings. Perhaps the most signif icant finding was t h a t , in e q u i l i b r i u m , there is a prevalence of MaxMin p r o d u c t di f ferent iat ion. T h a t is , the two firms tend to choose pos i t ions w h i c h w i l l represent m a x i m u m differ-e n t i a t i o n on one d imens ion and m i n i m u m di f ferent iat ion on the other d i m e n s i o n . T h i s so lu t i on impl i es that the m a x i m u m di f ferent iat ion so lut ions found i n one -d imens iona l models ( d ' A s p r e m o n t et a l 1979, Shaked a n d S u t t o n 1982) do not ex tend to two d i m e n -sions. M a x i m u m di f ferent iat ion on one of the two d imens ions appears to be sufficient to lessen the price c o m p e t i t i o n between firms. A l t h o u g h most e q u i l i b r i a e x h i b i t e d MaxMin p r o d u c t d i f ferent iat ion , i t was found that i n the t w o - d i m e n s i o n a l ve r t i ca l d i f ferent iat ion m o d e l , under cer ta in cond i t i ons , m a x i m u m produc t d i f ferent iat ion does occur . F u r t h e r -more , there are condi t ions i n w h i c h the firms dif ferentiate on b o t h d imens ions , but not fu l ly . T h i s la t ter finding appears to i l l u s t r a t e that there are h m i t s to the strategic effect (the desire to reduce pr i ce c ompet i t i on ) w h i c h leads to m a x i m u m di f ferent iat ion i n the one -d imens iona l case. F i n a l l y , the price e q u i h b r i a for the three models share a generahzed f o r m w i t h some parameter values depend ing o n the produc t d i f ferent iat ion assumpt ions used. T h i s finding, c ombined w i t h the MaxMin p r o d u c t d i f ferent iat ion result , i l lustrates that there are s imi lar i t i e s i n the market react ions to products based o n e i ther ver t i ca l or h o r i z o n t a l d i f ferent iat ion assumpt ions . T h e results of the e q u i l i b r i u m analysis prov ide several contr ibut i ons to the hterature on produc t a n d price c o m p e t i t i o n . F i r s t , the models ex tend the one -d imens iona l product d i f ferent iat ion models to two dimensions . Second , the models found p r o d u c t e q u i l i b r i a i n s i tuat ions where the compet i tors are a l lowed to choose a pos i t i on on b o t h character-is t i cs . E a r l i e r models w h i c h considered markets character ized by m u l t i p l e d imensions (e.g., C h o i , D e S a r b o a n d H a r k e r 1990, K u m a r a n d S u d h a r s h a n 1988, Hauser 1988) have e i ther ana lyzed the pr ice e q u i l i b r i u m alone or have s impl i f i ed the p r o d u c t e q u i l i b r i u m by cons ider ing on ly one d i m e n s i o n . For example , Hauser (1988) analyzes a two- d i m e n s i o n a l market i n w l i i c h products must l ie on a quarter c irc le inscr ibed i n the pos i t ive quadrant . T h i s res t r i c t i on imphes that the choice of posit ions can be represented by a single d i m e n -s ion : an angle between 0° and 90°. F i n a l l y , because three a l t e rnat ive models are analyzed ( two- d i m e n s i o n a l v e r t i c a l , two -d imens iona l h o r i z o n t a l a n d m i x e d ) , comparisons across d i f ferent iat ion assumpt ions are fa c i l i ta ted . 5 .1 .2 L i m i t a t i o n s T h e results of the economic models s h o u l d be v iewed i n hght of the mode l s ' h m i t a t i o n s . These l i m i t a t i o n s , most of whi ch concern the assumpt ions of the mode ls , are discussed be low: 1. A n i m p o r t a n t l i m i t a t i o n of the economic models is the a s s u m p t i o n of equa l m a r g i n a l costs regardless of pos i t i on . T h i s l i m i t a t i o n affects the v e r t i c a l character ist ics to a greater degree t h a n the h o r i z o n t a l character ist ics because a higher value on a v e r t i c a l character i s t i c impl ies a higher q u a l i t y level . It w o u l d be expected that h i g h q u a h t y products w o u l d cost more t h a n low cost products . T h e one -d imens iona l ve r t i ca l d i f ferent iat ion m o d e l developed by M o o r t h y (1988) incorporates a variable cost component . M o o r t h y ' s e q u i h b r i u m analysis shows that f irms choose products w h i c h are di f ferentiated ( though not m a x i m a l l y ) . In a d d i t i o n , the firms choose not to prov ide offerings w h i c h a p p e a l to the entire market (not a l l consumers purchase) . A n extens ion of his mode l to two d imensions w o u l d be of value. T h e constant cost a s s u m p t i o n is of less concern w h e n dea l ing w i t h h o r i z o n t a l character is t i cs because these character ist i cs emphasize var ie ty rather t h a n q u a l i t y differences. There is no reason to expect varieties to differ s y s t e m a t i c a l l y i n terms of cost. 2. T h e results i n the economic models are also affected by the choice of e q u i l i b r i u m so lu t i on concept . T h e economic models searched for perfect N a s h e q u i l i b r i u m so-lut ions . A l t h o u g h this is the most c o m m o n s o l u t i o n concept used i n models of this type , i t is i m p o r t a n t to note the i m p h c a t i o n s of this choice. It appears that the f indings of the models are affected by the N a s h pr ice game i n the second stage. A N a s h e q u i l i b r i u m assumes non-cooperat ive behavior o n the part of the f i rms. T h e s t rong price c o m p e t i t i o n w h i c h results gives the firms a s trong m o t i v a t i o n to dif-ferentiate. T h i s can be contrasted w i t h a C o u r n o t e q u i l i b r i u m (where firms choose quant i t ies rather t h a n prices) w h i c h tends to lessen the price c o m p e t i t i o n aspect. T h e C o u r n o t e q u i l i b r i u m m a y result i n less p r o d u c t d i f ferent iat ion . 