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Testing for structure in a multi-product industry with price expectations : the Canadian cattle industry Gordon, Daniel Vernon 1984

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TESTING FOR STRUCTURE IN A MULTI-PRODUCT INDUSTRY WITH PRICE EXPECTATIONS: THE CANADIAN CATTLE INDUSTRY by DANIEL VERNON GORDON B.A. The University of Lethbridge, 1977 M.A. The University of Saskatchewan, 1980 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Economics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1984 ©DANIEL VERNON GORDON, 1984 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requ i rements fo r an advanced degree at the U n i v e r s i t y of B r i t i s h Co lumb ia , I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e fo r r e f e r e n c e and s tudy . I f u r t h e r agree that p e r m i s s i o n f o r e x t e n s i v e copy ing of t h i s t h e s i s fo r s c h o l a r l y purposes may be g ran ted by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s unders tood tha t copy ing or p u b l i c a t i o n of t h i s t h e s i s for f i n a n c i a l ga in s h a l l not be a l l owed wi thout my w r i t t e n p e r m i s s i o n . Department of Economics The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P lace Vancouver , Canada V6T 1W5 Da te : August 20, 1984 i i ABSTRACT The aim of t h i s r e s e a r c h i s to deve lop a t h e o r e t i c a l p r o f i t maximiz ing model of a cow-cal f farm and then to determine and to es t imate e m p i r i c a l l y the dynamic shor t run supp ly response and investment behav iour of c a t t l e p r o d u c e r s . The theory of d u a l i t y i s used here to p rov i de a c o n s i s t e n t model of the cow-cal f i n d u s t r y . The model i s c o n s i s t e n t in that the e s t ima ted equa t ions are d e r i v e d from the p r o f i t maximiz ing farm mode l . A comparat ive s t a t i c a n a l y s i s i s c a r r i e d out to determine shor t run supp ly response of cow-cal f f a rmers . (Past s t u d i e s have argued the e x i s t e n c e of nega t i ve shor t run supp ly e l a s t i c i t i e s . ) In t h i s mode l , the s i gn of the shor t run e l a s t i c i t y of c a t t l e supp ly depends on th ree f a c t o r s : i ) the t e c h n o l o g i c a l s t r u c t u r e of the i n d u s t r y ; i i ) the s u b s t i t u t i o n p o s s i b i l i t i e s between p r o d u c t i o n today and p r o d u c t i o n tomorrow; and i i i ) f a rmers ' e x p e c t a t i o n s of c a t t l e p r i c e s . Consequen t l y , a sho r t run nega t i ve supp ly e l a s t i c i t y in the . cow-ca l f i n d u s t r y i s not a p r e d i c t i o n from economic t h e o r y . Rather the s i g n of the e l a s t i c i t y i s unknown and w i l l depend on p r i c e e x p e c t a t i o n s of p r o d u c e r s . The es t imated c o e f f i c i e n t s of the p r o f i t f u n c t i o n are used to t e s t f o r c e r t a i n c h a r a c t e r i s t i c s of the u n d e r l y i n g t r a n s f o r m a t i o n f u n c t i o n . I t i s de termined tha t the t e c h n o l o g i c a l s t r u c t u r e of cow-cal f p r o d u c t i o n in western Canada i s d e f i n e d by a non-homothet ic , non-homogeneous t r a n s f o r m a t i o n f u n c t i o n sub jec t to d e c r e a s i n g r e t u r n s to s c a l e and j o i n t p r o d u c t i o n between c rops and c a t t l e . Other c h a r a c t e r i s t i c s of the cow-ca l f i n d u s t r y are determined by c a l c u l a t i n g e l a s t i c i t i e s of c h o i c e . These e l a s t i c i t i e s conform to a l l a p r i o r i e x p e c t a t i o n s w i th output supp ly f u n c t i o n s hav ing non-negat ive s l o p e s , d e r i v e d input demand f u n c t i o n s hav ing non-pos t i ve s l o p e s , and a s u b s t i t u t e r e l a t i o n s h i p p r e d i c t e d between c a t t l e supp ly and end-o f-pe r i od i nven to r y demand. The t o t a l e l a s t i c i t y of c a t t l e supp ly i s a l s o c a l c u l a t e d . T h i s e l a s t i c i t y measure takes account not on l y of the e f f e c t of c a t t l e p r i c e f l u c t u a t i o n s , but a l s o the e f f e c t of changing e x p e c t a t i o n s of c a t t l e p r i c e s on c a t t l e s u p p l y . I t i s determined that a c coun t i ng fo r ad justments in e x p e c t a t i o n s of c a t t l e p r i c e s caused by changes in c u r r e n t c a t t l e p r i c e s w i l l a lways decrease the e l a s t i c i t y of c a t t l e s u p p l y . However, the re i s no ev idence to i n d i c a t e tha t t h i s tendency i s s i g n i f i c a n t l y s t rong enough to decrease shor t run e l a s t i c i t i e s of c a t t l e supply to ze ro or l e s s . TABLE OF CONTENTS ABSTRACT . i i TABLE OF CONTENTS i v LIST OF TABLES v i LIST OF FIGURES . v i i i ACKNOWLEDGEMENTS ix Chapter 1. INTRODUCTION 1 1 .1 O b j e c t i v e s 7 1.2 E x i s t i n g L i t e r a t u r e 7 1.3 T h e s i s O u t l i n e 9 Footnotes 12 2. THE CANADIAN CATTLE INDUSTRY 2.1 I n t r o d u c t i o n 14 2.2 Some C h a r a c t e r i s t i c s of the C a t t l e Indus t ry — 14 2.3 A l t e r n a t i v e P roduc t i on S t r a t e g i e s A v a i l a b l e to Cow-Calf P roducers 30 2.4 E x i s t i n g T h e o r e t i c a l Models of the Cow-Calf Indus t ry 34 Footnotes 43 3. A THEORETICAL MODEL OF THE COW-CALF INDUSTRY 3.1 I n t r o d u c t i o n 44 3.2 A S i n g l e Output P r o f i t F u n c t i o n fo r a Cow-Calf Producer 45 3.3 S e p a r a b i l i t y as a Ma in t a ined Hypothes i s 57 3.4 Aggrega t i on Over Farms 59 3.5 A S i n g l e Output P r o f i t F u n c t i o n f o r a Rep re sen t a t i v e Cow-Calf Producer 65 3.6 Some Comparat ive S t a t i c s 68 3.7 A M u l t i - O u t p u t , Mu l t i - I npu t Model of a Rep resen t a t i v e Cow-Calf Producer 74 3.8 C h a r a c t e r i z i n g the S t r u c t u r e of P roduc t i on . . . . 79 3.9 T e s t i n g fo r S t r u c t u r e us ing a M u l t i - O u t p u t , Mu l t i - I npu t V a r i a b l e P r o f i t Func t i on 82 Footnotes . . 85 VARIABLE SPECIFICATION AND FUNCTIONAL FORMS 4.1 I n t r o d u c t i o n 87 4.2 P r i c e E x p e c t a t i o n s 91 4.3 Data 98 4.4 S t o c h a s t i c S p e c i f i c a t i o n and E s t i m a t i o n Techn iques 111 Footnotes 122 PARAMETER ESTIMATES AND SUMMARY STATISTICS 5.1 I n t r o d u c t i o n 125 5.2 E m p i r i c a l R e s u l t s us ing a T r a n s l o g V a r i a b l e P r o f i t Func t i on 125 5.3 E m p i r i c a l R e s u l t s u s i ng T ime-Ser i es Data 151 Foo tno tes 166 SUMMARY AND CONCLUSIONS 167 BIBLIOGRAPHY . 176 APPENDIX A. Farm Expend i tu re Survey Q u e s t i o n n a i r e , 1981 . . . 184 B. C r o s s - S e c t i o n a l Data by S o i l Zone 206 C. T ime-Se r i es Data 228 D. Reg ress ion R e s u l t s u s i ng Cobb-Douglas and T r a n s l o g F u n c t i o n a l Forms: Almon Lag P r i c e P r e d i c t i o n s * 232 E. E s t ima ted Parameters : ARIMA Models 246 F. P r i c e P r e d i c t i o n s : ARIMA Models 253 v i L IST OF TABLES 2.1 Canadian Farm Cash Rece ip t s from the Sa le of C a t t l e and Ca l ves 15 2.2 Canadian Expor t s and Imports of L i v e Animals and Dressed Beef and Vea l 17 2.3 Va lue of Canadian Expor t s and Imports of L i v e An imals and Meat P roducts 18 2.4 Canadian T a r i f f S t r u c t u r e fo r D i f f e r e n t C a t e g o r i e s of An imals and Meat P roducts 20 4.1 E s t ima ted C o e f f i c i e n t s ARIMA(2,1,0) Mode l , S t e e r s , C a l v e s , Cows and H e i f e r s , Ca lga r y 97 4.2 Summary of FES Data 101 4.3 D e f i n i t i o n of V a r i a b l e s (T rans log ) 107 4.4 D e f i n i t i o n of V a r i a b l e s (T ime-Ser ies Data) 109 4.5 T e s t i n g fo r S t r u c t u r e wi th L i n e a r R e s t r i c t i o n s on the Share Equa t ions 117 5.1 Reg ress ion C o e f f i c i e n t s - T r a n s l o g P r o f i t Func t i on 126 5.2 Goodness of F i t S t a t i s t i c s 129 5.3 T e s t i n g fo r S t r u c t u r e 130 5.4 Hess i an C o e f f i c i e n t s and E i genva lues 132 5.5 E i genva lues fo r Hess ian Ma t r i x at each Obse r va t i on 133 5.6 Returns to Sca l e 136 5.7 E l a s t i c i t i e s of Cho ice (T rans log ) 138 5.8 Summary of Cross P r i c e and Own P r i c e E l a s t i c i t i e s 141 5.9 Summary C l a s s i f i c a t i o n of Farm Inputs 144 5.10 C l a s s i f i c a t i o n of Outputs w i th r espec t to Input Use 147 5.11 C l a s s i f i c a t i o n of Inputs w i th r espec t to Output Use 148 v i i 5.12 Regress ion C o e f f i c i e n t s , Quadra t i c P r o f i t Func t i on 153 5.13 E l a s t i c i t i e s of Cho ice (Quadra t i c ) 156 5.14 Summary of Own E l a s t i c i t i e s of Supply 158 5.15 T o t a l E l a s t i c i t i e s of C a t t l e Supply . . 161 5.16 Summary of C a t t l e Supply E l a s t i c i t i e s 164 D.1 E s t ima ted P r i c e P r e d i c t i o n Equa t ions us ing a Po l ynomia l D i s t r i b u t e d Lag 234 D.2 Example of P r e d i c t e d P r i c e s , S teer Equa t ion . . . . . . 235 D.3 Regress ion R e s u l t s : T r a n s l o g P r i c e Index 239 D.4 Output Supply and Cross P r i c e E l a s t i c i t i e s Ho ld i ng T o t a l Output Cons t an t , Means of the Exogeneous V a r i a b l e s 239 D.5 J o i n t E s t i m a t i o n : Norma l ized Cobb-Douglas P r o f i t F u n c t i o n and Net Input Demand Equa t ions 241 D.6 Own P r i c e E l a s t i c i t i e s , C ross P r i c e E l a s t i c i t i e s , and E l a s t i c i t i e s With Respect To the F i x e d Fac to r 242 D.7 T o t a l Supply E l a s t i c i t i e s : Output Component 242 D.8 Es t ima ted Parameters T r a n s l o g P r o f i t F u n c t i o n , Almon Lag P r i c e E x p e c t a t i o n s 244 D. 9 P r i c e E l a s t i c i t i e s , C ross P r i c e E l a s t i c i t i e s T r a n s l o g P r o f i t F u n c t i o n , Means of Exogeneous V a r i a b l e s 1981, Almon Lag P r i c e E x p e c t a t i o n s 245 E. 1 Es t ima ted Parameters : ARIMA(2,1,0) 248 E.2 P l o t s of the A u t o c o r r e l a t i o n Func t i on of the R e s i d u a l s 249 v i i i LIST OF FIGURES 2.1 Cho ice S teer P r i c e s in Canadian Funds Ca lga r y and Omaha 21 2.2 Aggregate Demand Fac ing Canadian C a t t l e P roducers 23 2.3 I n v e n t o r i e s of Beef Cows and H e i f e r s on Farms, Canada 25 2.4 I n v e n t o r i e s of Cows and H e i f e r s on Farms, Western and Eas te rn Canada 27 2.5 S teer and Female S l a u g h t e r , Canada 28 2.6 Female S l aughte r as a Percentage of S teer S l a u g h t e r , Canada 29 2.7 Flow Diagram of C a t t l e P roduc t i on D e c i s i o n s 32 3.1 Dynamic Behav ior of a Cow-Calf Producer 47 4.1 P l o t of A u t o c o r r e l a t i o n and P a r t i a l A u t o c o r r e l a t i o n F u n c t i o n s , S teer P r i c e s , Ca lga ry . . . 94 4.2 P l o t of A u t o c o r r e l a t i o n and P a r t i a l A u t o c o r r e l a t i o n F u n c t i o n s , F i r s t D i f f e r e n e c e d S teer P r i c e s , Ca lga ry 96 4.3 C a t t l e Supply o f f Farms 103 5.1 Supply Func t i on C r o s s - S e c t i o n a l Versus T ime-Ser i es 156 ix ACKNOWLEDGEMENTS I would l i k e to express my a p p r e c i a t i o n to R ick B a r i c h e l l o , Chuck B l a cko rby , John C ragg , and B i l l Schworm for t h e i r comments, s u g g e s t i o n s , and encouragements over the course of t h i s s tudy . Without t h e i r a s s i s t a n c e , t h i s d i s s e r t a t i o n would not have been comp le ted . T h i s d i s s e r t a t i o n a l s o b e n e f i t e d from d i s c u s s i o n s w i th other i n d i v i d u a l s . S p e c i f i c a l l y , I would l i k e to thank Erwin D iewer t , John Graham, Tim H a z l e d i n e , Kurt K l e i n , Ra lph L a t t i m o r e , R ick Lymer, and Cameron Short f o r t h e i r c o n s t r u c t i v e c r i t i c i s m s and c o o p e r a t i o n and Ray Bol lman fo r h i s comments and a s s i s t a n c e in o b t a i n i n g the d a t a . I am g r a t e f u l to the members and s tudents i n the departments of Economics and A g r i c u l t u r a l Economics fo r p r o v i d i n g an e x c e l l e n t environment in which to study economics . F i n a l l y , I would l i k e to thank my pa ren t s fo r encourag ing me to con t inue my educa t i on and my w i f e , G l o r i a , f o r her love and con t i nued suppor t d u r i n g many, sometimes t u r b u l e n t , yea rs of graduate s t u d i e s . T h i s d i s s e r t a t i o n i s d e d i c a t e d to h e r . 1 1. INTRODUCTION A number of economic s t u d i e s have ana l yzed the s t r u c t u r e and c h a r a c t e r i s t i c s of the Canadian cow-cal f i n d u s t r y and the dec i s ion-mak ing behav io r of c a t t l e p r o d u c e r s 1 (Kerr 1968, T r y f o s 1974, Ku l sh re sh tha 1976, Haack, M a r t i n , and MacAulay 1978, Pugh 1978, A g r i c u l t u r e Canada 1983, and o t h e r s ) . The i n t e r e s t in t h i s i n d u s t r y i s genera ted f i r s t of a l l by the need f o r economists to have knowledge of the s t r u c t u r a l c h a r a c t e r i s t i c s in order to determine the consequences of changes in p o l i c y and other pa ramete rs . Second, the re i s e v i dence , both t h e o r e t i c a l and e m p i r i c a l , which suggests that the e l a s t i c i t y of supp ly in the shor t run i s nega t i ve and g r a d u a l l y becomes p o s i t i v e over a long adjustment p e r i o d (Ma r sha l l 1964, R e u t l i n g e r 1966, J a r v i s 1969, Yver 1971, and Nelson and Spreen 1978). Three reasons are put forward to e x p l a i n nega t i ve shor t run supp ly responses in the c a t t l e i n d u s t r y : 1) the p r i c e e x p e c t a t i o n s of c a t t l e p roduce rs ( i . e . , changing p r i c e e x p e c t a t i o n s w i l l i n i t i a t e changes in investment d e c i s i o n s and c a t t l e i n v e n t o r i e s ) ; 2) the beef an imal i s both an input i n t o the p r o d u c t i o n p rocess as we l l as the output ( i . e . , a d d i t i o n a l output r e q u i r e s tha t cows and h e i f e r s be r e t a i n e d in the b reed ing herd i n o rder to produce more a n i m a l s : t h i s i m p l i e s lower c u r r e n t o u t p u t ) ; and 3) the b i o l o g i c a l c h a r a c t e r i s t i c s of c a t t l e r e p r o d u c t i o n ( i . e . , the e x i s t e n c e of a t ime l a g in the r e p r o d u c t i o n p rocess between when producers dec ide to i n c r ease t h e i r herd and when new an ima ls are brought to marke t ) . 2 E x i s t i n g s t u d i e s however, have had some problems in m o d e l l i n g and p r e d i c t i n g the dynamic shor t run supp ly response and investment behav io r of c a t t l e p r o d u c e r s . Kn ight (1961), in d e s c r i b i n g these prob lems, s t a t e d tha t "Research workers have p robab l y had more d i f f i c u l t y d e r i v i n g mean ingfu l and r e a l i s t i c s u p p l y - p r i c e e l a s t i c i t i e s fo r beef than fo r any of the o the r commod i t i e s " . In a d d i t i o n , Ne lson and Spreen (1978) have argued that p r e v i o u s e m p i r i c a l s t u d i e s of the c a t t l e i n d u s t r y have genera ted c o n t r a d i c t o r y r e s u l t s , "and a c o n t r o v e r s y s t i l l e x i s t s about the proper s p e c i f i c a t i o n of a sho r t- run supply r e l a t i o n f o r s l augh te r c a t t l e " . These problems can be a t t r i b u t e d to th ree f a c t o r s . 1) T h e o r e t i c a l s t u d i e s ( J a r v i s 1969, Yver 1971) which demonstrate the e x i s t e n c e of nega t i ve shor t run supp ly response a l l u d e to the importance of p r i c e e x p e c t a t i o n s of c a t t l e p roduce rs but do not e x p l i c i t l y take account of e x p e c t a t i o n s in t h e i r t h e o r e t i c a l a n a l y s i s . I t w i l l be shown in t h i s study that p r i c e e x p e c t a t i o n s of c a t t l e p roduce rs are the major c a u s a l f a c t o r gene r a t i ng nega t i v e supp ly responses i n the shor t r un . 2) E m p i r i c a l a t tempts to model the cow-cal f i n d u s t r y are c o m p l i c a t e d by the f a c t tha t beef an ima ls are s imu l t aneous l y an investment good and an output good. 3) Most e m p i r i c a l s t u d i e s are s t a t i c w i th some form of l a g s t r u c t u r e appended to the model in order to i n t r oduce dynamic e lements i n t o the a n a l y s i s . I n t e r t empora l a n a l y s i s i s r e q u i r e d to model c o n s i s t e n t l y the dynamic response and investment behav ior of c a t t l e p r o d u c e r s . T h i s w i l l a l l ow improved s p e c i f i c a t i o n of the econometr ic equa t i ons and presumably more accu ra te 3 r e s u l t s . The development of d u a l i t y theory (Shepard 1953, Gorman 1968, and McFadden 1978) o f f e r s the economist new t o o l s w i th which to approach the problem of m o d e l l i n g dynamic shor t run supp ly responses and inves tment 2 behav ior of c a t t l e p r o d u c e r s . G e n e r a l l y , d u a l i t y theory demonstrates tha t under c e r t a i n r e g u l a r i t y c o n d i t i o n s 3 and w i th the assumpt ion of p r o f i t .max im iza t i on , the p r o d u c t i o n p o s s i b i l i t i e s a v a i l a b l e to a farm can be comp le t e l y c h a r a c t e r i z e d by a p r o f i t f u n c t i o n . " A dua l r e l a t i o n s h i p between t h i s p r o f i t f u n c t i o n and a t r a n s f o r m a t i o n f u n c t i o n a l l ows e i t h e r to be d e r i v e d from the knowledge of the o t h e r . T h e o r e t i c a l l y , t h e r e f o r e , the t e c h n o l o g i c a l parameters of the cow-ca l f i ndus t r y can be recove red e i t h e r d i r e c t l y by e s t i m a t i n g the t r a n s f o r m a t i o n f u n c t i o n (the p r i m a l approach) or i n d i r e c t l y by e s t i m a t i n g the p r o f i t f u n c t i o n (the dua l a p p r o a c h ) . There are however, s e v e r a l d i sadvan tages to e s t i m a t i n g the t r a n s f o r m a t i o n f u n c t i o n d i r e c t l y 5 (Woodland 1976). I f the v e c t o r of i npu t s i n the t r a n s f o r m a t i o n f u n c t i o n are chosen by the fa rm, such i npu t s are endogenous in an econometr ic model and u n l i k e l y to be independent of the e r r o r s t r u c t u r e . In t h i s c a s e , o r d i n a r y l e a s t squares r e g r e s s i o n would be i n a p p r o p r i a t e and a l t e r n a t i v e and more c o m p l i c a t e d econometr ic t e c h n i q u e s , such as i n s t r umen ta l v a r i a b l e s , would be r e q u i r e d . I f t i m e - s e r i e s da ta are u s ed , i t i s l i k e l y tha t the i n p u t s w i l l be m u l t i c o l l i n e a r , c a u s i n g the s tandard e r r o r s of the r e g r e s s i o n c o e f f i c i e n t s to be l a r g e r (or sma l l e r ) than they o therw ise would be in the absence of m u l t i c o l l i n e a r i t y . 4 F i n a l l y , i f the farm maximizes p r o f i t s , t h i s behav io r i s not used in e s t i m a t i n g the t r a n s f o r m a t i o n f u n c t i o n un l ess i t i s mode l led d i r e c t l y . If one i s w i l l i n g to assume both p r o f i t maximiz ing and p r i c e - t a k i n g b e h a v i o r , then e m p i r i c a l f a c t o r demand and output supp ly equa t ions can be d e r i v e d as s o l u t i o n s to the f i r s t o rder c o n d i t i o n s in the max imiza t ion of p r o f i t s sub j ec t to the t r a n s f o r m a t i o n f u n c t i o n . However, because of the d i f f i c u l t y i n v o l v e d in s o l v i n g f i r s t o rder c o n d i t i o n s , one i s f o r c e d to p o s i t ve ry r e s t r i c t i v e f u n c t i o n a l forms f o r the t r a n s f o r m a t i o n f u n c t i o n ( e . g . , Cobb-Douglas or C . E . S . ) . 6 By us ing a dua l approach to recover the parameters of the t e c h n o l o g y , many of the problems a s s o c i a t e d w i th d i r e c t e s t i m a t i o n of the t r a n s f o r m a t i o n f u n c t i o n can be overcome. Under the ma in ta ined assumpt ions of p r o f i t max imiza t ion and p r i c e - t a k i n g market c o n d i t i o n s , the dua l approach s p e c i f i e s an (opt ima l ) p r o f i t f u n c t i o n d i r e c t l y and thereby avo ids the n e c e s s i t y of s o l v i n g f i r s t order c o n d i t i o n s in a maximiz ing p rob lem. C e r t a i n r e s t r i c t i o n s are imposed on the p r o f i t f u n c t i o n to ensure tha t i t s a t i s f i e s the c o n d i t i o n s of a "we l l -behaved " t r a n s f o r m a t i o n f u n c t i o n (Diewert 1973). Bes ides c i r cumven t i ng the need to so l v e f i r s t o rde r c o n d i t i o n s , the re are two o ther p r i n c i p a l advantages of d u a l i t y theory i n a p p l i e d economics (Diewert 1974). F i r s t , the d e r i v e d input demand and output supp ly equa t ions tha t are c o n s i s t e n t w i th farm p r o f i t max imiza t ion can be ob ta ined by d i f f e r e n t i a t i n g the p r o f i t f u n c t i o n w i th r e spec t to input and output p r i c e s . Because of the ease in d e r i v i n g input demand 5 and output supp ly e q u a t i o n s , d u a l i t y theory a l l ows a d i r e c t and c o n s i s t e n t r e l a t i o n s h i p between the t h e o r e t i c a l model and the econometr i c mode l . Second, comparat i ve s t a t i c r e s u l t s can e a s i l y be genera ted from the es t ima ted d e r i v e d input demand and output supply e q u a t i o n s . A number of r ecen t c o n t r i b u t i o n s to the theory of cos t and p r o d u c t i o n have enhanced and extended the use of d u a l i t y theory in e m p i r i c a l work. The i n t r o d u c t i o n of f l e x i b l e , f u n c t i o n a l forms (FFF) by Diewert (1971) and C h r i s t e n s e n , J o rgensen , and Lau (1973) a l lowed g e n e r a l i z a t i o n s away from p r e v i o u s more r e s t r i c t i v e f u n c t i o n a l forms. In f a c t , FFF can be used to t e s t s t a t i s t i c a l l y f o r the e x i s t e n c e of the more r e s t r i c t i v e fo rms. FFF p rov ide a second order approx imat ion to the u n d e r l y i n g t r a n s f o r m a t i o n f u n c t i o n and do not a p r i o r i impose h o m o t h e t i c i t y , s e p a r a b i l i t y , or r e s t r i c t i o n s on s u b s t i t u t i o n e l a s t i c i t i e s . 7 Moreover , FFF can be used to t e s t s t a t i s t i c a l l y f o r these r e s t r i c t i o n s on the u n d e r l y i n g t e c h n o l o g y . The e x t e n s i o n of d u a l i t y theory and FFF to a l low f o r m u l t i p l e ou tpu ts and i npu t s enab les the r esea r che r to model f i rms which employ a number of i npu ts and produce a number of ou tputs (Lau 1972, H a l l 1973, and Diewert 1 9 7 3 ) . 8 T h i s g e n e r a l i z a t i o n e l i m i n a t e s the need to a s s o c i a t e c e r t a i n expenses wi th the p r o d u c t i o n of c e r t a i n o u t p u t s . In a d d i t i o n , j o i n t p r o d u c t i o n p o s s i b i l i t i e s can be t e s t e d s t a t i s t i c a l l y . F i n a l l y , the development of v a r i a b l e or r e s t r i c t i v e p r o f i t f u n c t i o n s takes account of the M a r s h a l l i a n n o t i o n tha t in the shor t r un , some f a c t o r s are v a r i a b l e ( i . e . , the farm i s o p t i m i z i n g wi th r e spec t to the q u a n t i t y employed of each 6 v a r i a b l e input ) whereas other f a c t o r s are f i x e d ( i . e . , the farm may not be in e q u i l i b r i u m wi th r e spec t to q u a n t i t i e s employed of these f i x e d f a c t o r s ) (Gorman 1968). Us ing t h i s p ro cedu re , the shadow p r i c e of each f i x e d f a c t o r can be d e r i v e d by d i f f e r e n t i a t i n g the v a r i a b l e p r o f i t f u n c t i o n w i th r e spec t to the f i x e d f a c t o r . There are a number of econometr i c advantages to u s i n g the dua l approach combined w i th FFF . The c o e f f i c i e n t s of the p r o f i t f u n c t i o n can be es t ima ted from the d e r i v e d input demand and output supp ly e q u a t i o n s . These f u n c t i o n s are reduced form equa t ions w i th output and input q u a n t i t i e s as f u n c t i o n s of output and input p r i c e s and the q u a n t i t y of any f i x e d f a c t o r s . I f p r i c e s are exogenous, l e s s c o m p l i c a t e d econometr i c t echn iques can be used to es t imate the c o e f f i c i e n t s . A d d i t i o n a l l y , many types of FFF tha t are used to approximate the p r o f i t f u n c t i o n are l i n e a r in t h e i r c o e f f i c i e n t s and t h i s a l l ows the use of l i n e a r r e g r e s s i o n t e chn iques in e s t i m a t i n g these c o e f f i c i e n t s . However, because the independent v a r i a b l e s are monotonic t r ans fo rms of p r i c e s or p r i c e r a t i o s , m u l t i c o l l i n e a r i t y can be a s e r i o u s p rob lem. F i n a l l y , i t shou ld be noted tha t a l t hough one might expect p r i c e s to be independent of the e r r o r s t r u c t u r e in an econometr ic e q u a t i o n , i t i s l i k e l y tha t because of the symmetry r e s t r i c t i o n s imposed a c ros s e q u a t i o n s , the e r r o r s t r u c t u r e i s c o r r e l a t e d a c r o s s equa t ions in a system of input and output e q u a t i o n s . T h i s would i n d i c a t e tha t a systems method which accounts f o r t h i s e r r o r s t r u c t u r e shou ld be used when e s t i m a t i n g the c o e f f i c i e n t s from the d e r i v e d input demand and output supply 7 e q u a t i o n s . 9 1 . 1 OBJECTIVES The aim of t h i s r e sea r ch i s to deve lop a t h e o r e t i c a l p r o f i t maximiz ing model of a cow-cal f farm and then to determine and to es t ima te e m p i r i c a l l y the dynamic shor t run supp ly response and investment behav ior of c a t t l e p r o d u c e r s . S p e c i f i c a l l y , the o b j e c t i v e s are as f o l l o w s : i ) to c h a r a c t e r i z e the s t r u c t u r e of the Canadian cow-ca l f i n d u s t r y u s i n g a d i s c r e t e t ime , i n t e r t e m p o r a l model ( i g n o r i n g o ther s e c t o r s of the beef i n d u s t r y , such as f e e d l o t p r o d u c t i o n and meat p r o c e s s i n g ) ; i i ) to demonstrate t h e o r e t i c a l l y the importance of c a t t l e p r o d u c e r s ' p r i c e e x p e c t a t i o n s in g e n e r a t i n g the t ime path of the supp ly adjustment p rocess and to determine e m p i r i c a l l y c a t t l e p r o d u c e r s ' e x p e c t a t i o n s about f u t u r e beef p r i c e s ; i i i ) to recover the parameters of the t echno logy us ing the output supply and input demand equa t i ons tha t un ique l y d e f i n e the t r a n s f o r m a t i o n f u n c t i o n over the e c o n o m i c a l l y r e l e v a n t r e g i o n ; i v ) to undertake a compara t i ve s t a t i c a n a l y s i s of the changes in the op t ima l v a l ues of output supp ly and input demand as a r e s u l t of changes i n the exogenous v a r i a b l e s ; v) to generate a number of summary s t a t i s t i c s of output and input f l e x i b i l i t y i n c l u d i n g the shor t run e l a s t i c i t y of output supp ly and input demand and measures of s u b s t i t u t a b i l i t y of ou tputs and of i n p u t s . 1 . 2 EXISTING LITERATURE The present s tudy d i f f e r s from p r e v i o u s s t u d i e s of the 8 cow-ca l f i n d u s t r y in four ways. F i r s t , p r e v i ous s t u d i e s ( J a r v i s 1969 and Yver 1971) have deve loped t h e o r e t i c a l models of c a t t l e p r o d u c t i o n which maximize the net p resen t d i s c o u n t e d va lue of an animal at b i r t h or f o r i t s rema in ing l i f e t i m e . The endogenous v a r i a b l e s , op t ima l input q u a n t i t i e s and op t ima l s l a u g h t e r age, are s p e c i f i e d as f u n c t i o n s of the exogenous pa ramete r s . However, the e m p i r i c a l models do not f u l l y r e f l e c t the t h e o r e t i c a l r e s u l t s : they do not i n c l u d e equa t ions tha t r ep re sen t the endogenous v a r i a b l e s as f u n c t i o n s of the exogenous v a r i a b l e s . Ra the r , the e s t ima ted equa t ions are a r b i t r a r i l y s p e c i f i e d to determine average s l a u g h t e r we ight , number of an imals s l a u g h t e r e d in each c a t e g o r y , and expor t and domest ic demand. In c o n t r a s t , the theory of d u a l i t y i s used here to p rov ide a r i g o r o u s and c o n s i s t e n t model of the cow-c a l f i n d u s t r y . Because d u a l i t y theory a l l ows one to manage c o m p l i c a t e d f u n c t i o n s more e a s i l y , the t echno logy of c a t t l e p r o d u c t i o n can be mode l l ed in g r ea t e r d e t a i l and w i th more p r e c i s i o n than b e f o r e . The model i s c o n s i s t e n t in tha t the e s t ima ted equa t ions are d e r i v e d from the p r o f i t maximiz ing farm mode l . Second , R e u t l i n g e r (1966) argued tha t to ach ieve more a c cu r a t e r e s u l t s when e s t i m a t i n g c a t t l e p r o d u c t i o n mode ls , i t i s necessa r y to e s t ima t e output supp ly and c a t t l e i n ven to r y equa t i ons s i m u l t a n e o u s l y . P r ev ious s t u d i e s have e i t h e r assumed c a t t l e i n v e n t o r i e s to be exogenous (Langemeir and Thompson 1967) or have a r b i t r a r i l y s p e c i f i e d i nven to r y equa t i ons to be f u n c t i o n s of expected beef p r i c e s and feed c o s t s ( T r y f o s 1974). These s t u d i e s g e n e r a l l y a l low 9 i n v e n t o r i e s to approach an op t ima l l e v e l us ing a p a r t i a l adjustment p rocess (Ospina and Shumway 1978). In t h i s s tudy , c a t t l e i n v e n t o r i e s are determined endogenous ly . The importance of p r i c e e x p e c t a t i o n s in the c a t t l e i n d u s t r y has been we l l documented in the l i t e r a t u r e (Ma r sha l l 1964 and Elam 1975). However, l i t t l e has been done to demonstrate in a r i g o r o u s manner the t h e o r e t i c a l importance of p r i c e e x p e c t a t i o n s f o r the t ime path of adjustment adopted by c a t t l e p r o d u c e r s . T h e r e f o r e , a t h i r d i nnova t i on of t h i s study i s tha t p r i c e expec t a t i ons w i l l be i n t r o d u c e d i n t o the t h e o r e t i c a l mode l . The consequences of p r i c e e x p e c t a t i o n s f o r the dynamic shor t run response of c a t t l e p roduce rs w i l l be de te rm ined . F i n a l l y , e x i s t i n g s t u d i e s have focused on e s t i m a t i n g i n v e n t o r y , inves tment , or s l a u g h t e r equa t ions but have i gno red the demands by p roducers fo r f a c t o r i npu ts (Ku l sh resh tha and W i l son 1972, and Ospina and Shumway n . d . ) . In t h i s study output supply e q u a t i o n s , c a t t l e i n ven to r y e q u a t i o n s , and d e r i v e d input demand equa t i ons w i l l be e s t ima ted s i m u l t a n e o u s l y . The r e s u l t s of the e s t i m a t i o n w i l l p r o v i d e i n f o r m a t i o n on s t r u c t u r a l parameters of t h i s i n d u s t r y making i t p o t e n t i a l l y more u s e f u l to p o l i c y makers. 