3. T h o u g h not necessari ly h m i t a t i o n s , there are several assumpt ions w h i c h affect the e q u i l i b r i u m so lut ions . F i r s t , the choice of o r t h o g a n o l produc t d imensions and the consumer u t i l i t y funct ions does not consider interact ions between the two product d imensions . T h e development of e q u i l i b r i u m solut ions w o u l d be very di f f icult , i f not imposs ib le , i f in terac t ions were i n c l u d e d . Second, the a s s u m p t i o n of a u n i f o r m d i s t r i b u t i o n of taste parameters m a y be l i m i t i n g . T h e indifference l ine analysis procedure used i n chapter 2 can read i ly a c c o m m o d a t e n o n - u n i f o r m d i s t r ibut i ons on the taste parameters . However , n u m e r i c a l procedures w o u l d be required to search for the e q u i l i b r i u m solut ions. T h i r d , the issue of whether firms produce products w h i c h serve the entire market cannot be addressed as i t was assumed that a l l consumers must buy. R e l a x i n g this a s s u m p t i o n i n future research m a y be useful . F i n a l l y , there is a h m i t a t i o n concerning the generahzab ihty of the m o d e l results . T h e models ana lyze a res t r i c ted sett ing i n w h i c h there are o n l y two compet i tors i n a market where the p roduc t s are descr ibed on two d imensions . A l t h o u g h analysis of these models represent an extens ion to the current h t e r a t u r e , few " rea l w o r l d " s i tuat ions m a t c h the res tr i c ted mode l se t t ing . 5.1.3 F u t u r e R e s e a r c h T h e economic models a n a l y z e d i n chapter 2 represent a s t a r t i n g po int for the m a n y avenues of future research. These areas, w h i c h are not l i s t ed i n order of i m p o r t a n c e , are descr ibed below: 1. T h e economic models suggest that , i f a n e q u i l i b r i u m exists , it is l ike ly to exhib i t MaxMin p roduc t d i f ferent iat ion . A n interest ing research project w o u l d be to test whether this p h e n o m e n o n occurs i n a " r e a l w o r l d " set t ing . A n e m p i r i c a l analysis of a par t i cu lar m a r k e t w o u l d represent a s igni f icant c o n t r i b u t i o n . T h e r e have been few e m p i r i c a l tests of the i m p l i c a t i o n s of e conomic models . T h i s is p r o b a b l y due to the fact that f ind ing s i tuat ions w h i c h m a t c h m o d e l cond i t i ons is extremely dif f icult . A possible approach to d e t e r m i n i n g whether a p a r t i c u l a r market tends towards a MaxMin p roduc t e q u i l i b r i u m would be a h i s t o r i c a l analys is of p roduc t characteris-tics a n d prices. However , f ind ing an a p p r o p r i a t e market a n d d e t e r m i n i n g the range of possible produc t character ist ics c o u l d represent di f f icult prob lems . 2. A s discussed i n the l i m i t a t i o n s sect ion, the constant m a r g i n a l cost assumpt ion is restr ict ive , espec ia l ly for ver t i ca l p roduc t d imens ions . T h e development of a mode l which considered costs of a l ternat ive locat ions w o u l d be a c o n t r i b u t i o n . In this regard, an extens ion of M o o r t h y ' s (1988) m o d e l to two d imens ions appears to be the most p r o m i s i n g approach . In M o o r t h y ' s m o d e l , the var iab le cost of a par t i cu lar l ocat ion on a v e r t i c a l d imens ion , s, is def ined as us^. T h i s imphes that costs increase (at an increas ing rate) as q u a l i t y ( the value of 5) increases. It would be interest ing to de te rmine i f the e q u i l i b r i u m outcomes of a two -d imens iona l ver t i ca l m o d e l i n c o r p o r a t i n g costs i n this fashion paral le ls the results of M o o r t h y ' s (1988) one -d imens iona l m o d e l . M o o r t h y ' s e q u i l i b r i u m analys is shows that firms choose produc ts w h i c h are d i f ferent iated , but not m a x i m a l l y . 3. A s was o u t l i n e d i n the h te ra ture review, the h o r i z o n t a l mode l is very sensitive to the choice of the d i s tance f u n c t i o n ( E c o n o m i d e s 1986a). T h e two -d imens iona l h o r i z o n t a l d i f f erent iat ion m o d e l descr ibed here uses a q u a d r a t i c distance funct i on a n d is a d irect ex tens ion of the one -d imens iona l m o d e l a n a l y z e d by d ' A s p r e m o n t et a l (1979). T h e q u a d r a t i c d is tance f u n c t i o n was chosen to conform w i t h ideal po int models w h i c h are c o m m o n i n the m a r k e t i n g l i t e r a t u r e (e. g. G a v i s h , H o r s k y and S r i k a n t h 1983; C h o i , D e S a r b o a n d H a r k e r 1990, G r e e n a n d Sr in ivasan 1978). A n interes t ing extens ion to the two- d i m e n s i o n a l h o r i z o n t a l m o d e l w o u l d be the analysis of a m o d e l w h i c h uses a hnear d is tance f u n c t i o n . A l inear funct i on would be a direct ex tens ion to H o t e l h n g ' s (1929) o r i g i n a l m o d e l a n d be comparab le to the two-d i m e n s i o n a l v e r t i c a l m o d e l . E c o n o m i d e s (1986b) analyzes the pr ice e q u i l i b r i u m , but does not address the p r o d u c t e q u i l i b r i u m , i n a t w o - d i m e n s i o n a l " H o t e l l i n g " model . . 