1.3 THESIS OUTLINE The remainder of t h i s t h e s i s i s o r g a n i z e d as f o l l o w s . The c h a r a c t e r i s t i c s of the Canadian c a t t l e i n d u s t r y are d e s c r i b e d in Chapter Two. T h i s d i s c u s s i o n i n d i c a t e s the importance of c a t t l e p r o d u c t i o n w i t h i n Canadian a g r i c u l t u r e 10 and the i m p l i c a t i o n s f o r Canadian c a t t l e p r i c e s of r e l a t i v e l y f r e e i n t e r n a t i o n a l t rade in beef an ima ls and meat p r o d u c t s . T h i s chap te r i n c l u d e s a review of past t h e o r e t i c a l a t tempts to model c a t t l e p r o d u c t i o n . . In Chapter Th ree , a t h e o r e t i c a l p r o f i t maximiz ing model of a cow-cal f p roducer i s deve loped . I n i t i a l l y a number of s i m p l i f y i n g assumpt ions are imposed on the model in order to focus on the dynamic e lements of c a t t l e p r o d u c t i o n and to determine the t h e o r e t i c a l i m p l i c a t i o n s of p r i c e e x p e c t a t i o n s on shor t run supp ly b e h a v i o r . Subsequen t l y , the model i s extended to account fo r a m u l t i - o u t p u t , m u l t i - i n p u t p r o d u c t i o n techno logy from which an econometr ic model can be p o s t u l a t e d . A compara t i ve s t a t i c a n a l y s i s i s undertaken and a number of e l a s t i c i t y measurements fo r the m u l t i - o u t p u t , m u l t i - i n p u t model are d i s c u s s e d . The data r e q u i r e d to es t imate the output supp ly and d e r i v e d input demand equa t ions are r epo r t ed in Chapter Fou r . Data i n c l u d e the q u a n t i t y of d i f f e r e n t ou tpu ts produced by cow-ca l f farms and a s s o c i a t e d output p r i c e s , the q u a n t i t y of d i f f e r e n t i npu t s used on farms and a s s o c i a t e d input p r i c e s , and the i n v e n t o r i e s of c a t t l e on fa rms. The t r a n s f o r m a t i o n of the d a t a , in o rder to ob t a i n the a p p r o p r i a t e v a r i a b l e s r e q u i r e d fo r e m p i r i c a l a n a l y s i s in t h i s d i s s e r t a t i o n , are a l s o d e s c r i b e d . A d d i t i o n a l l y , Chapter Four i n c l u d e s a d i s c u s s i o n of the i s s u e s i n v o l v e d in e s t i m a t i n g the c o e f f i c i e n t s of the p r o f i t f u n c t i o n model . F u n c t i o n a l forms f o r the p r o f i t f u n c t i o n are s p e c i f i e d and the e s t i m a t i n g equa t ions are d e r i v e d . F i n a l l y , 11 the econometr i c methodology used to es t imate the system of equa t i ons i s d e t a i l e d as are the assumpt ions about the s t o c h a s t i c framework of the e q u a t i o n s . The r e s u l t s of the r e g r e s s i o n ana l y ses are r epo r t ed i n Chapter F i v e . In a d d i t i o n , a number of e l a s t i c i t y measurements are p resen ted and the hypotheses to be p o s t u l a t e d in Chapter Three are t e s t e d . The main c o n c l u s i o n s of the study are summarized in Chapter S i x . 1 2 FOOTNOTES TO CHAPTER ONE 1 A c a t t l e producer i s d e f i n e d as a farmer who owns a beef cow b reed ing herd and produces c a l v e s f o r s a l e . The c a t t l e producer may a l s o r e t a i n c a l v e s on the farm and s e l l heav i e r an ima ls at a l a t e r d a t e . The economic c h o i c e s a v a i l a b l e to the c a t t l e producer w i l l be d i s c u s s e d in Chapter Two. 2 The investment behav io r tha t i s of i n t e r e s t here i s the expans ion or r e d u c t i o n of the b reed ing h e r d . 3 These r e g u l a r i t y c o n d i t i o n s w i l l be d i s c u s s e d in Chapter Th ree . 4 Diewert (1974) s t a t e s tha t the essence of d u a l i t y theory r e s t s on a mathemat ica l theorem by M inkowsk i : " every c l o s e d convex set i n R n can be c h a r a c t e r i z e d as the i n t e r s e c t i o n of i t s s u p p o r t i n g h a l f s p a c e s " . 5 Some of these d i sadvan tages app l y e q u a l l y to e s t i m a t i o n of p r o f i t f u n c t i o n s . 6 These f u n c t i o n a l forms are r e s t r i c t i v e in the sense that they impose h o m o t h e t i c i t y , s e p a r a b i l i t y , or cons tan t e l a s t i c i t i e s of s u b s t i t u t i o n on the e s t i m a t i n g f u n c t i o n . 7 One can d i s t i n g u i s h two t ypes of a p p r o x i m a t i o n : i ) the Diewert a p p r o x i m a t i o n , where a f u n c t i o n a l form i s f l e x i b l e i f the parameters of the f u n c t i o n a l form can be chosen to make the v a l ues of i t s f i r s t and second order d e r i v a t i v e s equa l to the f i r s t and second order d e r i v a t i v e s of the f u n c t i o n be ing approximated at some p o i n t ; and i i ) the T a y l o r s e r i e s a p p r o x i m a t i o n , where the f u n c t i o n i s 13 approximated w i th a T a y l o r s e r i e s expans ion around some p o i n t . See B l a c k o r b y , P r imont , and R u s s e l l (1978) pp .290-300 f o r the d i s t i n c t i o n between the two d e f i n i t i o n s . 8 Given the m u l t i - p r o d u c t na ture of Canadian a g r i c u l t u r e , t h i s ex t ens i on w i l l prove v a l u a b l e in m o d e l l i n g the cow-c a l f i n d u s t r y . See Mundlak (1963) f o r an i n i t i a l attempt at m o d e l l i n g m u l t i - p r o d u c t p r o d u c t i o n f u n c t i o n s . 9 It shou ld be noted tha t the use of d u a l i t y in a p p l i e d economics has ga ined wide p o p u l a r i t y . For examples of a p p l i e d d u a l i t y i n both a g r i c u l t u r a l and n o n - a g r i c u l t u r a l markets see Be rndt , F u s s , and Waverman (1979) , Binswanger (1974), Caves and C h r i s t e n s e n (1980) , Caves , C h r i s t e n s e n , and Swanson (1981) , Fuss (1977), Lopez (1980) , McKay, Lawrence, and V l a s t i u m (1982) , S idhu and Baanante (1981) , Woodland (1975) , Woodland (1977) . One common f e a tu r e of a lmost a l l of these s t u d i e s i s the use of h i g h l y aggregated s e c t o r a l data ( i . e . , t o t a l a g r i c u l t u r e or t o t a l m a n u f a c t u r i n g ) . T h i s study w i l l use a more d i s agg rega t ed i n d u s t r y - l e v e l da ta s e r i e s to es t imate the mode l . 14 2. THE CANADIAN CATTLE INDUSTRY 2.1 INTRODUCTION The Canadian c a t t l e i n d u s t r y i s c h a r a c t e r i z e d by a l a r g e number of sma l l p r o d u c e r s , c y c l i c a l t rends in p r o d u c t i o n , and an open market f o r i n t e r n a t i o n a l t rade i n l i v e c a t t l e and bee f . These and o ther c h a r a c t e r i s t i c s of the c a t t l e i n d u s t r y are d i s c u s s e d in S e c t i o n (2.2) of t h i s c h a p t e r . The economic o p t i o n s a v a i l a b l e to cow-ca l f p roducers when de t e rm in ing p r o d u c t i o n s t r a t e g y are o u t l i n e d in Se c t i on ( 2 . 3 ) . F i n a l l y , S e c t i o n (2.4) c o n s i s t s of an examinat ion of pas t a t tempts to model the economic behav ior of cow-cal f p r o d u c e r s . 2.2 SOME CHARACTERISTICS OF THE CATTLE INDUSTRY The c a t t l e i n d u s t r y i s an important s e c t o r of a g r i c u l t u r a l p r o d u c t i o n in Canada. Tab le 2.1 l i s t s farm cash r e c e i p t s fo r Canada from the s a l e of c a t t l e and c a l v e s f o r s e l e c t e d yea rs between 1970 to 1982. C a t t l e and c a l f s a l e s f o r t h i s p e r i o d r ep resen t from 18.4% to 34.9% of t o t a l farm cash r e c e i p t s , second on ly to the g r a i n s (wheat, b a r l e y , e t c . ) i n d u s t r y . In 1982, the r e c e i p t s from the sa l e of c a t t l e and c a l v e s accounted f o r 3 0 . 5 % , 12.6%, and 17.6% of t o t a l farm cash r e c e i p t s fo r A l b e r t a , Saskatchewan, and Mani toba r e s p e c t i v e l y . 1 Another i n d i c a t i o n of the importance of the Canadian c a t t l e i n d u s t r y i s that i n t e r n a t i o n a l t rade in beef an ima ls and meat p roduc t s has i n c r ea sed s i g n i f i c a n t l y in recent y e a r s . 15 TABLE 2.1 Canadian Farm Cash Receipts from the Sale of Cattle and Calves Year 1970 1975 1980 1981 1982 Receipts from the Sale of Cattle and Calves ($ million) 1,469.6 1,873.9 3,665.0 3,537.0 3,586.0 Total Farm CAsh Receipts ($ million) 4,208.4 10,142.4 15,837.0 18,835.0 18,840.0 Receipts from the Sale of Cattle and Calves as a Percentage of Total Receipts 34.9 18.4 23.0 18.8 19.0 Source: Stat is t ics Canada, Farm Cash Receipts, Cat. No. 21-001, Ottawa, Queen's Printer, annual. 16 Tab le 2.2 l i s t s the numbers of c a t t l e and c a l v e s and pounds of d r e s s e d beef and v e a l expor ted and imported fo r s e l e c t e d yea rs between 1970 to 1982. T h i s t a b l e i n d i c a t e s that throughout t h i s p e r i o d , Canada has been a net expo r t e r of l i v e an ima ls and tha t these expor t s have been i n c r e a s i n g at a s i g n i f i c a n t l y g r ea t e r r a te than impo r t s . Fur thermore , in 1970 and 1975 Canada was a net importer of d ressed beef and vea l but i n the l a t e ' 7 0 ' s and e a r l y ' 8 0 ' s , Canada changed to a net expo r t e r in t h i s c a t ego ry as w e l l . The s i g n i f i c a n c e of i n t e r n a t i o n a l t rade to the Canadian c a t t l e i n d u s t r y i s demonstrated in Tab l e 2.3 which l i s t s , in m i l l i o n s of d o l l a r s , the va lue of expo r t s and imports of l i v e an imals and meat p r o d u c t s . Throughout t h i s p e r i o d , the va lue of l i v e animal expor t s exceeded imports but the va lue of imports i n c r e a s e d at a s i g n i f i c a n t l y g r e a t e r r a te than e x p o r t s . These f i g u r e s r ep resen t the f a c t tha t Canada expor t s l a r g e q u a n t i t i e s of low q u a l i t y beef and imports h igh q u a l i t y beef from the U . S . 2 F i n a l l y , in 1977-78 the va lue of imports of meat p roducts exceeded expor t s but t h i s has changed s i g n i f i c a n t l y . In recent y e a r s , the va lue of meat p roduc t s expo r t s has i n c r eased to more than tw ice the va lue of impo r t s . The U.S. i s Canada 's l a r g e s t t r a d i n g pa r tne r i n beef p roduc t s a c coun t i ng f o r approx imate l y 90% of t o t a l expo r t s of c a t t l e and c a l v e s and 85% of t o t a l d r essed beef and v e a l . Canada 's success in i n t e r n a t i o n a l t r ade in l i v e an ima l s and meat p roduc t s depends on low t rade b a r r i e r s wi th i t s major t r a d i n g p a r t n e r s . 3 Except f o r a few p e r i o d s where h igh t a r i f f s or import r e s t r i c t i o n s were imposed, beef p roducers have 17 TABLE 2.2 Canadian Expor t s and Imports of L i v e An imals and Dressed Beef and Vea l Year 1970 1975 1980 1981 1982 EXPORTS C a t t l e and Ca l ves ( thousand Head) 247.0 223.6 357.8 353.0 . 504.9 Dressed Beef and Vea l ( m i l l i o n l b s . ) 119.1 45.1 114.3 174.7 183.5 IMPORTS C a t t l e and Ca l ves ( thousand head) 53.3 92.6 52.7 171.1 83.9 Dressed Beef and V e a l ( m i l l i o n l b s . ) 157.4 139.8 129.7 133.8 140.6 Sou r ce s : S t a t i s t i c s Canada, L i v e s t o c k and Animal P roducts S t a t i s t i c s , C a t . No. 23-203, Ottawa, Queen 's P r i n t e r , a n n u a l . A g r i c u l t u r e Canada, L i v e s t o c k Market Review, Ot tawa, Queen 's P r i n t e r , a n n u a l . 18 TABLE 2.3 Value of Canadian Exports and Imports of Live Animals and Meat Products Year . 1977 1978 1979 1980 1981 1982 EXPORTS ($ million) Live Animals 135. 0 196. 0 224. 0 229. 0 201 . 0 299.0 Meat Products 222. 0 309. 0 428. 0 514. 0 620. 0 776.0 IMPORTS ($ million) Live Animals 30. 0 57. 0 48. 0 88. 0 170. 0 105.0 Meat Products 295. 0 331 . 0 332. 0 287. 0 301 . 0 297.0 Source: Stat is t ics Canada, Selected Agriculture Stat is t ics Canada and the Provinces, Ottawa, Queen's Printer, 1983. 19 enjoyed r e l a t i v e l y f r ee t rade in beef p r o d u c t s . In Tab le 2 .4 , an example of the 1982 t a r i f f s t r u c t u r e i s p resen ted fo r Canada and i t s maj'or t r a d i n g p a r t n e r s fo r d i f f e r e n t c a t e g o r i e s of an imals and meat p r o d u c t s . Canadian import t a r i f f s fo r d i f f e r e n t c a t e g o r i e s of l i v e s t o c k and meat and fo r d i f f e r e n t c o u n t r i e s are e i t h e r ze ro or approx imate l y $.02 per pound. U.S. t a r i f f on Canadian p roduc t s v a r i e s from ze ro to 10% of the p r i c e per pound. But f o r the two important c a t e g o r i e s of l i v e an ima ls and d r e s sed beef and v e a l , the t a r i f f i s $.01 and $.02 per pound r e s p e c t i v e l y . Canada produces approx imate l y 10% of t o t a l Nor th American beef o u t p u t . Because of the s i z e and p r o x i m i t y of the U.S. market and the v i r t u a l f r e e t rade in beef c a t t l e between the two c o u n t r i e s , Canadian beef p r i c e s are c l o s e l y r e l a t e d to U.S. beef p r i c e s . F i g u r e 2.1 i l l u s t r a t e s t h i s r e l a t i o n s h i p w i th q u a r t e r l y c h o i c e s t ee r p r i c e s in Canadian funds , in Ca lga r y and Omaha, f o r the p e r i o d 1977 to 1982. I f . changes in supp ly or demand c o n d i t i o n s fo r beef in Canada r e s u l t in Canadian p r i c e s becoming s i g n i f i c a n t l y h ighe r than U.S. beef p r i c e s , a r b i t r a g e w i l l r e s u l t in U.S. c a t t l e e n t e r i n g the Canadian market and consequen t l y d e c r e a s i n g Canadian beef p r i c e s . One would expect tha t U.S. c a t t l e would be imported to Canada i f the Canadian beef p r i c e i s g r ea t e r than the U.S. p r i c e p l u s t r a n s p o r t a t i o n c o s t s to Canadian markets p l u s t r a n s a c t i o n c o s t s , which i n c l u d e a sma l l import t a r i f f . The r e l a t i o n s h i p between p r i c e v a r i a t i o n s and shipments of c a t t l e between Canada and the U.S. can be r ep resen ted in a s imple d i ag r am. * In F i gu re 2 .2 , DD' r ep resen t s the . Canadian 20 TABLE 2.4 Canadian T a r i f f S t r u c t u r e fo r D i f f e r e n t C a t e g o r i e s of An imals and Meat P roducts Commodity B r i t i s h A u s t r a l i a M . F .N . * U.S. T a r i f f on New Zea land U.S. Candian Goods B reed ing An imals F ree Free Free Free L i v e C a t t l e ( exc ludes d a i r y cows) Free Free $ .01/ lb $.01/Ib Beef and V e a l F r e sh and F rozen $ .02/ lb $ .02/ lb $ .02/ lb Prime or Cho ice Prepared f o r R e t a i l $ .02/ lb $ .02/ lb $ .02/ lb $ .02/ lb 4.0% Beef P repared and P rese r ved Free Free $ .01/ lb $.02 or 10.0%** Beef Canned 15.0% Free 15.0% 3.0% Beef S a l t e d in B a r r e l s Free Free Free $.022 or 10 .0%*** C a t t l e H ides Free Free Free Free * Most F a v o r i t e Na t ion * * $ .02/ lb when p r i c e i s $ .30/ lb or l e s s ; 10.0% when p r i c e i s over $ . 3 0 / l b . * * * $ .022/ lb when p r i c e i s $ .30/ lb or l e s s ; 10.0% when p r i c e i s over $ . 3 0 / l b . Sou r ce : A g r i c u l t u r e Canada, L i v e s t o c k Market Review, Ottawa, Queen 's P r i n t e r , 1982. 21 FIGURE 2.1 Choice Steer Prices, in Canadian Funds, Calgary and Omaha $/CWT 90.0 85.0 80.0 75.0 70.0 65.0 60.0 55.0 50.0 45.0 40.0 35.0 Omaha Calgary 1977 1978 1979 1980 1981 1982 Source: Agriculture Canada, Canadian Livestock and Meat Trade Report, Ottawa, Queen's Printer, annual. 22 domest ic demand f u n c t i o n fo r beef p r o d u c t s . The import c e i l i n g p r i c e (P 1 ) r ep re sen t s the p r i c e of beef p roduc t s i n the U.S. p l u s t r a n s p o r t a t i o n c o s t s to Canadian markets p l u s a sma l l import d u t y . The expor t f l o o r p r i c e (P E ) r ep resen t s the p r i c e of beef p roduc t s in the U.S. l e s s t r a n s p o r t a t i o n c o s t s to U.S. markets l e s s U.S. import du t y . P' and P E r ep resen t the range in which the Canadian p r i c e w i l l change r e l a t i v e to tha t of the U.S. beef p r i c e . The l a rge s i z e of the U.S. market r e l a t i v e to the Canadian market has a number of important i m p l i c a t i o n s for the shape of the t o t a l demand curve f a c i n g Canadian c a t t l e p r o d u c e r s . If Canadian p r i c e s vary w i t h i n the range P ' to P E , the r e l e v a n t demand curve i s domest ic demand. I f Canadian p r i c e s f a l l below P E , then Canadian beef becomes c o m p e t i t i v e in U.S. markets and the r e l e v a n t demand curve fo r Canadian p roduce rs i s the domest ic demand p l u s U.S. demand fo r Canadian bee f . T h i s demand i s drawn as h o r i z o n t a l at p r i c e P E (segment CE) to i n d i c a t e the assumpt ion tha t Canadian expor t s to the U.S. w i l l not a f f e c t U.S. beef p r i c e s . On the o ther hand, i f Canadian p r i c e s r i s e above p r i c e P 1 , U.S. beef becomes c o m p e t i t i v e on Canadian marke ts . A r e d u c t i o n in Canadian beef supp ly below Oq would r e s u l t in U.S. beef e n t e r i n g the Canadian market and p r i c e s be ing reduced to P 1 . Consequen t l y , the r e l e v a n t demand curve f o r Canadian p roduce rs i s h o r i z o n t a l at p r i c e P 1 (segment AB) . T h e r e f o r e , the demand curve f a c i n g Canadian beef p roducers i s r ep resen ted as ABCE in F i gu re 2.2. T h i s d iagram has three important i m p l i c a t i o n s f o r t h i s s tudy . F i r s t , on l y v a r i a t i o n s w i t h i n a c e r t a i n output range P r i c e 23 FIGURE 2.2 Aggregate Demand F a c i n g Canadian C a t t l e P roducers Import C e i l i n g Quantity 24 in the q u a n t i t y of beef s u p p l i e d by Canadian p roduce rs w i l l a l t e r the p r i c e of beef in Canada. O the rw i se , changes in output supp ly have no e f f e c t on beef p r i c e s . Second, s i n c e Canadian beef p r i c e s are not the p r i c e s at wh ich 'Canad ian demand and supp ly are e q u a l i z e d but are l a r g e l y determined exogenous ly by the U.S. market , demand and supp ly f u n c t i o n s are independent f u n c t i o n s and may be es t ima ted s e p a r a t e l y . F i n a l l y , because one can t r e a t Canadian beef p r i c e s as p r ede t e rm ined , such p r i c e s can be assumed to be exogenous not on l y at the farm l e v e l but a l s o exogenous at the Canadian i n d u s t r y l e v e l . T h i s s i m p l i f i e s the econometr ic model . One d i s t i n c t i v e f e a t u r e of the c a t t l e i n d u s t r y i s l a r g e v a r i a t i o n s over time i n c a t t l e p r o d u c t i o n . T h i s has become known as the "beef c y c l e " . The beef c y c l e i s r ep resen ted in F i g u r e 2.3 by the i n v e n t o r i e s of cows and h e i f e r s on farms in Canada fo r the p e r i o d 1950-82. Female i n v e n t o r i e s were at a c y c l i c a l low po in t in 1950 (the p r e v i o u s peak was 1945): they reached a peak in 1965, a r e l a t i v e low p o i n t i n 1 9 6 8 , and aga in peaked in 1975. Inc luded in F i g u r e 2.3 i s a curve r e p r e s e n t i n g the r a t i o of cho i ce s t e e r p r i c e s to the p r i c e of f eed b a r l e y over the p e r i o d 1950-82. G e n e r a l l y , the p r i c e r a t i o i s the r e c i p r o c a l of i n ven to r y movements, but p r i c e s precede the t u r n i n g p o i n t s of i n v e n t o r i e s by s e v e r a l y e a r s . The response l ag of i n v e n t o r i e s f o l l o w i n g changes in p r i c e s r e f l e c t s the b i o l o g i c a l l a g between when cow-ca l f farmers make p r o d u c t i o n p l ans and when such p l ans are r e f l e c t e d in herd s i z e . A b e t t e r d e s c r i p t i o n of the beef c y c l e i s ga ined from N u m b e r o f A n i m a l s ( , 0 0 0 ) F i g u r e 2 . 3 I n v e n t o r i e s o f B e e f Cows a n d H e i f e r s o n F a r m s , C a n a d a 6 , 6 0 0 . 0 6 , 2 0 0 . 0 _ 5 , 8 0 0 . 0 _ 5 , 4 0 0 . 0 5 , 0 0 0 . 0 4 , 6 0 0 . 0 4 , 2 0 0 . 0 _ 3 , 8 0 0 . 0 3 , 4 0 0 . 0 _ 3 , 0 0 0 . 0 _ 2 , 6 0 0 . 0 _ 2 , 2 0 0 . 0 _ 1 , 8 0 0 . 0 _ 1 , 4 0 0 . 0 _ P r i c e o f S t e e r s P r i c e o f B a r l e y 5 0 . 0 S t a t i s t i c s C a n a d a , L i v e s t o c k a n d A n i m a l P r o d u c t S t a t i s t i c s , C a t . N o . 2 3 - 2 0 3 , O t t a w a , Q u e e n ' s P r i n t e r , a n n u a l . S t a t i s t i c s C a n a d a , H a n d b o o k o f A g r i c u l t u r a l S t a t i s t i c s , C a t . N o . 2 1 - 5 1 6 , P a r t 1 , O t t a w a , Q u e e n ' s P r i n t e r , a n n u a l . 26 examining changes in female i n v e n t o r i e s in the beef herds in western Canada compared to herds i n eas te rn Canada. F i g u r e 2.4 shows changes in female i n v e n t o r i e s fo r the two r eg ions f o r the p e r i o d 1950-1982. A l though there are some c y c l i c a l t r ends in the eas te rn beef h e r d , the more pronounced v a r i a t i o n s occur in the western h e r d . T h i s r e f l e c t s the f a c t tha t 80 pe rcen t of the Canadian beef b r eed ing herd i s in western Canada. Consequen t l y , changes in Canadian beef p r o d u c t i o n are due p r i m a r i l y to i n ven to r y changes in the beef herd in western C a n a d a . 5 To ga in some i n s i g h t i n t o the causes of the beef c y c l e , c o n s i d e r F i g u r e 2.5 which i l l u s t r a t e s s t e e r and female s l augh te r f o r the p e r i o d 1960-82. S teer s l a u g h t e r i s more s t a b l e than female s l a u g h t e r . T h i s i n d i c a t e s tha t as the herd expanded (say between 1970 and 1975), female an ima ls were h e l d back from the market and r e t a i n e d in the b reed ing herd to produce new an ima l s . Consequen t l y , du r i ng t h i s p e r i o d of the c y c l e , female s l augh te r i s l e s s than s t e e r s l a u g h t e r . However, the d e c l i n e in the herd a f t e r 1975 c o i n c i d e s w i th farmers r educ ing t h e i r b reed ing herds ( c u l l i n g cows and s l a u g h t e r i n g h e i f e r s ) r e s u l t i n g i n a l a rge female s l a u g h t e r . The p o s i t i o n of the beef i n d u s t r y a l ong a c y c l e can g e n e r a l l y be i d e n t i f i e d by the s l a u g h t e r of females as a r a t i o of s t ee r s l a u g h t e r . F i g u r e 2.6 shows t h i s r a t i o f o r the p e r i o d 1960-82. Dur ing an expans ionary phase of the c y c l e , f o r example between 1970 and 1975, female s l a u g h t e r i s s i g n i f i c a n t l y l e s s than s t e e r s l augh te r whereas d u r i n g a c o n t r a c t i o n a r y phase of the c y c l e , a f t e r 1975, female Figure 2.4 Number of Animals (,000) Inventories of Cows and Heifers on Farms, Western and Eastern Canada 4,500.0 _ 4,000.0 _ 3,500.0 _ 3,000.0 _ 2,500.0 _ 2,00O.O_ 1,500.0 _ 1,00 O.c? Western Canada 1,200.0 1,000.0 800.0 600.0 400.0 200.0 1950 1960 1970 1980 Source: Statistics Canada, Livestock and Animal Product Statistics, Cat. No. 23-203, Ottawa, Queen's Printer, annual. N u m b e r o f A n i m a l s ( , 0 0 0 ) 1 , 9 0 0 . 0 1 , 8 0 0 . 0 1 , 7 0 0 . 0 1 , 6 0 0 . 0 1 , 5 0 0 . 0 1 , 4 0 0 . 0 1 , 3 0 0 . 0 1 , 2 0 0 . 0 1 , 1 0 0 . 0 1 , 0 0 0 . 0 9 0 0 . 0 F i g u r e 2 . 5 S t e e r a n d F e m a l e S l a u g h t e r , C a n a d a 1960 1 9 7 0 1 9 8 0 S o u r c e : S t a t i s t i c s C a n a d a , L i v e s t o c k a n d A n i m a l P r o d u c t S t a t i s t i c s , C a t . N o . 2 3 - 2 0 3 , O t t a w a , Q u e e n ' s P r i n t e r , a n n u a l . F i g u r e 2 . 6 S o u r c e : S t a t i s t i c s C a n a d a , L i v e s t o c k a n d A n i m a l P r o d u c t S t a t i s t i c s , C a t . N o . 2 3 - 2 0 3 , O t t a w a , Q u e e n ' s P r i n t e r , a n n u a l . 30 s l a u g h t e r i s s i g n i f i c a n t l y g r ea t e r than s t ee r s l a u g h t e r . A r a t i o of female to s t ee r s l a u g h t e r of l e s s than one i n d i c a t e s an expans ionary phase . C o n v e r s e l y , a r a t i o of more than one i n d i c a t e s a c o n t r a c t i o n a r y phase . Both F i g u r e 2.5 and 2.6 suggest tha t there i s a s i g n i f i c a n t r e l a t i o n s h i p between the beef c y c l e and the s l a u g h t e r or r e t e n t i o n of female a n i m a l s . M a r s h a l l (1964) d e s c r i b e s t h i s r e l a t i o n s h i p as f o l l o w s : "When the p r i c e of c a t t l e i s h i g h r e l a t i v e to o ther p r o d u c t i o n p o s s i b i l i t i e s the tendency i s to h o l d back cows and h e i f e r s fo r b r e e d i n g . I n ven to r i e s are thus augumented, market ings reduced and p r i c e s s t r e n g t h e n e d . As i n ven to r y numbers b u i l d up and the progeny of i n c r e a s e d cow numbers reach market weight market ings i n c r e a s e . E v e n t u a l l y i n c r e a s e d market ings reduce p r i c e s to a po in t that d i s c o u r a g e s f u r t h e r expans ion and e v e n t u a l l y some l i q u i d a t i o n of i n v e n t o r i e s takes p l a c e . The f o l l o w i n g d e c l i n e in market ings r e s u l t s , in p r i c e s i n c r e a s i n g and the beg inn ing of a new c y c l e . " C a t t l e p roducers have always had to ad ju s t and respond to the beef c y c l e as pa r t of the b i o l o g i c a l and economic environment in which they o p e r a t e . The remainder of t h i s chap te r w i l l be an examinat ion of the economic o p t i o n s and d e c i s i o n s faced by cow-cal f p roduce rs and p r e v i o u s t h e o r e t i c a l a t tempts to model t h i s b e h a v i o r . 2.3 ALTERNATIVE PRODUCTION STRATEGIES AVAILABLE TO COW-CALF PRODUCERS The cow-ca l f farmer i s engaged i n the pr imary a c t i v i t y of r ep roduc ing an ima ls and s e l l i n g the progeny . A secondary a c t i v i t y i s the s e l l i n g of c u l l cows (and b u l l s ) . These a c t i v i t i e s are d i s t i n c t from the s p e c i a l i z e d feeder ope ra to r 31 whose pr imary r o l e i s the p r o d u c t i o n of f i n i s h e d bee f . The b a s i c d e c i s i o n of the cow-cal f farmer i s whether to s e l l a c a l f now or feed to heav i e r weights be fo re s e l l i n g . T h i s d e c i s i o n w i l l depend on the p r e v a i l i n g and expected economic c o n d i t i o n s : the p r i c e of an ima ls at d i f f e r e n t we igh ts ; the a v a i l a b i l i t y of pas tu re and i t s q u a l i t y ; the p r i c e of a s s o c i a t e d i n p u t s ; and the o p p o r t u n i t y c o s t of the fa rmer . At any p o i n t in t ime , t h e r e f o r e , i t i s l i k e l y tha t a cow-cal f farmer w i l l have a v a r i e t y of an imals in h i s herd ( e g . , b u l l s , cows, s t e e r s , h e i f e r s , c a l v e s ) at d i f f e r e n t weights and ages . In managing the h e r d , the cow-cal f farmer i s f aced wi th th ree major d e c i s i o n s (Yver 1971): a) de t e rm in ing op t ima l herd s i z e (and a s s o c i a t e d op t ima l input l e v e l s ) ; b) de te rm in ing the op t ima l numbers of d i f f e r e n t types of an ima ls in the h e r d ; and c) de te rm in ing whether an an imal shou ld be s o l d or r e t a i n e d in the herd fo r the purpose of p roduc ing more a n i m a l s . The f i r s t and t h i r d d e c i s i o n s are t y p i c a l p r o d u c t i o n d e c i s i o n s ( i . e . , de t e rm in ing the s i z e of p l a n t and output r a te ) whi le the second i s b a s i c a l l y a p o r t f o l i o d e c i s i o n . F i g u r e 2.7 he lp s to d e s c r i b e the economic o p t i o n s a v a i l a b l e to the cow-cal f p r o d u c e r . The focus of a cow-ca l f f a r m e r ' s management d e c i s i o n s i s the r e p r o d u c t i v e herd which i n c l u d e s b u l l s , cows, and h e i f e r s . 6 The number of c a l v e s produced in any one year depends on the number of cows and h e i f e r s bred n ine months e a r l i e r . A s u c c e s s f u l c a l v i n g r a te of 85% i s c o n s i d e r e d ave rage . G e n e r a l l y , because of Canadian weather c o n d i t i o n s , c a l v i n g i s t imed to take p l a ce in the F i g u r e 2 . 7 F l o w D i a g r a m o f C a t t l e P r o d u c t i o n D e c i s i o n s C u l l B u l l s S e l l C a l v e s ( 3 0 0 - 5 0 0 l b s . ) R e p r o d u c t i v e H e r d > C a l v e s C u l l Cows R e t a i n F e m a l e C a l v e s B r e e d i n g H e r d M a i n t a i n C a l v e s , S e l l Y e a r l i n g s ( 5 0 0 - 6 5 0 l b s . ) M a i n t a i n Y e a r l i n g s , S e l l L o n g Y e a r l i n g s ( 6 5 0 - 7 5 0 l b s . ) R e t a i n M a l e C a l v e s B u l l s B r e e d i n g H e r d > S t e e r s M a i n t a i n C a l v e s , S e l l Y e a r l i n g s ( 6 0 0 - 7 5 0 l b s . ) M a i n t a i n Y e a r l i n g s , S e l l L o n g Y e a r l i n g s ( 7 5 0 - 9 0 0 l b s . ) 33 early spring. The new calves can be sold to feedlots in the f a l l of the year in which they are born or retained in the herd over the winter. The cow-calf farmer has available a number of production alternatives for the retained calves. Bull calves can be retained for breeding within the reproductive herd or they can become steers. Steers can be sold to feedlots as yearlings at approximately 600-750 pounds or maintained on pasture and sold as long yearlings at approximately 750-900 pounds. (Feedlots s e l l finished steers at approximately 1000-1100 pounds). Female calves can be kept as replacement heifers or sold to feedlots. Heifers can be sold as yearlings at approximately 500-650 pounds or maintained on pasture and sold as long yearlings at approximately 650-750 pounds. (Feedlots s e l l finished heifers at approximately 850-950 pounds). Of course, the decision on whether to use a heifer as a replacement can be made up to the time the animal is sold. In the case of steers, the decision of the farmer is quite straightforward: he must decide on the optimal weight and time to s e l l the animal. In the case of bul ls , cows, and heifers, the decision is more complicated. He must decide whether to s e l l the animal, retain i t for further fattening (heifers), or incorporate i t into the breeding herd for producing calves. A number of economic studies have attempted to model the economic options available to cow-calf producers. The next section w i l l examine two important contributions in this area. 34 2.4 EXISTING THEORETICAL MODELS OF THE COW-CALF INDUSTRY There. have been a number o£ important t h e o r e t i c a l a t tempts to model the c h a r a c t e r i s t i c s of the cow-cal f i n d u s t r y . J a r v i s (1968) and Yver (1971) use a b a s i c c a p i t a l -t h e o r e t i c approach to model t h i s i n d u s t r y . The emphasis of t h e i r models i s the p o s s i b l e e x i s t e n c e of nega t i ve shor t run supply e l a s t i c i t i e s . Ca rva lho (1972) on the o ther hand, i s i n t e r e s t e d in c a p t u r i n g the dynamic c h a r a c t e r i s t i c s of the cow-cal f i n d u s t r y by us ing dynamic programming t e c h n i q u e s . In a d d i t i o n , Ca r va lho combines t h i s approach w i th time s e r i e s a n a l y s i s to i n c o r p o r a t e p r i c e e x p e c t a t i o n s i n t o the model . Because many e x i s t i n g e m p i r i c a l s t u d i e s of the c a t t l e i n d u s t r y are based e i t h e r on the J a r v i s and Yver models or on the Ca rva lho model , t h e i r main r e s u l t s are summarized below. The Yver model , a l t hough s i m i l a r to the J a r v i s model , i s l e s s comp l i c a t ed and i s d i s c u s s e d in p l a ce of the J a r v i s m o d e l . 7 Yver d e f i n e s the problem faced by the c a t t l e producer as one of de te rm in ing the q u a n t i t y of feed inpu ts used and the time of s a l e of the a n i m a l . T h i s problem i s e q u i v a l e n t to the max imiza t ion of the present net d i s c o u n t e d va lue of the an ima l a t b i r t h . For s t e e r s t h i s problem can be r ep resen ted as f o l l o w s . tm I2**' Vm(0) = qW(tm)e~ r t m - p/ f ( x ) e ~ r x dx, 0 where Vm(0) i s the d i s coun ted va lue at b i r t h , q and p are r e s p e c t i v e l y the p r i c e of beef and feed per un i t of we ight , W i s the weight of the a n i m a l , tm i s the s l a u g h t e r age , f (x ) i s the feed input at any po in t in t ime , and r i s the i n t e r e s t 35 rate. The f i r s t term on the right hand side of (2 .1) is the total revenue from the sale of the animal at age tin discounted to the present. The model assumes that the farmer knows the price of beef (q) with certainty. The second term on the right hand side represents the cost of feeding the animal over i t s l i fet ime, discounted to the present. The model assumes that the price of feed is constant over the lifetime of the animal. If one assumes that the animal is fed optimally throughout i ts l i fet ime, the f i r s t order condition for the maximization of Vm(0) requires that: (2 .2 ) 3Vm(0) •T " e " r t m [qW (tm)-rqW(tm)-pf(tm)] = 0. Equation (2 .2) indicates that a steer w i l l be slaughtered when the percentage increase in its weight equals the rate of interest plus feed costs per dol lar ' s worth of animal, or (2 .3 ) 9w(tm) 1 = r+pf(tm). 9t W(tm) qW(tm) The second order condition for the maximization of Vm(0) i s : (2 .4 ) 3tm^ 9Vm(0) - e~ r t m[qW f ,(tm) - rqW (tm) -pf'(tm)] < 0. At slaughter age tm , it is l i k e l y that both the weight W(tm) of the steer and feed intake f(tm) w i l l be increasing (W'(tm), f'(tm) > 0) . Therefore, in order to satisfy ( 2 . 4 ) , i t is sufficient that the steer be increasing in weight at a decreasing rate at slaughter age tm ( i . e . , W'(tm) < 0). 36 Yver considers the effect of changes in beef and feed prices on the optimal slaughter age of steers. Using Equation (2.2) and the implicit function theorem, he is able to show that (2.5) dtm = -pf(tm) (ding - dlnp) , [qW'(tm) - rqW'(tm) - pf'(tm)] where the denominator is negative from the second order condition ( 2 . 4 ) . In Equation ( 2 . 5 ) , pf(tm) represents feed costs at slaughter age tm and is posit ive. Furthermore, the negative sign on the right hand side is cancelled by the negative sign of the denominator. Therefore, this equation indicates that an increase in beef prices or a decline in feed costs w i l l increase the optimal slaughter age of a steer. Consequently, this result demonstrates that a negative supply response is expected in the short r u n . 8 This model can be extended to represent female animals by taking into account the female animals' additional output in the form of calves in the discounted value function. After accounting for this additional factor, Yver is again able to show a negative supply response in the short run for female animals. In addition, Yver reaches a number of conclusions with regard to changes in the capital price of cattle and changes in beef and feed prices. The algebra used in generating these conclusions is tedious and w i l l not be presented here. However, the conclusions can be summarized as follows: 1 ) The e las t ic i ty of capital price with respect to beef 37 p r i c e i s : i ) p o s i t i v e and h i ghes t at b i r t h , d e c l i n i n g m o n o t o n i c a l l y towards u n i t y as the an imal approaches the optimum s l a u g h t e r age ; i i ) l a r g e r f o r females than fo r male a n i m a l s . 2) The e l a s t i c i t y of c a p i t a l p r i c e wi th r espec t to feed p r i c e i s : i ) nega t i ve and l a r g e s t in abso lu t e va lue at b i r t h , d e c l i n i n g m o n o t o n i c a l l y toward ze ro as the an imal approaches the optimum s l a u g h t e r age ; i i ) l a r g e r in abso lu t e va lue fo r female than f o r male a n i m a l s . 3) An i n c r ease in beef p r i c e or a d e c l i n e in feed p r i c e w i l l i n c r ease the optimum s l a u g h t e r age of a l l an ima ls in the h e r d . To summarize, the Yver (and J a r v i s ) r e s u l t s i n d i c a t e that an i n c r ea se in the p r i c e of beef (expected to p e r s i s t i n t o the f u tu r e ) i n c r e a s e s the marg ina l va lue product of the a n i m a l , thereby i n c r e a s i n g the op t ima l s l a u g h t e r a g e . 9 Under these c o n d i t i o n s the c a t t l e producer w i l l f i n d i t p r o f i t a b l e to r e t a i n an ima ls in the herd tha t o therw ise may have been s o l d . For s t e e r s , t h i s i m p l i e s keeping the an ima l longer and f a t t e n i n g to heav i e r we igh t s . For h e i f e r s and cows, i t i m p l i e s e i t h e r f a t t e n i n g to heav i e r weights ( h e i f e r s ) or b reed ing , the an imals to ob t a i n c a l v e s . In the aggregate and in the shor t r u n , t h i s i n d i c a t e s that there w i l l be a decrease in the s l a u g h t e r of a l l a n i m a l s . In the long r un , the supp ly e l a s t i c i t i e s of beef w i l l be p o s i t i v e due to the i n c r ease in 38 herd s i z e and average we igh t s . The Yver and J a r v i s models were i n i t i a l a t tempts to model the c a t t l e i ndus t r y and to p r o v i d e some t h e o r e t i c a l j u s t i f i c a t i o n fo r the nega t i ve sho r t run supp ly e l a s t i c i t i e s ob ta ined i n past e m p i r i c a l work. These models focused p r i m a r i l y on the sho r t run behav io r i n the i n d u s t r y and d i d not account fo r a number of important f a c t o r s such as the dynamic nature of the i n d u s t r y and the importance of p r i c e e x p e c t a t i o n s in d e c i s i o n - m a k i n g . Ca r va lho (1972) a t tempted to i n c l u d e these two f a c t o r s in an economic model of the c a t t l e i n d u s t r y by a l l o w i n g a dynamic r e l a t i o n s h i p to be d e r i v e d from p r o f i t maximiz ing farmer b e h a v i o r . An econometr ic system of equa t ions i s ob ta ined as a s o l u t i o n to the max imiz ing p rob l em. In a d d i t i o n , he i n t r o d u c e d the n o t i o n of q u a s i - r a t i o n a l e x p e c t a t i o n s to account f o r f a rmers ' e x p e c t a t i o n s of p r i c e s . The C a r v a l h o 1 0 model assumes tha t the farmer i s a p r o f i t maximizer over a l l t ime p e r i o d s d u r i n g which he i s in o p e r a t i o n . The farmer opera tes h i s farm fo r m p e r i o d s and then r e t i r e s . At any p o i n t in t ime , the farmer i s n p e r i o d s from r e t i r i n g . The farm has th ree k inds of an imals a c c o r d i n g to age : I D j , an ima ls born in p e r i o d j which cannot be s o l d i n t h i s p e r i o d ; I 1 j , an imals l e s s than one year of age at the beg inn ing of p e r i o d j which can be s o l d at market p r i c e C J ; and an ima ls over one year of age i n p e r i o d j . In a d d i t i o n , a l l an ima ls can be d i v i d e d i n t o th ree c a t e g o r i e s : (1) an ima ls i n the b reed ing h e r d ; (2) feeder c a t t l e to be s o l d now or in the f u t u r e ; and (3) c a l v e s . 39 Carva lho assumes that the p r o f i t s generated over the t o t a l time the farm i s in o p e r a t i o n can be approx imated , in p e r i o d n, by a q u a d r a t i c f u n c t i o n a s : V ( S n , £ . n , V n , C n | K n , F n , I n , n ) = q n V n + P n S n +c n C n - . 5a (K n + & n - v" n ) 2 - . 5 b ( K n - V n ) 2 - . 5 d ( l 0 n ) 2 - . 5 f ( F n + I i n - & n - C n - S n ) 2 - . 5 g ( F n - S n ) 2 + a E n [ V ( S n _ 1 , V n M , C n _ , | K n . , . F n _ , , I n - , , n-1)] f sub jec t to the f o l l o w i n g i d e n t i t i e s : F n = F n + 1 + I n+1 _ £ <n+1 " C n + 1 ~ S n+ 1 ' K n = K n+1 + S ,n+1 " V n + 1 ' 1 On = ^ K n c a l v i n 9 r a t e ) , 1 In = X 0n+1 ' where: K n = number of an imals in the b reed ing h e r d , & n = new an imals added to the h e r d , V = an imals c u l l e d from the h e r d , n F „ = an imals on f e ed , S = number of feeder an ima ls s o l d , C n = number of c a l v e s s o l d fo r s l a u g h t e r , F j = number of feeder c a l v e s next p e r i o d (= F +1 -C -6 -S ), n n n n n q n = p r i c e of c u l l s , P n = p r i c e of f e e d e r s , c = p r i c e of c a l v e s , n V ( . ) i s the expected p resen t va lue of p r o f i t s when there are n p e r i o d s l e f t u n t i l r e t i r e m e n t , q V +P S +c C = t o t a l revenue, ^ n n n n n n .5a[K +& -V ] 2 = maintenance cos t of an ima ls kept in n n n s to ck , , 5 b [ K n - V n ] 2 = aging cost of animals kept in stock, 40 . 5 d [ I Q n 32 = cos t of p roduc ing c a l v e s , •5f(F +1 -& -C -S ) 2 = f eed ing c o s t fo r an ima ls on f e e d , n In n n n . 5 g ( F n - S n ) 2 = ag ing c o s t of an imals on f e e d , a = one p e r i o d d i s coun t r a t e , E = e x p e c t a t i o n opera to r at p e r i o d n, and n [ V ( . n _ i | . n _ i ] = va lue of next p e r i o d s p r o f i t s . Us ing a q u a d r a t i c f u n c t i o n ensures a maximum or minimum by the g l o b a l c o n v e x i t y or c o n c a v i t y of t h i s f u n c t i o n . As w e l l , the s i m p l i c i t y of the p r o f i t f u n c t i o n a l l ows s o l u t i o n by dynamic programming t e c h n i q u e s . Ca rva lho a l s o shows that t h i s f u n c t i o n s a t i s f i e s the c o n d i t i o n s fo r f i r s t - p e r i o d c e r t a i n t y e q u i v a l e n c e . The maximiz ing s o l u t i o n r e q u i r e s s o l v i n g the model in the l a s t year be fo re r e t i r e m e n t , t h e n , working backwards, s o l v i n g i t in each p e r i o d u n t i l the s o l u t i o n s conve rge . In t h i s manner the f o l l o w i n g gene ra l s o l u t i o n s are o b t a i n e d : s n = < i / g ) P n - ( i / g ) c n - ( i / g ) a 2 E n ( p n _ 2 ) + F n , &n = ( l / b ) g n - [ ( l / a + A 2 a d ) + ( l /b ) ] cn + ( l /a + A 2 a d ) a E n ( q n - i ) ( l / a + A 2 a d ) a 2 E n ( c n _ 2 ) + [ 1/a+A2a d) + 1/d) ] a 2 E n ( P n _ 2 ) , V n " d / b ) q n - ( l / b ) c n + K n , C n = [ d / a + A 2 a d ) + ( l/b) + ( l / f ) + ( 1 / g ) ] c n - ( l / g ) P n - ( 1 / b ) q n -(1/f ) a E n ( P n _ l ) - ( 1 / a + A 2 a d ) a E n ( q n _ l ) - ( l / a + X 2 a d ) a 2 E n ( c n _ 2 ) - [ ( l / a A 2 a d ) + ( l /b ) + ( l / f ) + ( 1/g)] a 2 E n ( p n - 2 ) + I l n -A number of fu tu re p r i c e s appear as exogenous v a r i a b l e s in the s o l u t i o n e q u a t i o n s . These p r i c e s are genera ted as c o n d i t i o n a l e x p e c t a t i o n s from past p r i c e s a c c o r d i n g to 41 e x p e c t a t i o n s formed by a q u a s i - r a t i o n a l e x p e c t a t i o n p rocess (Ner love 1972). G e n e r a l l y , q u a s i - r a t i o n a l e x p e c t a t i o n s imply tha t a n t i c i p a t e d va lues of v a r i a b l e s may be r e p l a c e d by t h e i r maximum-mean-square-error p r e d i c t i o n s . The s o l u t i o n equa t ions form the b a s i s of the econometr ic mode l . Ca r va lho p rov i des u s e f u l i n t e r p r e t a t i o n s of the c o e f f i -c i e n t s i n these s o l u t i o n equa t ions which are p e r t i n e n t to the study at hand. 1) S teer s a l e s w i l l i n c r ease i f the expected change in s t ee r p r i c e s i n c r e a s e s or i f there i s a l a rge number of young s t e e r s r each ing n ine months of age . 2) H e i f e r s a l e s w i l l i n c r ea se as the a c t u a l p r i c e of h e i f e r s i n c r e a s e s , p r o v i d e d t h i s i n c rease overwhelms the expec ted i n c r ease i n h e i f e r p r i c e s . 3) I f p r i c e e x p e c t a t i o n s f o r s t e e r s and h e i f e r s are h igh compared to a c t u a l p r i c e s , h e i f e r and s t e e r s a l e s w i l l d e c r e a s e . 4) Cow s a l e s w i l l i n c r e a s e as the p r i c e of cows i n c r e a s e s and t h e r e f o r e fewer h e i f e r s need to be s o l d f o r a g i ven t o t a l revenue. The c o n t r i b u t i o n of the Ca rva lho model i s t w o f o l d . F i r s t , one need not be s a t i s f i e d w i th s t a t i c models i n c o r p o r a t i n g some form of d i s t r i b u t e d l a g s t r u c t u r e to account f o r dynamic e lements . I n s t ead , the dynamics can be d e r i v e d from a p r o f i t maximiz ing model . Second, in c o n t r a s t to the Yver model , Ca r va lho i s ab l e to show that shor t run supp ly behav io r depends on p r i c e e x p e c t a t i o n s of c a t t l e p r o d u c e r s . There are however, two main d e f i c i e n c i e s i n the Ca r va lho mode l . F i r s t , i t c o n c e n t r a t e s on gene ra t i ng output supply and 42 i n ven to ry equa t i ons but i gnores the d e r i v e d demand by p roducers f o r a s s o c i a t e d i n p u t s . T h i s i s necessa ry due to the comp lex i t y of the p r ima l model used in the a n a l y s i s . Second, the importance of the e f f e c t of p r i c e e x p e c t a t i o n s on the shor t run supp ly response i s not deve loped in a r i g o r o u s t h e o r e t i c a l manner. Ra the r , i t i s determined ex p o s t , from the i n t e r p r e t a t i o n of the r e g r e s s i o n c o e f f i c i e n t s . In the next c h a p t e r , an attempt w i l l be made to overcome these problems by us ing the theory of d u a l i t y to model the cow-ca l f i n d u s t r y . 43 FOOTNOTES TO CHAPTER TWO 1 S t a t i s t i c s Canada , S e l e c t e d A q r i c u l t u r e S t a t i s t i c s Canada  and the P r o v i n c e s , Ottawa, 1983. 2 A l b e r t a A g r i c u l t u r e , The Beef Cow-Calf Manual , Edmonton, Agdex No. 420/10, 1976, p . 4 . 3 Canada ' s major t r a d i n g p a r t n e r s in beef and an imal p roduc t s are the U . S . , A u s t r a l i a , New Zea l and , and Eng l and . 4 See Ma r t i n (1981) . 5 Because of t h i s c h a r a c t e r i s t i c , one can cap tu re the e s s e n t i a l f e a t u r e s of the Canadian cow-cal f i n d u s t r y by a n a l y z i n g western Canadian cow-cal f p r o d u c t i o n . 6 A h e i f e r becomes a cow a f t e r i t s f i r s t c a l f i s b o r n . 7 The J a r v i s model a l l ows fo r the q u a n t i t y of i npu t s fed to the an imal to be an endogenous v a r i a b l e : o therw ise both models are i d e n t i c a l . 8 It shou ld be noted that Yver q u a l i f i e s these r e s u l t s and l i s t s a number of reasons why the e s t ima ted s i g n s of shor t run supp ly e l a s t i c i t e s may not be nega t i ve ( p r i c e e x p e c t a t i o n s of f a rmers , data p rob lems , and f a c t o r input c o n s t r a i n t s ) . 9 T h i s i s t rue on ly under c e r t a i n r e q u l a r i t y c o n d i t i o n s of the p r o d u c t i o n f u n c t i o n and i f the g rad ing system permi t s f l e x i b l e s l a u g h t e r we igh t s . 10 T h i s i s a s i m p l i f i e d v e r s i o n of the model e s t ima ted by Ca r va lho but i t does cap tu re the main c h a r a c t e r i t i e s of h i s mode l . See Ca rva lho (1972) or N e r l o v e , G r e t h e r , and Ca r va lho (1979) . 44 3. A THEORETICAL MODEL OF THE COW-CALF INDUSTRY 3.1 INTRODUCTION The purpose of t h i s chapte r i s to deve lop a t h e o r e t i c a l model which d e s c r i b e s the shor t run supply and d e r i v e d input demand behav io r of a r e p r e s e n t a t i v e cow-cal f p roduce r . An attempt i s made to extend e x i s t i n g t h e o r e t i c a l models by c o n c e n t r a t i n g on three a r e a s : 1) mode l l i ng both the output supp ly and input demand by cow-ca l f p roducers w i t h i n a m u l t i -o u t p u t , m u l t i - i n p u t p r o f i t f u n c t i o n ; 2) de te rm in ing the t h e o r e t i c a l i m p l i c a t i o n s of f a rmers ' p r i c e e x p e c t a t i o n s fo r shor t run supp ly b e h a v i o r ; and 3) a n a l y z i n g the model w i t h i n an i n t e r t e m p o r a l framework from which a t r a c t a b l e econometr ic model can be d e r i v e d . In the f i r s t s e c t i o n ( 3 . 2 ) , an i n i t i a l attempt w i l l be made to model cow-cal f f a rmers ' shor t run behav io r u s i n g a f a rm- l e ve l v a r i a b l e p r o f i t f u n c t i o n but assuming on l y a s i n g l e output p r o f i t f u n c t i o n . T h i s w i l l a l low the dynamic a spec t s of cow-ca l f p r o d u c t i o n to be emphasized and w i l l f a c i l i t a t e the subsequent development of a m u l t i - o u t p u t , m u l t i - i n p u t p r o f i t f u n c t i o n . In order to assume the e x i s t e n c e of an i n d u s t r y p r o f i t f u n c t i o n (which i s ob ta ined by agg rega t i ng from the farm l e v e l to the i n d u s t r y l e v e l ) two i s sues must be a d d r e s s e d : i ) agg rega t i on of i n p u t s ; and i i ) agg rega t i on a c ros s fa rms . S e c t i on (3.3) w i l l address input agg rega t i on by examining the importance artd i n p l i c a t i o n s of s e p a r a b i l i t y as a ma in ta ined h y p o t h e s i s . R e s t r i c t i o n s on the u n d e r l y i n g farm-l e v e l t e chno logy which r e s u l t from c o n s i s t e n t agg rega t i on from 45 the farm l e v e l to the r e p r e s e n t a t i v e (aggregate ) p roducer l e v e l w i l l be determined in S e c t i o n ( 3 . 4 ) . In S e c t i on ( 3 . 5 ) , a s i n g l e output p r o f i t f u n c t i o n fo r a r e p r e s e n t a t i v e cow-ca l f producer w i l l be p o s t u l a t e d . The i m p l i c a t i o n s fo r shor t run behav io r of changes in p r o d u c e r s ' p r i c e e x p e c t a t i o n s as we l l as o ther comparat ive s t a t i c s u s i ng t h i s r e p r e s e n t a t i v e p r o f i t f u n c t i o n w i l l be d e r i v e d in S e c t i o n ( 3 . 6 ) . In the f o l l o w i n g s e c t i o n ( 3 . 7 ) , the s i n g l e output r e p r e s e n t a t i v e p r o f i t f u n c t i o n w i l l be extended to accommodate the m u l t i - o u t p u t , m u l t i - i n p u t techno logy of the cow-ca l f i n d u s t r y . T h i s s e c t i o n a l s o i n c l u d e s a d e s c r i p t i o n of the r e s t r i c t i o n s imposed on the model due to the b i o l o g i c a l na ture of p r o d u c t i o n . A number of e l a s t i c i t y measurements a p p r o p r i a t e to the techno logy of cow-ca l f p roduc t i on w i l l be r epo r t ed in S e c t i o n ( 3 . 8 ) . F i n a l l y , a number of t e s t a b l e hypo theses , genera ted from r e s t r i c t i o n s on the t h e o r e t i c a l m u l t i - o u t p u t , m u l t i - i n p u t p r o f i t f u n c t i o n , w i l l be p o s i t e d i n S e c t i on ( 3 . 9 ) . 3.2 A SINGLE OUTPUT PROFIT FUNCTION FOR A COW-CALF PRODUCER Before d e s c r i b i n g the t h e o r e c t i c a l mode l , i t shou ld be emphasized that a number of c h a r a c t e r i s t i c s of the cow-ca l f i n d u s t r y w i l l impose dynamic r e s t r i c t i o n s on the model . The e x i s t e n c e of " second hand" markets ( auc t ion markets) f o r a l l c a t e g o r i e s of a n i m a l s , except b reed ing f ema les , i m p l i e s tha t at the farm l e v e l the stock of an ima l s can be i n c r e a s e d by n a t u r a l r e p r o d u c t i o n or by pu r chas ing a n i m a l s . 1 However, a t the i n d u s t r y l e v e l the aggregate herd can on l y be i n c r e a s e d by 46 natural reproduction. 2 These conditions impose a dynamic constraint at both the farm level (the number of replacement he i f e r s next period i s determined by the number of female animals bred t h i s period) and the industry l e v e l (next period's beginning stock of animals i s determined by the number of animals l e f t over at the end of the period). To account for these dynamic constraints in the the o r e c t i c a l model, one assumes that the objective of the cow-c a l f producer is to maximize expected p r o f i t s over a two-period planning horizon subject to the constraint that next period's beginning stock of animals i s decided t h i s period on the basis of expected price next period. Subsequently, the entire period in which the farmer is in business can be viewed as overlapping two-period planning horizons. The basic problem facing a cow-calf farmer i s to determine whether i t i s more pr o f i t a b l e to s e l l an animal t h i s period at known (certain) output price or retain the animal for sale in the future at an uncertain p r i c e . These simple dynamics are i l l u s t r a t e d in Fiqure 3.1. The farmer i s assumed to have a given stock of animals at the beginning of period zero ( C b ) . Moreover, the farmer knows o (with certainty) output price in period zero ( P Q ) and input prices in period zero (W Q). But in period zero, the farmer does not know output price in period one ( P ^ ) . Rather, in period zero, he forms some expectation of what output price w i l l be in period one (EgP-^) . 47 F i g u r e 3 .1 Dynamic Behav ior of a Cow-Calf producer TIME PERIOD 0 TIME PERIOD 1 o P W o o q C 6 o O q l c l Yo Y l 1 2 < „ _ _ The farmer combines the i n i t i a l s tock of an ima ls (C b ) o with a v e c to r of v a r i a b l e inputs ( q Q ) . Then , r espond ing to an economic environment w i th output p r i c e P Q , input p r i c e W , and h i s e x p e c t a t i o n s about p r i c e next p e r i o d , the farmer de te rmines the s tock of an imals r e t a i n e d at the end of the f i r s t p e r i o d ( C Q ) a n a " the output supply (Y ) d u r i n g p e r i o d zero (which i s d e f i n e d as the r e s i d u a l from the max imiza t ion p r o c e s s ) . I t i s important to note that end-o f-pe r i od s tocks are va lued at the expected output p r i c e p r e v a i l i n g next p e r i o d but tha t c u r r e n t output supply i s va lued at output p r i c e in p e r i o d z e r o . Given the f a r m e r ' s e x p e c t a t i o n of output p r i c e next p e r i o d ( E Q P ) , he may dec ide to purchase o ther an ima ls (C^) to augment end-o f-pe r i od s tocks (C^). T h i s w i l l determine b e g i n n i n g - o f - p e r i o d s tocks in p e r i o d one In p e r i o d one, the farmer combines beg inn ing s tock (C^) w i th a v e c to r of v a r i a b l e i npu ts (q^), w i th input p r i c e s ( W ^ ) , and, g i ven h i s e x p e c t a t i o n of p r i c e in the next p e r i o d ( E j ^ ) , he de te rmines the end of p e r i o d s tock of an ima ls (C e ) and the 1 q u a n t i t y of an imals s u p p l i e d d u r i n g p e r i o d one (Y-^) aga in as a r e s i d u a l of the max imiza t ion p r o c e s s . Note tha t output supp ly in p e r i o d one (Y^ ) i s aga in va lued at known output p r i c e ( P - ^ . Consequen t l y , the beg inn ing s tock of an ima ls in any p e r i o d i s j u s t the p r e v i ous p e r i o d ' s ending s tock of an imals 48 plus any animals purchased at the beginning of the next period Output supply in any period i s just the beginning-of-period stock of animals minus the end-of-period stock of animals or: The intertemporal problem faced by the farmer can be viewed as the maximization of each period's p r o f i t s , subject to price expectations and to the dynamic constraint. This simple model of dynamic behavior can be characterized using a discrete, two-period, variable p r o f i t function in the framework of Hicks (1946), Malinvaud (1953), Diewert (1972), and Diewert and Lewis (1981). Assume for t h i s i n i t i a l analysis that the farm's c a p i t a l stock consists only of cows and that breeding a cow th i s period gives r i s e to two cows next period. The output of the farm w i l l be a flow supply of beef. In addition, the following assumptions are employed in the model. i) The stock of animals i s quasi-fixed in the sense that the stock in any period is chosen before the output price of beef is observed (Hartman 1976). That i s , the farmer determines the stock of animals at the beginning of next period given today's expectation of output (beef) prices next •period. This assumption is not u n r e a l i s t i c in the c a t t l e industry given that a cow-calf farmer must decide on whether to breed a cow to obtain another animal in the future, based on his expectations of the p r e v a i l i n g price when the progeny is sold. 49 i i ) In any p e r i o d , v a r i a b l e i npu t s are chosen g iven complete knowledge of output p r i c e and input p r i c e s in that p e r i o d . T h i s assumpt ion a l l ows the farmer to ad jus t employment of v a r i a b l e i npu t s a f t e r output p r i c e s are known. Consequen t l y , v a r i a b l e -input usage can be a d j u s t e d to accommodate e r r o r s in s tock d e c i s i o n s (Hartman 1976). i i i ) V a r i a b l e input p r i c e s are known wi th c e r t a i n t y . i v ) The farmer i s a p r i c e taker in a l l output and input marke ts . v) There are no c o s t s to a d j u s t i n g the s tock of a n i m a l s . The dynamics of the model d e r i v e from the assumpt ion that the s tock of an ima ls i s de termined wi th r e spec t to expected fu tu re p r i c e ; they do not a r i s e from convex adjustment c o s t s . T h i s l a s t assumpt ion r e q u i r e s f u r t h e r comment. As a f i rm a l t e r s i t s c a p i t a l s tock i t may i ncu r a d d i t i o n a l c o s t s over and above the purchase p r i c e of the new c a p i t a l . These c o s t s of c a p i t a l s tock adjustment are based on the assumpt ion that the re are c o s t s a s s o c i a t e d wi th r e o r g a n i z a t i o n and r e t r a i n i n g w i th the adop t ion of new equipment ( N i c k e l l 1978, p . 2 5 ) . I t i s g e n e r a l l y assumed tha t these c o s t s i n c r ease at an i n c r e a s i n g r a te as the speed of adjustment i n c r e a s e s ( B r e c h l i n g 1975). In terms of c a t t l e p r o d u c t i o n , the assumpt ion of zero ad justment c o s t s at the farm l e v e l appears to be r a the r i nnocuous . The farmer can decrease or i n c r ease h i s c a t t l e he rd by t r a n s p o r t i n g an ima l s to and from the neares t a u c t i o n market . Because i t i s assumed that the c a t t l e producer i s a p r i c e t ake r i n a l l marke ts , he can a l t e r a s s o c i a t e d input 50 l e v e l s w i thout i n c u r r i n g a d d i t i o n a l c o s t s . At the i n d u s t r y l e v e l however, t h i s assumption i s l e s s t e n a b l e . At the i n d u s t r y l e v e l , the herd can expand on ly as f a s t as i t s r e p r o d u c t i v e p o t e n t i a l w i l l a l l o w . But as the i ndus t r y expands i t w i l l i n c r ease i t s demand fo r i n p u t s . If the i n d u s t r y i s not a p r i c e t aker in a l l input markets ( e . g . , l a n d ) , then as i ndus t r y demand f o r inputs i n c r e a s e s , some input p r i c e s w i l l i n c r e a s e . T h i s must t r a n s l a t e i n t o an adjustment c o s t a s s o c i a t e d wi th i n c r e a s i n g the s i z e of the aggregate herd ( N i c k e l l 1978, p . 3 5 ) . The i n t e r t e m p o r a l model deve loped in t h i s chapte r c o u l d be m o d i f i e d to handle adjustment c o s t s . However, because such c o s t s are not the pr imary focus of t h i s r e s e a r c h , i t w i l l be assumed tha t adjustment c o s t s are not a s i g n i f i c a n t f a c t o r at e i t h e r the farm or i n d u s t r y l e v e l s . M o d e l l i n g and e s t i m a t i o n of adjustment c o s t s w i l l be r e se r ved fo r another s tudy . F o l l o w i n g E p s t e i n (1977) and E p s t e i n and Denny (1980) , the t echno logy of the farm can be d e s c r i b e d by a concave p r o d u c t i o n f u n c t i o n f ( q , C b , C e ) = Y, where q i s a v e c to r of i n p u t s , C b i s b e g i n n i n g - o f - p e r i o d s tock of cows, C e i s end-of-p e r i o d s tock of cows, and Y i s the output of beef du r i ng that p e r i o d . The p r o d u c t i o n f u n c t i o n f ( . ) shows the t e c h n o l o g i c a l p o s s i b i l i t i e s a v a i l a b l e fo r combin ing the v e c to r of i nputs wi th the beg inn ing s tock of cows to determine end-o f-pe r i od s tocks and output supply of bee f . f i s s t r i c t l y i n c r e a s i n g in q and C b , i n d i c a t i n g that the marg ina l p roduc t s of i nputs and beg inn ing s tocks are s t r i c t l y p o s i t i v e , f i s d e c r e a s i n g in C e , i n d i c a t i n g tha t the more cows a v a i l a b l e at the end of the 51 period ( C e ) , the less output supplied (Y) during the period. At any point in time, current beef prices and factor prices are known but next period's beef prices are uncertain. The farmer i s assumed to have a subjective probability d i s t r i b u t i o n concerning these prices and to select a strategy to maximize the expected value of the discounted sum of anticipated p r o f i t s over a two-period future planning horizon (subject to the i n i t i a l stock of cows (C^), the animal accumulation equation, and his price expectations). At the farm l e v e l , the farmer can purchase cows (C^) to augment end-of-period stocks at price P t. However, i t w i l l be assumed that farmers only purchase animals at the beginning of each period. No animals are purchased in the f i r s t period (C^=0). These c h a r a c t e r i s t i c s can be described as: ( 3 . 1 ) Max E i - i - [P tf (q t,C b,C^) - - P ^ ] , e p (1+r) V C t , t j t s . t . c£ = ( l + X ) ^ + (1+X)CP, C b > 0, o C P = 0, o where: q t i s a vector of inputs chosen during period t given that the farmer knows with certainty current output and input prices; W i s a vector of factor input prices; is the end-of-period stock of animals and i s determined with respect to the farmer's expectation of beef prices next period; C p i s the number of cows purchased at the beginning of period t: i t i s determined according to the farmer's desired 52 fu tu r e l e v e l s of an imal s tocks sub jec t to e x p e c t a t i o n s of f u tu re p r o f i t s and beef p r i c e s ; i s the b e g i n n i n g - o f - p e r i o d stock of an imals and , except fo r p e r i o d ze ro in which s tock i s g i ven (CQ > 0 ) , the beg inn ing s tock of cows in p e r i o d t i s de termined in the b e n p r e v i o u s p e r i o d (t-1) by the formula C t = ( 1 ) C t - l + ( 1 + X)C% which takes account of the r e p r o d u c t i v e a b i l i t y (X) of cows to produce news cows, 0 £ X _< 1. T h i s formula i n d i c a t e s that the number of cows at the beg inn ing of any p e r i o d t i s equa l to the number of cows r e t a i n e d in the l a s t p e r i o d p lus the progeny of those cows p l u s any cows bought at the beg inn ing of the p e r i o d and t h e i r progeny ; P i s the p r i c e of beef per hundredweight ; P t i s the s tock p r i c e of a cow and i s not on l y a f u n c t i o n of beef p r i c e s but w i l l a l s o i n c l ude a component that r ep r e sen t s the a n i m a l ' s a b i l i t y to produce new a n i m a l s ; E i s the mathemat ica l e x p e c t a t i o n o p e r a t o r ; and r i s the d i s c o u n t r a t e , assumed cons tan t and known wi th c e r t a i n t y . A f t e r r e a r r a n g i n g the an imal accumula t ion c o n s t r a i n t as Ct = [ C b /(1+X)]-C^_1 and s u b s t i t u t i n g i n t o the max imiza t ion prob lem, Equa t ion (3.1) can be r e w r i t t e n a s : , W C t t = ° ( 1 + r ) OffA) The max imiza t ion problem in Equat ion (3.2) can be viewed as a two-stage o p t i m i z a t i o n p rocedu re . In the f i r s t s t age , the farmer views the number of cows a v a i l a b l e i n any p e r i o d as be ing f i x e d or p rede te rm ined . He must dec ide on the opt ima l 53 q u a n t i t y of i nputs to combine wi th the f i x e d s tock of cows from which he determines op t ima l i nven to ry c a r r y o v e r s (end-of-p e r i o d s tocks ) and c u r r e n t p e r i o d output as the r e s i d u a l . Opt ima l i n ven to r y c a r r y o v e r s are va lued by the farmer at the output p r i c e he expects to p r e v a i l next p e r i o d d i s c o u n t e d to the p resen t o r : z t = life)- V W In the second stage of the o p t i m i z a t i o n p rocedu re , the farmer de te rmines op t ima l beg inn ing s tocks fo r the next p e r i o d . T h i s w i l l i n v o l v e the purchase of an imals to augment e x i s t i n g s t o c k s . The f i r s t s tage in max imiz ing Equat ion (3.2) can be d e f i n e d as f o l l o w s : (3.3) " <P »W »Z ;cj) = Max e P f ( q ^ C ^ C * ) - w j ^ + ZfcC^ q ,C n (.) i s d e f i n e d as the v a r i a b l e p r o f i t f u n c t i o n dua l to f ( . ) . 3 Samuelson (1953-54) i n t r o d u c e d the concept of a v a r i a b l e p r o f i t f u n c t i o n wh i le Gorman (1968) and McFadden (1970) determined i t s p r o p e r t i e s . In o rder fo r there to e x i s t a dua l r e l a t i o n s h i p between the p r o d u c t i o n p o s s i b i l i t y se t and the v a r i a b l e p r o f i t f u n c t i o n , c e r t a i n r e g u l a r i t y c o n d i t i o n s must be s a t i s f i e d by each f u n c t i o n (Lau 1972, and Diewert 1973 and 1974) .* For ease in e x p o s i t i o n of the r e g u l a r i t y c o n d i t i o n s and f o r g r e a t e r g e n e r a l i t y , r e d e f i n e the p r o d u c t i o n p o s s i b i l i t y set as f o l l o w s : f ( Y , X ; v ) , where f ( . ) i s the p r o d u c t i o n p o s s i b i l i t y set and Y = ( Y I , . . . , Ym) i s an M-dimensional 54 v e c to r denot ing v a r i a b l e o u t p u t s . X = ( X I , . . . , Xn) i s an N-d imens iona l v ec to r deno t i ng v a r i a b l e i n p u t s , V = ( V 1 , . . . , Vj ) i s a J -d imens iona l v e c to r deno t ing the f i x e d i n p u t s , and z = (Y ,x ; v ) i s the M+N+J-dimensional v e c to r of a l l ou tputs and i n p u t s . The f o l l o w i n g assumpt ions are made on f : 5 f l ) f i s a c l o s e d non-empty subset of M+N+J-dimensional space , f2) f i s a convex s e t , f3) i f z ' e T , z " < z ' then z " e T , f4) i f ( Y , x ; v ) e f then the components of Y are bounded from above fo r v f i x e d . An economic i n t e r p r e t a t i o n of each assumpt ion i s p r o v i d e d by Diewert (1973 and 1974). C o n d i t i o n ( f l ) i s a mathemat ica l r e g u l a r i t y c o n d i t i o n , ( f2) i n d i c a t e s tha t the techno logy e x h i b i t s n o n - i n c r e a s i n g marg ina l r a t e s of t r a n s f o r m a t i o n , ( f3) i m p l i e s f r ee d i s p o s a l , and ( f4) i n d i c a t e s that a bounded v e c to r of i npu ts can produce on l y a bounded vec to r of o u t p u t s . C o n t i n u i n g wi th the above n o t a t i o n , i f the farmer f aces p o s i t i v e p r i c e s fo r the v a r i a b l e ou tputs p = ( p 1 r . . . , , p m ) , p o s i t i v e p r i c e s fo r the v a r i a b l e i npu ts w = ( w l r . . . ,w n ) , and the f i x e d inpu ts are f i x e d at v , the v a r i a b l e p r o f i t f u n c t i o n can be d e f i n e d a s : (3.4) n(P,W;V) = max [P TY - WTX: (Y,X;V)ef], P > > Om, W > > On. If f s a t i s f i e s c o n d i t i o n s ( f l ) to ( f4) and the v a r i a b l e p r o f i t f u n c t i o n s a t i s f i e s Equa t ion ( 3 . 