4. T h e m o d e l s t r u c t u r e used i n the analys is of the t w o - d i m e n s i o n a l models can be read i ly e x p a n d e d to ana lyze s i tuat ions i n w h i c h there are several compet i tors or several p r o d u c t d imens ions . T h e indif ference hne approach used i n the chapter 2 models extends easi ly to a c c o m m o d a t e e i ther a d d i t i o n a l compet i tors or p r o d u c t d i -mensions . However , the added complex i t i es w o u l d p r o b a b l y require that the price e q u i l i b r i u m be es tabhshed t h r o u g h n u m e r i c a l procedures . T h e e q u i h b r i u m i m p l i -cat ions of i n c l u d i n g several compet i to rs or several d imensions is u n k n o w n a p r i o r i . I m p o r t a n t research questions i n c l u d e : Does the MaxMin p roduct e q u i h b r i u m hold when there are three d imens ions a n d two compet i t o rs? n d imensions? Does the MaxMin p roduc t e q u i h b r i u m result h o l d w h e n there are three compet i tors and two dimensions? 5.2 Set t ing the Strategic D i r e c t i o n in a P r o d u c t - S e r v i c e F i r m 5.2.1 C o n c l u s i o n s a n d C o n t r i b u t i o n s T h e S D M m o d e l is designed to a id c ombined product - serv i ce f irms i n m a k i n g offering pos i t i on ing a n d p r i c i n g decisions. D r a w i n g on the o p t i m a l produc t pos i t i on ing h tera ture , the m o d e l uses an a n a l y t i c a l approach to the reso lut i on of the strategic quest ion of whether to invest i n p r o d u c t or service i m p r o v e m e n t s . T h e S D M m o d e l is fundamenta l l y different f rom o p t i m a l product pos i t i on ing models . T h e S D M mode l opt imizes a f irm's strategic d i rec t ion whereas o p t i m a l produc t pos i -t i on ing models search for an o p t i m a l new p r o d u c t l o cat i on . T h i s strategic focus adds a number of d imensions to the modehng p r o b l e m . F i r s t , the S D M analyzes the pos i t i on ing prob lem is ana lyzed f rom the perspective of the customer and the company. W i t h i n the company, managers at b o t h the i m p l e m e n t a t i o n a n d senior management levels combine to assess the appropr iate strategic d irect ion for the f i r m . Second, the S D M m o d e l views services as a c r i t i ca l component i n the company ' s offering. A s technological product differences are reduced, f irms must look to services to ob ta in compet i t ive advantage. F inaUy, the S D M m o d e l allows for the cons iderat ion of compet ing i n m u l t i p l e markets . E a c h of these markets m a y differ i n terms of size, n u m b e r of competitors a n d the struc-ture of customer perceptions and preferences. In a d d i t i o n , the ab ih ty to m o d i f y services at the regional level adds flexibihty to the company ' s pos i t ion ing opt ions . O n e of the p r i m a r y cont r ibut i ons of the S D M m o d e l is the nature of its speci f icat ion of the l i n k between phys i ca l and perceptua l spaces. In the offering improvement phase, the m o d e l develops a n u m b e r of p r o m i s i n g offering improvements a n d subsequent ly esti -mates the i r l o c a t i o n i n p e r c e p t u a l space. T h i s approach is the reverse of o p t i m a l product p o s i t i o n i n g models w h i c h t y p i c a l l y search for an o p t i m a l product l o ca t i on i n perceptua l space a n d a t t e m p t to relate this to a phys i ca l p roduc t . A l t h o u g h the S D M m o d e l does not find the o p t i m a l per cep tua l l o c a t i o n , i t does address the m a j o r c r i t i c i sms of o p t i -m a l p r o d u c t p o s i t i o n i n g models i n c l u d i n g the ident i f i ca t i on of the character ist ics of the p h y s i c a l offering a n d an accurate es t imate of p r o d u c t i o n costs. T h e S D M m o d e l also contr ibutes to the research on g loba l m a r k e t i n g by p r o v i d i n g an a n a l y t i c a l , firm-specific approach to the development of a g lobal product - serv i ce strategy. T h e m o d e l takes the v iew that an offering, espec ia l ly its service component , need not be s t a n d a r d i z e d across regions. M o r e i m p o r t a n t l y , the mode l determines a company ' s s t ra tegy by cons ider ing the pos i t i on of the firm's offering re lat ive to c ompet i t i ve offerings as wel l as other reg ional market condi t ions . 5.2.2 L i m i t a t i o n s T h e S D M m o d e l represents a n i n i t i a l step i n the development of an a n a l y t i c a l procedure to a i d a product - serv i ce firm i n se t t ing an appropr ia te strategic d i re c t i on . In its current stage of deve lopment , there are a n u m b e r of l i m i t a t i o n s to the S D M mode l . These l i m i t a t i o n s are o u t h n e d below: 1. Because of cross-offering synergies w h i c h can be reahzed i n b o t h p r o d u c t i o n and the de l ivery of services, the strategic d i r e c t i o n dec is ion s h o u l d be a c ompany -wide decis ion. However , the S D M m o d e l developed i n chapter 3 assumes that there is o n l y one offering for the f i r m . Since most product -serv ice f irms market a range of offerings, the development of a m o d e l w h i c h considers m u l t i p l e offerings is necessary. 2. A signif icant h m i t a t i o n of the S D M mode l is the s tat i c nature of the analys is . T h e m o d e l determines the o p t i m a l s trategic d i rec t ion by c o m p a r i n g what the customer wants w i t h what the f i r m is capable of offering at a p a r t i c u l a r point i n t ime . T h e S D M m o d e l does not consider d y n a m i c issues hke changing customer preferences a n d the p o t e n t i a l for s ignif icant technolog ica l breakthroughs . W h e n a n a l y z i n g the improvement programs , the S D M m o d e l does not consider the t ime required to de-velop the improvements , the rate at w h i c h improvements are accepted by customers a n d the offering-based act ions or reactions of compet i tors . M o d e l improvements i n these areas w o u l d represent a signif icant c o n t r i b u t i o n . 3. T h e S D M m o d e l requires i n f o r m a t i o n f rom a wide var iety of sources. These inc lude customers as wel l as managers i n m a r k e t i n g , p r o d u c t i o n a n d research and devel-opment . If m u l t i p l e regions are considered, i n f o r m a t i o n f rom b o t h customers and managers i n each regions is r equ i red . C o - o r d i n a t i o n of these i n f o r m a t i o n sources represents a signif icant task w h i c h requires a s t rong c o m m i t m e n t f rom a l l levels of the o r g a n i z a t i o n . In a d d i t i o n , contro l l ing for agency effects (the tendency for managers to act i n the ir o w n best interest ) w o u l d be di f f icult . 5.2.3 F u t u r e R e s e a r c h T h e ob jec t ive the chapter 3 was to descr ibe the components of the S D M i n d e t a i l . A d -d i t i o n a l research is required i n a n u m b e r of areas before the m o d e l can be i m p l e m e n t e d i n an a c t u a l c o m p a n y se t t ing . These areas are o u t l i n e d below. 1. A n approach to the deve lopment of an i n d i v i d u a l - l e v e l customer decision mode l needs to be deve loped . T h i s research requirement was addressed i n the chapter 4. 2. T h e development of i m p r o v e m e n t programs requires a d d i t i o n a l e m p i r i c a l research. T h e improvement p r o g r a m s are c r i t i c a l to the success of the model . To be of value, the p r o d u c t a n d service i m p r o v e m e n t programs must be specific enough to ident i fy the most p r o m i s i n g a l t e rnat ives , but s imple enough to be of value i n a m o d e h n g procedure . I n a c o m p a n y w h i c h is not c u r r e n t l y invo lved i n a qua l i ty funct i on deployment s y s t e m , a procedure s imi lar to the one developed by N a r a s i m h a n a n d Sen (1990) appears to be the most p r o m i s i n g . 3. A n u m e r i c a l p rocedure for the development of a pr ice e q u i l i b r i u m has not been de-ve loped. T h e c r i t i c a l c o m p o n e n t of this research step is the development of accurate cost assessments for the c o m p e t i t i v e offerings. T h e customer mode l developed i n the chapter 4 can be used as synthet i c d a t a to i l l u s t r a t e how the price e q u i l i b r i u m analysis w o u l d operate . 4. F i n a l l y , a d d i t i o n a l research is necessary to e x t e n d the current mode l to the analysis of m u l t i p l e regions. C o n c e p t u a l l y , this extens ion i n s t ra ight forward as an a d d i t i o n a l level of analys is can be a c c o m m o d a t e d by a l l phases of the mode l . T h e development of improvement p r o g r a m s w o u l d p r o b a b l y present the most di f f iculty i n this ex ten -sion as m u l t i p l e m a r k e t s w o u l d c o m p o u n d the n u m b e r of projects which warrant cons iderat ion . O n c e the research o u t l i n e d above has been c o m p l e t e d , an obvious extension w o u l d be to app ly the S D M m o d e l i n a n a c t u a l s i t u a t i o n . T h e e m p i r i c a l a p p l i c a t i o n should inc lude b o t h improvement programs a n d the customer dec is ion mode l . In this regard, an extens ion of the combine harvester example to i n c o r p o r a t e improvements may be possible. In a d d i t i o n to c omple t ing the research necessary to i m p l e m e n t the S D M m o d e l , re-search is necessary to address the issues raised i n the l i m i t a t i o n s sect ion. T h e S D M m o d e l , at i ts current stage of deve lopment , is concerned w i t h d e t e r m i n i n g the o p t i m a l strategic d i rec t i on for a one offering firm. However , most product - serv i ce firms market a range of offerings. Because of the p o t e n t i a l for p roduc t -based or service-based synergies, the strategic d i rec t i on decision shou ld incorpora te this added complex i ty . Therefore , a more comprehensive mode l needs to be developed. F i n a l l y , research a imed at i n c o r p o r a t i n g t i m e d y n a m i c s in to the analysis is needed. T h e s tat i c analys is issue has always been a concern i n p o s i t i o n i n g research a n d reso lv ing the associated m o d e h n g problems has proven to be di f f i cult . I n the S D M m o d e l , i n i t i a l efforts to incorporate t ime d y n a m i c s into the analysis s h o u l d occur in the R O I analys is phase. Here , assumpt ions can be made regard ing the rate of improvement acceptance by customers a n d the length of t i m e u n t i l c ompet i tors react to these improvements . These modi f i cat ions w o u l d require a net present value analysis i n the assessment of the i m p a c t of p o t e n t i a l improvements . 