4 ) , then Diewert (1973) has shown tha t n( . ) s a t i s f i e s the f o l l o w i n g c o n d i t i o n s : 55 111) n-(PfW,;v) i s a non-negat ive f u n c t i o n for p » 0 m , w » 0 n , and any v, 112) n ( . ) i s nondecreas ing in p, n3) n(«) i s n o n i n c r e a s i n g in w, Jl4) n ( . ) i s homogeneous of degree one in p and w, 115) n ( . ) i s convex in p and w, 116) n ( . ) i s concave in v fo r every f i x e d p and w. C o n d i t i o n 11(1) i s a r e g u l a r i t y c o n d i t i o n which i s c o n s i s t e n t w i th economic p r o f i t max im iza t i on , n( 2) i n d i c a t e s tha t i f p ' > p ' ' then n ( p ' , w ; v ) > n ( p ' ' , w ; v ) , n( 3) i n d i c a t e s tha t i f w '>w" then n(p,w' ;v) <n(p,w' ' ;v) , and n( 4) i n d i c a t e s tha t fo r every X>0, n(XPr Xw;v) = xn (p f w, ;v) . Moreover , f e x h i b i t s cons tan t r e tu rns to s c a l e i f and on ly i f II(.) i s homogeneous of degree one in v or X > 0, Il(p, w;Xv) = XII (p, w;v) . (JI5) and (II6) ensure tha t the p r o f i t f u n c t i o n i s we l l-behaved fo r sma l l changes in p r i c e s and that there e x i s t s a maximum fo r each g i ven vec to r of p r i c e s and f i x e d i n p u t s . Diewert ( 1973) proves that g iven any f u n c t i o n II s a t i s f y i n g c o n d i t i o n s (n i ) to (116), there e x i s t s a unique f s a t i s f y i n g c o n d i t i o n s ( f1) to ( f4) that genera tes n through Equa t ion ( 3 . 4 ) . Thus f and n a re e q u i v a l e n t r e p r e s e n t a t i o n s of t echno logy and t h e r e f o r e n may be used to c h a r a c t e r i z e the techno logy and t e s t f o r s t r u c t u r e . Re tu rn ing to the i n t e r t e m p o r a l problem of the c a t t l e p roduce r , the dua l r e l a t i o n s h i p d e f i n e d in Equa t ion (3.3) can be used to r ew r i t e Equat ion (3.2) a s : (3.5) Max E 1 Z t=o (1+r)t 1 [n(P t.w t ,z t ;cJ) - P t cJ ]. (l+X) 56 G e n e r a l l y , the i n t e r t e m p o r a l problem (3.5) i s so l ved fo r each p e r i o d but on ly the p lans fo r t=0 are c a r r i e d out because of e r r o r s in e x p e c t a t i o n s ( Eps te in and Denny 1980). Fu r the rmore , i f the v a r i a b l e p r o f i t f u n c t i o n d e f i n e d by Equat ion (3.3) s a t i s f i e s c o n d i t i o n s (ni ) to (116) and i s , in a d d i t i o n , d i f f e r e n t i a b l e wi th r e spec t to o u t p u t , i n p u t , and expected output p r i c e s , then Equa t ion (3.3) can be so l ved fo r the op t ima l q u a n t i t i e s of output s u p p l y , input demand, and end of p e r i o d i n v e n t o r i e s by a p p l y i n g H o t e l l i n g ' s Lemma ( H o t e l l i n g 1932). These op t ima l s o l u t i o n s are d e f i n e d a s : (3.6) * Y t = n p t(P t , w t , z t ; c b ) , * qt • - n W t(P t , w t , z t ; c b ) , <?• n z < P t ' W C t > » where n i denotes the p a r t i a l d i f f e r e n t a t i o n of Il(.) w i th respec t to p f c , wt., and r e s p e c t i v e l y . Y * t ' Q*£» a n ^ c t represen t the p r o f i t maximiz ing q u a n t i t i e s of output s u p p l y , input demand, and end-o f-pe r i od s tock demand r e s p e c t i v e l y , as f u n c t i o n s of the p r i c e s ( p t , w t , and z t ) and the l e v e l of the f i x e d f a c t o r C ^. Equa t ion (3.6) e x p l i c i t l y d e f i n e s the f i r s t s tage of the o p t i m i z i n g problem f a c i n g the fa rmer . In the second stage of the o p t i m i z a t i o n , the farmer has on ly to determine next p e r i o d ' s op t ima l beg inn ing s tock of cows. R e c a l l that beg inn ing an imal s tock in p e r i o d one i s chosen in p e r i o d ze ro to maximize the expected va lue of p r o f i t in p e r i o d one o r : < 3- 7) b b Eo[n(P 1,w 1Z1;cJ) - PjCj/d+A)]. 57 b* Next p e r i o d ' s op t ima l animal s tock i s determined by d i f f e r e n t i a t i n g Equa t ion ( 3 . 7 ) w i th r espec t to Cj and then s o l v i n g the f i r s t o rder c o n d i t i o n fo r Cj o r : ( 3 . 8 ) = En c b (P 1 ,W 1 , Z 1 ;C b * ) . ( l+X) . I t i s i n t e r e s t i n g to note that the p r o d u c t i o n f u n c t i o n i s homogeneous of degree one i f and on l y i f the v a r i a b l e p r o f i t f u n c t i o n can be w r i t t e n as C b n (p t ,w ,z ). T h e r e f o r e , i f there are cons tan t r e t u r n s to s c a l e in p r o d u c t i o n , i t i s c l e a r tha t C b in Equat ion ( 3 . 8 ) would v an i sh and consequen t l y C b i s not d e f i n e d . T h i s problem can be avo ided by assuming that the v a r i a b l e p r o f i t f u n c t i o n i s s t r i c t l y concave in the f i x e d i n p u t . An econometr ic model can be p o s t u l a t e d , u s i ng Equa t ions ( 3 . 6 ) and ( 3 . 8 ) , by s p e c i f y i n g a f u n c t i o n a l form fo r II( .) , de te rm in ing p r i c e e x p e c t a t i o n s of c a t t l e p r o d u c e r s , and s p e c i f y i n g the s t o c h a s t i c d i s t u r b a n c e s f o r each e q u a t i o n . However, as i s o f t en the c a s e , the data a v a i l a b l e fo r e s t i m a t i n g the econometr i c equa t i ons r e l a t e to aggregate v a r i a b l e s r a the r than farm l e v e l v a r i a b l e s . Rather than es t imate a farm l e v e l mode l , one must p o s t u l a t e the e x i s t e n c e of an aggregate " r e p r e s e n t a t i v e " fa rm. However, be fo re s p e c i f y i n g an aggregate p r o f i t f u n c t i o n , the r e s t r i c t i o n s imposed by agg rega t i on must be examined. 3.3 SEPARABILITY AS A MAINTAINED HYPOTHESIS In most s t u d i e s of aggregate t e c h n o l o g y , s e p a r a b i l i t y of the p r o f i t and p r o d u c t i o n f u n c t i o n s p l a y s a s i g n i f i c a n t r o l e . 58 S e p a r a b i l i t y i s p o s t u l a t e d to l e s sen econometr ic problems such as m u l t i c o l l i n e a r i t y and to f a c i l i t a t e e s t i m a t i o n . If s e p a r a b i l i t y can be assumed, aggregate commodit ies can be d e f i n e d , thereby reduc ing the i n f o rma t i on necessary to es t imate a g iven system of e q u a t i o n s . 6 Mic ro i npu ts can be aggregated i f the marg ina l r a t e of s u b s t i t u t i o n between any two inpu ts ( i , j ) i s e s s e n t i a l l y u n a f f e c t e d by the l e v e l of use of a t h i r d input (k ) . The mic ro p a i r ( i , j ) i s then separab le from k ( L eon t i e f 1947 ) . 7 F o r m a l l y , l e t f i r m Z have a p r o d u c t i o n f u n c t i o n ; (3.9) f z = f z ( X z , . . . , X Z ) and X z = (X z , . . . , X z ) , where f i s output and X i are micro i n p u t s . Next p a r t i t i o n X z i n t o n subgroups : ( 1 X Z , . . . , n X z ) , and p a r t i t i o n the p r i c e v e c to r c o r r e s p o n d i n g l y a s : (3.10) q = ( q i , . . . , qm) = ( i q , . . . , n q j . Equa t ion (3.9) can be r e w r i t t e n a s : (3.11) f z = f z ( 1 X z , . . . , n X z ) . Now l e t ty1, . . . be homogeneous q u a n t i t y aggrega to rs and Q 1 , . . . , Q n be homogeneous p r i c e aggrega to r s d e f i n e d over ( 1 X Z , . . . ^ X 2 ) and ( x q, . . . , n q ) r e s p e c t i v e l y . Then, the p r o d u c t i o n f u n c t i o n of f i r m Z can be w r i t t e n a s : (3.12) f z = f z ( V » 1 ( 1 X z ) f / ( n X z ) ) . S ince f i s i n c r e a s i n g in i t s arguments and each aggregator i • ~ z f u n c t i o n \p i s l i n e a r homogeneous, f i s h o m o t h e t i c a l l y sepa rab l e ( B l a cko rby , P r imont , and R u s s e l l 1978, Chapter T h r e e ) . The economic i m p l i c a t i o n of assuming h o m o t h e t i c a l l y sepa rab l e p r o d u c t i o n f u n c t i o n s i s : 59 f z / X X Z (—Z—i ~) = 0 i . J E X , re X , aV 3f Z /3 1X. Z r J That i s , the marg ina l r a te of s u b s t i t u t i o n between the i t h and j t h input in the 1th aggregator f u n c t i o n i s independent of the r t h input in the kth aggregator f u n c t i o n . It has been shown ( B l ackorby , P r imont , and R u s s e l l 1978 and B lackorby 1982) tha t t h i s t reatment of mic ro i npu ts i s c o n s i s t e n t w i th p r o f i t maximiz ing behav io r at the aggregate l e v e l i f and on ly i f the aggregate p r o f i t and p r o d u c t i o n f u n c t i o n s are sepa rab l e in the same a p p r o p r i a t e p a r t i t i o n of commodit ies and p r i c e s . 8 T h e r e f o r e , the p r o f i t f u n c t i o n wi th output p r i c e (P) and output q u a n t i t y (Y) can be w r i t t e n a s : (3.13) nZ(P,q) = max [ PY - qTXZ : f Z ( X Z ) > fo ] = nZ(P,Q1(1q) QVq)). 3.4 AGGREGATION OVER FARMS Aggregate p r o d u c t i o n f u n c t i o n s and t h e i r dua l p r o f i t f u n c t i o n s are t h e o r e t i c a l c o n s t r u c t s w ide ly used in a p p l i e d economic r e s e a r c h . However, these aggregate f u n c t i o n s are a p u r e l y f i c t i t i o u s concep t . A mic ro p r o d u c t i o n f u n c t i o n , because i t f u l l y d e s c r i b e s the t echno logy used by a fa rm, i s s i g n i f i c a n t l y d i f f e r e n t than i t s aggregate c o u n t e r p a r t . At the aggregate l e v e l , no one maximizes the p r o f i t of the i n d u s t r y or min imizes i t s c o s t . The supply of outputs and demand f o r i n p u t s , at the i n d u s t r y l e v e l , are d e r i v d from the 60 d e c i s i o n s of the v a r i o u s i n d i v i d u a l farms which are assumed to be p r o f i t max im ize r s . T h e r e f o r e , in what con tex t i s i t a p p r o p r i a t e to th ink of an "aggregate p r o d u c t i o n f u n c t i o n " as a complete r e p r e s e n t a t i o n of i n d i v i d u a l farm p r o d u c t i o n f u n c t i o n s ? Two types of agg rega t i on can be c o n s i d e r e d : i ) exact agg rega t i on and i i ) f i c t i t i o u s a g g r e g a t i o n . 9 Exact aggrega t ion (Gorman 1968, B l a c k o r b y , Pr imont and R u s s e l l 1978, and B lackorby and Schworm 1982a, 1982b, and 1983) i m p l i e s that one can p o s t u l a t e the e x i s t e n c e of a r e p r e s e n t a t i v e producer whose p r o f i t max imiz ing b e h a v i o r , w i th rega rd to output supp ly and input demand, i s i d e n t i c a l to the p r o f i t maximiz ing behav io r of a l l i n d i v i d u a l farms combined. Cons ide r an i n d u s t r y tha t c o n s i s t s of Z farms wi th t echno logy se t s f z . Each f z i s a f u n c t i o n of ( X z , K z ) where X z i s a N-dimensional v e c to r of outputs and inpu ts (outputs are de s i gna t ed by p o s i t i v e s i g n s , and inpu ts are des i gna t ed by nega t i v e s i gns ) and K z i s the f i x e d input v e c to r fo r each f i r m Z = 1 . . . z . Let P = ( P 1 , . . . , Pn) be the c o r r e s p o n d i n g p r i c e v e c t o r pa ramet r i c to a l l fa rms. At the micro l e v e l , each farm has a p r o d u c t i o n p o s s i b i l i t y set f z = f z ( X z , K z ) . , G iven tha t the r e g u l a r i t y c o n d i t i o n s are s a t i s f i e d , the techno logy can be d e s c r i b e d c o m p l e t e l y us ing a dua l p r o f i t f u n c t i o n : n Z(P,K Z) = max [PX/ (X,K) e f Z ] x where the op t ima l net output v e c to r i s d e f i n e d a s : ^ ! f ^ l = X Z i = l . . . n . 9 P i 1 61 The question of exact aggregation i s : what are the conditions imposed on individual farm technologies for which the following holds?: (3.14) IKP.KCK1 KZ)) = 1 nZ(P,KZ) = E m a X [PXZ/(XZ,KZ)efZ] , Z Z X Y - FY Z - 9n(p,K(.)), n(p,K(.)) = m * x tpx/(x,k) et] , given the vector of prices P, the vector of fixed factors ( K 1 , ...,KZ) and no external economies or diseconomies. The necessary and s u f f i c i e n t conditions under which (3.14) i s s a t i s f i e d were provided by Gorman (1968) (see Blackorby, Primont, and Russell 1978) where i t i s demonstrated that (3.14) holds i f and only i f a l l farms are i d e n t i c a l at the margin. This indicates that each farm must have a -quasi-homothetic production function ( i . e . , Gorman Polar Form (GPF)) with a p r o f i t function of the form: ( 3 . 1 5 ) nz(p,Kz) = n z(p)K z(K z) + n z o(p) Moreover, the aggregate p r o f i t function for the industry must be of the form: (3.16) n(p,k(io) = znz(p,Kz) = zn z(p)k z(k z) + zn z o(p). z z z Equations (3.15) and (3.16) indicate that each farm's p r o f i t function must be a f f i n e in the fixed factor and that a l l farms value an extra unit of the fixed factor equally ( i . e . , the shadow price of the fixed factor i s the same for a l l farms). F i n a l l y , the assumption that a l l farms are operating with constant returns to scale implies that the 62 f o l l o w i n g r e s t r i c t i o n s are imposed on (3.15) and (3.16) r e s p e c t i v e l y (Gorman 1968): n z o(p) - o and E n z o (P) = 0 . z The aggregate net output vec to r can now be w r i t t e n a s : n i7) Y — an(p,k(k)) _ Ek z (k z ) an 2(p) , z 9n z o(p), i = I ... N . * J' W ; Xi " 9 P ± " z 2 3 P i I t i s worthwhi le at t h i s po in t to emphasize an important r e s t r i c t i o n of the GPF. Because each farm must use the f i x e d f a c t o r e q u a l l y e f f i c i e n t l y , a r e d i s t r i b u t i o n of f i x e d f a c t o r s amongst the farms w i l l have a n e u t r a l e f f e c t on aggregate p r o f i t but w i l l change the net output v e c t o r s and the p r o f i t s earned by i n d i v i d u a l fa rms. What t h i s i m p l i e s i s that once an aggregate p r o f i t f u n c t i o n has been d e f i n e d a s : n(p,k) = JI(P)k(k) + n ° ( P ) , i t i s i n v a r i a n t to changes in the d i s t r i b u t i o n of the f i x e d f a c t o r s amongst i n d i v i d u a l farms and t h u s , i s comp le t e l y de t e rm ined . Of c o u r s e , n(P, K) i s on l y .an " e x a c t " r e p r e s e n t a t i o n of the aggregate t echno logy as long as the u n d e r l y i n g micro p r o f i t f u n c t i o n s , n z ( p f K ) rema in . Consequen t l y , assuming that a l l farms are i d e n t i c a l at the margin in t h e i r techno logy and that the parameters of H(p,K) can be i d e n t i f i e d , knowledge of aggregate data a lone i s s u f f i c i e n t to ob t a i n an exact c h a r a c t e r i z a t i o n of the mic ro p r o d u c t i o n p r o c e s s e s . I t i s c l e a r tha t the c o n d i t i o n s under which an exact aggregate can be ob ta ined are q u i t e r e s t r i c t i v e . 63 Consequen t l y , the very e x i s t e n c e of such an aggrega tor i s not at a l l c e r t a i n (Gorman 1968). In a s i t u a t i o n where the c o n d i t i o n s of p r o d u c t i o n d i f f e r s i g n i f i c a n t l y from farm to farm, the a b s t r a c t i o n of a r e p r e s e n t a t i v e producer l o s e s i t s meaning. In t h i s c a s e , on l y the knowledge of a l l d e t a i l s p e r t a i n i n g to the p r o d u c t i o n p rocess would permi t an exact model of the i n d u s t r y . Cons ide r an aggregate p r o f i t function,-.II (P,K) , which i s not ob t a i ned by the r e s t r i c t i o n s of exact agg rega t i on ( i . e . , f i c t i t i o u s a g g r e g a t i o n ) . What are the p r o p e r t i e s of n ( P ,K ) ? F i r s t , because i t i s not an exact a g g r e g a t o r , the s t r u c t u r a l form of n ( P ,K ) does not r e v e a l the s t r u c t u r a l form of the i n d i v i d u a l f a rm ' s p r o f i t f u n c t i o n s . Because IT(p,K) i s not e x a c t , the u n d e r l y i n g micro p r o d u c t i o n f u n c t i o n s are not quas i-homothe t i c and consequen t l y , a l l farms are not i d e n t i c a l a t the marg in . T h e r e f o r e , some farms may d i f f e r s i g i n i f i c a n t l y in t h e i r t e chno logy . Second, n ( P ,K ) does not convey any i n f o rma t i on on s p e c i f i c t e c h n o l o g i e s and i t s s t r u c t u r a l form i s u n i n f o r m a t i v e . T h i r d , i f an aggregate p r o f i t f u n c t i o n n ( P , R ) i s e x a c t , i t i s i n v a r i a n t to a r e d i s t r i b u t i o n of the f i x e d f a c t o r s amongst i n d i v i d u a l fa rms. However, t h i s i s not the case fo r n ( P , K ) . There may e x i s t d i f f e r e n t s t r u c t u r a l forms of n (P ,K) f o r d i f f e r e n t d i s t r i b u t i o n s of K. T h e r e f o r e , n ( P ,K ) i s c o n t i n g e n t upon K. Consequen t l y , even i f n ( p ,K ) i s "we l l -behaved " and shows a l l the usua l p r o p e r t i e s of a p r o f i t f u n c t i o n , the aggregate 64 f u n c t i o n to which i t i s dua l i s a l s o con t i ngen t upon K. Moreoever , there are p r i c e paths and an i n i t i a l d i s t r i b u t i o n of f i x e d f a c t o r s tha t would generate aggregate data that cannot be r a t i o n a l i z e d by a t echno logy s a t i s f y i n g the r e g u l a r i t y c o n d i t i o n s (B lackorby and Schworm 1982b). The reason fo r t h i s i s q u i t e s i m p l e . The aggregate A p r o d u c t i o n f u n c t i o n i s ob ta ined from n ( P ,K ) wh ich , when e s t i m a t e d , p i c k s up aggregate i npu ts demanded and outputs s u p p l i e d and the c o r r e s p o n d i n g p r i c e v e c t o r s (g iven the i n i t i a l d i s t r i b u t i o n of f i x e d f a c t o r s ) and at tempts to measure s u b s t i t u t i o n p o s s i b i l i t i e s . But as the f i x e d f a c t o r s are r e d i s t r i b u t e d among fa rms, the aggregate demand and supp ly f o r a l l f a c t o r s and f o r a l l farms changes (a l though of c o u r s e , P i s unchanged) . When n ( P , K ) i s not an exact aggrega to r f u n c t i o n , i t i s r e a l l y a bogus f u n c t i o n . However, v i r t u a l l y a l l e m p i r i c a l r e s e a r c h us ing aggregate data se t s r e l i e s on f i c t i t i o u s a g g r e g a t i o n . The hope i s that such f u n c t i o n s are u s e f u l in the ne ighborhood of some i n i t i a l d i s t r i b u t i o n of f i x e d f a c t o r s and t h e r e f o r e w i l l p ro v i de an approx imat ion of the behav io r of aggregate q u a n t i t i e s . The a p p l i e d r e sea r che r who has a v a i l a b l e on l y aggregate data i s r e a l l y faced w i th two c h o i c e s beyond abandoning the p r o j e c t : 1) he can impose the r e s t r i c t i o n tha t a l l farms va lue a marg ina l u n i t of a f i x e d f a c t o r e q u a l l y and t h e r e f o r e r e l y on exact a g g r e g a t i o n ; or 2) he can assume the da ta are genera ted by a r e p r e s e n t a t i v e producer and impose homothet ic s e p a r a b i l i t y on the t echno logy set (B lackorby 1982). If c o n d i t i o n (1) ho lds over a l l f a rms , then the 65 a p p r o p r i a t e procedure i s exact a g g r e g a t i o n . However, i f i t does not h o l d , then the re i s , at p r e s e n t , no way to determine which procedure w i l l generate the best r e s u l t s . The r e s e a r c h e r ' s cho i ce w i l l depend g e n e r a l l y on the o b j e c t i v e of the study and the c h a r a c t e r i s t i c s of the data (B lackorby and Schworm 1982a). The important po in t i s that e m p i r i c a l r e s u l t s genera ted us ing aggregate data must be i n t e r p r e t e d as c o n d i t i o n a l upon the r e s t r i c t i o n s imposed by the aggrega t ion p rocedu re . 3.5 A SINGLE-OUTPUT PROFIT FUNCTION FOR A REPRESENTATIVE COW-CALF PRODUCER Assume there e x i s t s an aggregate p r o d u c t i o n techno logy d e f i n e d f o r the cow-ca l f i n d u s t r y . T h i s r e p r e s e n t a t i v e farm can be d e s c r i b e d by an aggregate p r o d u c t i o n f u n c t i o n Y = F ( q , C b , C e ) where Y i s an aggregate q u a n t i t y index of beef s u p p l i e d and F i s the p r o d u c t i o n p o s s i b i l i t y se t d e f i n e d fo r a v e c to r of aggregate i npu ts (q ) , a q u a n t i t y index of the beg inn ing s tock of cows ( C b ) , and a q u a n t i t y index of end ing s tock of cows ( C e ) . F i s i n c r e a s i n g in q and C b but d e c r e a s i n g in C e . Assume tha t F s a t i s f i e s c o n d i t i o n s ( f l ) to ( f4) in S e c t i o n ( 3 . 2 ) . The problem faced by the r e p r e s e n t a t i v e farm at the i n d u s t r y l e v e l i s i d e n t i c a l to that f aced by the i n d i v i d u a l c a t t l e producer except that the a d d i t i o n a l r e s t r i c t i o n on herd expans ion must be imposed. These c h a r a c t e r i s t i c s can be d e s c r i b e d a s : 66 1 ( 3' 1 8 ) r Vo ^ 7 [ P t Y t " W tq t:(q tcJ,cJ.Y t) EF], Y t,q t,C t t=0 (1+r) s.t. Cht = (l+A)C*_ l f c b > 0 o A l l v a r i a b l e s are as d e f i n e d in Sec t i on (3.2) except tha t each v a r i a b l e , where a p p l i c a b l e , shou ld now be i n t e r p r e t e d as the aggregate r e p r e s e n t a t i o n fo r the i n d u s t r y . Fu r the rmore , the an imal accumula t ion c o n s t r a i n t r e s t r i c t s the i n d u s t r y ' s a b i l i t y to i n c r ease next p e r i o d ' s beg inn ing an imal s tocks to the r e p r o d u c t i v e c a p a c i t y of l a s t p e r i o d ' s ending female s t o c k s . ' 0 A d d i t i o n a l l y , t h i s c o n s t r a i n t reduces the max imiza t ion problem of the r e p r e s e n t a t i v e farm from a two-stage max imiza t ion problem ( fo r the i n d i v i d u a l farm) to a one-stage max imiza t ion prob lem. That i s , the farmer views the number of cows at the beg inn ing of any p e r i o d as be ing f i x e d or p r ede te rm ined . He must dec ide on the op t ima l q u a n t i t y of i npu t s to combine wi th the f i x e d s tock of cows. From t h i s he de te rmines op t ima l i n ven to r y c a r r y o v e r s ( end-of-per iod s t o c k s ) , l e a v i n g cu r r en t p e r i o d output as the r e s i d u a l . A g a i n , op t ima l i nven to ry c a r r y o v e r s are va lued at 6t (1+r) t t + 1 As b e f o r e , the i n t e r t e m p o r a l problem ( 3 . 1 8 ) , i s so l v ed a c r o s s the two p e r i o d s but on l y the p l ans f o r t=0 are a c t u a l l y c a r r i e d out because e r r o r s in e x p e c t a t i o n s n e c e s s i t a t e r e v i s i o n of p l ans once the second p e r i o d a r r i v e s . A dua l p r o f i t f u n c t i o n can aga in be used to r e p r e s e n t , i n any p e r i o d t , the max imiz ing behav io r of the r e p r e s e n t a t i v e farm . T h i s 67 i s d e f i n e d a s : (3.19) n(P t,W t,Z t;C b) = maxe V ( V ^ ° t ) ~ V t + g C*. q t C t The i n d u s t r y ' s op t ima l output s u p p l y , input demand, and end-o f - p e r i o d i nven to ry can be determined by a p p l y i n g H o t e l l i n g ' s Lemma to Equa t ion ( 3 . 19 ) . These i ndus t r y equa t ions are d e f i n e d a s : (3.20) Y* = n p t(P t,W t,Z t;C b), q* = - n w t ( P t w t , z t ; c b t ) , ct*= n«t(pt»wt»zt;cf>-where n i ( . ) i s the p a r t i a l d i f f e r e n t i a l of n ( . ) w i th r e spec t to p t , wt, and z t r e s p e c t i v e l y . Y*t, q * t , and C^* denote the r e p r e s e n t a t i v e f a rm ' s p r o f i t max imiz ing q u a n t i t i e s of output s u p p l y , input demand, and end—of — p e r i o d i nven to r y demand r e s p e c t i v e l y , as f u n c t i o n s of the p r i c e s (p t , wt, and z t ) and the l e v e l of the f i x e d f a c t o r C b . t D u a l i t y t e chn iques can be used to generate a formula to p r e d i c t when the i n d u s t r y w i l l be i n c r e a s i n g or r educ ing the number of an imals in the h e r d . The i n d u s t r y ' s op t ima l shadow p r i c e of an an imal in the herd can be determined (Diewert 1974) by d i f f e r e n t i a t i n g Equa t ion (3.19) w i th respec t to b e g i n n i n g - o f - p e r i o d animal s tocks ( C b ) , (3.21 ) n b ( p ,w ,Z ;Cb) m shadow p r i c e of an an imal in the h e r d , c t t t t An i n c r e a s e in herd s i z e can be p r e d i c t e d i f the i n d u s t r y ' s shadow p r i c e i s g r ea t e r than the ( f low) p r i c e of an an imal o r : (3 .22) I L b ( P ,W ,Z ;Cb) > p r i c e of an a n i m a l , c t t t t 68 A decrease in herd s i z e can be p r e d i c t e d i f the o p p o s i t e o c c u r s . 1 1 Equa t ion (3.21) has an i n t e r e s t i n g p r o p e r t y . The cow-c a l f model c h a r a c t e r i z e d in Equa t i on (3.20) i s d e f i n e d as a sho r t run model : consequen t l y econometr ic r e s u l t s must be i n t e r p r e t e d sub jec t to the l e v e l of the f i x e d f a c t o r . However, i t i s p o s s i b l e to o b t a i n long run es t ima tes by combin ing the i n f o r m a t i o n con t a i ned in Equa t i on (3.21) and Equa t i on (3.20). (See Berndt , M o r r i s o n , and Watkins 1982, and Brown and C h r i s t e n s e n 1981). In long run e q u i l i b r i u m (at op t ima l herd s i z e ) , the op t ima l shadow p r i c e of an an imal must equa l the ( f low) p r i c e (Pt) o r : (3.23) n cb(P t,W t,Z t;C b*) = P t . The op t ima l p r o f i t max imiz ing herd s i z e C f c can be d e r i v e d by s o l v i n g Equat ion (3.23) g i ven p t , wt, z t , and Pt a s : (3.24) cb*= n*(P t,w t,z t,P t) , Long run c h a r a c t e r i s t i c s of the i n d u s t r y can be ob t a i ned by s u b s t i t u t i n g C ° i n t o Equa t i on (3.20) and d e r i v i n g the d e s i r e d measurements. S i m i l a r l y , the response of C b * to changes in p r i c e can be ob ta ined d i r e c t l y form Equa t ion (3.24), 3.6 SOME COMPARATIVE STATICS Us ing Equat ion (3.20), comparat ive s t a t i c r e s u l t s can be o b t a i n e d f o r changes in the op t ima l l e v e l s of the endogenous v a r i a b l e s caused by a change in the exogenous pa ramete rs . In an at tempt to s i gn these r e s u l t s , the r e s t r i c t i o n s imp l i ed by 69 d u a l i t y theory and n e o - c l a s s i c a l p r o d u c t i o n theory w i l l be imposed on the s i n g l e output p r o f i t mode l . To f a c i l i t a t e e x p o s i t i o n , Equa t ion (3.20) w i l l be r e p e a t e d : (3.20) Y * = n P (P ,W , Z ; C b ) , q * = - n w t ( P t , w t , z t ; c b ) , c t * = n? t<' p t»VV ct>-F i r s t , c o n s i d e r a change in c u r r e n t output supp ly (Y*t ) due to a change in cu r r en t p r i c e ( p t ) . D i f f e r e n t i a t i n g Y*t w i th r espec t to pt r e s u l t s i n : (3.25) < - n p p ( P t , W t , Z t ; C b ) + H p z ( P t , W t , Z t ; C b ) .A. d? t 1 t t where n p (.) r ep resen t s the change in Y*t from a change in t t c u r r e n t p r i c e (pt) h o l d i n g a l l o ther v a r i a b l e s cons tan t ( i . e . , the second d e r i v a t i v e ) , n (.) i s p o s i t i v e by c o n v e x i t y of t t the p r o f i t f u n c t i o n , imp l y i ng c u r r e n t output w i l l i n c r ease when c u r r e n t p r i c e i n c r e a s e s . n p z (.) r ep resen t s the change in Y*t from a change in t t expected p r i c e (z t ) h o l d i n g a l l o ther v a r i a b l e s c o n s t a n t . G e n e r a l l y , the s i gn of n (.) i s unknown and w i l l depend t t on whether c u r r e n t output i s a s u b s t i t u t e or a complement wi th end-o f-pe r i od s tock of a n i m a l s . However, the r e s t r i c t i o n s imposed by the b i o l o g i c a l nature of c a t t l e p roduc t i on i n d i c a t e s tha t in order to supp ly more cu r r en t ou tpu t , fewer an ima ls w i l l be r e t a i n e d in the herd at the end of the p e r i o d . Consequen t l y , c u r r e n t output supp ly and end-o f-pe r i od s tock of 70 animals are substitutes and the sign of n p z i s negative. This indicates that current output supply w i l l decrease when expected future output price increases. 3Zt represents the change in expectations about future price caused by a change in current output pr i c e . The 371 sign of w i l l depend on how the farmer uses current price in revising his expectations of the future and may be pos i t i v e , negative, or zero. If |^|. = 0, t h i s implies no change in expected price following a change in current price. The sign of w i l l thus be determined by the sign of ^ p P t(«) which i s postive, implying that current output w i l l increase given an increase in current p r i c e . If 3 Z t < 0, the farmer expects future price to decrease given an increase in current p r i c e . In thi s case, current output w i l l again increase because the positive sign of Hp p(.) i s reinforced by the positive sign o f n P z (.) t t t t 3pt F i n a l l y , i f .?.z.t. > 0, the farmer expects the future 3Pt price of animals to increase given an increase in current * price, then the sign of <*Yt w i l l be as follows: * 9 p t 3zt i f 3Zt > o then 9X1 £ 0 i f f n p p > n 3Pt 3Pt < P t P t < P t Z t d P t * 3Zt That i s , i f "gp-jT > 0, a negative supply response i s expected in the short run i f the magnitude of Itp « i s smaller t t than n 7 3 Z t *t t 3 P t It i s of some interest to transform Equation (3.25) into an e l a s t i c i t y measurement: 71 (3.26) T o t a l E l a s t i c i t y Direct E l a s t i c i t y Cross E l a s t i c i t y E l a s t i c i t y of of Supply of Supply of Output Expectation r8Yt . Ft, = r9IlPt . Pt-. r9HPt . Zt, f 3Zt . Ft. 9Pt Y t J 1 9Pt Yt J 1 9Zt Y t J * L 9Pt Z t J ' Equa t i on (3.26) can be i n t e r p r e t e d in the f o l l o w i n g manner. The t o t a l e l a s t i c i t y of supp ly i s not on l y dependent on the t e c h n o l o g i c a l s t r u c t u r e of the i n d u s t r y , as measured by the d i r e c t e l a s t i c i t y of supp l y , but i s a l s o dependent on the s u b s t i t u t i o n p o s s i b i l i t i e s between p r o d u c t i o n today and p r o d u c t i o n tomorrow, as measured by the c r o s s e l a s t i c i t y of output supp ly w i th r e spec t to ending s tock of a n i m a l s , and the s e n s i t i v i t y of f a rmers ' p r i c e e x p e c t a t i o n s w i th r e spec t to changes in c u r r e n t p r i c e , as measured by the e l a s t i c i t y of e x p e c t a t i o n s . The importance of t h i s d i s c u s s i o n i s to demonstrate tha t in t h i s model , the c o n v e x i t y of the p r o f i t f u n c t i o n does not ensure a p o s i t i v e t o t a l e l a s t i c i t y of supp ly ( i . e . , an upward s l o p i n g supp ly c u r v e ) . Ra ther , the s i gn of the t o t a l e l a s t i c i t y of supp ly w i l l depend on the s i g n of the e l a s t i c i t y of e x p e c t a t i o n s . T h e r e f o r e , a shor t run nega t i ve supp ly e l a s t i c i t y in the cow-cal f i n d u s t r y i s not a p r e d i c t i o n from economic t h e o r y : r a the r the s i gn of the e l a s t i c i t y i s unknown and w i l l depend on p r i c e e x p e c t a t i o n s of p r o d u c e r s . G iven t h i s r e s u l t , how i s i t p o s s i b l e tha t the J a r v i s (1969) and Yver (1971) models are ab l e to p r e d i c t a nega t i ve supp ly e l a s t i c i t y in the shor t run? R e c a l l tha t t h e i r r e s u l t s are o b t a i n e d by a l l o w i n g the f u tu r e p r i c e of beef to change h o l d i n g o the r v a r i a b l e s c o n s t a n t . Or in the con tex t of the 72 model deve loped in t h i s c h a p t e r , they focus on the consequences fo r c u r r e n t output g iven a change in expected p r i c e : 9Y* 3 Z t P Z t t t T h i s d e r i v a t i v e was s igned in Equa t ion (3.25) and shown to be nega t i ve i n d i c a t i n g that an i n c r ea se in expected fu tu re p r i c e , h o l d i n g a l l o ther v a r i a b l e s c o n s t a n t , w i l l decrease c u r r e n t output s u p p l y . Consequen t l y , the J a r v i s and Yver models are not i n c o r r e c t but r a the r they m i s i n t e r p r e t the v a r i a b l e s on which c u r r e n t output d e c i s i o n s depend. Two o ther comparat i ve s t a t i c s are of i n t e r e s t : i ) a change in c u r r e n t input demand due to a change in c u r r e n t output p r i c e ; 3 g * = anwt anwt azt 3Pt 3Pt 3Zt * 3 P t ' and i i ) a change in ending p e r i o d s tock of an imals due to a change in c u r r e n t p r i c e ; 3 C e = 3IIz + 3IIz . 