5.3 A n I n d i v i d u a l L e v e l C u s t o m e r D e c i s i o n M o d e l 5.3.1 C o n c l u s i o n s a n d C o n t r i b u t i o n s C h a p t e r 4 develops and tests a n i n d i v i d u a l level customer dec is ion m o d e l . M e t h o d o l o g i -cal ly , the m o d e l extends the research on customer decis ion models i n a number of ways. F i r s t , t l i e analys is is conducted at the i n d i v i d u a l level . A l t h o u g h the perceptual space is shared by a l l respondents ( in a p a r t i c u l a r region), the specif ic perceptual locat ions of the offerings a n d the preference func t i on are unique to the i n d i v i d u a l . T h i s level of ana lys i s is a p p r o p r i a t e i n s i tuat ions where there is a large degree of heterogeneity i n b o t h percept ions a n d preferences. M a r k e t s character ized by product - serv i ce f irms fal l in to this category. T h e i n d i v i d u a l level m o d e l h n g approach also al lows for the development of a cus tomer dec is ion mode l s imula tor s i m i l a r to choice s imulators avai lable on c o m m e r c i a l conjoint packages. G r e e n a n d S r i n i v a s a n (1990) suggest that the a v a i l a b i l i t y of choice s imulators is one of the m a i n reasons for the p o p u l a r i t y of conjoint analysis i n industry . Second , the use of a con f i rmatory analys is i n the development of the perceptual space represents a n advance i n p e r c e p t u a l m a p p i n g research. In most perceptua l m a p p i n g s i tuat i ons , a s ignif icant amount of i n f o r m a t i o n is k n o w n about the market under con-s idera t i on pr i o r to d a t a co l lect ion . C o n f i r m a t o r y factor analys is takes advantage of this k n o w n i n f o r m a t i o n to develop a m o d e l w h i c h can be tested s ta t i s t i ca l ly . In a d d i t i o n , the s t r u c t u r e al lows for the e s t i m a t i o n of corre lated perceptua l d imensions whi le e l i m i n a t -i n g the r o t a t i o n a l i n d e t e r m i n a c y of c o m m o n factor analysis and p r i n c i p a l components analys is . I n the e m p i r i c a l study, the use of con f i rmatory factor analys is s t a t i s t i c a l l y con-firmed hypothes i zed factor p a t t e r n as wel l as the i m p o r t a n c e of the corre la t i on between p e r c e p t u a l d imens ions . T h i r d , the m o d e l uses conjoint measurement to es t imate customers ' preference weight-ings for each of the perceptual d imensions and price . Desp i te the fact that the use of conjoint measurement i n the development of customer dec is ion models was suggested over a decade ago by Shocker and S r i n i v a s a n (1979), customer dec is ion models have not i n c o r p o r a t e d this f o rm of preference measurement . A vector preference m o d e l , ra ther t h a n the t r a d i t i o n a l p a r t - w o r t h m o d e l , is used. T h e vector m o d e l simphfies the d a t a co l lect ion procedure a n d increases the r e l i a b i l i t y of parameter est imates . F i n a l l y , the customer decision m o d e l improves on past procedures i n the way it i n -corporates price . T h e pr ice parameter is e s t imated i n the conjoint measurement task i n w h i c h price a n d other p e r c e p t u a l d imensions are factors. T h i s improves on earher preference measurement approaches , l ike the b r a n d "at a st icker pr i ce " r a n k i n g or r a t i n g tasks , w h i c h i n a d v e r t e n t l y t end to place more re la t ive ly more emphasis on the price d i -mens ion as c o m p a r e d to o ther d imens ions of the offering. In a d d i t i o n , because the pr ice parameter is e s t i m a t e d over a range of pr ice levels, the customer dec is ion m o d e l is s t i l l v a l i d as current prices are ad justed to i n c o r p o r a t e price c o m p e t i t i o n between brands. T h e customer dec is ion m o d e l developed i n this research should be of interest to m a r -k e t i n g researchers a n d prac t i t i oners . B u i l d i n g o n wel l k n o w n research tools l ike percep-t u a l m a p p i n g a n d conjoint ana lys i s , the m o d e l provides an i n t u i t i v e , easy to unders tand i n t e r p r e t a t i o n of the preference decisions made by customers i n the m a r k e t . In a d d i t i o n , the p o t e n t i a l for the development of a choice s i m u l a t o r is appeahng . A p p l i c a t i o n of the m o d e l s h o u l d not pose any s u b s t a n t i a l di f f icult ies . T h e methodo logy uses s tandard d a t a co l lect ion techniques. In a d d i t i o n , g iven that p o p u l a r stat ist ics packages are m a k i n g con f i rmatory factor analys is packages avai lab le (e.g. S P S S w i t h L I S R E L , S Y S T A T w i t h E Z P A T H ) , the d a t a analys is procedures are re lat ive ly s t ra ight f o rward . 5.3.2 L i m i t a t i o n s T h e r e are a n u m b e r of h m i t a t i o n s w h i c h i m p a c t the i n d i v i d u a l level customer decision m o d e l a n d the e m p i r i c a l results o u t l i n e d i n chapter 4. These h m i t a t i o n s are discussed below: 1. T h e e m p i r i c a l a p p l i c a t i o n of the customer decision mode l y i e lded good predict ive results i n the combine harvester market . However , this represents on ly one h m i t e d a p p l i c a t i o n . To better determine the strengths and weaknesses of the mode l , several a d d i t i o n a l app l i ca t i ons need to be under taken . These app l i ca t i ons should s tudy a wide range of s i tuat ions and compare the i n d i v i d u a l level m o d e l performance w i t h more aggregate level models . 