3 z . t t t t 3P 3P 3z 3P t t t ( i ) The s i gn of p ^ i s unknown and depends on whether the input i s a normal or i n f e r i o r i n p u t . I f the input i s norma l , then the s i gn of i s p o s i t i v e and c o n v e r s e l y , the s i gn i s nega t i ve i f i t i s an i n f e r i o r i n p u t . T h e r e f o r e , assuming n o n - i n f e r i o r i npu t s i m p l i e s tha t the demand fo r i npu ts w i l l i n c r e a s e . The second term on the r i g h t hand s i d e i s easy to h a n d l e . V a r i a b l e i npu t s are chosen in the model a f t e r output l e v e l s are de te rm ined . T h e r e f o r e , the op t ima l input l e v e l i s 73 independent of expected f u t u r e p r i c e s and consequen t l y , 3nwt g z t = 0. T h i s comparat ive s t a t i c i n d i c a t e s that in terms of input demand, the s t r u c t u r e of techno logy a lone determines the r equ i r emen ts , independent of changes in p r i c e expec ta t i o n s . ( i i ) The r e s u l t s of t h i s comparat ive s t a t i c are oppos i t e * 3Yt to the r e s u l t s ach ieved f o r 7 ^ . However, i t i s p resen ted to show c o n s i s t e n c y in the p r o f i t mode l . A p p l y i n g Young 's theorem to the f i r s t term on the r i g h t hand s i de i n d i c a t e s that artzt = anpt 3 P t 3 Z t 3npt From the d i s c u s s i o n of Equa t ion ( 3 .25 ) , the s i g n of 3 Z t i s nega t i ve and t h e r e f o r e , " ^ f ^ * s a ^ s o n e g a t i v e . T h i s i n d i c a t e s tha t there i s a decrease in end-o f-pe r i od s to cks of an ima ls when c u r r e n t p r i c e i n c r e a s e s , c e t e r i s p a r i b u s . drc,Zt i s the change in end-o f-pe r i od s tock of an ima ls 3Zt g i ven a change in expected p r i c e . T h i s d e r i v a t i v e i s p o s i t i v e from the c o n v e x i t y of the p r o f i t f u n c t i o n . F i n a l l y , ||iL r e p r e s e n t s a change in p r i c e e x p e c t a t i o n s g i ven a change in c u r r e n t p r i c e . The s i gn of d Z t , which can be p o s i t i v e , n e g a t i v e , or z e r o , i s i d e n t i c a l to the d i s c u s s i o n p resen ted e a r l i e r . T h e r e f o r e , the s i g n of iL^ I does not on l y depend on the s t r u c t u r e of 3Pt t echno logy but as wi th Equa t ion ( 3 .25 ) , depends on p r i c e e x p e c t a t i o n s of p r o d u c e r s . 74 3.7 A MULTI-OUTPUT, MULTI-INPUT MODEL OF A REPRESENTATIVE COW-CALF PRODUCER It i s now q u i t e s t r a i g h t f o r w a r d to extend the s i n g l e output model of the c a t t l e producer to d e s c r i b e a m u l t i -o u t p u t , m u l t i - i n p u t cow-cal f p roduce r . T h i s s e c t i o n w i l l ma in ta in a l l of the assumpt ions set out in S e c t i on (3.2) except that the c a p i t a l s tock of the farmer now c o n s i s t s of f i v e c a t e g o r i e s of an imals ( i . e . , b u l l s , cows, h e i f e r s , s t e e r s , and c a l v e s ) and c o r r e s p o n d i n g l y , output supply w i l l a l s o c o n s i s t of the f i v e animal c a t e g o r i e s . The o b j e c t i v e of the m u l t i - o u t p u t , m u l t i - i n p u t cow-cal f p roducer i s to maximize the expected net p resen t va lue of h i s o p e r a t i o n from the s a l e of an imals over two time p e r i o d s . The mu l t i -ou tpu t producer i s faced wi th two b a s i c p rob lems : i ) d e t e rm in ing the type of an imal ( i . e , out of which ca tegory ) to be s o l d ; and i i ) de t e rm in ing whether i t i s more p r o f i t a b l e to s e l l the an imal t h i s p e r i o d at a known output p r i c e or r e t a i n the an imal fo r s a l e in the fu tu re at an u n c e r t a i n p r i c e . G e n e r a l i z i n g E p s t e i n (1977) and E p s t e i n and Denny (1980) to the m u l t i - o u t p u t , m u l t i - c a p i t a l s tock c a s e , the techno logy of the farm can be d e s c r i b e d by a concave t r a n s f o r m a t i o n f u n c t i o n F ( q , A b , / f ,Y) = 0, where q i s an I-d imens iona l v e c to r of i npu t s q = (q1 , . . . , q i ) , Ab i s an N-dimensional v e c to r of b e g i n n i n g - o f - p e r i o d s tock of a n i m a l s , A e i s an N-dimens ions l v e c to r of end-o f-pe r i od s tock of an ima l s , and Y i s an N-d imens i ona l v e c to r of output supp ly d u r i n g tha t p e r i o d . The aggregate t r a n s f o r m a t i o n f u n c t i o n F ( . ) shows the t e c h n o l o g i c a l p o s s i b i l i t i e s a v a i l a b l e fo r combin ing the vec to r of i npu t s 75 wi th the vec to r of beg inn ing s tock of an imals to determine the ve c to r of end-o f-pe r iod s tock of cows and the v e c t o r of output supp ly as the r e s i d u a l . F ( . ) i s i n c r e a s i n g in the i n d i v i d u a l components of the v e c t o r s of q and Ab ; i t i s d e c r e a s i n g in the i n d i v i d u a l components of the v e c to r of A e . At any po in t in t ime , the v e c t o r s of c u r r e n t output and f a c t o r p r i c e s are known but the v e c to r of next p e r i o d ' s output p r i c e s i s u n c e r t a i n . The producer i s assumed to have a s u b j e c t i v e p r o b a b i l i t y d i s t r i b u t i o n conce rn ing t h i s v e c to r of p r i c e s and to s e l e c t a s t r a t e g y to maximize the expected va lue of the d i s coun ted sum of a n t i c i p a t e d p r o f i t s over a two-per iod f u tu r e p l ann ing h o r i z o n , sub jec t to the i n i t i a l v e c to r of an imal s t o c k s , the v e c to r of p r i c e e x p e c t a t i o n s , and the an imal accumula t ion equa t ions and i d e n t i t i e s . T h i s s t r a t e g y can be summarized a s : 1 (3.27) maxe E E t-0" (lb [ p X - w t V ( V A t ' A t ' V E F l sub jec t to A b >> 0, and . the f o l l o w i n g i d e n t i t y r e s t r i c t i o n s : b e , e i ) B t = Bt_^ +X 1 (Jt-1 , i i ) C b = + RHt_ 1 , . . . . b e , e i l l ) S t = +A2Ca t _ j . . b e e , e i v ) H t = H,.^ -RH,..! +*3Ca t _ 1 » _ b c / e e v) €3^.= § (C t _ 1 + R H t _ 1 ) , where p t i s a c u r r e n t p e r i o d vec to r of output p r i c e s assumed known in p e r i o d t , w t i s a c u r r e n t p e r i o d vec to r of input p r i c e s assumed known in p e r i o d t , 7 6 ^ i i s the percentage of c a l v e s that become b u l l s , s t e e r s , and h e i f e r s r e s p e c t i v e l y , ' 2 § i s the percentage of cows and replacement h e i f e r s bred in p e r i o d t-1 that s u c c e s s f u l l y c a l v e d in p e r i o d t , b denotes beg inn ing of p e r i o d , e denotes end of p e r i o d , A i s a v e c to r of an ima ls s t o c k s c o n s i s t i n g of f i v e c a t e g o r i e s of a n i m a l s , B i s the s tock of b u l l s , C i s the s tock of cows, S i s the s tock of s t e e r s , H i s the s tock of h e i f e r s , Ca i s the s tock of c a l v e s , and RH i s the s tock of replacement h e i f e r s . The an imal accumula t ion c o n s t r a i n t s are s i g n i f i c a n t l y more c o m p l i c a t e d in the mu l t i -ou tpu t case and r e f l e c t the i n t e r r e l a t i o n s h i p s between the d i f f e r e n t c a t e g o r i e s of a n i m a l s . C o n s t r a i n t i ) shows that the number of b u l l s a v a i l a b l e in p e r i o d t i s i d e n t i c a l l y equa l to the number of b u l l s l e f t over at the end of the p r e v i o u s p e r i o d p l u s the percentage of c a l v e s that are r e t a i n e d as b u l l s at the end of the p r ev i ous p e r i o d . C o n s t r a i n t i i ) i n d i c a t e s tha t the number of cows a v a i l a b l e in p e r i o d t i s i d e n t i c a l l y equa l to the number of cows l e f t over at the end of the p r e v i o u s p e r i o d p l u s the number of h e i f e r s e n t e r i n g the b reed ing herd at the end of the p r e v i o u s p e r i o d . 77 C o n s t r a i n t i i i ) shows that the number of s t e e r s at the beg inn ing of p e r i o d t i s i d e n t i c a l l y equa l to the number of s t e e r s at the end of the p r e v i ous p e r i o d p l u s the percentage of c a l v e s at the end of the p r e v i o u s p e r i o d that become s t e e r s . C o n s t r a i n t i v ) i n d i c a t e s that the number of h e i f e r s at the beg inn ing of p e r i o d t i s i d e n t i c a l l y equa l to the number of h e i f e r s at the end of p e r i o d t-1 p l u s the percentage of c a l v e s at the end of the p r e v i o u s p e r i o d which are fema le , minus replacement h e i f e r s that enter the b r eed ing h e r d . F i n a l l y , c o n s t r a i n t v) shows that the number of c a l v e s at the beg inn ing of p e r i o d t i s equa l to the percentage of cows and replacement h e i f e r s bred in p e r i o d t-1 tha t s u c c e s s f u l l y c a l v e d at the beg inn ing of p e r i o d t . In any p e r i o d t , the farmer views the number of an imals in each ca tegory as be ing f i x e d or p r ede t e rm ined . He must dec ide on the op t ima l q u a n t i t y of i npu t s to combine wi th the f i x e d s tock of an imals from which he de t e rm ines , f o r each ca t ego r y of a n i m a l , the op t ima l en d-o f -pe r i od s tock and c u r r e n t p e r i o d output as the r e s i d u a l . End-o f-pe r i od s tocks of an ima ls in each ca tegory a re va lued by the farmer at the output p r i c e he expects fo r each animal c a t ego r y next p e r i o d d i s c o u n t e d to the p resen t o r : (3 .28) z i t = [ 1 1 ( 1 + r ) * E t ( * i t - 1 ) ] ' 1 = l f ••' ' n ' where z J = (z, z ) i s d e f i n e d as a v e c t o r of expected i t i t nt p r i c e s . A m u l t i - o u t p u t , m u l t i - i n p u t dua l p r o f i t f u n c t i o n can be 78 used to r e p r e s e n t , in any p e r i o d t , the maximiz ing behav io r of the r e p r e s e n t a t i v e p roduce r . T h i s i s d e f i n e d a s : (3.29) n(P ,W t,z ;Ap = max [P'Y - W'q. + z» A*: (q ,A£,A* Y )€F]/ Y t ' q t ' A t The r e p r e s e n t a t i v e f a rm ' s vec to r of output supp l y , input demand, and end of p e r i o d i nven to ry can be determined by a p p l y i n g H o t e l l i n g ' s Lemma to Equat ion ( 3 . 2 9 ) . These equa t ions are d e f i n e d a s : (3.30) * b Y i t " "p ( P t , W t , z t s V i = l , . . . , n , <j\ = - n w. t (V W t'V A t ) i = 1 1, A l t = ^ t ' W ^ i = l , . . . , n , where Y * t , q * t , and A* are the r e p r e s e n t a t i v e p r o d u c e r ' s p r o f i t maximiz ing q u a n t i t i e s of output s u p p l y , input demand, and end of p e r i o d s tock demand r e s p e c t i v e l y , as f u n c t i o n s of the ve c to r of p r i c e s (p f c , w t , and ^ ) and the l e v e l s of the f i x e d s tock of an ima l s , A b . It shou ld be noted tha t s i m i l a r to Equa t ion (3.21) in S e c t i o n ( 3 . 5 ) , a shadow p r i c e f o r each ca t ego r y of an imal can be ob t a i ned by d i f f e r e n t i a t i n g Equa t ion (3.29) wi th respec t to the a p p r o p r i a t e s t o c k . Moreover , long run s t r u c t u r a l e s t ima tes of the techno logy can aga in be determined as d e s c r i b e d i n Se c t i on ( 3 . 5 ) . The system of equa t ions in (3.30) can be used to p o s t u l a t e an econometr ic model by s p e c i f y i n g a f u n c t i o n a l form fo r n ( . ) , de te rm in ing the vec to r of p r i c e e x p e c t a t i o n s of c a t t l e p r o d u c e r s , and s p e c i f y i n g the s t o c h a s t i c d i s t u r b a n c e s fo r each e q u a t i o n . However, be fo re a t t empt ing to es t imate 79 t h i s system of e q u a t i o n s , the e l a s t i c i t i e s and other summary s t a t i s t i c s a v a i l a b l e to d e s c r i b e the s t r u c t u r e of the u n d e r l y i n g t r a n s f o r m a t i o n f u n c t i o n w i l l be p r e s e n t e d . 3.8 CHARACTERIZING THE STRUCTURE OF PRODUCTION In d e s c r i b i n g the techno logy of an i n d u s t r y , r e sea r che r s are i n t e r e s t e d in de te rm in ing how the r e l a t i o n s h i p s among i npu t s and among outputs change g i ven changes in exogenous v a r i a b l e s . G e n e r a l l y , these measures determine the s t r u c t u r e and cu r va tu r e p r o p e r t i e s of i soquan ts and t r a n s f o r m a t i o n cu rves ( i . e . , the ra te at which i npu ts or ou tputs may be s u b s t i t u t e d in p r o d u c t i o n ) . A d d i t i o n a l l y , o ther measures of i n t e r e s t are the p r i c e e l a s t i c i t i e s of input demand and output s u p p l y . Of c o u r s e , such measurements are c o n d i t i o n a l on the assumpt ions of p r o d u c t i o n ( i . e . , f i x e d f a c t o r s ) . One measure of the ease w i th which i npu t s may be s u b s t i t u t e d in p r o d u c t i o n i s the H i c k s - A l l e n e l a s t i c i t y of s u b s t i t u t i o n (a^j ) which measures the no rma l i zed change of the input r a t i o s (q±/q^) w i th respec t to changes in the marg ina l r a te of s u b s t i t u t i o n (F i/F j ) . The n o r m a l i z a t i o n i s such that a . . = a . , and that a., i s i n v a r i a n t to changes in the s c a l e of i j j i i j 3 measurement of the i n p u t s : I a±j =£ = 1 <Vk !•*«!> 1 lFl> 9F - _ where F, = , F i s the bordered hes s i an of F and F i s the c o f a c t o r of 8 2F / dq^q^ in |F|. Diewert (1974) extended and g e n e r a l i z e d the no t i on of e l a s t i c i t y of s u b s t i t u t i o n to the m u l t i - o u t p u t , m u l t i - i n p u t 80 v a r i a b l e p r o f i t f u n c t i o n by d e f i n i n g the f o l l o w i n g e l a s t i c i t i e s : i ) an e l a s t i c i t y of t r a n s f o r m a t i o n between output and v a r i a b l e input q u a n t i t i e s i and h d e f i n e d fo r each p e r i o d t : ° i h ( P t » W t , z t » ; A t ) = n ( p t » w t ' z t ; A t ) * 3 2 n(')/3P ±3P h , Ih - l , . . . , n . [3n(.)/3P±] • [3n(.)/3P h l . i i ) an e l a s t i c i t y of s u b s t i t u t i o n between f i x e d inpu ts j and k d e f i n e d fo r each p e r i o d t : = n ( , ) ' 9 2 n ( » ) / 9 A ^ A ^ . j k = l , . . . , n . [3n(.)/3Aj] . [3II(.)/3A£] i i i ) an e l a s t i c i t y of i n t e n s i t y between v a r i a b l e q u a n t i t y i and f i x e d f a c t o r j d e f i n e d fo r each p e r i o d t : Y i j ( p t ' w t ' z t ; A t ) = n(.)a 2n(.)/3P 13A b , i j » 1 n. [3n(.)/3p±] • [ a n ( . ) / 3 A b ] These e l a s t i c i t i e s p rov ide measures of the r e spons i veness of v a r i a b l e o u t p u t s , i n p u t s , and shadow p r i c e s of f i x e d f a c t o r s to changes in p r i c e s of v a r i a b l e o u t p u t s , i n p u t s , and changes in q u a n t i t i e s of f i x e d f a c t o r s . With the h e l p of H o t e l l i n g ' s Lemma and the usua l symmetry c o n d i t i o n s , a l l th ree e l a s t i c i t i e s are no rma l i zed to be i n v a r i a n t to the s c a l e of measurement and fur thermore the f o l l o w i n g r e s u l t s are o b t a i n , a i h = a h i ' V • V a n d Y i j " Y J I -Diewert (1979) has a l s o shown t h a t : a) the mat r ix [a ] ih of e l a s t i c i t i e s of t r a n s f o r m a t i o n i s p o s i t i v e s e m i d e f i n i t e and of rank at most equa l to n-1: c o n s e q u e n t l y , a ^ > 0, v i ; and 81 b) the mat r ix [ $ j k ] of e l a s t i c i t i e s of s u b s t i t u t i o n i s nega t i ve s e m i d e f i n i t e of rank at most equa l to n-1: c o n s e q u e n t l y , 3jj £ Q, vj • In a d d i t i o n to the above measures of s u b s t i t u t i o n , a number of non-normal ized p a r t i a l e l a s t i c i t i e s can be d e f i n e d to p r o v i d e a l t e r n a t i v e measures of the cu r va tu re p r o p e r t i e s : i ) the e l a s t i c i t y of output supply (Y i ) w i th respec t to p r i c e (Ph) d e f i n e d fo r each p e r i o d t : £ i h = 9 Y i * P h ' =• l , . . . , n . Of c o u r s e , t h i s e l a s t i c i t y can be d e f i n e d fo r input demand (q) and end of p e r i o d s tock of an ima ls (A e ) u s ing the a p p r o p r i a t e p r i c e s . i i ) the i nve r se p r i c e e l a s t i c i t y of f i x e d f a c t o r j and k d e f i n e d f o r each p e r i o d t : n j k " ' ^ ' = l , . . . , n . .b where Rj i s the shadow p r i c e of the j t h f i x e d f a c t o r . i i i ) the e l a s t i c i t y of the v a r i a b l e q u a n t i t y i w i th r e spec t to the j t h f i x e d f a c t o r d e f i n e d for each p e r i o d t : S j^ = • A b i j = l , . . . , n . 3Ab Y J i i v ) the e l a s t i c i t y of f i x e d f a c t o r j ' s shadow p r i c e w i th r e spec t to the p r i c e of the i t h v a r i a b l e q u a n t i t y d e f i n e d fo r each p e r i o d t : . - i i . • I*. F i n a l l y , i t can be shown that the f o l l o w i n g r e l a t i o n s h i p s ho ld 82 between the no rma l i zed and non-normal ized e l a s t i c i t i e s (see K o h l i 1976): a i h "-. eih 1 S h = e h l 1 S i ' B j k " V 1 s k = \ j 1 V Y i j = C i 3 ' 8J = PJ1 / S i , where S i = P i Y i/n i s v a r i a b l e q u a n t i t y i ' s share of revenue and Sj = R j A j / n i s f i x e d input j ' s share of revenue. 3.9 TESTING FOR STRUCTURE USING A MULTI-OUTPUT, MULTI-INPUT VARIABLE PROFIT FUNCTION It has been p r e v i o u s l y s t a t e d that i f a p r o f i t f u n c t i o n s a t i s f i e s c e r t a i n r e g u l a r i t y c o n d i t i o n s , the parameters of the u n d e r l y i n g t r a n s f o r m a t i o n f u n c t i o n can be r e c o v e r e d . T h i s r e s u l t i n d i c a t e s tha t p r o p e r t i e s such as homogenei ty , h o m o t h e t i c i t y , s e p a r a b i l i t y , and j o i n t n e s s of the techno logy can be determined by t e s t i n g fo r the s t r u c t u r e of the dua l p r o f i t f u n c t i o n . In t h i s s e c t i o n , a number of theorems w i l l be p resen ted which d e s c r i b e these p r o p e r t i e s . T h i s s e c t i o n r e l i e s on Lau (1972) where p roo f s of the theorems may be found . Be fore s t a t i n g the theorems, s e v e r a l d e f i n i t i o n s must be e s t a b l i s h e d : D e f i n i t i o n 1 ) : A f u n c t i o n F (Y ,q ,A ) where Y i s a v e c to r of o u t p u t s , q i s a v e c to r of i n p u t s , and A i s a v e c to r of f i x e d f a c t o r s , i s s a i d to be almost homogenous of degrees k i , k2, k3, and k4 i f f F (A k l Y, A k 2 q , A k 3 A) = A k 4 F ( Y ,q ,A ) fo r any s c a l a r * > 0. D e f i n i t i o n 2 ) : An a lmost homogenous f u n c t i o n s a t i s f i e s a 83 m o d i f i e d Eu l e r Theorem: kl£3F Y. + k2E3F q., + k3E3F A = k4F. i q i 1 3Y± 3q± 3A± D e f i n i t i o n 3 ) : A m u l t i - o u t p u t , m u l t i - i n p u t t echno logy i s s a i d to be separab le in outputs and inpu t s ( v a r i a b l e and f i x e d ) i f there e x i s t f u n c t i o n s f and q such t h a t : f(Y) - g(g,A) = 0. D e f i n i t i o n 4 ) : A f u n c t i o n F (Y ,q ,A ) i s s a i d to be non-j o i n t in inputs i f there e x i s t i n d i v i d u a l p r o d u c t i o n f u n c t i o n s : Y i = f l ( X i l X i n V V l j ' w i th the p r o p e r t i e s : i ) there are no economies of j o i n t n e s s ; and i i ) there are no d i seconomies of j o i n t n e s s . Assume tha t the r e g u l a r i t y c o n d i t i o n s are s a t i s f i e d fo r both F ( . ) and n ( . ) . Then the f o l l o w i n g theorems can be s t a t e d . Theorem 1) : A p r o d u c t i o n f u n c t i o n i s homogenous of degree k in A, k>0, i f f the v a r i a b l e p r o f i t f u n c t i o n i s a lmost , homogenous of degree 1 and 1/k in p r i c e s and f i x e d f a c t o r s r e s p e c t i v e l y . Theorem 2 ) : A p r o d u c t i o n f u n c t i o n i s h o m o t h e t i c a l l y s epa rab l e in Y, q , and A or F (G (Y ) , J ( q ) ,H (A ) ) where G, J , and H are homogenous of degree one, i f f the v a r i a b l e p r o f i t f u n c t i o n i s d e f i n e d a s : n* = n(G(P), J(q), H(A)). Theorem 3 ) : A m u l t i - o u t p u t , m u l t i - i n p u t techno logy i s sepa rab l e in D e f i n i t i o n 3) i f f the v a r i a b l e p r o f i t f u n c t i o n i s 84 d e f i n e d a s : n(f(P), g(g,A)), which i m p l i e s that the output supp ly equa t ions are independent of q and tha t the input demand equa t ions are independent of p. Theorem 4 ) : A p r o d u c t i o n f u n c t i o n i s non- jo in t in i npu ts i f f the f o l l o w i n g d i f f e r e n t i a t i o n of the v a r i a b l e p r o f i t f u n c t i o n h o l d s : 92n(P,g,A) = O i r j , V i j . 3VPJ To make these theorems e m p i r i c a l l y o p e r a t i o n a l , a f u n c t i o n a l form fo r n( . ) must be p o s t u l a t e d ( i . e . , a f u n c t i o n a l form tha t does not impose the p r o p e r t i e s to be t e s t ed ) and then the r e s t r i c t i o n s on the parameters of the f u n c t i o n a l form co r r e spond ing to these p r o p e r t i e s must be de t e rm ined . A p p r o p r i a t e s t a t i s t i c a l t e s t s can be performed to t e s t each p r o p e r t y . Such a p rocedure w i l l be c a r r i e d out in Chapter Four , which a l s o i n c l u d e s a d i s c u s s i o n of the da ta and t r a n s f o r m a t i o n s of the data necessa ry to undertake the e m p i r i c a l a n a l y s i s . 85 FOOTNOTES TO CHAPTER THREE 1 Cow-calf farmers p r e f e r to reproduce female an ima ls from e x i s t i n g s tock in o rde r to ma in ta in the gene t i c base of the h e r d . 2 Very few an imals are imported fo r the purposes of b r e e d i n g . In 1982 there where on ly 1830 an imals imported fo r t h i s purpose ( A g r i c u l t u r e Canada 1982). 3 The v a r i a b l e p r o f i t f u n c t i o n i s a l s o d e f i n e d by some au thors as a g ross or r e s t r i c t e d p r o f i t f u n c t i o n . 4 T h i s s e c t i o n r e l i e s e n t i r e l y on Diewert (1973) and (1974) . 5 For a l t e r n a t i v e assumpt ions on f ( . ) see Lau (1974) . 6 S e p a r a b i l t y i s c o n s i s t e n t wi th d e c e n t r a l i z e d d e c i s i o n -making-- see B l a cko rby , P r imont , and R u s s e l l (1978) Chapter Th ree . 7 See B l a cko rby , P r imont , and R u s s e l l (1978) fo r an a l t e r n a t i v e d e f i n i t i o n . 8 There have been a number of a t tempts to t e s t f o r c o n s i s t e n t s e p a r a b l i t y in c o s t and p r o f i t f u n c t i o n s — see Berndt and C h r i s t e n s e n (1973) , Denny and Fuss (1977), and Woodland (1978) . 9 A number of au thors have used the term " f i c t i t i o u s " when d e s c r i b i n g agg rega t i on problems (Gorman (1968) and B l a cko rby , P r imont , and R u s s e l l (1978) ) . 10 F o l l o w i n g a change in an exogeneous v a r i a b l e the r e s t r i c t i o n on herd expans ion w i l l l i m i t the i n d u s t r y to i n c r ease i t s s tock of an ima l s , over a number of time p e r i o d s , to reach a new e q u i l i b r i u m l e v e l . It shou ld be 86 noted however, that the i ndus t r y can r a p i d l y decrease the herd by s l a u g h t e r i n g a n i m a l s . 11 Equa t i on (3.22) i n d i c a t e s tha t i f the farmer p l a ces a g r e a t e r va lue on the animal in the herd than the va lue he c o u l d ob t a i n by s e l l i n g i t , the farmer w i l l r e t a i n the a n i m a l . 12 Assume that the p r o b a b i l i t y that a cow w i l l g i v e b i r t h to a male (or female) an imal i s 0 . 5 . T h i s assumption i s c o n s i s t e n t wi th t y p i c a l b i o l o g i c a l r e p r o d u c t i o n of male and female a n i m a l s . 87 4. VARIABLE SPECIFICATION AND FUNCTIONAL FORMS 4.1 INTRODUCTION The purpose of t h i s chapter i s to d i s c u s s the methodology employed in p o s t u l a t i n g an econometr ic model and to d e s c r i b e the data used in gene ra t i ng the econometr ic r e s u l t s . The f i r s t stage in e s t i m a t i n g the system of equa t ions in (3.30) r e q u i r e s s p e c i f y i n g some e x p e c t a t i o n p rocess to be used in p r e d i c t i n g next p e r i o d ' s c a t t l e p r i c e s . In S e c t i o n ( 4 . 2 ) , a " q u a s i - r a t i o n a l " e x p e c t a t i o n p rocess i s p o s i t e d to p r e d i c t e x a c t l y the p r i c e e x p e c t a t i o n s of cow-cal f p r o d u c e r s . T h i s e x p e c t a t i o n procedure i s based on a Box and J enk ins (1976) time s e r i e s method whereby an a u t o r e g r e s s i v e i n t e g r a t e d moving average (ARIMA) model i s h ypo thes i zed to represen t the e x p e c t a t i o n p r o c e s s . In S e c t i on ( 4 . 3 ) , two a l t e r n a t i v e data s e t s , c r o s s -s e c t i o n a l and t i m e - s e r i e s , are i d e n t i f i e d and r e p o r t e d . As w e l l , the t r a n s f o r m a t i o n s necessary to f a c i l i t a t e econometr i c e s t i m a t i o n are d i s c u s s e d . S p e c i f i c a l l y , to es t imate the system of equa t ions in ( 3 .30 ) , the f o l l o w i n g i n f o rma t i on i s r e q u i r e d : i ) the q u a n t i t y of d i f f e r e n t ou tputs produced by cow-cal f farms and a s s o c i a t e d output p r i c e s ; i i ) the q u a n t i t y of d i f f e r e n t i npu t s used on farms and a s s o c i a t e d input p r i c e s ; i i i ) the end-o f-pe r i od s tocks of c a t t l e and a s s o c i a t e d expected p r i c e s ; and iv ) the beg inn ing s tocks of c a t t l e . F i n a l l y , in S e c t i on ( 4 . 4 ) , f u n c t i o n a l forms are s p e c i f i e d f o r d i f f e r e n t v e r s i o n s of the model and the s t o c h a s t i c s p e c i f i c a t i o n of the econometr ic equa t ions i s examined. 88 Fur the rmore , n u l l hypotheses are p resen ted fo r t e s t i n g s t a t i s t i c a l l y the v a r i a b l e p r o f i t f u n c t i o n fo r symmetry, l i n e a r homogeneity in p r i c e s , non- jo i n t p r o d u c t i o n in o u t p u t s , "a lmost homothe t i c " in o u t p u t s , and "a lmost homogeneous" in o u t p u t s . Before examining e x p e c t a t i o n s f o r m a t i o n , i t would be a p p r o p r i a t e to summarize the procedure tha t was f o l l owed in gene r a t i ng the f i n a l s t a t i s t i c a l r e s u l t s . The comp lex i t y of the t h e o r e t i c a l model n e c e s s i t a t e d (as an i n i t i a l p rocedure ) the s p e c i f i c a t i o n of a s imple f u n c t i o n a l form to r ep resen t the m u l t i - o u t p u t , m u l t i - i n p u t v a r i a b l e p r o f i t f u n c t i o n . A Cobb-Douglas form was chosen . T h i s was combined w i th the assumpt ion tha t e x p e c t a t i o n s of p r i c e s next p e r i o d are e x a c t l y r ep resen ted by the p r e d i c t i o n s of a po l ynomia l d i s t r i b u t e d l ag model (Almon 1965) of past annual o w n - p r i c e s . 1 I t i s we l l known tha t the Cobb-Douglas f u n c t i o n a l form imposes r e s t r i c t i v e cu r va tu re p r o p e r t i e s on the p r o d u c t i o n techno logy set ( i . e . , complementar i t y amongst inputs and an e l a s t i c i t y of s u b s t i t u t i o n equa l to one ) . However, i t i s not as we l l known, tha t fo r the mu l t i -ou tpu t Cobb-Douglas p r o f i t f u n c t i o n to s a t i s f y c o n v e x i t y in output p r i c e s , the r e s t r i c t i o n that the r a t i o of t o t a l revenue of the i t h output to o v e r a l l p r o f i t be g rea te r than one fo r a l l i , i s r e q u i r e d . In o ther words, the revenue genera ted from each output must be g r ea t e r than the o v e r a l l p r o f i t genera ted by the f i r m . I t i s c l e a r that t h i s c o n d i t i o n i s always s a t i s f i e d in the s i n g l e output c a s e 2 but i s u n l i k e l y to be s a t i s f i e d in the m u l t i -output c a s e . Casua l o b s e r v a t i o n of the data sample used in 89 t h i s study r e vea l ed that these convex i t y c o n d i t i o n s would not be s a t i s f i e d . To c i rcumvent t h i s p rob lem, i t was dec ided to generate an aggregate output p r i c e index us ing a t r a n s l o g f u n c t i o n a l fo rm 3 but m a i n t a i n i n g a Cobb-Douglas s t r u c t u r e on the input s i d e . The t r a n s l o g f u n c t i o n a l form i s a member of the group of f l e x i b l e f u n c t i o n s and, as such , does not r e q u i r e r e s t r i c t i o n s on revenue shares to s a t i s f y c o n v e x i t y . T h i s aggregate index was e s t ima ted fo r the th ree-output case and a f t e r check ing second order c o n d i t i o n s ( i . e . , check ing the s i gns of the c h a r a c t e r i s t i c roo t s of the Hess ian m a t r i x ) , i t was determined that in f a c t , the es t ima ted aggregate p r i c e index was convex in p r i c e s . T h i s aggregate p r i c e index was then employed in e s t i m a t i n g a norma l i zed Cobb-Douglas v a r i a b l e p r o f i t f u n c t i o n . W i th in the r e s t r i c t i v e nature of the Cobb-Douglas , the r e s u l t s of the e s t i m a t i o n were very s a t i s f a c t o r y . These r e s u l t s , as we l l as the es t imated aggregate t r a n s l o g p r i c e index and the es t imated po l ynomia l d i s t r i b u t e d l ag p r i c e e x p e c t a t i o n model , are r epo r t ed in Appendix D. With the i n i t i a l success of the Cobb-Douglas s p e c i f i c a t i o n , i t was dec ided to a l low g rea t e r f l e x i b i l i t y of s t r u c t u r e in input p r i c e s whi le m a i n t a i n i n g both a f l e x i b l e s t r u c t u r e in output p r i c e s and a po l ynomia l d i s t r i b u t e d l ag e x p e c t a t i o n p r o c e s s . T h i s g r ea t e r f l e x i b i l i t y i s a ch i e ved by s p e c i f y i n g a m u l t i - o u t p u t , m u l t i - i n p u t v a r i a b l e t r a n s l o g p r o f i t f u n c t i o n ( C h r i s t e n s e n , J o rgenson , and Lau 1971 and Diewert 1974). T h i s f u n c t i o n a l form can p rov ide a second-order l o c a l approx imat ion to an a r b i t r a r y f u n c t i o n . In 90 a d d i t i o n , i t has a s u f f i c i e n t number of parameters to a l l ow e s t i m a t i o n of the f i r s t and second order d e r i v a t i v e s of an a r b i t r a r y f u n c t i o n at the po in t of approx imat ion (Hanoch 1975). T h i s i m p l i e s that r e s t r i c t i o n s are not imposed a p r i o r i on e l a s t i c i t i e s of c h o i c e . Us ing a combined c r o s s - s e c t i o n a l , t i m e - s e r i e s data base , a t r a n s l o g p r o f i t f u n c t i o n was es t ima ted for the t h r ee-ou tpu t , t h r e e - i n p u t , one f i x e d f a c t o r c a s e . An examinat ion of the e m p i r i c a l r e s u l t s generated us i ng t h i s f l e x i b l e f u n c t i o n a l form, combined w i th an Almon l ag e x p e c t a t i o n p r o c e s s , v e r i f i e d that the model performed w e l l . These r e s u l t s , i n c l u d i n g es t ima tes of e l a s t i c i t i e s of c h o i c e , are a l s o r epo r t ed in Appendix D. The use of an Almon l a g model to generate p r i c e e x p e c t a t i o n s assumes a r a the r na ive p rocess fo r p r e d i c t i n g p r i c e s . It was dec ided that a more " r a t i o n a l " p r i c e e x p e c t a t i o n p rocess would more a c c u r a t e l y r ep resen t a c t u a l p r i c e e x p e c t a t i o n s of cow-cal f p roducers and consequen t l y p rov i de more e f f i c i e n t econometr ic r e s u l t s . T h i s was ach i eved by adop t ing N e r l o v e ' s " q u a s i - r a t i o n a l " e x p e c t a t i o n s approach (Ne r love , et a l . 1 9 7 9 ) . It i s assumed that p r i c e e x p e c t a t i o n s are r ep resen ted e x a c t l y by the p r e d i c t i o n s of a time s e r i e s (ARIMA) model . T h i s e x p e c t a t i o n p r o c e s s , combined wi th a m u l t i - o u t p u t , m u l t i - i n p u t v a r i a b l e t r a n s l o g p r o f i t f u n c t i o n , p r o v i d e s the main e m p i r i c a l s p e c i f i c a t i o n of the t h e o r e t i c a l mode l . Econometr ic r e s u l t s are generated us ing a c r o s s -s e c t i o n a l , t i m e - s e r i e s data base and are r epo r t ed in Chapter F i v e . 91 In a d d i t i o n to the c r o s s - s e c t i o n a l d a t a , a t i m e - s e r i e s da ta set i s a l s o u t i l i z e d in the e s t i m a t i o n . Because of the c y c l i c a l nature of beef p r o d u c t i o n , t h i s data set w i l l a l l ow e l a s t i c i t y measurements oyer the beef c y c l e which can be compared to the c r o s s - s e c t i o n a l r e s u l t s du r i ng a s i n g l e p e r i o d of the c y c l e . However, a number of v a r i a b l e s r e q u i r e d to es t imate the p r o f i t f u n c t i o n are not a v a i l a b l e on a t i m e - s e r i e s b a s i s . S p e c i f i c a l l y , t h i s data set does not i n c l ude i n fo rma t i on on t o t a l p r o f i t s , c r op p r o d u c t i o n , or the q u a n t i t i e s of i npu t s used on cow-ca l f fa rms. I t does i n c l u d e i n f o rma t i on on c u r r e n t c a t t l e p r i c e s , expected c a t t l e p r i c e s , c rop p r i c e s , input p r i c e s fo r l a b o u r , c a p i t a l , and m a t e r i a l s and s e r v i c e s , and i n v e n t o r i e s of c a t t l e on cow-ca l f farms. From the a v a i l a b l e t i m e - s e r i e s d a t a , net output supp ly equa t ions w i l l be s p e c i f i e d fo r t o t a l c a t t l e output supply and t o t a l end-o f-pe r i od i nven to ry demand. It i s un fo r tuna te that because the p r o f i t v a r i a b l e i s absent from the d a t a , a t r a n s l o g f u n c t i o n a l form c o u l d not be s p e c i f i e d f o r the v a r i a b l e p r o f i t f u n c t i o n . I n s t e ad , a no rma l i zed q u a d r a t i c f u n c t i o n a l form w i l l be used . To complete the e m p i r i c a l r e s e a r c h , these equa t ions are es t ima ted wi th the t i m e - s e r i e s da ta sample m a i n t a i n i n g a " q u a s i - r a t i o n a l " e x p e c t a t i o n p r o c e d u r e . These r e s u l t s are r e p o r t e d and compared to the c r o s s - s e c t i o n a l r e s u l t s in Chapter F i v e . 4.2 PRICE EXPECTATIONS In s p e c i f y i n g the v a r i a b l e s used in the econometr ic 92 model , i t would be p r e f e r a b l e to d e f i n e a market-determined r e p r e s e n t a t i o n of expected p r i c e s . The market does p rov ide f u tu r e s p r i c e s fo r beef a n i m a l s . However, two problems p r e c l uded t h e i r use in t h i s s tudy : a) f u t u r e s p r i c e s are a v a i l a b l e fo r on ly one ca tegory of feeder an imal ( s t ee r s ) whereas t h i s study r e q u i r e s p r i c e p r e d i c t i o n s fo r a l l c a t e g o r i e s of an imals on farms; and b) f u t u r e s p r i c e s are quoted in U.S. funds and t h i s i m p l i e s that t h e i r use in Canadian s t u d i e s must i n c l u d e a p r e d i c t i o n fo r expected exchange r a t e s . Consequen t l y , i t i s necessa ry in t h i s r e sea r ch to d e f i n e some p rocess fo r p r e d i c t i n g these unobservab le p r i c e s . It w i l l be assumed that cow-ca l f f a rmers ' e x p e c t a t i o n of f u tu re c a t t l e p r i c e s can be r ep resen ted e x a c t l y by the p r e d i c t i o n s of a t ime s e r i e s model genera ted us i ng a combinat ion of weighted averages of past p r i c e s go ing back p p e r i o d s and of random d i s t u r b a n c e s going back q p e r i o d s , as d e s c r i b e d by Box and J enk ins (1976) . I n t e r e s t i n g l y , N e r l o v e , et a l . (1979) shows tha t such an a u t o r e g r e s s i v e i n t e r g r a t e d moving average (ARIMA) model e x h i b i t s many of the p r o p e r t i e s of Muth ' s (1961) r a t i o n a l e x p e c t a t i o n s mode l . Moreover , a t ime s e r i e s approach does not r e q u i r e s o l v i n g the complete model to determine e x p e c t a t i o n format ion ( i . e . , expected p r i c e as a f u n c t i o n of the exogeneous pa ramete r s ) . T h i s i s an important advantage because i t a l l ows one to app ly more e a s i l y the time s e r i e s approach to e m p i r i c a l r e sea r ch yet ma in ta in the b a s i c p r o p e r t i e s of a f u l l y r a t i o n a l e x p e c t a t i o n approach . Ner love r e f e r s to t ime s e r i e s e x p e c t a t i o n fo rmat ion as " q u a s i -9 3 r a t i o n a l " . F o r t h i s s t u d y , t h e p r o c e d u r e w i l l b e t o e s t i m a t e a n A R I M A ( p , q ) f u n c t i o n f o r e a c h e x p e c t e d p r i c e v a r i a b l e i n t h e m o d e l . T h e g e n e r a l s p e c i f i c a t i o n o f a n A R I M A ( p , q ) m o d e l c a n b e w r i t t e n a s : (1 - <\>l - <|>2$2 - . . . - <f>p3P)AdY t = 6 t ( l - 0 X 3 - 0 2 3 2 - . . o - 0 q 3 q ) e t ' w h e r e B i s t h e b a c k s h i f t o p e r a t o r , .d . A Y t i s t h e o b s e r v e d v a r i a b l e d i f f e r e n c e d d t i m e s , ^ t i s a r a n d o m d i s t u r b a n c e t e r m , <$t i s a n i n t e r c e p t t e r m , a n d <l ) i a n d 0^ a r e t h e c o e f f i c i e n t s t o b e e s t i m a t e d . T h i s m o d e l c a n b e c o n v e n i e n t l y r e w r i t t e n a s : A d Y t = 6 + 0(3) e t . <f>(8) A v e r a g e a n n u a l p r i c e s , f o r t h e p e r i o d 1 9 4 6 t o 1 9 8 3 , f o r f i v e m a j o r a u c t i o n m a r k e t s i n w e s t e r n C a n a d a ( C a l g a r y , E d m o n t o n , R e g i n a , S a s k a t o o n , a n d W i n n i p e g ) w e r e p r o v i d e d b y A g r i c u l t u r e C a n a d a . A n A R I M A ( p , q ) m o d e l w a s e s t i m a t e d f o r e a c h c a t e g o r y o f a n i m a l i n e a c h m a r k e t l o c a t i o n . " T h e e s t i m a t e d r e s u l t s w e r e n o t s i g n i f i c a n t l y d i f f e r e n t i n e a c h m a r k e t l o c a t i o n . T h e r e f o r e , o n l y t h e r e s u l t s f o r t h e C a l g a r y m a r k e t w i l l b e p r e s e n t e d h e r e . T h e e s t i m a t e d e q u a t i o n s f o r t h e o t h e r m a r k e t l o c a t i o n s a r e r e p o r t e d i n A p p e n d i x E . I n F i g u r e 4 . 1 , a g r a p h o f t h e a u t o c o r r e l a t i o n a n d p a r t i a l a u t o c o r r e l a t i o n f u n c t i o n s f o r t h e s t e e r p r i c e s e r i e s i s p r e s e n t e d . A n e x a m i n a t i o n o f t h e s t r u c t u r e o f t h e s e f u n c t i o n s 9* FIGURE 4.1 Plot of Autocorrelation and P a r t i a l A utocorrelation Function, Steer Price Series, Calgary PLOT OF PARTIAL AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 LAG CORR. + + • + + * * * + * * I 1 0.859 4- IXXXXXXX+XXXXXXXXXXXXX 2 -0.265 +XXXXXXXI 4 3 0.040 4- IX 4< 4 -O.116 + XXXI 4-5 0.237 4- IXXXXXX 4-6 0.058 + IX 4-7 -0.113 + XXXI 4-8 -0.030 + XI 4-9 -0.088 4- XXI 4-10 -0.017 4- I 4-1 1 O.067 + IXX 4-12 -0.129 + XXXI 4-13 -0.069 4- XXI 4-14 -O.083 + XXI 4-15 O. 104 4- 1XXX 4-16 -0.061 4- XXI 4-17 -0.088 4- XXI 4-18 -0.036 4- XI 4-19 0.036 4- IX + 20 -0.025 4- XI 4-21 -O.087 4- XXI 4. 22 -0.018 4- I + 23 -O.093 4- XXI + 24 -0.067 4- xx^ 4-25 0.022 4- IX + 26 O. 109 4- IXXX 4 27 -0.012 • + I 4-28 -0.084 4. XXI 4-29 -0.117 4- XXXI 4-30 0.068 4 1 XX 4 31 0. 1 15 + IXXX 4-32 -0.033 + XI + PLOT OF AUTOCORRELATIONS - 1 . 0 - 0 . 8 - 0 . 6 - 0 . 4 - 0 . 2 0.0 0.2 0.4 0.6 0.8 1.0 LAG CORR. + 4- + + + 4. 4- + + 4- + I 1 0. .859 + IXXXXXXX+XXXXXXXXXXXXX 2 0. .669 4- IXXXXXXXXXXXX+XXXX 3 0. .510 4- IXXXXXXXXXXXXX 4-4 0. .360 4^  IXXXXXXXXX 4-5 0. ,290 4- IXXXXXXX 4-6 O. . 28 1 4- IXXXXXXX 4- • 7 O. .251 4- IXXXXXX 4-8 O. .210 + IXXXXX 4-9 O. 147 4- IXXXX 4-10 0. 065 4- IXX 4-1 1 0. 017 4- I + 12 -0. 026 4- XI 4-13 -0. 078 4- XXI + 14 -O. . 123 4- XXXI 4-15 -0. . 146 • XXXXI 4-16 -0. 167 4- XXXXI 4-17 -0. 192 4- XXXXXI 4-18 -0. 209 4- XXXXXI 4-19 -0. 214 4- XXXXXI 4 20 -0. 22 1 4- XXXXXXI 4-21 -0. 239 4- XXXXXXI 4-22 -0. 247 + XXXXXXI 4. 23 -0. 264 • XXXXXXXI 4-24 -o. 294 4- XXXXXXXI + 25 -0. 306 4- XXXXXXXXI 4-26 -0. 275 4. XXXXXXXI 4-27 -0. 223 4- XXXXXXI 4-28 -0. 178 4- XXXXI 4-29 -0. 169 4- XXXXI 4-30 -0. 17 1 4> XXXXI + 31 -0. 150 4- XXXXI 4-32 -o. 127 4- XXXI 4-95 suggests that the s e r i e s i s n o n - s t a t i o n a r y . In an attempt to c o r r e c t t h i s p rob lem, the s e r i e s i s t r ans fo rmed by f i r s t d i f f e r e n c e s . 5 A graph of the a u t o c o r r e l a t i o n and p a r t i a l a u t o c o r r e l a t i o n f u n c t i o n s r e p r e s e n t i n g the t rans formed s e r i e s i s reproduced in F i gu re 4 .2 . It appears tha t t h i s problem has been c o r r e c t e d . T h e r e f o r e , i t i s assumed tha t the f i r s t d i f f e r e n c e d p r i c e s e r i e s i s s t a t i o n a r y . The p l o t of the p a r t i a l a u t o c o r r e l a t i o n f u n c t i o n p resen ted in F i gu re 4.2 can be used to p r o v i d e an i n i t i a l s p e c i f i c a t i o n of the ARIMA model . The l a r g e s tandard e r r o r s in the f i r s t and second l ags may i n d i c a t e an a u t o r e g r e s s i v e p rocess of ( 2 , 1 , 0 ) . Subsequent l y , a v a r i e t y of a u t o r e g r e s s i v e s p e c i f i c a t i o n s were f i t t e d to the d a t a . In a d d i t i o n , a moving average component was e v e n t u a l l y i n c l u d e d in an attempt to f i n d the best s p e c i f i c a t i o n . 6 A f t e r d i a g n o s t i c checks were comp le ted , the" most a p p r o p r i a t e ARIMA s p e c i f i c a t i o n remained ( 2 , 1 , 0 ) . Fu r the rmore , the ARIMA(2,1,0) model p r o v i d e d the best f i t f o r each an imal p r i c e s e r i e s . T h i s i s not unexpected g i ven the i n t e g r a t e d nature of these markets . The ARIMA(2,1,0) s p e c i f i c a t i o n can be w r i t t e n as f o l l o w s : A P i t = * l A P i t - l + * 2 A P l t - 2 + £ i t ' where A i n d i c a t e s f i r s t d i f f e r e n c e s , ? ± i s the p r i c e s e r i e s fo r the i t h an imal c a t e g o r y , and $^  + $ 2 < 1 i s a necessa ry c o n d i t i o n f o r s t a t i o n a r i t y . The es t imated c o e f f i c i e n t s fo r each ARIMA(2,1,0) model , f o r each animal c a t e g o r y , are r epo r t ed in Tab le 4 . 1 . A l l FIGURE 4.2 Plot of Autocorrelation and Partial Autocorrelation Functions, First Differenced Steer Price Series, Calgary PLOT OF PARTIAL AUTOCORRELATIONS -1.0 -0.8 -0.G -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 LAG CORR. * + + + + + + + + • + I 1 0.266 4 IXXXXXXX4-2 -0.417 XX+XXXXXXXI 4 3 -0.060 4 XXI 4 4 -0.252 4 XXXXXXI • 5 0.043 + IX + 6 0.022 4 IX + 7 -0.080 4 XXI 4-8 0.095 4 IXX + 9 -0.070 4 XXI + 10 0. 141 4 IXXXX + 11 -0.030 4 XI + 12 0.081 4 IXX + 13 -0.056 4. XI + 14 0.007 4 I 4 15 -0.027 4 XI • 16 -0.034 4. XI 4 17 -0.049 4 XI + 18 -0.128 4 XXXI 4 19 -0.022 4 XI + 20 -0.043 4 XI 4 21 -0.029 4 XI 4-22 0.059 + IX 4-23 -0.049 * XI 4-24 0.010 4 I + 25 -0.116 4 XXXI + 26 -0.222 4 XXXXXXI 4-27 0.024 4 IX + 28 0.031 4 JX • 29 -0.122 4. XXXI • 30 0.013 4 I 4-PLOT OF AUTOCORRELATIONS -I.O -0.8 -0.6 -0.4 -0.2 O.O 0.2 0.4 0.6 0.8 1.0 LAG CORR. * • • + • + + 4- 4- 4- • I 1 O. 266 4 IXXXXXXX4 2 -O. 317 4XXXXXXXXI 4 3 -O. 277 4> XXXXXXXI 4 4 -O. 181 + XXXXXI 4 5 0. 031 4- IX 4 6 0. 198 4- 1XXXXX 4 7 . O. 053 4- IX 4 8 -0. OOO • I 4 9 -0. 04 1 4- XI 4 10 0. 006 4- I 4 11 O. 04 1 4- IX 4 12 0. .032 4. IX 4 13 -O. .043 4- XI 4 14 -0. .057 4- XI 4 15 -0 .036 4- XI . 4 16 O. ,005 4. I 4 17 -0. 006 4. I 4 18 -0. .060 4- xxt 4 19 -O. .051 4- XI 4 20 0 028 4- IX 4 21 0. .029 4- IX 4 22 O .068 4- IXX 4 23 0 .008 4- I 4 24 -0. .083 4 XXI 4 25 -0 , 124 4 XXXI 4 26 -0 .202 4 XXXXXI 4 27 -0 .029 4 XI 4 28 0 .237 4 IXXXXXX 4 29 0 .079 4 IXX 30 -0 .049 4 XI TABLE 4.1 Es t imated C o e f f i c i e n t s ARIMA(2,1,0) Mode l , S t e e r s , C a l v e s , Cows, and H e i f e r s ; Ca lga r y Equat ion Es t imated Coef f i c i e n t s S tandard E r r o r S t ee r s $1 $2 .4199 -.3962 . 164* .163* Ca l ves $1 $2 .5262 -.5853 .153* .160* Cows $1 $ 2 . 3343 -.3589 . 168** .166** Hei f e r s $1 $2 .3022 -.3017 . 171* * . 169**. * s i g n i f i c a n t at 10 percent l e v e l * * s i g n i f i c a n t at 5 percent l e v e l 98 es t imated c o e f f i c i e n t s are s i g n i f i c a n t at e i t h e r the 10 percent or 5 pe rcent l e v e l . Moreover , the necessary c o n d i t i o n fo r s t a t i o n a r i t y $^  + $^  < l i s s a t i s f i e d in each es t ima ted e q u a t i o n . From these es t ima ted e q u a t i o n s , a p r e d i c t i o n i s generated fo r each animal c a t e g o r y , fo r each yea r , to co r respond wi th the data base used in the econometr ic e s t i m a t i o n . P r i c e p r e d i c t i o n s fo r a l l cases are r epo r t ed in Appendix F. For s t e e r s and c a l v e s , the p r e d i c t e d ARIMA p r i c e i s d i s c o u n t e d back one p e r i o d and d e f i n e d as the expected p r i c e fo r each a n i m a l . For cows and h e i f e r s , however, i t i s assumed tha t farmers va lue a female animal next p e r i o d at i t s own expected p r i c e p l u s the p r i c e expected from the s a l e of i t s newborn c a l f . T h i s expected va lue i s d i s c o u n t e d back one p e r i o d and d e f i n e d as the expected p r i c e fo r each female a n i m a l . These expected p r i c e s e r i e s w i l l be combined wi th the main da ta base to complete the data requ i rements necessary fo r econometr i c e s t i m a t i o n . 4.3 DATA The main data base used in e s t i m a t i n g the econometr ic models was assembled from a v a r i e t y of s o u r c e s . Two surveys conducted by S t a t i s t i c s Canada (Farm Expend i tu re Survey (FES) and N a t i o n a l L i v e s t o c k Survey (NLS) 7 ) were the pr imary sources fo r i n ven to r y and expend i tu re data on cow-cal f farms. G e n e r a l l y , p r i c e s of farm inpu ts were ob t a i ned from the main Cansim f i l e s of S t a t i s t i c s Canada and c a t t l e output p r i c e s 99 were ob ta ined from market quo t a t i ons r epo r t ed in the L i v e s t o c k Market Review. The FES i s a p r o b a b i l i t y survey conducted annua l l y in the th ree p r a i r i e p r o v i n c e s and the Peace R i ve r r eg ion of B r i t i s h Co lumb ia . It i s des igned to p rov ide i n f o rma t i on on t o t a l a g r i c u l t u r e r e c e i p t s , farm input e x p e n d i t u r e s , i n v e n t o r i e s of l i v e s t o c k on farms, and land use in western Canada. T h i s survey i s d e f i n e d as an area frame su rvey . T h i s imp l i e s that a sample of farms from a s p e c i f i c a g r i c u l t u r a l census r eg ion i s s e l e c t e d in a random f a s h i o n for p a r t i c i p a t i o n in the su r vey . Some l a r g e farms are t a r g e t e d to be i n c l u d e d in the survey r e g a r d l e s s of whether they are s e l e c t e d in the random sample. Data are c o l l e c t e d by p e r s o n a l i n t e r v i ews from each p a r t i c i p a t i n g farm. From these d a t a , an es t imate fo r each v a r i a b l e i s genera ted fo r each s p e c i f i c a g r i c u l t u r a l census r e g i o n . The accuracy of the FES i s measured a g a i n s t the Census of A g r i c u l t u r e survey which i s taken every f i v e y e a r s . The es t ima tes generated by the FES are w i th i n approx imate l y 10 percent of the census bench m a r k s . 8 An example of the q u e s t i o n n a i r e fo r the 1981 FES and a map of the s o i l zones in western Canada appears in Appendix A. For purposes of e x t r a c t i n g i n fo rma t i on on b e e f - c a t t l e p r o d u c t i o n from the FES, a cow-ca l f farm was d e f i n e d to have t h i r t y or more beef breed ing cows in i n v e n t o r y . Acco rd ing to t h i s d e f i n i t i o n , S t a t i s t i c s Canada p rov ided data on f o r t y -seven v a r i a b l e s fo r four teen s o i l zone l o c a t i o n s f o r the p e r i o d 1978 to 1981. T h i s r e s u l t e d in a t o t a l c r o s s -100 s e c t i o n a l , t i m e - s e r i e s sample of f i f t y - s i x o b s e r v a t i o n s . Tab le 4.2 p rov i des summary i n fo rma t i on on each v a r i a b l e c o l l e c t e d . At tempts to "estimate output supp ly equa t ions fo r each an imal ca tegory were u n s u c c e s s f u l due to s e r i o u s m u l t i c o l l i n e a r i t y p rob lems . I t was dec i ded t h e r e f o r e , to s p e c i f y three aggregate output g roups : 1) t o t a l c a t t l e supp ly s o l d o f f fa rms; 2) t o t a l end-o f-pe r i od i n ven to r y demand; and 3) t o t a l c rop s u p p l y . 9 The FES does not p rov ide d i r e c t i n f o r m a t i o n on c a t t l e s o l d o f f f a r m s . 1 0 However, us ing a combina t ion of i nven to ry d a t a , c a l v i n g r a t e s , and growth r a t e s of an ima ls in d i f f e r e n t c a t e g o r i e s , va lues f o r t h i s v a r i a b l e can be gene ra t ed . F i g u r e 4.3 p r o v i d e s a d iagrammatic i l l u s t r a t i o n of how t h i s v a r i a b l e i s de t e rm ined . S p e c i f i c a l l y , the supply of an imals i s determined as f o l l o w s : Female Supp ly : Cows in p e r i o d t are e i t h e r s o l d in p e r i o d t or are ma in ta ined on farms and become pa r t of the cow inven to r y in t+1. H e i f e r s in p e r i o d t are e i t h e r s o l d in p e r i o d t or become cows in p e r i o d t and ma in ta ined on farms to become pa r t of cow i n ven to r y in t+1. Consequen t l y , female supp ly i s equa l to the number of cows and h e i f e r s in p e r i o d t minus the number of cows in p e r i o d t+1. S tee r Supp l y : S t e e r s are norma l l y s o l d o f f farms f o r f i n i s h i n g at approx imate l y n ine hundred pounds. Consequen t l y , s t e e r s r e p o r t e d on farms in p e r i o d t w i l l be s o l d du r i ng the p e r i o d and t h e r e f o r e not r epo r t ed as i n ven to r y i n t+1. C a l f Supp l y : Ca l ves r epo r t ed on farm in p e r i o d t w i l l 101 TABLE 4.2 Summary of FES Da t a : C r o s s - S e c t i o n a l V a r i a b l e Mean Minimum Maximum Cash r e c e i p t s from Custom Work $ 1 ,869,000 19,548 25,377,000 M i s c e l l a n e o u s Farm Expenses $ 1 , 133,500 116,310 5,232,300 Cash Wage, H i r e d Labour § 6,155,200 341 , 1 10 24,513,000 Cash Wage, Fami ly Labour $ 1,650,800 25,571 6,180,800 Cash V a l u e , H i r e d Labour Room and Board $ 413,360 30,686 2,372,100 P e s t i c i d e Expend i tu re $ 3,864,700 49,032 15,202,000 Custom Work Expenses $ 3,570,700 222,840 15,158,000 Feed and Supplements Expenses $ 12,817,000 267,290 73,786,000 V e t e r i n a r y medic ine and A r t i f i c i a l Inseminat ion Expenses $ 1,491,900 74,612 5, 105,900 Expend i tu r e on Loans$ 1,3831,000 470,260 63,170,000 Te lephone Expenses $ 700,480 31,288 1,702,900 E l e c t r i c i t y Expenses $ 1 ,802,500 53,395 4,628,800 F u e l Expenses $ 1 , 147,900' 55,020 4 ,188,200 Insurance Premiums $ 3,379,500 68,834 10,846,000 P rope r t y Taxes $ 3,649,100 116,780 9,890,500 C a p i t a l Cost A l lowance $ 31 ,451,000 1,294,600 82,233,000 T o t a l Ac res Seven G r a i n s 1 ,032,400 27,970 2,599,300 Ac res Tame Hay 294,600 28,481 902,700 Ac res Land Renta l 1 ,534,400 67,474 4,076,000 Repa i r s to Farm B u i l d i n g s $ 2, 121,900 66,505 7,906,600 Repa i r t o Fences $ 1 ,309,800 27,204 3,758,900 Expend i tu re Twine and Wire $ 783,390 38,084 1,856,400 Expend i tu re Hardware $ 1,484,900 59,141 3,995,100 102 Tab le 4.2 ( con t . ) Summary of FES Da t a : C r o s s - S e c t i o n a l V a r i a b l e Mean Minimum Maximum Acres of Other Crops 25,177 898 87,378 Acres of Summer Fa l low 508,120 6,693 1,637,000 Acres A l l Crops 1,864,000 71 ,841 3,927,800 Acres Improved Pasture 203,090 26,874 809,560 T o t a l Other Land 1,928,300 119,470 4,792,600 Ren ta l Expenses $ 7,546,700 339,300 26,578,000 Machinery Expenses $ 22,922,000 1,480,200 69,540,000 Seed Expenses $ 2,331,600 171,020 6,675,600 F e r t i l i z e r Expenses $ 9,938,500 458,540 46,615,000 I r r i g a t i o n Expenses $ 175,000 0 1,894,700 Other Ope ra t i ng Expenses $ 301,870 9,496 1,844,200 T o t a l A g r i c u l t u r e Re ce i p t s $ 195,230,000 10,758,000 618,420,000 P o r t i o n of Rece ip t s from the Sa le of G ra ins $ 74,194,000 1 ,716,800 243,950,000 T o t a l Ac res A l l Land 3,990,200 230,320 8,931,600 Oats Fed bu . 3,788,900 131 ,520 11,085,000 Ba r l e y Fed bu . 4 ,723,000 106,200 31,828,000 Wheat Fed bu . 203,130 0 786,410 Ca l ves # 154,120 7,650 333,920 T o t a l C a t t l e and Ca l ves # 147,030 24,569 974,960 Ca l ves Born A l i v e Las t S ix Months # 159,120 7,835 331,550 Cows and H e i f e r s Expected to Ca lve Next S ix Months # 7,611 0 36,672 Beef Cows # 182,550 9,269 517,090 B u l l s # 8,629 853 24,512 S t ee r s # 41,051 2,634 146,540 103 FIGURE 4.3 C a t t l e Supply o f f Farms Inventory t Inventory t+1 Cows t H e i f e r s t S t ee r s t Ca l v e s t C a l v e s Born t Cows t+1 H e i f e r s t+1 S t e r s t+1 Ca l ves t+1 Ca l v e s Born t+1 104 e i t h e r be s o l d du r i ng the p e r i o d or enter h e i f e r or s t ee r i n v e n t o r i e s in t + 1 . Ca l ves born du r i ng p e r i o d t w i l l e i t h e r be s o l d or enter c a l f i n v e n t o r i e s in t + 1 . Consequen t l y , c a l f supply i s equa l to the number of c a l v e s in p e r i o d t p l u s the number, of c a l v e s born in p e r i o d t l e s s the number of h e i f e r s , s t e e r s , and c a l v e s in i n ven to r y in t + 1 . T o t a l c a t t l e supply i s d e f i n e d as the sum of an imals s o l d in each c a t e g o r y . Annual average c a t t l e p r i c e s from f i v e major western Canadian a u c t i o n m a r k e t s 1 1 ( Ca lga r y , Edmonton, Reg ina , Saska toon , and Winnipeg) are a v a i l a b l e fo r each an imal c a t e g o r y . These p r i c e s were used to generate a weighted average p r i c e fo r a l l c a t t l e . The weights r ep resen ted the number of an imals in each ca tegory m u l t i p l i e d by the average weight ( in pounds) of an animal in each c a t e g o r y . T o t a l revenue ob t a i ned from the s a l e of c a t t l e i s determined by the number of an imals ( m u l t i p l i e d by the average weight of an an imal ) m u l t i p l i e d by the weighted average p r i c e of a l l c a t t l e . The t o t a l number of an ima ls in i n ven to r y at the end of the p e r i o d i s taken d i r e c t l y from the FES and i s equa l to the sum of an ima ls in each c a t e g o r y . For econometr i c s p e c i f i c a t i o n , i t was dec ided tha t r a the r than u s i n g the expected p r i c e of c a t t l e next p e r i o d , i t would be p r e f e r a b l e to generate a v a r i a b l e r e p r e s e n t i n g the expected ga in from ma in t a i n i ng the an imal on the farm and s e l l i n g i t next p e r i o d . T h i s expected ga in v a r i a b l e was d e f i n e d by f i r s t s u b t r a c t i n g the revenue r e c e i v e d from the s a l e of an ima ls from 105 the va lue of the beg inn ing s tock of a n i m a l s . Next , the d i s c o u n t e d va lue of the end-o f-pe r i od s tock of an imals was genera ted us ing (ARIMA) expected p r i c e s from which the reduced va lue of the beg inn ing herd was s u b t r a c t e d . Us ing t h i s p rocedu re , the t o t a l d i s c o u n t e d expected ga in was gene ra ted . F i n a l l y , the d i s c o u n t e d expected ga in per head was generated by d i v i d i n g t o t a l d i s c o u n t e d expected ga ins by the number of an ima ls at the end of the p e r i o d , m u l t i p l i e d by the average weight of an animal in each c a t e g o r y . A q u a n t i t y index of c rop output i s genera ted by d i v i d i n g the t o t a l r e c e i p t s from the sa l e of c r o p s , as r epo r t ed in the FES, by an aggregate c rop p r i c e i ndex . The aggregate c rop p r i c e index was p rov ided by A g r i c u l t u r e Canada and i s d e f i n e d to equa l 100 in 1971. The FES r e p o r t s expend i tu re data f o r twenty-four input v a r i a b l e s . Farm input p r i c e indexes were t h e r e f o r e r e q u i r e d to co r r e spond to these twenty-four expend i tu re v a r i a b l e s . These p r i c e indexes were ob ta ined from S t a t i s t i c s Canada 's Cansim data f i l e on a p r o v i n c i a l b a s i s f o r each year 1978 to 1981. A l l p r i c e indexes are set to 100 in the base year of 1971 . It was dec ided to aggregate expend i t u r e s i n t o th ree g roups : l a b o u r , c a p i t a l , and m a t e r i a l s and s e r v i c e s . Labour expenses i n c l u d e d expend i t u r e s on h i r e d l a b o u r , f a m i l y l a b o u r , and room and boa rd . The h i r e d l abour wage ra te was used as the l abour p r i c e index and i t was assumed that t h i s wage was p a i d to both h i r e d and f am i l y l a b o u r . C a p i t a l expenses i n c l u d e d expend i t u r e s on r e p a i r s to 106 b u i l d i n g s , r e p a i r s to f e n c e s , c a p i t a l d e p r e c i a t i o n , machinery expenses , t a x e s , custom work, f i n a n c i a l loan expenses , l and r e n t a l , and a f low v a r i a b l e r e p r e s e n t i n g the s e r v i c e s from a g i ven s tock of l a n d . 1 2 The c a p i t a l p r i c e index i s generated us i ng a Cobb-Douglas aggregator f u n c t i o n ' 3 and r ep resen t s fo r each v a r i a b l e in t h i s c a t e g o r y , the r e n t a l p r i c e of annual per u n i t f lows of s e r v i c e s . M a t e r i a l s and s e r v i c e s expenses i n c l u d e d expend i tu res on feed and supplements , v e t e r i n a r y m e d i c i n e s , a r t i f i c i a l i n s e m i n a t i o n , t e l ephone , e l e c t r i c i t y , f u e l , i r r i g a t i o n , hardware, m i s c e l l a n e o u s farm expenses , and o ther ope r a t i ng expenses . The m a t e r i a l s and s e r v i c e s p r i c e index was a l s o genera ted us ing a Cobb-Douglas aggrega tor f u n c t i o n fo r the d e f i n e d v a r i a b l e s . I t was d e c i d e d , f o r a t r a c t a b l e s p e c i f i c a t i o n , to s p e c i f y on l y one o v e r a l l f i x e d s tock v a r i a b l e r a the r than separate ones for each an imal c a t e g o r y . T h i s v a r i a b l e was d e f i n e d as the number of beg inn ing an imals in a l l c a t e g o r i e s and i s ob ta ined d i r e c t l y from the FES. F i n a l l y , an es t ima te of p r o f i t i s genera ted by t ak i ng t o t a l revenue (the sum of revenue from c a t t l e s a l e s , c r op s a l e s , and t o t a l d i s c o u n t e d expected ga ins ) and s u b t r a c t i n g t o t a l expend i tu r e s on v a r i a b l e i n p u t s . A l l v a r i a b l e s are d e f i n e d in r e a l terms by d i v i d i n g by the consumer p r i c e index (1971=100). The d e f i n i t i o n s of each expend i tu re and p r i c e v a r i a b l e are summarized in Tab l e 4 . 3 . In a d d i t i o n , a complete l i s t i n g of a l l data used i n the t r a n s f o r m a t i o n s i s r epo r t ed in 107 TABLE 4.3 D e f i n i t i o n of V a r i a b l e s (T rans log ) Var i a b l e D e f i n i t i o n P C a t t l e Output P r i c e Index Weighted Average P r i c e Index A l l C a t t l e P^  Expected C a t t l e P r i c e Index Weighted Average Expected Gain A l l C a t t l e P 3 Crop Output P r i c e Index Index of the P r i c e of a l l Crops Produced P Labour Input P r i c e Index Index of the Hour l y wage Rate P C a p i t a l Input P r i c e Index P M a t e r i a l s and S e r v i c e s 6 Input P r i c e Index A b Beg inn ing C a t t l e I n ven to r i e s Si C a t t l e Revenue Share S 2 Expected C a t t l e Revenue Share S3 Crop Revenue Share S4 Labour Expend i tu re Share S5 C a p i t a l Expend i tu re Share Index of the Ren ta l P r i c e of C a p i t a l Index of the P r i c e of A l l M a t e r i a l s and S e r v i c e s T o t a l Number of An imals Beg inn ing of Each Pe r i od T o t a l Revenue from the Sa le of A l l C a t t l e D i v i d e d by T o t a l P r o f i t T o t a l Expected Gain Revenue from the Sa le of C a t t l e Next P e r i od D i v i d e d by T o t a l P r o f i t T o t a l Revenue from the Sa le of A l l Crops D i v i d e d by T o t a l P r o f i t T o t a l Expend i tu re fo r H i r e d and Fami ly Labour P lus Room and Board D i v i d e d by T o t a l P r o f i t E s t ima ted Expend i tu re of the Flow of C a p i t a l S e r v i c e s D i v i d e d by T o t a l P r o f i t S6 M a t e r i a l s and S e r v i c e s Expend i tu re Share T o t a l Expend i tu re on A l l M a t e r i a l s and S e r v i c e s D i v i d e d by T o t a l P r o f i t 108 Appendix B. The NLS p r o v i d e s an a l t e r n a t i v e source from which to o b t a i n es t ima tes of c a t t l e i n v e n t o r i e s . T h i s p u b l i c a t i o n r epo r t s the t o t a l number of an ima ls on farms in each ca tegory fo r each p rov ince on a t i m e - s e r i e s b a s i s . For the purposes of t h i s s tudy , c a t t l e i n v e n t o r i e s were c o l l e c t e d fo r western Canada, fo r the p e r i o d 1956 to 1982. Inc luded in the i n ven to r y data were es t ima tes of c a l v i n g r a t e s . The NLS does not p rov ide i n fo rma t i on on farm input expend i tu r e s or t o t a l c r op output supply f o r cow-cal f fa rms . The consequence of t h i s l i m i t e d data base i s that econometr i c equa t ions can on ly be s p e c i f i e d for two output e q u a t i o n s : 1) t o t a l c a t t l e output s u p p l y ; and 2) t o t a l end-of-p e r i o d inven to ry demand. Both v a r i a b l e s were genera ted a c c o r d i n g to the procedures o u t l i n e d fo r the c o r r e s p o n d i n g v a r i a b l e s ' in the FES c a s e . In a d d i t i o n , the output p r i c e fo r each v a r i a b l e i s determined on a t i m e - s e r i e s b a s i s f o l l o w i n g the p rocedures p r e v i o u s l y o u t l i n e d . A g r i c u l t u r e Canada p r o v i d e d aggregate p r i c e indexes c o r r e s p o n d i n g to the three input groups d e f i n e d in the FES c a s e . These p r i c e indexes r ep resen t p r i c e changes , fo r the th ree input g roups , fo r western Canada over the p e r i o d 1956 to 1982. Each index has a base of 100 in 1971. F i n a l l y , b e g i n n i n g - o f - p e r i o d s tocks of c a t t l e fo r each y e a r , f o r western Canada, were ob ta ined d i r e c t l y from the NLS. D e f i n i t i o n s of the output and p r i c e v a r i a b l e s are summarized in Tab l e 4 .4 . In a d d i t i o n , a complete l i s t i n g of the t ime-s e r i e s da ta , i s r epo r t ed in Appendix C. 109 TABLE 4.4 D e f i n i t i o n of V a r i a b l e s (T ime-Ser ies Data) V a r i a b l e D e f i n i t i o n Pj^  C a t t l e Output P r i c e Index —e P 2 Expected C a t t l e P r i c e Index P-j Crop Output P r i c e Index P4 Labour Input P r i c e Index P5 C a p i t a l Input P r i c e Index P6 M a t e r i a l s and S e r v i c e s Input P r i c e Index A b Beg inn ing C a t t l e I n v e n to r i e s Qc Q u a n t i t y of C a t t l e Produced A e End-o f-Pe r i od I n v e n t o r i e s Weighted Average Time-S e r i e s P r i c e Index A l l C a t t l e Weighted Average Time-S e r i e s Expec ted Gain A l l C a t t l e T ime-Ser ies Index of the P r i c e of a l l Crops Produced T ime-Ser ies Index of the Hour l y Wage Rate Time S e r i e s Index of the Ren ta l p r i c e of C a p i t a l T ime-Ser ies Index of the P r i c e of a l l M a t e r i a l s and S e r v i c e s T o t a l Number of An imals Beg inn ing of Each P e r i o d , T ime-Ser i es Output of a l l C a t t l e , T ime-Ser ies T o t a l Number of a l l Animal at the End of the P e r i o d , T ime-Ser ies 110 Before p roceed ing wi th the econometr ic s p e c i f i c a t i o n of the model , i t i s i n t e r e s t i n g to c o n s i d e r the consequences of u s i ng a c r o s s - s e c t i o n a l (FES) ve rsus t i m e - s e r i e s (NLS) data base i n the e s t i m a t i o n . In the c r o s s - s e c t i o n a l d a t a , beg inn ing s tocks of c a t t l e are d e c l i n i n g over the four year p e r i o d . One would expect tha t because p roducers are not r e s t r i c t e d in r educ ing herd s i z e , beg inn ing s tocks of c a t t l e can be c o n s i d e r e d to be at some op t ima l l e v e l g i ven the l e v e l of the exogeneous v a r i a b l e s . Consequen t l y , e l a s t i c i t i e s of c h o i c e shou ld be i n t e r p r e t e d under the assumption of a f u l l y a d j u s t e d beg inn ing s tock of a n i m a l s . In the t i m e - s e r i e s d a t a , beg inn ing s tocks of c a t t l e have g e n e r a l l y i n c r ea sed over the t ime p e r i o d c o n s i d e r e d . However, the r a te at which herd s i z e can i n c r ease i s r e s t r i c t e d by the b reed ing c a p a b i l i t y of the female h e r d . Consequen t l y , e l a s t i c i t i e s of cho i c e shou ld be i n t e r p r e t e d under the assumpt ion tha t beg inn ing s tocks of c a t t l e may not have a d j u s t e d comp le te l y to changes in the exogeneous v a r i a b l e s . G iven the Le C h a t e l i e r P r i n c i p l e ( S i l b e r b e r g 1978), one can conc lude tha t own e l a s t i c i t i e s of supp ly e s t ima ted u s i n g c r o s s - s e c t i o n a l data (FES) w i l l be g rea te r than (or at l e a s t equa l to) co r r e spond ing es t ima tes u s i ng t i m e - s e r i e s da ta ( N L S ) . 1 " T h i s a p r i o r i p r e d i c t i o n on the magnitude of e l a s t i c i t i e s of cho i c e w i l l be c h a l l e n g e d e m p i r i c a l l y in Chapter F i v e . 111 4.4 STOCHASTIC SPECIFICATION AND ESTIMATION TECHNIQUES The t r a n s c e n d e n t a l l o g a r i t h m i c f u n c t i o n a l form i s p o s t u l a t e d for the m u l t i - o u t p u t , m u l t i - i n p u t v a r i a b l e p r o f i t f u n c t i o n . The r e s t r i c t e d t r a n s l o g p r o f i t f u n c t i o n i s d e f i n e d as a second order l o g a r i t h m i c T a y l o r s e r i e s expans ion . For the t h r e e - o u t p u t , t h r e e - i n p u t , one f i x e d f a c t o r c a s e , i t can be w r i t t e n a s : « U - ° _ b ° _ 6 6 lnIl(P,A ) = a. + E a.lnP. + hZ Z y^lrtAnP^ ° 6 1=1 1 1 1=1 h=l i h 1 h Z 6,lnP.lnA b + B, l n A b + , l n A b l n A b , i 1 k kk where n ( P,A b) i s r e s t r i c t e d p r o f i t ( t o t a l revenues minus t o t a l c o s t s of v a r i a b l e i n p u t s ) , P i s a s i x - d i m e n s i o n a l v ec to r r e p r e s e n t i n g output p r i c e s of c a t t l e , expected p r i c e of c a t t l e and c r o p s , and input p r i c e s of l a b o u r , c a p i t a l , and m a t e r i a l s . A b i s the beg inn ing s tock of c a t t l e on farms. Symmetry of the Hess i an mat r ix r e q u i r e s Y ih = Y h i , f o r a l l i and h and homogeneity of degree one in p r i c e s r e q u i r e s the f o l l o w i n g r e s t r i c t i o n s on the pa ramete rs : (4.2) D O o Z a. = l . Z Y = n. h = i fi. r t 6 6 . 