2. T h e use of respondents ' s tated preferences as a proxy for choice i n f o r m a t i o n is l i m i t i n g . It is unc lear whether these responses provide a n accurate representation of how customers would respond i n a choice s i t u a t i o n . Access to t ime ly choice i n f o r m a t i o n is preferred, but diff icult to o b t a i n i n m a n y s i tuat i ons . E v e n i f choice i n f o r m a t i o n were avai lable , the p r o b l e m of o b t a i n i n g an accurate representat ion of customer choice does not d isappear since there exists the p r o b l e m of respondents us ing post -hoc reasoning. 3. T h e r e are some specific aspects of the e m p i r i c a l s tudy w h i c h affected mode l perfor-mance . F i r s t , by h a v i n g respondents rate a l l four combine brands , it was assumed that a l l b r a n d were i n each respondents choice set. O f a l l types of f a rm equip-ment , the combine harvester is the most l ike ly to receive the most prepurchase cons iderat i on . However , since some farmers choose the same b r a n d for a l l of their f a r m equ ipment needs, the inc lus i on of choice sets i n the m o d e l w o u l d be of value. Second , the preference parameters measured t h r o u g h the conjo int analys is have a re la t ive ly l ow level of rehabihty . For each respondent , three parameters (and a constant ) were e s t imated f rom an eva luat i on of 12 profiles. In future studies , i f no in terac t i ons are assumed, f rac t i ona l fac tor ia l designs s h o u l d be used i n this phase of the ana lys i s . F i n a l l y , the use of re lat ive prices ins tead of a c t u a l prices may be l i m i t i n g . T l i o u g h b o t h farmers and combine dealers felt comfortable using the rel -at ive price scales, the effect that this choice had on the i m p o r t a n c e of the price parameter is u n k n o w n . 5 .3 .3 F u t u r e R e s e a r c h T h e development and a p p l i c a t i o n of the customer dec is ion m o d e l provides several oppor -tuni t i es for future research: 1. T h e a p p l i c a t i o n of the customer decis ion m o d e l i n o ther sett ings should be one of the m a i n pr ior i t ies of future research. These studies cou ld be used to determine the a p p l i c a b i l i t y of the m o d e l i n diverse s i tuat ions i n c l u d i n g non product -serv ice sett ings. Several ad justments to the specific cus tomer dec is ion m o d e l can be made. These ad justments are p r i m a r i l y i n response to l i m i t a t i o n 3 above. A more in -depth conjoint measurement procedure a n d a review of how prices are in corpora ted should be a pr ior i ty . F u t u r e research m a y also want to consider choice sets issues. 2. O n e of the key aspects of the customer decis ion m o d e l is the use of perceptual factors i n the conjoint measurement phase. T h i s al lows for the p a r a m e t e r i z a t i o n of a preference m o d e l based o n percept ions . In th is procedure , i t is i m p o r t a n t that the labels used i n the conjoint measurement task i m p l y the relevant a t t r ibutes i n the minds of the respondent . T h e current a p p l i c a t i o n used a secondary survey to check the a t t r i b u t e - factor associat ions. However , more research is necessary to determine better ways of ensur ing that the a p p r o p r i a t e factors are used i n the preference measurement procedure. 3. T h e customer decis ion mode l o u t h n e d i n chapter 4 considers b o t h heterogeneous preferences a n d percept ions i n developing a m o d e l of choice. T h e i n d i v i d u a l nature of the d a t a allows for the development of a s i m u l a t o r s i m i l a r to the choice s imulators which are avai lable w i t h c o m m e r c i a l conjoint p rograms . T h e d a t a avai lable t h r o u g h the customer decis ion mode l is p o t e n t i a l l y r icher t h a n the d a t a der ived f rom a conjoint s tudy as the i n d i v i d u a l ' s percept ions of e x i s t i n g offerings is also i n c l u d e d . G i v e n the p o p u l a r i t y of these s i m u l a t o r s , development of a sys tem wou ld be of benefit to prac t i t i oners . In C o n c l u s i o n T h i s d i sser tat ion has concentrated on p o s i t i o n i n g i n produc t - serv i ce f i rms. To date , re-search i n this area has been h m i t e d . However , as f irms search for new ways of c reat ing a n d m a i n t a i n i n g c o m p e t i t i v e advantage , issues re la t ing to produc t - serv i ce f irms w i l l increase i n i m p o r t a n c e . It is bel ieved that the research developed i n this d i sser ta t i on contr ibutes to our u n d e r s t a n d i n g of some of these issues. B i b l i o g r a p h y [1] A g a r w a l , M . a n d B . T . R a t c h f o r d (1980), " E s t i m a t i n g D e m a n d Funct i ons for P r o d -uct C h a r a c t e r i s t i c s , " Journal of Consumer Research, 7 (December ) , 249- 262. 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In a W o r l d of N a t i o n s ? , " Sloan Management Review, ( F a l l ) , 29-41. 