6 E " It E Y,, = 0, h = 1....6, Z 6 J = 0. 1=1 1 1=1 l h 1=1 M u l t i c o l l i n e a r i t y problems g e n e r a l l y p rec lude d i r e c t econometr i c e s t i m a t i o n of the parameters in Equat ion ( 4 . 1 ) . However, i f one assumes that the t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n s a t i s f i e s (at l e a s t l o c a l l y ) c o n d i t i o n s (J[ ) to (Tl6) of Chapter T h r e e , the revenue share equa t ions fo r each output and expend i tu re share equa t ions for each input can be ob t a i ned by a p p l y i n g H o t e l l i n g ' s Lemma to ( 4 . 1 ) : U . 3 ) a i r J I ( ? , A b ) = s. = ? l q i i » 8lnP ± n 1 12 where Pi i s the p r i c e of the i t h output or i n p u t , q i i s the q u a n t i t y of the i t h output or i n p u t , and expend i tu re shares are a f f i x e d wi th negat i ve s i g n s . For econometr ic e s t i m a t i o n , the t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n w i l l be c o n s i d e r e d an exact r e p r e s e n t a t i o n of the t rue p r o f i t f u n c t i o n . If the t r a n s l o g f u n c t i o n i s assumed to approximate the t rue p r o f i t f u n c t i o n in the econometr ic a n a l y s i s , then the e r r o r terms appended to each equa t ion must account f o r e r r o r s in approx imat ion as we l l as random e r r o r s in p r o f i t maximiz ing b e h a v i o r . In s p e c i f y i n g s t o c h a s t i c d i s t u r b a n c e s fo r the equa t ions in ( 4 . 3 ) , i t i s assumed that any d e v i a t i o n of a c t u a l revenue or expend i tu re shares from p r o f i t maximiz ing l e v e l s i s due to random e r r o r s in o p t i m i z a t i o n . These random d i s t u r b a n c e s are modeled by appending a d d i t i v e d i s t u rbance terms ( e i ) to each share equa t ion in ( 4 . 3 ) . Fu r the rmore , i t i s assumed that e i ' s are norma l l y d i s t r i b u t e d w i th zero means and a p o s i t i v e s e m i d e f i n i t e v a r i a n c e - c o v a r i a n c e ma t r i x , ft . The v a r i a n c e -c o v a r i a n c e mat r ix must be p o s i t i v e s e m i d e f i n i t e because the adding-up c o n s t r a i n t on the share equat ions i m p l i e s tha t i t w i l l be s i n g u l a r . The s i n g u l a r i t y of ft i s avo ided in the econometr i c procedure by d ropp ing one share equa t ion in the e s t i m a t i o n . F i n a l l y , the v e c to r of e r r o r s i s assumed to be contemporaneous ly c o r r e l a t e d a c ros s equa t ions but t empora l l y independent . These c o n d i t i o n s can be w r i t t en a s : e ± ~ N(0,a*), E ( e l t e J t ) = 0 l j ' a n d  E ( e l t e j s ) = 0 V fc * s ' 113 The c r o s s - s e c t i o n a l , t i m e - s e r i e s nature of the sample u t i l i z e d in the econometr ic e s t i m a t i o n of Equa t ion (4.3) n e c e s s i t a t e s the use of c o v a r i a n c e e s t i m a t o r s 1 5 to take account of y e a r l y d i f f e r e n c e s in the d a t a . • To save degrees of f reedom, the c o v a r i a n c e e s t ima to r s take the form of y e a r l y dummy v a r i a b l e s and are a t t a ched to the cons tan t term in each share e q u a t i o n . The share equa t ions fo r c a t t l e , end-o f-pe r i od i n v e n t o r i e s , c r o p s , l a b o u r , c a p i t a l , and m a t e r i a l s can now be r e w r i t t e n i n c o r p o r a t i n g e r r o r terms and y e a r l y dummy v a r i a b l e s a s : (4.4) 6 3 S i ' a i + I / i h l n P h + 6 i l n A + I A i Dk + e i 1 = 1 6> n=l k=l where Dk i s a dummy v a r i a b l e f o r year k ( i . e . , Dk takes the va lue 1 in year k and ze ro o therw ise ) and a l l o ther v a r i a b l e s are as p r e v i o u s l y d e f i n e d . The c r o s s equa t ion c o n s t r a i n t s imposed by the symmetric Hess i an mat r i x and o ther r e s t r i c t i o n s to be d i s c u s s e d below, n e c e s s i t a t e the use of a m u l t i v a r i a t e g e n e r a l i z e d l e a s t squares procedure to es t imate ( 4 . 4 ) . To ensure e f f i c i e n t e s t i m a t i o n of the pa ramete rs , Z e l l n e r ' s seemingly u n r e l a t e d r e g r e s s i o n (SUR) t echn ique i s employed. The m a t e r i a l s ' share equa t i on i s dropped in the e s t i m a t i o n to ensure non-s i n g u l a r i t y of ft . Z e l l n e r ' s SUR es t ima tes of the parameters are i n v a r i a n t to which equa t ion i s dropped and are a s y m p t o t i c a l l y e q u i v a l e n t to maximum l i k e l i h o o d es t ima tes i f the c o e f f i c i e n t s are i t e r a t e d u n t i l convergence (Barten 1969). 1 14 In order f o r there to e x i s t a dua l r e l a t i o n s h i p between the v a r i a b l e p r o f i t f u n c t i o n and the u n d e r l y i n g t r a n s f o r m a t i o n f u n c t i o n , Equa t ion 4.1 must s a t i s f y the p r o p e r t i e s of symmetry, homogeneity of degree one in p r i c e s , m o n o t o n i c i t y , and c o n v e x i t y in p r i c e s . These p r o p e r t i e s must a l s o ho ld in the es t ima ted system of share equa t ions ( 4 . 4 ) . However, fo r the t r a n s l o g f u n c t i o n , these p r o p e r t i e s do not h o l d g e n e r a l l y but may ho ld over an a r b i t r a r y set of d a t a . A necessary and s u f f i c i e n t c o n d i t i o n f o r the t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n to s a t i s f y symmetry i s that the H e s s i a n mat r ix of (4.4) wi th r e spec t to p r i c e s be symmetr ic . T h i s i m p l i e s that the es t imated share equa t ions shou ld s a t i s f y the p r o p e r t y that Yih = yhi, f o r a l l i and h. The p rope r t y of homogeneity of degree one in p r i c e s for the v a r i a b l e p r o f i t f u n c t i o n i m p l i e s tha t the share equa t ions are homogeneous of degree zero in p r i c e s . T h i s c o n d i t i o n imposes the f o l l o w i n g r e s t r i c t i o n s on the es t imated pa ramete rs : 6 Z Y.. = 0 i = 1 6, h=l i n 6 Z y = 0 h = 1,...6, and 1=1 6 Z 6 = 0 i = 1,...,6. 1=1 In a d d i t i o n , the f o l l o w i n g adding up r e s t r i c t i o n s are imposed on the dummy v a r i a b l e s : 3 Z 3 = 0 i = 1,...,6 and k=l fcl 6 Z B = 0 k = 1,2,3. 1=1 The p r o p e r t i e s of mono ton i c i t y and c o n v e x i t y are not p r o p e r t i e s which are e a s i l y summarized as l i n e a r r e s t r i c t i o n s 115 on the share e q u a t i o n s . Ra ther , the c o n s i s t e n c y of these p r o p e r t i e s w i th the share equa t ions w i l l be eva lua t ed a f t e r e s t i m a t i o n . To s a t i s f y m o n o t o n i c i t y , the p r e d i c t e d shares must be p o s i t i v e fo r revenues and nega t i ve fo r e x p e n d i t u r e s . A necessa ry c o n d i t i o n fo r convex i t y in p r i c e s i s tha t own supply e l a s t i c i t i e s are p o s i t i v e and own d e r i v e d demand e l a s t i c i t i e s are n e g a t i v e . A necessary and s u f f i c i e n t c o n d i t i o n f o r convex i t y i s that the Hess i an of the v a r i a b l e p r o f i t f u n c t i o n wi th respec t to p r i c e s i s p o s i t i v e s e m i d e f i n i t e . T h i s Hess ian mat r ix [H] can be c o n v e n i e n t l y c h a r a c t e r i z e d in terms of the es t ima ted c o e f f i c i e n t s in (4.4) and the p r e d i c t e d revenue and expend i tu re s h a r e s . [H] i s w r i t t e n a s : Y n + S 1 ( S 1 - l ) Y 1 2 + S l S z ... Y 1 6 + S l S e Y 2 1 + S 2 S 1 Y 2 2 + S 2 ( S 2 - 1 } Y 2 6 + S 2 S 6 [H] = ' . • • Y61 + S 6 S 1 Y62 + S 6 S 2 W W " 1 * where [H] must be p o s i t i v e s e m i d e f i n i t e . Rather than m a i n t a i n i n g the hypotheses of symmetry and homogeneity of degree zero in p r i c e s , i t i s p r e f e r a b l e to t e s t s t a t i s t i c a l l y f o r these p r o p e r t i e s . Tab le 4.5 summarizes the l i n e a r r e s t r i c t i o n s on the share equa t ions as n u l l hypo theses . A l i k e l i h o o d r a t i o t e s t w i l l be used fo r h ypo thes i s t e s t i n g . The l i k e l i h o o d r a t i o t e s t compares the va lue of the l i k e l i h o o d f u n c t i o n under the n u l l h ypo thes i s (Lo) ( i . e . , w i th r e s t r i c t i o n s imposed on the model) to the va lue of the u n r e s t r i c t e d l i k e l i h o o d f u n c t i o n ( La ) . I t i s we l l known that 1 16 -2( InLa-lnLo) i s a s y m p t o t i c a l l y d i s t r i b u t e d as Ch i - squa r ed . The n u l l h ypo thes i s i s r e j e c t e d or not r e j e c t e d depending on whether the va lue of -2( InLa-lnLo) i s g r e a t e r or l e s s than a c r i t i c a l va lue of x 2 w i th k degrees of f reedom, where k i s the number of independent r e s t r i c t i o n s . A f t e r t e s t i n g f o r these p r o p e r t i e s , symmetry and homogeneity of degree zero in p r i c e s w i l l be imposed on the es t imated model and f u r t h e r s t a t i s t i c a l t e s t i n g w i l l be done under these ma in ta ined hypotheses . Once the c o n d i t i o n s fo r p r o f i t max imiza t ion have been s a t i s f i e d , the es t ima ted share equa t ions can be used to d e s c r i b e c e r t a i n p r o p e r t i e s of the u n d e r l y i n g t r a n s f o r m a t i o n f u n c t i o n . Of p a r t i c u l a r i n t e r e s t in t h i s s tudy i s whether the u n d e r l y i n g t r a n s f o r m a t i o n f u n c t i o n can be d e s c r i b e d a s : i ) "a lmost homothe t i c " in 'outputs ; i i ) "a lmost homogeneous" in o u t p u t s ; and i i i ) e x h i b i t i n g j o i n t p r o d u c t i o n between c rops and c a t t l e supp l y , as d e f i n e d in S e c t i on (3.9) of Chapter Th ree . These c h a r a c t e r i s t i c s of the t r a n s f o r m a t i o n f u n c t i o n are t e s t e d by imposing l i n e a r r e s t r i c t i o n s on the parameters of the es t ima ted share e q u a t i o n s . Tab le 4.5 summarizes the l i n e a r r e s t r i c t i o n s on Equa t ion (4.4) which are s u f f i c i e n t c o n d i t i o n s f o r the t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n to be c o n s i s t e n t wi th these three p r o p e r t i e s . A l i k e l i h o o d r a t i o t e s t w i l l aga in be used to t e s t each p r o p e r t y . The es t ima ted parameters of the revenue share equa t ions can a l s o be used to p rov ide a measure of sho r t run r e tu rns to s c a l e (RTS) in the cow-cal f i n d u s t r y . G e n e r a l l y , e s t ima tes of r e tu rns to s c a l e are determined under the ma in ta ined 117 TABLE 4.5 T e s t i n g for S t r u c t u r e wi th L inea r R e s t r i c t i o n s on the Share Equa t ions P roper ty L i nea r R e s t r i c t i o n s on Share E q u a t i o n s ( 4 . 4 ) : N u l l Hypotheses Symmetry Ho: T i h " Y h j = 0 v i ' h » = 1 6 Homogeneity o-f Degree b Zero in P r i c e s Ho: E Y ,u = 0 Vi = 1.....6 h=1 n Almost Homothe t i c i t y in 3 Output P r i c e s Ho: E Y i h = 0 h = 1,2,3 Almost Homogeneity in Output P r i c e s i = 1 H o : E Y j h = 0 h - 1,2,3 i = 1 H o : E Y-u = 0 h = i»,5,6 i-4 , h Ho: E 6. = 0 Vi = 1 6 1-1 ' J o i n t P roduc t i on Technology in Crops and Beef HO: a i 3 = 0 ' = 1.2 Ho: a 3 h = 0 h = 1,2 1 18 hypo thes i s of homogeneity in t e chno logy . However, Weaver (1982) has d e r i v e d a formula to measure r e t u r n s to s ca l e in non-homothet ic mu l t i -ou tpu t t e c h n o l o g i e s . Fur thermore , r e s t r i c t i o n s are imposed on the formula to ensure that the measurement i s taken a long the expans ion p a t h . For the mu l t i -ou tpu t v a r i a b l e t r a n s l o g p r o f i t f u n c t i o n , a measure of r e tu rns to s c a l e can be es t ima ted us ing the f o l l o w i n g f o rmu l a : 3 RTS = .1 - 1/Z S , k=l K where Sk i s d e f i n e d over revenue shares o n l y . A measure of r e tu rns to s c a l e f o r each s o i l zone w i l l be c a l c u l a t e d . F i n a l l y , o ther c h a r a c t e r i s t i c s of the techno logy set can be d e s c r i b e d by e l a s t i c i t i e s of c h o i c e . For the t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n , these e l a s t i c i t i e s w i l l be f u n c t i o n s of the es t ima ted parameters and the p r e d i c t e d revenue and expend i tu re sha r e s . The e l a s t i c i t y of net output i w i th r espec t to p r i c e Ph can be w r i t t e n a s : e i h (P ,A b ) = S h - Y i h / S ± i = 1.. . .6, h = 1,. . .6, i ^ h. Own e l a s t i c i t y of net output supp ly can be w r i t t e n a s : e ± i (P ,A b ) = S ± + ? l i / S i - 1 i = 1 6. The own e l a s t i c i t y of c a t t l e supply ( e i i ) i s generated under the assumpt ion tha t p r i c e e x p e c t a t i o n s are not a d j u s t e d . I f changes in p r i c e e x p e c t a t i o n s are a l l o w e d , an es t imate of the t o t a l own e l a s t i c i t y of c a t t l e supp ly ( n i i ) can be de t e rm ined . For the t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n , t h i s formula can be w r i t t e n a s : 1 19 T o t a l E l a s t i c i t y D i r e c t E l a s t i c i t y C r o s s E l a s t i c i t y E l a s t i c i t y o f E x p e c t a t i o n s n 11 [ § i + V / g i i ] + [ s 2 - Y ^ ] 0 P* P x l . where r ep re sen t s the percentage chang e in the expected p r i c e of c a t t l e caused by a percentage change in the c u r r e n t p r i c e of c a t t l e . A l t e r n a t i v e es t imates of the e l a s t i c i t i e s of c h o i c e can be genera ted us ing the t i m e - s e r i e s data sample. However, because some v a r i a b l e s are not a v a i l a b l e on a t i m e - s e r i e s b a s i s , i t was necessary to s p e c i f y an a l t e r n a t i v e f u n c t i o n a l form fo r the v a r i a b l e p r o f i t f u n c t i o n in t h i s c a s e . I t was dec ided that a norma l i zed q u a d r a t i c f u n c t i o n a l form (as deve loped by Lau (1974)) would be a p p r o p r i a t e f o r t h i s pu rpose . The no rma l i zed q u a d r a t i c f u n c t i o n i s a member of the group of f l e x i b l e f u n c t i o n a l forms and w i l l p rov ide a second order approx imat ion to an a r b i t r a r y f u n c t i o n . The v a r i a b l e no rma l i zed q u a d r a t i c p r o f i t f u n c t i o n fo r the t h r e e - o u t p u t , t h r ee- inpu t one f i x e d f a c t o r case can be w r i t t e n a s : where II' i s n/p" and P' i s P./P, and a l l v a r i a b l e s are as 6 i i 6 p r e v i o u s l y d e f i n e d . The no rma l i zed q u a d r a t i c f u n c t i o n a l form ma in ta ins l i n e a r homogeneity of the p r o f i t f u n c t i o n in p r i c e s (4.5) + i $ a o o A b 2 + E P ! A b , i = l 1 120 but symmetry of the Hess ian mat r ix r e q u i r e s the r e s t r i c t i o n b i j = b j i , f o r a l l i and j . In a d d i t i o n , i f the q u a d r a t i c v a r i a b l e p r o f i t f u n c t i o n s a t i s f i e s at l e a s t l o c a l l y the c o n d i t i o n s (11^) to (n 6 ) i n Chapter Th ree , the net output supp ly equa t ions can be ob ta ined by a p p l y i n g H o t e l l i n g ' s Lemma to ( 4 . 5 ) : U - 6 ) M-(P,A b) -Y,. where Y i i s the i t h net output q u a n t i t y . Assuming a s t o c h a s t i c s p e c i f i c a t i o n fo r ( 4 . 6 ) s i m i l a r to that p r e v i o u s l y d i s c u s s e d for the t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n and , in a d d i t i o n , appending a time t r end v a r i a b l e to each equa t ion in ( 4 . 6 ) to account , in a rud imentary way, f o r t e c h n o l o g i c a l change in the cow-calf i n d u s t r y , the net output equa t ions can now be r e w r i t t e n a s : ( 4 . 7 ) 5 Y i • b± + i = 1 V j + a o / + V + £ i i = 1 ' 2 ' where t i s a t ime t r end v a r i a b l e and ei i s a random e r r o r te rm. Econometr ic e s t i m a t i o n of ( 4 . 7 ) can proceed as d e s c r i b e d in the t r a n s l o g case but symmetry and homogeneity of degree ze ro in p r i c e s w i l l be imposed as ma in ta ined hypotheses . Because the Hess i an of the q u a d r a t i c v a r i a b l e p r o f i t f u n c t i o n i s the same at a l l o b s e r v a t i o n s , the e l a s t i c i t i e s of c h o i c e can eas i l y " be d e r i v e d d i r e c t l y from the es t imated net output e q u a t i o n s . The own p r i c e e l a s t i c i t y of supp ly i s d e f i n e d a s : e q = fi F' /Y i = l 2 e i i D i i i / x i 1 121 The e l a s t i c i t y of net output Y i w i th respec t to p r i c e Pj d e f i n e d a s : is ' i j i j j V i , j i r< j . The e l a s t i c i t y of net output Y i wi th r e spec t to the f i x e d b f a c t o r (A ) i s d e f i n e d as : F i n a l l y , a l l o w i n g fo r adjustments i n e x p e c t a t i o n s , an es t ima te of t o t a l e l a s t i c i t y of supply can aga in be generated a s : Total E l a s t i c i t y Direct E l a s t i c i t y 1 11J [6 P ' /Y ] 1 11 r 1J Cross E l a s t i c i t y + t 8 1 2 7 2 / Y l ] E l a s t i c i t y of Expectations x [521] X P j , [ 3 F 1 ^ ] where a l l v a r i a b l e s are as p r e v i o u s l y d e f i n e d . T h i s completes the d i s c u s s i o n of s t o c h a s t i c and f u n c t i o n a l form s p e c i f i c a t i o n and data t r a n s f o r m a t i o n . We can now tu rn to a d i s c u s s i o n of the econometr ic r e s u l t s . 122 FOOTNOTES TO CHAPTER FOUR 1 The Almon l a g e x p e c t a t i o n model was chosen fo r two r easons : f i r s t , t h i s model i s commonly used i n a g r i c u l t u r a l economics f o r gene ra t i ng p r i c e p r e d i c t i o n s (Ospina and Shumway, n . d . ) ; and second, s p e c i f i c a t i o n and e s t i m a t i o n of the model i s s t r a i g h t f o r w a r d . 2 For an example of the one output Cobb-Douglas v a r i a b l e p r o f i t f u n c t i o n see Yo topou los , Lau , and L i n (1976) . 3 Fuss (1977) employs a s i m i l a r t echn ique to generate an aggregate input p r i c e index fo r a vec to r of energy i n p u t s . 4 It was dec i ded to es t imate p r i c e e x p e c t a t i o n s f o r each market l o c a t i o n because i t was observed tha t p r i c e s v a r i e d s y s t e m a t i c a l l y between market l o c a t i o n s . 5 The s e r i e s was d i f f e r e n c e d a number of t i m e s : however, these t r a n s f o r m a t i o n s added no new i n f o r m a t i o n . 6 The a d d i t i o n of h ighe r order a u t o r e g r e s s i v e and moving average components e i t h e r reduced the s i g n i f i c a n c e of or changed the s igns of the es t ima ted c o e f f i c i e n t s . Futhermore , in some cases the necessa ry c o n d i t i o n fo r s t a t i o n a r i t y was v i o l a t e d . 7 See S t a t i s t i c s Canada, Methodology Paper Number 3, Data C o l l e c t i o n and E s t i m a t i n g Procedures of the. L i v e s t o c k E s t i m a t i o n U n i t , A g r i c u l t u r e S t a t i s t i c s D i v i s i o n , Ottawa, 1 982. 8 S t a t i s t i c s Canada, Methodology Paper Number 3, p .117 . 9 It was necessa ry to i n c l u d e a t o t a l c r op supp ly v a r i a b l e because on examina t i on , the data r e vea l ed tha t the cow-cal f 123 farm as d e f i n e d generated approx imate l y 30 to 40 percent of t o t a l revenue from the s a l e of c r o p s . 10 The number of b u l l s in the aggregate Canadian herd has remained s t a b l e at approx imate l y 5 p e r c e n t . G iven t h i s f a c t and the s p e c i a l i z e d na ture of the b u l l market , i t was dec ided to e l i m i n a t e b u l l s from the a n a l y s i s . 11 These p r i c e s are r epo r t ed in L i v e s t o c k Market Review, A g r i c u l t u r e Canada, Ottawa, v a r i o u s i s s u e s . 12 The r e n t a l p r i c e of l and i s d e f i n e d a s : P t = (r - Pt)/(1 + r)P where p = r e n t a l p r i c e of l a n d , P~ = asse t p r i c e of l a n d , P t = r a t e of growth of l and p r i c e s , set equa l to 3% ( B a r i c h e l l o 1979), r = i n t e r e s t r a t e . 13 The Cobb-Douglas p r i c e aggrega to r f u n c t i o n i s d e f i n e d a s : P(P±) = np™ 1, where P( . ) i s the aggregate p r i c e index , P i i s the p r i c e of the i t h i n p u t , and a i = P i x j / 2 P j x j ; (x i i s the i t h input q u a n t i t y ) . 14 It shou ld be noted tha t two a d d i t i o n a l f a c t o r s may a f f e c t the magnitude of these e l a s t i c i t i e s . F i r s t , the c r o s s -s e c t i o n a l sample i s d e f i n e d to i n c l u d e on ly cow-ca l f farms wi th t h i r t y or more beef cows whereas the t i m e - s e r i e s data i n c l u d e s a l l farms w i th beef c a t t l e in western Canada. Consequen t l y , there i s g r e a t e r p o t e n t i a l f o r output v a r i a t i o n s in the c r o s s - s e c t i o n a l data caused by farms o u t s i d e the sample moving i n t o the c r o s s - s e c t i o n a l 124 c l a s s i f i c a t i o n . T h e r e f o r e , output e l a s t i c i t i e s c a l c u l a t e d us ing t h i s data set shou ld be l a r g e r in magnitude than those u s i n g the t i m e - s e r i e s sample. Second, f o r each data s e t , i t i s necessary to s p e c i f y a d i f f e r e n t f u n c t i o n a l form fo r the v a r i a b l e p r o f i t f u n c t i o n ; the e f f e c t of the a l t e r n a t i v e f u n c t i o n a l form s p e c i f i c a t i o n on the magnitudes of the c a l c u l a t e d e l a s t i c i t i e s i s not c e r t a i n . 15 Two t echn iques have been proposed to ensure e f f i c i e n t e s t i m a t i o n when us ing a combined c r o s s - s e c t i o n a l , t ime-s e r i e s sample : 1) cova r i ance e s t i m a t i o n ; and 2) e r r o r components. The pr imary d i f f e r e n c e between the two methods i s tha t the cova r i ance model assumes tha t the c r o s s -s e c t i o n a l parameters are f i x e d whereas the e r r o r components model assumes that such parameters are s t o c h a s t i c ( Judge, e t a l . 1980). Covar i ance e s t i m a t o r s are used i n t h i s study s imply because they are more e x p e d i e n t . T a b l e 5.1 R e g r e s s i o n C o e f f i c i e n t s - T r a n s l o g P r o f i t F u n c t i o n s h a r e P r i c e s Dummy V a r i a b l e s C a t t l e I n v e n t o r i e s C r o p s L a b o u r C a p i t a l M a t e r i a l s S t o c k C o n s t a n t 1 9 8 1 1 9 8 0 1979 Cattle .86 -.241 -.33 -.078 .077 -.288 .037 .787 .156 -.004 -.151 (8,4)* (8.2) (5.1) (4.6) (4.9) (6.1) (5.2) (6.3) (6.9) (.42) (7.1) I n v e n t o r i e s -.241 .289 -.107 .014 -.01 .054 -.036 1.09 -.053 .02 .033 (8.2) (7.5) (2.6) (2.9) (2.1) (4.9) (3.4) (8.2) (3.5) (1.1) (1.7) C r o p s -.33 -.107 .315 .015 -.039 .147 .011 -.585 -.048 -.008 .056 (5.1) (2.6) (4.8) (1.4)" (4.0) (6.3) (.90) (3.8) (2.4) (4.3) (2.2) Labour -.078 .014 .015 .02 -.007 .037 -.002 -.095 -.019 -.002 .02 (4.6) (2.9) (1.4) (2.3) (1.4) (2.2) (1.7) (3.8) (4.6) (1.1) (5.9) Capital .077 -.01 -.039 -.007 -.02 -.001 .002 .055 .019 -.006 -.013 (4.9) (2.1) (4.0) (1.4) (3.3) (.05) (1.5) (2.5) (5.1) (3.5) (4.0) Materials -.288 .054 .147 .037 -.001 .051 -.012 -.252 -.055 0 .055 * t-statistics in parentheses 1 25 5. PARAMETER ESTIMATES AND SUMMARY STATISTICS 5.1 INTRODUCTION In t h i s c h a p t e r , e m p i r i c a l r e s u l t s are r epo r t ed and d i s c u s s e d f o r each model s p e c i f i e d in S e c t i o n (4.4) of Chapter Fou r . In S e c t i o n ( 5 . 2 ) , the es t imated parameters of the share equa t ions f o r the m u l t i - o u t p u t , m u l t i - i n p u t v a r i a b l e t r a n s l o g p r o f i t f u n c t i o n are p r e s e n t e d . S t a t i s t i c a l t e s t i n g to determine the t e c h n i c a l s t r u c t u r e of the cow-ca l f i n d u s t r y i s c a r r i e d out and i n c l u d e s e s t ima tes of e l a s t i c i t i e s of cho i c e and r e tu rns to s c a l e . These r e s u l t s c o n s t i t u t e the main e m p i r i c a l f i n d i n g s of t h i s d i s s e r t a t i o n . In the l a s t S e c t i on ( 5 . 3 ) , the t i m e - s e r i e s based econometr ic r e s u l t s e s t ima ted us ing net output supply equa t ions which are d e r i v e d from a m u l t i - o u t p u t , m u l t i - i n p u t v a r i a b l e no rma l i zed q u a d r a t i c p r o f i t f u n c t i o n are r e p o r t e d . Measurements of e l a s t i c i t i e s of cho i c e are aga in genera ted and compared to e a r l i e r r e s u l t s . j 5.2 EMPIRICAL RESULTS USING A TRANSLOG VARIABLE PROFIT FUNCTION Es t ima tes of the parameters of the f i v e revenue and expend i tu re share equa t ions d e r i v e d us ing Z e l l n e r ' s (SUR) procedure f o r e s t i m a t i n g systems of equa t ions are g iven in Tab l e 5 .1 . Seven i t e r a t i o n s were r e q u i r e d fo r convergence. ' These c o e f f i c i e n t s r ep resen t the ma in ta ined hypotheses of symmetry and homogeneity of degree zero in p r i c e s . The parameter e s t ima tes fo r the m a t e r i a l s and s e r v i c e s expend i tu re 1 27 equa t ion are d e r i v e d us ing symmetry, homogeneity , and the add ing up c o n s t r a i n t s . Asymptot i c t - s t a t i s t i c s are g i ven in p a r e n t h e s e s . 1 A l l own output p r i c e c o e f f i c i e n t s are p o s i t i v e and s t a t i s t i c a l l y s i g n i f i c a n t at the 5 percent l e v e l . T h i s i s a necessa ry c o n d i t i o n fo r p o s i t i v e own output supp ly e l a s t i c i t i e s . The asymptot i c t - s t a t i s t i c s fo r own input p r i c e c o e f f i c i e n t s a l s o i n d i c a t e s t a t i s t i c a l s i g n i f i c a n c e at the 5 percent l e v e l . Moreover , of the remain ing p r i c e c o e f f i c i e n t s , 84 pe rcen t are s t a t i s t i c a l l y s i g n i f i c a n t at the 10 percent l e v e l of s i g n i f i c a n c e . The es t ima ted c o e f f i c i e n t s fo r the beg inn ing s tock of c a t t l e are h i g h l y s i g n i f i c a n t in both t o t a l c a t t l e output supp ly and t o t a l end of p e r i o d i nven to r y demand e q u a t i o n s . But t h i s c o e f f i c i e n t i s not s t a t i s t i c a l l y d i f f e r e n t from ze ro in the t o t a l c r op revenue share e q u a t i o n . For the l abour and c a p i t a l expend i tu re share e q u a t i o n s , the es t ima ted beg inn ing c a t t l e s tock c o e f f i c i e n t s are m a r g i n a l l y s i g n i f i c a n t w i th asymptot i c t - s t a t i s t i c s of 1.7 and 1.5 r espec t i v e l y . G e n e r a l l y , the s t a t i s t i c a l s i g n i f i c a n c e of the p r i c e and beg inn ing c a t t l e s tock c o e f f i c i e n t s p rov ide support f o r the econometr ic s p e c i f i c a t i o n of the v a r i a b l e and f i x e d i npu t s as def i n e d . I t i s i n t e r e s t i n g to examine the es t ima ted c o e f f i c i e n t s f o r the c o v a r i a n c e e s t ima to r s in Tab le 5 .1 . These c o e f f i c i e n t s are s t a t i s t i c a l l y s i g n i f i c a n t at the 10 pe rcen t l e v e l f o r a l l input share equa t ions fo r the yea rs 1981 and 1979. But they are s t a t i s t i c a l l y i n s i g n i f i c a n t , except fo r 128 the c a p i t a l share e q u a t i o n , f o r the year 1980. These r e s u l t s p rov ide s t rong ev idence tha t the i n t e r c e p t c o e f f i c i e n t s have v a r i e d between the base year (1978) and 1 9 79 , and aga in v a r i e d between the base year and 1981. T h i s i n d i c a t e s tha t the data are not drawn from a homogeneous sample and consequen t l y , to generate e f f i c i e n t parameter e s t i m a t e s , i t i s necessary to ma in t a i n the dummy v a r i a b l e s p e c i f i c a t i o n in the e s t i m a t i o n . G o o d n e s s - o f - f i t summary s t a t i s t i c s are p r o v i d e d in Tab le 5 .2. T h i s t a b l e i n d i c a t e s tha t the e s t ima ted equa t i ons account fo r 7 2 . 2 , 6 4 . 6 , 4 4 . 9 , 6 1 . 6 , and 56.9 percent of the v a r i a t i o n in the shares fo r c a t t l e , end-o f-pe r i od i n v e n t o r y , c r o p , l a b o u r , and c a p i t a l share equa t ions r e s p e c t i v e l y . G iven the c r o s s - s e c t i o n a l data u t i l i z e d in the e s t i m a t i o n , these R 2 measurements can be c o n s i d e r e d q u i t e adequate . In a d d i t i o n , Tab le 5.2 r e p o r t s the r e s u l t from t e s t i n g the n u l l h y p o t h e s i s tha t a l l e s t ima ted c o e f f i c i e n t s are equa l to z e r o . The n u l l h y p o t h e s i s i s soundly r e j e c t e d . These s t a t i s t i c a l r e s u l t s p rov ide p r e l i m i n a r y v a l i d a t i o n of the model . However, i t i s necessa ry to t e s t the e s t ima ted equa t i ons to ensure tha t the c o n d i t i o n s f o r d u a l i t y a re s a t i s f i e d . Symmetry of the Hess ian mat r ix and l i n e a r homogeneity in p r i c e s are t e s t e d us i ng the n u l l hypotheses d e f i n e d in Tab le 4.5 of Chapter Fou r . The r e s u l t s of these t e s t s are r epo r t ed in the f i r s t h a l f of Tab le 5.3 fo r two c r i t i c a l va lues of the Ch i-squared s t a t i s t i c and i n d i c a t e the gene ra l c o n s i s t e n c y of these p r o p e r t i e s in the es t imated share e q u a t i o n s . The on l y excep t i on i s tha t homogeneity of p r i c e s i s r e j e c t e d at a 5 percent l e v e l of s i g n i f i c a n c e . TABLE 5.2 Goodness of F i t S t a t i s t i c s 129 Share Equat ion R : SEE C a t t l e End-Of-Per iod I n ven to r i e s Crops Labour C a p i t a l .7220 .6463 .4493 .61 56 .5690 .0358 .061 5 .0672 .0054 .0049 Ho: A l l C o e f f i c i e n t s x 2 d . f . X 2 ( . 01 ) Equa l to Zero 198.01 30 50.98 Dec i s ion Re jec t 130 TABLE 5.3 T e s t i n g fo r S t r u c t u r e Test Ho: . A* d . f . x 2 ( - 0 5 ) D e c i s i o n x 2 ( . 0 1 ) D e c i s i o n Homogeneous of Degree One in P r i c e s Symmetry 12.46 5 11.07 Re jec t 15.09 Accept 15.26 10 18.31 Accept 23.21 Accept "A lmost Homothet i c " "A lmost Homogeneous' Non-Joint P roduc t i on 31.82 3 7.82 Re jec t 11.35 Re jec t 35.70 4 9.49 Re jec t 13.28 Re jec t 31.02 4 9.49 Re jec t 13.28 Re jec t * X = -2 ( l nLa - InLo) 131 S ince the p r o p e r t i e s of symmetry and homogeneity are not s t a t i s t i c a l l y r e j e c t e d at the 10 pe rcen t l e v e l in the u n r e s t r i c t e d model , i t i s not unreasonable to impose these p r o p e r t i e s in the e s t i m a t i o n in order to per form a d d i t i o n a l t e s t s . Check ing r e g u l a r i t y c o n d i t i o n s , the p r e d i c t e d revenue shares are p o s i t i v e and expend i tu re shares are nega t i ve fo r a l l o b s e r v a t i o n s which i n d i c a t e s that the t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n s a t i s f i e s the mono ton i c i t y p r o p e r t y . Convex i t y of t h i s v a r i a b l e p r o f i t f u n c t i o n in p r i c e s i s checked by computing the e i genva lues of the Hess ian mat r ix of the p r o f i t f u n c t i o n wi th respec t to p r i c e s . The Hess ian mat r ix i s convex i f a l l e i genva lues are non-nega t i ve . Tab le 5.4 r e p o r t s the e lements of the Hess ian matr ix (us ing p r e d i c t e d shares determined at the means of the exogeneous v a r i a b l e s ) and es t imates of the e i g e n v a l u e s . U n f o r t u n a t l y , these r e s u l t s i n d i c a t e tha t the f u l l v a r i a b l e p r o f i t f u n c t i o n i s not convex in p r i c e s . 2 I t i s worth n o t i n g however, that the 3x3 Hess ian of output p r i c e s and the 3x3 Hess ian of input p r i c e s are convex. The e igenva lues fo r these sub-matr i ces are a l s o r epo r t ed in Tab le '5 .4 . G iven tha t at the means of the exogeneous v a r i a b l e s the Hess i an mat r ix i s non-convex, t h i s p rope r t y shou ld be checked at each sample p o i n t . In Tab le 5.5 the e i genva lues for the Hess ian mat r ix are r epo r t ed for each o b s e r v a t i o n . These r e s u l t s i l l u s t r a t e that at each sample po in t f i v e e igenva lues are p o s i t i v e but one va lue i s n e g a t i v e ; aga in i n d i c a t i n g a non-convex Hess ian m a t r i x . However, i t i s i n t e r e s t i n g to note 1 TABLE 5.4 Hess i an C o e f f i c i e n t s and E i genva lues Hess ian c o e f f i c i e n t s C a t t l e Inven. Crops Labour C a p i t a l M a t e r i a l s C a t t l e .615 -.013 -.261 -.095 .068 -.330 Inven. -.013 .04 -.022 -.007 -.021 .002 Crops -.261 -.022 .181 .009 -.042 .131 Labour -.095 - .007 .009 .062 - .006 .041 C a p i t a l .068 -.021 -.042 -.006 .002 .001 M a t e r i a l s -.33 .002 .131 .041 .001 .16 E igenva lues Hess i an Ma t r i x : .9228 .0932 .0569 .0363 -.0439 - .0069 Output P r i c e Sub-Matr ix : .737 .076 .022 Input P r i c e Sub-Matr ix : .162 .060 .0008 TABLE 5.5 , • E i genva lues f o r Hess ian Ma t r i x at each Obse r va t i on 0.92746 0.92659 0.88902 0.88348 0.90472 0.92363 0.91942 0.90425 0.91351 0.89467 0.91187 0.92406 0.91199 0.93385 0.91502 0.93252 0.88055 0.88311 0.90214 0.89024 0.89305 0.91269 0.90104 0 . 