129] Z e i t h a m l , V . A . , L . L . B e r r y a n d A . P a r a s u r a m a n (1988), " C o m m u n i c a t i o n and C o n t r o l Processes i n the D e l i v e r y of Service Q u a h t y , " Journal of Marketing, 52 ( A p r i l ) , 35-48. [130] Z u f r y d e n , F . S. (1982), " Z I P M A P — A Z e r o - O n e Integer P r o g r a m m i n g M o d e l for M a r k e t Segmenta t i on a n d P r o d u c t P o s i t i o n i n g , " Journal of the Operational Research Society, 30 ( J a n u a r y ) , 63-76. A p p e n d i x A P r i c e E q u i l i b r i u m A n a l y s i s T h i s a p p e n d i x provides the m a t h e m a t i c a l details of the price e q u i l i b r i a discussed in the text (sect ion 2.4). F i r s t , the a s y m m e t r i c character ist ics case w i l l be ana lyzed w i t h charac ter i s t i c x dominance be ing presented before character is t i c y dominance . Second, the d o m i n a t e d character ist ics case w i l l be presented. In some instances , second order cond i t i ons are ca l cu la ted to show that they are satisf ied. In a l l other instances , they are a n a l y z e d by inspec t i on . A . l A s y m m e t r i c C h a r a c t e r i s t i c s Case 1: C h a r a c t e r i s t i c x D o m i n a n c e C h a r a c t e r i s t i c x d o m i n a n c e imphes that k{ai — a,) > (62 — In terms of the angle of c o m p e t i t i o n this impl ies that a > 45°. T h i s s i t u a t i o n is dep i c ted i n the fo l lowing g r a p h . 1 G W i t h i n c l iaracter is t i c x d o m i n a n c e , there are three regions i n w h i c h a price e q u i l i b r i u m may occur R]., Rl a n d Rl. T h e d e m a n d for f i r m 1 i n these regions is developed in section 2.4.1 of the text and are defined by equat ions (2.13), (2.15) a n d (2.17) respect ively . These equations are l i s ted below: 1 _ 1 / P2- Pi+ j + rnka " 2 cot a Dl = - cot a + mka — mb J (1 - c o t a ) = 1 - - cot a + - ^P2 -Pi+ j mb •\ 2 cot a ( A . l ) T h e d e m a n d for firm 2 i n these regions is s i m p l y 1 — D e m a n d i . Since m a r g i n a l costs are assumed to be zero regardless of p o s i t i o n , the profit funct ion for firm i {i = 1,2) is def ined as U.i{pi,pj) = piDi{pi,pj) for i ^ j. A noncooperat ive price e q u i l i b r i u m is a p a i r of prices {pî,Pj) such t h a t : MPhPj) > n i ( p i , p - ) , V P i > 0; i,j = 1,2 ; a n d , i 7^  j T h e pr ice e q u i h b r i u m analys is w i l l beg in w i t h Rl. A . 1 . 1 P r i c e E q u i l i b r i u m in R C o n s i d e r firm 1: / I / P2 — Pl + i\ = P l - cot a + 1 + ^\ l \2 \ mka - mb/ (1 - c o t a ) T h e first order c o n d i t i o n of this profit f u n c t i o n is : ^ I I i 1 ,^ , , -s / 1 - c o t a — - = - cot a + (1 - cot a ) + (p2 - P l + j ) — -C p i z \mka — m o / I — cot a \mka — mb Iso lat ing p i y ie lds : 1 / 1 - cot a \mka — mb ^ cota + ^{mka - mb + p2 + j) (A .2 ) N o w consider firm 2 a n d conduct a s i m i l a r ana lys i s . n2 = P 2 ( l - Z > ? ) 1 ^ " ^ ^ mka — m 6 (1 - c o t a ) ^ dUj 1 dp2 — ''' cot a ( + ') f ^ ~ ) / 1 — cot a \ 2 \mka — mb) \mka — mb) = 0 1 / 1 - cot a P2 = 4 \mka : t a \ 1, — j c o t a + - ( p i - j ) (A .3 ) S o l v i n g for p i a n d p, i n (A .2 ) and (A .3 ) y ie lds (note that cot a = ^ ) 3 f mka-mb^ 2 PI = -y 1—cota y cot a + 2{mka — mb) + j 3 imka — mb + 2j 6 (A .4 ) P2 = l ( ^ T ^ ) cota + mka-mb-j 3 2mka + mb — 2j 6 (A .5 ) These e q u i h b r i u m prices are shown i n equat ions (2.18) and (2.19) i n section 2.4.1 of the t ex t . In the t ex t , these equat ions are fo l lowed by a discussion of the condit ions w h i c h are necessary for th is e q u i l i b r i u m to be v a l i d . W h e n the e q u i l i b r i u m is v a h d , the profits for the firms are o b t a i n e d by m u l t i p l y i n g the e q u i l i b r i u m prices by the d e m a n d equations . S u b s t i t u t i n g the e q u i l i b r i u m prices a n d cot ot — in to the d e m a n d equations Df and Dl y ie lds : ^ 2 4mfca — mb + 2j ^ 6mka Dl = l - D l 2mka + mb — 2j 6mka Pro f i t s for the firms w h e n this e q u i l i b r i u m holds are: HI = plD\ (imka — mb + 2j)^ 36mka ^^'^^ {2mka - mb - 2jf Z^mka A . 1 . 2 P r i c e E q u i l i b r i u m i n Rl C o n s i d e r f i r m 1. D e m a n d is g iven by (2.13) i n the text (sect ion 2.4.1) a n d ( A . l ) above. P r o f i t s i n this region for f i r m 1 are: = P i \ 2 v P2 - Pi - j + mka\ mb cot a I I T h e first order c o n d i t i o n for profit m a x i m i z a t i o n is : dp f = {P2-Pi+J + mkaY / | c o t a ^ + Pi / | c o t a \ {2pi - 2p2 - 2j - 2mka) = 0 E x p a n d i n g this equat ion y ie lds , 3p? - Pi(4p2 + 4 ; + imka) + pi + f + (mka)^ +P2J + 2p2mka + 2jmka = 0 ( A . 8 ) ( A . 8 ) is a q u a d r a t i c equat i on of t l ie f orm fp^ + gpi + / i = 0. T h i s can be solved us ing t l ie q u a d r a t i c f o rmula : -g ± s/g' -\fh p i = Yf T h e two roots to (A .8 ) are: Pl = ^ (A .10 ) In ( A . 9 ) , P l = p" , the price at w h i c h d e m a n d for f i r m 1 is equa l to zero (see sect ion 2.4.1 of t ex t ) . ( A . 10) max imizes profit a n d is used i n the analys is below. N o w consider firm 2. T h e profit f u n c t i o n a n d associated first order c o n d i t i o n are: = P2 1 -/ i - cot a \2 ^ P2 — Pl + j + mka^ mb ' f dpi 'l~{^-coio> iv2-Pi^i^rnka mb • 2\ I +P2 / - ^ c o t a \ , ^ ' (2p2 - 2p i + 2j + 2mka) = 0 {mby M u l t i p l y i n g by and e x p a n d i n g y ie lds : 3p2 + P2 (4 i + 4mka - ipi) + j + {mkaf + p\ + 2jmka ^ . , , 2{mhf ^ —2pij — 2p\mka = 0 cot a S u b b i n g the equal i ty for pi f rom ( A . 10) into the above equat ion yields (recal l that c o t a = ^ ) : 9 + P2(5 j + bmka) + [j + mkaf - -m^kab = 0 T h i s equat ion is quadra t i c i n p2 a n d can be solved us ing the q u a d r a t i c f o rmula . T h e larger of the two roots m a x i m i z e s 112 ^ 0). S o l v i n g for th is root a n d s u b s t i t u t i n g th is value of p2 into (A .10 ) yie lds the fo l lowing price e q u i l i b r i u m : j -)- mka + JiJ + mkaf + Sm^kab Pl = ^ (A .11 ) -5j - 5mka + ZJij + mkaV + Sm^kab Pl = (A .12 ) These e q u i h b r i u m prices are shown i n equations (2.23) and (2.24) i n sect ion 2.4.1 of the text . In the text , these equat ions are fol lowed by a d iscuss ion of the condi t ions w h i c h are necessary for this e q u i h b r i u m to be v a h d . W h e n the e q u i h b r i u m is v a h d , the profits for the firms are ob ta ined by m u l t i p l y i n g the e q u i h b r i u m prices by the d e m a n d equations . S u b s t i t u t i n g the e q u i l i b r i u m prices and cot « = ^ into the d e m a n d equat ions and Dl y ie lds : (^j + mka + + mkaY + Sm^fcaft) 22m-^kab {Z2m^kab) - {j + mka + + mfca)^ + Sm^kab mn^kab T h e profit for f i rm 1 is : = piDl (^j + mka + ^(j -f- mkaY + Sm^kab^ 256m^kab (A .13 ) T h e profit for f i r m 2, as can be seen f r o m the equat i on for D], is a complex equat ion . A s is shown i n the produc t e q u i h b r i u m sections of the text (sect ion 2.5.3, A p p e n d i x B ) , i t is not requ ired for the d e t e r m i n a t i o n of the produc t e q u i l i b r i u m . A . 1 . 3 P r i c e E q u i l i b r i u m in Rl T h e price e q u i h b r i u m i n Rl is a complex q u a d r a t i c f u n c t i o n of pr ice . T h e exact so lu t i on has not been ca l cu la ted as it is not required for the p r o d u c t e q u i h b r i u m (see sections 2.5.1, 2.6.1, 2.7.1 of the text ) . A . 2 C a s e 2 : C h a r a c t e r i s t i c s y D o m i n a n c e W h e n character i s t i c y d o m i n a n c e holds , a < 45°. T h i s impl ies that k{ai - a,) < (62 -^i)-T h e same price equations ho ld (equations 2.8-2.11 i n the text ) but now p" > p" > pT' > Pi since as firm 1 decreases its pr ice f rom p" (given P2), the indifference l ine passes t h r o u g h the o r i g i n before i t passes t h r o u g h po int (1, 1). T h i s s i t u a t i o n is depicted i n the fo l lowing g r a p h . Indifference Line Demand 2 Demand 1 a U s i n g the same procedure as o u t l i n e d under character is t i c x dominance , d e m a n d i n each of the regions can be defined as a f u n c t i o n of prices and a . T h e r e are three regions i n w h i c h a pr ice e q u i l i b r i u m m a y occur , R^, R^ a n d R^. T h e d e m a n d for firm 1 i n these regions is developed i n sect ion 2.4.2 of the text a n d defined by equations (2.26), (2.27) and (2.28) respectively. These equat ions are l i s ted below: 1 ^ P2 - P i + J I , 1 H ; t a n a mka I (A .14) I>i = - t a n a + 'h - P i + m 6 — mÂ;a (1 - t a n a ) i ) 3 ^ 1 _ t a n a + - P2 — P i + i + 771^  + Tnka mka t a n a A . 2 . 1 P r i c e E q u i l i b r i u m in R} C o n s i d e r f i r m 1. Pro f i t s for th is f i r m i n are: = p , ( i t a n a + ( ^ i - ^ ) ( l - t a n a ) ) \2 \mb — mka/ J T h e der ivat ive of this profit func t i on w i t h respect to p i is : ^ I I i 1 , 1 — t a n a 1 — t a n a = - t a n a + (p2 - p i + j ) — ^ - 7 — - p i — — = 0 I so la t ing for p i y ie lds : mh — mka mb — mka P i = ( mb — mka\ 1 1 — I t a n a + - ( p 2 + i ) — t a n a I I (A .15 ) N o w consider f i r m 2 a n d per form a s i m i l a r analys is . n 2 = P2{l-Dl) = P2 M t a n a — —; ;— ^ V 2 \mh~mka) (1 - t a n a) 9112 1 . 1 — t a n a l - t a n a = - t a n a + 1 - t a n a - [p, - P i + j)—r • (p2 - c,)—: — = 0 dp2 2 mb — mka mb — mka P2 = mb - mka 1 — t a n a ) t a n a + - ( p i + mb — mka — j) (A .16 ) S o l v i n g for p i and p2 i n ( A . 15) and (A .16 ) yie lds the fo l l owing price e q u i l i b r i u m (note that t a n a = ^ ) : P l = l ( n f e ^ ) t^na + mb-mka + j 2mb + mka + 2j 6 (A .17 ) P2 = tan a+ 2{mb-mka)-j imb — mka + 2j (A .18 ) These e q u i h b r i u m prices are shown i n equat ions (2.29) a n d (2.30) i n sect ion 2.4.2 of the text . In the text , these equat ions are fol lowed by a d iscuss ion of the condi t ions w h i c h are necessary for this e q u i l i b r i u m to be v a l i d . W h e n the e q u i l i b r i u m is v a h d , the profits for the f irms are o b t a i n e d by m u l t i p l y i n g the e q u i l i b r i u m prices by the d e m a n d equations. S u b s t i t u t i n g the e q u i l i b r i u m prices and cot oc — ^ into the d e m a n d equations and vie lds : 2 2mb + mka + 2j " 6mb imb — mka — 2j 6mkb Prof i t s for the firms w h e n this e q u i l i b r i u m holds are: ( 2 m a + ma + 2jf 36mkb ^^'^^^ n: = PTDl ( 4 m a + mka - 2jY 36mb (A .20 ) A . 2 . 2 P r i c e E q u i l i b r i u m in U s i n g the fact that t a n a = a n d that c o t a = it can be shown that the chniiand for f i rm 1 in R^ (defined by (2.26) in the te.xt a n d (.^.14) above) is equal to the demand for f i rm 1 in R], (defined by (2.13) and ( A . l ) above) . There fore , the demands for firm 2 in b o t h of these regions are equal as wel l . S ince profits are defined as PiDl, T h e price e q u i l i b r i u m i n R^ is i d e n t i c a l to the price e q u i l i b r i u m in R],. T h i s e q u i l i b r i