8 8 1 6 5 0.90167 0.90456 0.89725 0.90214 0.94763 0.98123 0.92820 0.92364 0.95250 0.95157 0.96264 0.93718 0.95429 0.93047 0.95249 0.97379 0.95767 0.98458 0.96825 0.99325 0.93761 0.93860 0.97837 0.96089 0.98904 0.95162 0.99734 0.94313 0.98830 0.95834 0.93973 0.94574 -0.08158 0.09111 -0.06818 0.07085 -0.08110 -0.07411 -0.07741 -0.07169 -0.07677 -0.06949 -0.08022 -0.07805 -0.07336 -0.07944 -0.07719 0.10822 0.07087 0.07378 -0.07358 0.06892 -0.07254 -0.07046 -0.07300 0.06997 -0.07536 -0.07520 -0.06991 -0.07429 0.10956 0.17964 0.08791 0.08288 -0.07229 0.10290 0.07903 0.09400 -0.07258 0.08425 -0.07543 0.11181 0.09423 0.11562 0.1051 1 0.16478 0.07718 0.09178 0.09870 0. 11081 0.09913 0.11010 0.09857 0.07667 0.10929 0.07945 0.0691 1 0.07320 0.05807 -0.05993 0.06693 -0.06380 0.05937 0.061 1 4 0.06032 0.06324 0.05916 0.06387 0.06010 0.05682 0.05734 0.05283 0.06467 0.06044 -0.06607 -0.06131 0.06249 -0.06876 0.06473 0.06365 0.06258 -0.06582 0.06419 0.06004 0.06343 0.06166 -0.06680 -0.05663 -0.05879 -0.05722 0.07137 -0.06138 -0.07356 -0.06031 0.07031 -0.05891 0.07383 -0.07297 -0.06689 -0.07034 -0.06893 -0.06278 -0.06007 -0.05609 -0.06683 -0.06043 -0.07140 -0.05788 -0.07213 -0.06034 -0.07047 -0.07010 -0.06474 -0.06608 0.03151 0.05898 0.04109 0.04558 0.02968 0.04038 0.03462 0.03729 0.03153 0.03791 0.03134 0.03563 0.03411 0.02903 0.04570 -0.05765 0.04672 0.04828 0.03636 0.04446 0.03879 0.04391 0.03689 0.04589 0.03856 0.03964 0.04348 0.04158 0.04847 0.04408 0.04592 0.04372 0.04176 0.04421 0.04135 0.04507 0.04060 0.04436 0.04341 0.03945 0.03902 0.03683 0.05123 0.04801 0.05093 .0.05304 0.04772 0.05228 0.04639 0.05420 0.04458 0.04978 0.04764 0.04357 0.04352 0.04370 0.01281 0.01832 0.01797 0.01915 0.01409 0.01375 0.01417 0.01323 0.01285 0.01581 0.01437 0.01288 0.01135 0.00871 0.02020 0.02838 0.02427 0.02415 0.01706 0.02114 0.01907 0.01760 0.01734 0.02331 0.01890 0.01758 0.01971 0.01875 0.01502 0.01071 0.01553 0.01504 0.01108 0.01016 0.01076 0.01202 0.01008 0.01358 0.01278 0.01026 0.00944 0.00758 0.01238 0.00932 0.01323 0.01469 0.01011 0.01057 0.01067 0.01241 0.00936 0.01124 0.01119 0.00971 0.00995 0.00940 0.00014 0.00016 0.00014 0.00016 0.00015 0.00015 0.00015 0.00014 0.00014 0.00015 0.00014 0.00015 0.00015 0.00014 0.00016 0.00017 0.00015 0.00016 0.00015 0.00016 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.0001 5 0.00016 0.00015 0.00015 0.00016 0.00016 0.00016 0.00015 0.00016 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00016 0.00015 0.00015 0.00014 0.00015 134 that fo r each o b s e r v a t i o n one e igenva lue i s s i g n i f i c a n t l y l a r g e r then the o ther va lues and c l o s e to one in magni tude, whereas the remain ing va lues are r e l a t i v e l y c l o s e to z e r o . These p o i n t e s t ima tes do not prove tha t the t rue u n d e r l y i n g p r o f i t f u n c t i o n i s non-convex in p r i c e s . Wales (1977) has shown tha t a non-convex r e s u l t may not i n d i c a t e an absence of o p t i m i z i n g b e h a v i o r , r a the r i t may i n d i c a t e that the FFF does not p rov ide a good approx imat ion to the t rue f u n c t i o n . N e v e r l e s s , Wales conc ludes that t h i s r e s u l t does not p r e c l ude o b t a i n i n g good e l a s t i c i t y e s t i m a t e s . In sum, the es t imated c o e f f i c i e n t s of the revenue and expend i tu re share equa t ions are g e n e r a l l y s t a t i s t i c a l l y s i g n i f i c a n t wi th the share equa t ions p r o v i d i n g a good f i t to the d a t a . Fu r the rmore , s t a t i s t i c a l t e s t i n g i n d i c a t e s tha t the es t ima ted v a r i a b l e p r o f i t f u n c t i o n s a t i s f i e s the r e q u i r e d d u a l i t y p r o p e r t i e s of symmetry, l i n e a r homogeneity in p r i c e s , and m o n o t o n i c i t y . F i n a l l y , i t w i l l be assumed tha t the t rue p r o f i t f u n c t i o n i s convex in p r i c e s . Consequen t l y , one can conc lude that the es t imated share equa t ions have per formed w e l l and tha t they adequate l y r ep resen t the p r o f i t max imiz ing behav io r of cow-cal f p r o d u c e r s . Us ing the es t ima ted c o e f f i c i e n t s of the revenue and expend i tu re share e q u a t i o n s , one can t e s t fo r c e r t a i n c h a r a c t e r i s t i c s of the u n d e r l y i n g t r a n s f o r m a t i o n f u n c t i o n as d e f i n e d in Tab le 4.5 of Chapter Fou r . These s t a t i s t i c a l t e s t s are r epo r t ed in the bottom h a l f of Tab le 5 .3 . "A lmost-homothe t i c " in ou tputs i s r e j e c t e d at both the 5 and the 10 pe rcen t l e v e l of s i g n i f i c a n c e . Subsequent l y , i t must f o l l ow 135 tha t "a lmost-homogeneous" in outputs i s a l s o r e j e c t e d . T h i s i s due to the f a c t tha t almost-homogeneous i s nested w i t h i n the a lmost-homothet ic h y p o t h e s i s . These r e s u l t s are c o n s i s t e n t wi th the f i n d i n g s of o ther economic s t u d i e s (Lopez (1980) , Kunimoto (1983)) on Canadian a g r i c u l t u r e . These t e s t s support the c o n t e n t i o n tha t cow-cal f p r o d u c t i o n t e c h n o l o g i e s are not c h a r a c t e r i z e d by cons tan t r e t u r n s to s c a l e . However, f o l l o w i n g the d e f i n i t i o n of r e t u r n s to s ca l e in S e c t i o n (4.4) of Chapter F o u r , an es t imate of a r e t u r n s - t o - s c a l e measure can be de t e rm ined . In Tab le 5 .6 , e s t ima tes of the r e tu rns to s c a l e in 1981 are p rov ided fo r each of the fou r t een s o i l zone l o c a t i o n s . These es t imates are generated us i ng the p r e d i c t e d revenue shares for each o b s e r v a t i o n . The r e s u l t s c l e a r l y i n d i c a t e d e c r e a s i n g r e tu rns to s c a l e fo r a l l s o i l zone l o c a t i o n s . What t h i s means i s that a g i ven i nc rease in ou tpu ts r e q u i r e s inputs to be i n c r eased in a s i g n i f i c a n t l y g r ea t e r p r o p o r t i o n . The author i s unaware of past Canadian s t u d i e s which p rov ide s i m i l a r measures of r e tu rns to s c a l e in a g r i c u l t u r e . However, these e s t i m a t e s , a l though sma l l in magni tude, are c o n s i s t e n t w i th U.S. a g r i c u l t u r a l s t u d i e s which a l s o r epor t d e c r e a s i n g r e t u r n s to s c a l e (Ray 1982 and Weaver 1983). The l a s t s t r u c t u r a l t e s t a ssesses j o i n t p roduc t i on p o s s i b i l i t i e s between c rops and c a t t l e on cow-ca l f farms. R e s u l t s from the s t a t i s t i c a l t e s t i n g of the non- jo in t p r o d u c t i o n hypo thes i s are a l s o r epo r t ed in Tab l e 5.3 and i n d i c a t e that non- jo i n t p r o d u c t i o n of c rops and c a t t l e can be r e j e c t e d at both the 5 and the 10 pe rcen t l e v e l s of TABLE 5.6 Returns to Sca l e S o i l Zone Returns to S ca l e 1 .065 2 .094 3 .093 4 . 1 02 5 .071 6 .072 7 .071 8 .079 9 .072 10 .088 1 1 .071 1 2 .065 1 3 .072 1 4 .058 137 s i g n i f i c a n c e . T h i s i n d i c a t e s that there i s a s i g n i f i c a n t b e n e f i t to j o i n t l y p roduc ing c rops and c a t t l e on cow-cal f fa rms. A c rop cow-cal f p r o d u c t i o n system a l l ows the farmer the o p t i o n of market ing g r a i n d i r e c t l y or through c a t t l e in the form of bee f . The author i s aga in not aware of p u b l i s h e d r e s u l t s t e s t i n g f o r j o i n t p r o d u c t i o n p o s s i b i l i t i e s in Canadian a g r i c u l t u r e . However, in a working paper , Lopez (1981) does t e s t f o r t h i s c h a r a c t e r i s t i c and r e j e c t s j o i n t p roduc t i on between c rops and c a t t l e . H i s r e s u l t must be i n t e r p r e t e d c a r e f u l l y because i t i s based on h i g h l y aggregated data and does not r e f l e c t the t echno logy of a s p e c i f i c a l l y d e f i n e d farm as do the r e s u l t s fo r t h i s s tudy . Summar iz ing, the t e c h n o l o g i c a l s t r u c t u r e of cow-cal f p r o d u c t i o n in western Canada i s d e f i n e d by a non-homothet ic , non-homogeneous t r a n s f o r m a t i o n f u n c t i o n sub jec t to d e c r e a s i n g r e t u r n s to s c a l e and j o i n t p r o d u c t i o n between c rops and c a t t l e . The s t a t i s t i c a l t e s t s p resen ted above p rov i de i n fo rma t i on which i s necessa ry to c h a r a c t e r i z e cow-cal f p r o d u c t i o n . Of equa l i n t e r e s t are measures of input s u b s t i t u t i o n and r e spons i v eness of cow-cal f farmers to changes in p r i c e s . These p a r t i a l e l a s t i c i t i e s of cho i c e (computed at the means of the exogeneous v a r i a b l e s ) are g iven in Tab le 5 .7 . Approximate s tandard e r r o r s fo r each es t imate are in p a r e n t h e s e s . 3 These e s t ima tes are genera ted us i ng the f i t t e d t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n and consequen t l y shou ld be i n t e r p r e t e d as shor t run e l a s t i c i t i e s . 138 TABLE 5.7 E l a s t i c i t i e s of Cho i ce (T rans log ) C a t t l e Invent . Crop Labour C a p i t a l M a t e r i a l s A B C a t t l e 1 .43 _ .03 .602 .021 . 1 58 .769 ( .237)* (. 067) ( .149) ( .019) ( .036) ( .021 ) I nvent . -.025 .075 - .042 — .014 _ .04 .003 (.055) (. 072) ( .078) ( .009) ( .008) ( .02) Crops -1 .63 - .139 1 . 1 3 .054 — .265 .820 ( .402) (. 261 ) ( .408) ( .063) ( .061 ) ( .144) Labour 2.48 .28 .215 _ . 1 54 . 1 54 -1 .024 (.42) ( .12) (.25) ( .216) (.13) ( .416) C a p i t a l -3.24 1 .01 2 .02 .293 — .116 _ .05 (.74) (. 223) ( .466) ( .248) ( .288) ( .575) M a t e r i a l s 3.34 - .015 -1 .32 - .414 _ .011 -1 .61 ( .47) ( .109) ( .233) ( .168) ( .122) ( .523) c * s t anda rd e r r o r in parentheses D 139 Before p roceed ing w i th a d i s c u s s i o n of t h i s t a b l e , r e c a l l tha t the t h e o r e t i c a l model deve loped in Chapter Three p r o v i d e d a number of a p r i o r i p r e d i c t i o n s about the s i gns of these e l a s t i c i t i e s . S p e c i f i c a l l y , output supp ly f u n c t i o n s must have non-negat ive s l o p e s , d e r i v e d input demand f u n c t i o n s must have n o n - p o s i t i v e s l o p e s , and there i s a nega t i ve or s u b s t i t u t e r e l a t i o n s h i p between c a t t l e supply and end-o f-pe r i od i nven to ry demand. An examinat ion of Tab le 5.6 i n d i c a t e s that a l l a p r i o r i e x p e c t a t i o n s are c o n f i r m e d . In d e s c r i b i n g the e l a s t i c i t i e s i n Tab le 5 .7 , i t i s conven ien t to d i v i d e the t a b l e i n t o four sub-matr i ces (A, B, C , and D) as d e f i n e d . In sub-matr ix A, the own e l a s t i c i t i e s of supply and c r o s s p r i c e e l a s t i c i t i e s f o r c a t t l e , end-o f-pe r i od i n v e n t o r y , and c r o p supp ly are g i v e n . Own e l a s t i c i t i e s of supply fo r c a t t l e (1.43) and c rops (1.13) are s t a t i s t i c a l l y s i g n i f i c a n t at the 5 pe rcen t l e v e l and are p o s i t i v e and g r ea t e r than one i n d i c a t i n g an e l a s t i c response to changes in own p r i c e s . T h i s i m p l i e s tha t output q u a n t i t i e s of c a t t l e and c rops are s i g n i f i c a n t l y a l t e r e d in response to changes in c u r r e n t p r i c e s . The own e l a s t i c i t y of end-o f-pe r i od i n v e n t o r i e s however, i s p o s i t i v e but l e s s than one ( . 075 ) , (with a con f i dence l e v e l of 85 pe r cen t ) i n d i c a t i n g an i n e l a s t i c response to changes in expec ted c a t t l e p r i c e s . T h i s i m p l i e s that end-o f-pe r i od i n v e n t o r i e s of c a t t l e are not s u b s t a n t i a l l y a l t e r e d in response to changes in expected c a t t l e p r i c e s . From the magnitude of these own e l a s t i c i t i e s , one can argue tha t cow-cal f f a rmers ' output response to changes in 1 40 expected c a t t l e p r i c e i s r e l a t i v e l y minor ( i . e . , there i s no s i g n i f i c a n t output adjustment in an attempt to counter the c a t t l e c y c l e ) . Ra the r , output supply responds p r i m a r i l y to changes in c u r r e n t c a t t l e p r i c e ( i . e . , changes in c a t t l e output are p o s i t i v e l y c o r r e l a t e d wi th p r i c e f l u c t u a t i o n s over the c a t t l e c y c l e ) . In o ther words, these r e s u l t s support the e x i s t e n c e of a c a t t l e c y c l e . In de te rm in ing output s u b s t i t u t i o n p o s s i b i l i t i e s , r e c a l l tha t nega t i ve c r o s s p r i c e e l a s t i c i t i e s between two q u a n t i t i e s imply that they are s u b s t i t u t e s and p o s i t i v e c ro s s p r i c e e l a s t i c i t i e s imply comp lementa r i t y . Us ing t h i s d e f i n i t i o n , the es t imated c r o s s p r i c e e l a s t i c i t i e s i n d i c a t e a s u b s t i t u t e r e l a t i o n s h i p amongst a l l output c a t e g o r i e s . For example, a one percent i n c r ease in c rop p r i c e s r e s u l t s i n a decrease in end-o f-pe r i od i n v e n t o r i e s and c a t t l e output of -.042% and -.602% r e s p e c t i v e l y . A one percent i n c r ease in c a t t l e p r i c e s causes a sma l l r e d u c t i o n in i n v e n t o r i e s (-.025%) but a major s h i f t away from c rop p r o d u c t i o n (-1.63%) . F i n a l l y , a one pe rcen t i n c r ease in expected c a t t l e p r i c e s r e s u l t s in a sma l l decrease in c a t t l e and c rop supp ly of -0 .03% and - .139% r e s p e c t i v e l y . However, the magnitude of the s tandard e r r o r s i m p l i e s that on ly c a t t l e and c rop outputs are s t a t i s t i c a l l y s i g n i f i c a n t s u b s i t u t e s at the 5 pe rcen t l e v e l . One can conc lude from these c r o s s p r i c e e l a s t i c i t i e s tha t there i s s i g n i f i c a n t scope fo r changing the output compos i t i on between c rops and c a t t l e on cow-cal f farms in western Canada. In Tab le 5 .8 , a summary of the c r o s s p r i c e and own p r i c e e f f e c t s are p r e s e n t e d . TABLE 5.8 Summary o f C r o s s P r i c e and Own P r i c e E l a s t i c i t y C a t t l e I n v e n t o r i e s C r o p C a t t l e I n v e n t o r i e s C r o p E l a s t i c S u b s t i t u t e S u b s t i t u t e S u b s t i t u t e I n e l a s t i c S u b s t i t u t e S u b s t i t u t e S u b s t i t u t e E l a s t i c 142 Es t ima tes of c r o s s p r i c e and own p r i c e input demand e l a s t i c i t i e s are shown in sub-matr ix D in Tab le 5 .7 . The own p r i c e input demand e l a s t i c i t i e s fo r labour and m a t e r i a l s a re s i g n i f i c a l l y nega t i ve and g rea te r than one in abso lu t e va lue at a 5 percent l e v e l of s i g n i f i c a n c e , i n d i c a t i n g an e l a s t i c d e r i v e d demand fo r both i n p u t s . T h i s i m p l i e s tha t in response to an i n c r ea se in input p r i c e s , cow-cal f farmers decrease the q u a n t i t y of labour and m a t e r i a l i npu ts u t i l i z e d s u b s t a n t i a l l y . On the o ther hand, own d e r i v e d demand e l a s t i c i t y f o r c a p i t a l i nputs i s nega t i ve but l e s s than one in a b s o l u t e va lue i n d i c a t i n g an i n e l a s t i c demand fo r t h i s i n p u t . However, t h i s es t imate i s not s t a t i s t i c a l l y s i g n i f i c a n t l y d i f f e r e n t from z e r o . In o ther words, the q u a n t i t y of c a p i t a l i npu t s used i s not s e n s i t i v e to changes in own p r i c e . The magnitude of these c o e f f i c i e n t s i n d i c a t e s that employment of c a p i t a l i npu ts i s more s t a b l e r e l a t i v e to employment of l abour and m a t e r i a l i n p u t s . The s i g n s of the c r o s s p r i c e e l a s t i c i t i e s in sub-matr ix D d e f i n e s i npu t s as s u b s t i t u t e s or complements. On the input s i d e , a nega t i ve c r o s s p r i c e e l a s t i c i t y i m p l i e s complementar i t y and a p o s i t i v e c r o s s p r i c e e l a s t i c i t y i m p l i e s s u b s t i t u t i b i l i t y . A one percent i n c r ease in the p r i c e of c a p i t a l i n c r e a s e s the q u a n t i t y of labour demanded by .154% (with a s tandard e r r o r of . 1 3 ) . C o n v e r s e l y , a one percent i n c r ea se in the p r i c e of l abour i n c r e a s e s the q u a n t i t y of c a p i t a l demanded by .293% (with a s tandard e r r o r of . 248 ) . These two measures d e f i n e , at the 85 percent c o n f i d e n c e l e v e l , a s u b s t i t u t e r e l a t i o n s h i p between labour and c a p i t a l . For a 143 g iven set of r e l a t i v e p r i c e s , the s t r eng th of the s u b s t i t u t i o n e f f e c t between labour and c a p i t a l i m p l i e s , muta t i s mutand i s , that cow-cal f farms are s u b s t i t u t i n g away from labour and towards g rea te r c a p i t a l i z a t i o n . On the o ther hand, a one percent i n c r ease in the p r i c e of m a t e r i a l s reduces the q u a n t i t y demanded of both l abour and c a p i t a l by -1.024% and - .051% r e s p e c t i v e l y . The magnitude of these e l a s t i c i t i e s combined w i th the sma l l s tandard e r r o r s fo r the l abour es t imate i m p l i e s a s t ronge r complementar i t y between m a t e r i a l s and labour than between m a t e r i a l s and c a p i t a l . Fu r the r ev idence of the degree of complementar i t y between m a t e r i a l s and the other i npu ts i s p r o v i d e d by the f a c t tha t a one percent i n c rease in the p r i c e of l abour or c a p i t a l reduces the q u a n t i t y of m a t e r i a l s employed by -.414% and - .011% r e s p e c t i v e l y . A g a i n , the complementar i t y between l abour and m a t e r i a l s i s s t a t i s t i c a l l y s i g n i f i c a n t at the 5 pe rcen t l e v e l whereas the es t imated complementar i ty between c a p i t a l and m a t e r i a l s i s not s t a t i s t i c a l l y s i g n i f i c a n t . Tab le 5.9 summarizes the r e l a t i o n s h i p s between i npu t s fo r cow-cal f f a rms . Tu rn i ng now to examine sub-matr ix B, which p r o v i d e s va lues of the e l a s t i c i t i e s of output supp ly wi th r espec t to input p r i c e s , cons ide r a one percent i n c r ea se in the p r i c e of l a b o u r . T h i s r e s u l t s in a r e d u c t i o n in the l e v e l of end-of-p e r i o d i n v e n t o r i e s and c a t t l e supply of -.014% ( s t a t i s t i c a l l y s i g n i f i c a n t at the 5 percent l e v e l ) and - .021% ( s t a t i s t i c a l l y s i g n i f i c a n t at the 15 percent l e v e l ) r e s p e c t i v e l y , but i t r e s u l t s in an inc rease in c rop p r o d u c t i o n of .054% (a l though TABLE 5.9 Summary C l a s s i f i c a t i o n of Farm Inputs Labour C a p i t a l M a t e r i a l s Labour E l a s t i c S u b s t i t u t e Complement C a p i t a l S u b s t i t u t e I n e l a s t i c Complement M a t e r i a l s Complement Complement E l a s t i c 145 t h i s r e s u l t i s not s i g n i f i c a n t l y d i f f e r e n t from z e r o ) . T h i s i m p l i e s tha t c a t t l e p r o d u c t i o n , and to a l e s s e r e x t e n t , end-o f - p e r i o d i n v e n t o r i e s , a re labour i n t e n s i v e o p e r a t i o n s . On the other hand, a one pe rcen t i n c r ea se in the f low p r i c e of c a p i t a l r e s u l t s in a l a rge decrease in q u a n t i t y of c rops s u p p l i e d (-.265%) and a minor decrease in end-o f-pe r i od i n v e n t o r i e s (-.04%) but now c a t t l e supp ly i n c r e a s e s by .158%. These es t ima tes are a l l s t a t i s t i c a l l y s i g n i f i c a n t at the 5 pe rcen t l e v e l and imply tha t c r op p r o d u c t i o n and a g a i n , to a l e s s e r e x t e n t , end of p e r i o d i n v e n t o r i e s , a re c a p i t a l i n t e n s i v e o p e r a t i o n s . F i n a l l y , a one pe rcen t i n c r ease in the p r i c e of m a t e r i a l s has the e f f e c t of s i g n i f i c a n t l y i n c r e a s i n g t o t a l c r op supply by .820%, but r e s u l t s in a s i g n i f i c a n t l y l a r g e decrease in c a t t l e supply of - . 7 6 9 % . ( End-of-per iod i n v e n t o r i e s would i n c r ea se by .003% but t h i s es t imate i s not s i g n i f i c a n t l y d i f f e r e n t from z e r o . ) T h i s r e s u l t would imply tha t c a t t l e p r o d u c t i o n i s a l s o m a t e r i a l i n t e n s i v e . Fu r the rmore , t h i s r e s u l t suppor ts the argument (by c a t t l e m e n ' s groups) that changes in the p r i c e of i n t e rmed ia te inputs s i g n i f i c a n t l y a f f e c t s the cos t of c a t t l e p r o d u c t i o n and subsequen t l y , the supp ly of c a t t l e . G e n e r a l l y , p o l i c i e s tha t d i s t o r t downwards the r e l a t i v e p r i c e of an input have the e f f e c t of i n c r e a s i n g the supp ly of tha t output which uses the input more i n t e n s i v e l y . For example, the Canadian government 's p o l i c y of s u b s i d i z i n g the i n t e r e s t ra te on farm loans would tend to decrease the p r i c e of farm c a p i t a l r e s u l t i n g in an i n c r ea se in the p r o d u c t i o n of 1 46 c rops and a decrease (a l though sma l l e r in magnitude) in the p r o d u c t i o n of c a t t l e . C l a s s i f i c a t i o n of outputs a c c o r d i n g to input i n t e n s i t i e s i s summarized in Tab le 5 .10. The f i n a l sub-matr ix (C ) , p rov i des e s t ima tes of the e l a s t i c i t i e s of input demand wi th r espec t to output p r i c e s . These e l a s t i c i t i e s w i l l be used to c l a s s i f y i npu t s as s u p e r i o r ( e i j > 1 ), normal (0 £ e i j <_ 1 ), or i n f e r i o r ( e i j < 0) . Cons ide r a one percent i n c r ease in expected i nven to ry p r i c e s . T h i s w i l l r e s u l t in an i n c r ease in the q u a n t i t y of l abour and c a p i t a l demanded by .18% and 1.01% r e s p e c t i v e l y but in a dec rease in the q u a n t i t y of m a t e r i a l i npu t s demanded by - . 0 1 5 % . However, s t a t i s t i c a l t e s t s i n d i c a t e tha t a l l th ree i npu t s can be d e f i n e d as normal i npu ts in the p r o d u c t i o n of end-o f-pe r i od i n v e n t o r i e s . I n c reases in the p r i c e s of c a t t l e and c rops have c o n s i d e r a b l y l a r g e r e f f e c t s on the demand f o r i n p u t s . In the p r o d u c t i o n of c a t t l e , l abour and m a t e r i a l s can be c l a s s i f i e d as s u p e r i o r i n p u t s : however, c a p i t a l appears to be an i n f e r i o r i n p u t . S t a t i s t i c a l t e s t s on each v a r i a b l e suppor t s t h i s c l a s s i f i c a t i o n . T h i s c l a s s i f i c a t i o n i s r e ve r sed in the p r o d u c t i o n of c rops where c a p i t a l i s now d e f i n e d as s u p e r i o r and m a t e r i a l s c a l c u l a t e d to be i n f e r i o r . A d d i t i o n a l l y , the l a rge s tandard e r r o r s fo r the l abour es t imate r e s u l t s in the c l a s s i f i c a t i o n of l abour as a normal i n p u t . These input demand e l a s t i c i t i e s w i th r espec t to output supp ly are c o n v e n i e n t l y summarized in Tab le 5 .11. The c l a s s i f i c a t i o n of l abour as a s u p e r i o r input in the p r o d u c t i o n of c a t t l e i s c o n s i s t e n t wi th the major emphasis TABLE 5.10 C l a s s i f i c a t i o n of Outputs With Respect to Input Use Labour Capi t a l M a t e r i a l s C a t t l e I n v e n t o r i e s Crops I n t ens i v e Less I n t ens i v e Less I n t ens i v e I n t ens i v e I n t ens i v e 1 48 TABLE 5.11 C l a s s i f i c a t i o n of Inputs With Respect to Output Use C a t t l e Inventor i e s Crop Labour C a p i t a l Ma t e r i a 1 Supe r i o r I n f e r i o r Supe r i o r Normal Normal Normal Normal Super i o r I n fe r i o r 1 49 s t i l l p l a c ed on the cowboy in the p r o d u c t i o n of c a t t l e in western Canada whereas in the p r o d u c t i o n of c r o p s , l a b o u r ' s i n f e r i o r c l a s s i f i c a t i o n combined wi th c a p i t a l ' s s u p e r i o r c l a s s i f i c a t i o n i s c o n s i s t e n t wi th a net m i g r a t i o n of l abour o f f the farm and an emphasis on i n c r e a s i n g c a p i t a l i z a t i o n . P o l i c i e s des igned to i n c r ease farm p r i c e s of e i t h e r c a t t l e or c rops w i l l have q u i t e d i f f e r e n t e f f e c t s on r u r a l deve lopment . I n c r e a s i n g c rop p r i c e s w i l l g i v e r i s e to s u b s t i t u t i o n away from labour which w i l l encourage i n c r eased m i g r a t i o n o f f farms and i n c r e a s i n g c a p i t a l i z a t i o n . Inc reased c a t t l e p r i c e s , on the o ther hand, w i l l r e s u l t in i n c r ea sed farm employment. I t would be h e l p f u l to compare the e l a s t i c i t y e s t ima tes p resen ted in t h i s s e c t i o n wi th other s t u d i e s on Canadian a g r i c u l t u r e . However, the author i s unaware of any past r e s e a r c h which r e p o r t s e s t ima tes of e l a s t i c i t i e s of cho i ce fo r such d i s agg rega t ed outputs and inpu ts combined w i th s p e c i f i c farm d a t a . Complet ing the r e p o r t i n g of e m p i r i c a l r e s u l t s f o r the m u l t i - o u t p u t , m u l t i - i n p u t t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n r e q u i r e s a c a l c u l a t i o n of the t o t a l e l a s t i c i t y of c a t t l e supp ly as d e f i n e d in S e c t i o n (4.4) of Chapter Fou r . R e c a l l tha t t h i s e l a s t i c i t y measure takes account not on l y of the e f f e c t of c a t t l e p r i c e f l u c t u a t i o n s , but a l s o the e f f e c t of changing e x p e c t a t i o n s of c a t t l e p r i c e s on c a t t l e s u p p l y . For conven i ence , the formula fo r e s t i m a t i n g the t o t a l e l a s t i c i t y of c a t t l e supp ly i s reproduced h e r e : T o t a l D i r e c t 150 Cross E l a s t i c i t y of E l a s t i c i t y n u " - 1 1 E l a s t i c i t y E l a s t i c i t y Expectations [ e „ ] + [ £ 1 2 ] * ^ l 1 t « i + V § i - 1 1 + [ g 2 - V g i ] ' • [3 Pj P21 The dir e c t e l a s t i c i t y of supply [ e ^ ] and cross e l a s t i c i t y of supply C e ] 2 3 are calculated, at the means of the exogenous variables, to be 1.43 and -.03 respectively (Table 5.6). Thus, a l l that i s required to generate an estimate of this t o t a l e l a s t i c i t y i s a measure of the e l a s t i c i t y of expectations. This i s determined by f i r s t taking a weighted average of the f i r s t derivatives of each ARIMA model estimated in Section (4.2) of Chapter Four. This defines an estimate —e — 1 • for 3P 2 /3P which i s then transformed using the mean of each — —g price series P1 and P 2 to provide a point estimate of the e l a s t i c i t y of expectations. This value is calculated to be .4186. Given that the cross e l a s t i c i t y of supply i s negative and that the e l a s t i c i t y of expectations i s po s i t i v e , this indicates that accounting for adjustments in expectations of c a t t l e prices caused by changes in current c a t t l e price w i l l always decrease the e l a s t i c i t y of c a t t l e supply. However, th i s effect i s not strong enough to reduce the t o t a l e l a s t i c i t y of c a t t l e supply to zero or le s s . The to t a l e l a s t i c i t y i s calculated to be 1.41. Therefore, the results of the estimation do not support a perverse short run supply response. Rather, the evidence c l e a r l y indicates a positive short run supply function for c a t t l e in western Canada. Some speculative reasons for this 151 r e s u l t w i l l be o f f e r e d a f t e r the t i m e - s e r i e s based r e s u l t s have been examined. 5.3 EMPIRICAL RESULTS USING TIME-SERIES DATA Be fore d i s c u s s i n g the r e s u l t s genera ted us ing a no rma l i z ed q u a d r a t i c v a r i a b l e p r o f i t f u n c t i o n , i t i s important to emphasize the reasons fo r e s t i m a t i n g these a d d i t i o n a l t ime-s e r i e s pa ramete rs . The c r o s s - s e c t i o n a l r e s u l t s may not f u l l y cap tu re the i n f l u e n c e of two c h a r a c t e r i s t i c s in the cow-ca l f i n d u s t r y . The f i r s t i s the c y c l i c a l nature of c a t t l e p r o d u c t i o n r e s u l t i n g in we l l d e f i n e d p r i c e f l u c t u a t i o n s . The second i s tha t c a t t l e i n v e n t o r i e s have i n c r ea sed s i g n i f i c a n t l y over the l a s t t h i r t y y e a r s . The t o t a l number of c a t t l e on farms in 1956 was approx imate l y 11 m i l l i o n head : t h i s number i n c r e a s e d to 13 m i l l i o n head by 1982." G iven tha t p r i c e p r e d i c t i o n s are genera ted us i ng time s e r i e s p r o c e d u r e s , the f i r s t c h a r a c t e r i s t i c may not go undetec ted in the c r o s s - s e c t i o n a l r e s u l t s . However, the t ime-s e r i e s sample w i l l c e r t a i n l y a l l ow fo r g r ea t e r v a r i a b i l i t y in c a t t l e p r i c e data used in the econometr ic e s t i m a t i o n . The second c h a r a c t e r i s t i c i s more impor tan t . Us ing a t i m e - s e r i e s da ta sample, e l a s t i c i t i e s of cho i c e can be c a l c u l a t e d under the c o n d i t i o n of i n c r e a s i n g c a t t l e i n v e n t o r i e s . Or in o ther words, under the c o n s t r a i n t that beg inn ing i n v e n t o r i e s have not a d j u s t e d f u l l y to changes in exogenous pa ramete rs , these va lues can then be compared to e l a s t i c i t i e s genera ted g iven the assumpt ion of an op t ima l beg inn ing i nven to r y ( i . e . , c r o s s -1 52 s e c t i o n a l r e s u l t s ) . I n i t i a l e s t ima tes of the parameters of the two net output supply e q u a t i o n s , t o t a l c a t t l e supply and t o t a l end-o f-pe r iod i nven to ry demand, we re ,de r i v ed us ing Z e l l n e r ' s SUR t e chn ique . However, the Durbin-Watson t e s t i n d i c a t e d f i r s t - o r d e r a u t o c o r r e l a t i o n in each e q u a t i o n . To c o r r e c t t h i s prob lem, a l l v a r i a b l e s used in the e s t i m a t i o n were t rans fo rmed 5 us ing P = 1 6 and the model r e - e s t i m a t e d . Us ing the f i r s t -d i f f e r e n c e d t r a n s f o r m a t i o n i n d i c a t e s tha t the es t imated i n t e r c e p t term can be i n t e r p r e t e d as a t r end v a r i a b l e (Kmenta 1971, p .290 ) . Consequen t l y , the time t r end v a r i a b l e can be droped in the e s t i m a t i o n . The e s t ima ted parameters are p resen ted in Tab le 5.12. Three i t e r a t i o n s were r e q u i r e d fo r convergence . These equa t ions are e s t ima ted under the ma in ta ined hypotheses of symmetry of the Hess i an mat r ix and homogeneity of degree ze ro i n p r i c e s . Asympto t i c t - s t a t i s t i c s are g iven in pa r en theses . The s i gns of the es t ima ted p r i c e c o e f f i c i e n t s are c o n s i s t e n t w i th a p r i o r i e x p e c t a t i o n s . That i s , own p r i c e c o e f f i c i e n t s are p o s i t i v e : the c a t t l e p r i c e c o e f f i c i e n t i s s t a t i s t i c a l l y s i g n i f i c a n t at the 5 percent l e v e l and the end-o f - p e r i o d i nven to ry c o e f f i c i e n t i s s t a t i s t i c a l l y s i g n i f i c a n t at the 10 pe rcen t l e v e l of s i g n i f i c a n c e . The c rop p r i c e c o e f f i c i e n t i s s t a t i s t i c a l l y s i g n i f i c a n t at the 5 percent l e v e l in both e q u a t i o n s . However, the input p r i c e c o e f f i c i e n t s are not s t a t i s t i c a l l y s i g n i f i c a n t in e i t h e r e q u a t i o n . Con t r a r y to the t r a n s l o g c a s e , p o s i t i v e own output p r i c e c o e f f i c i e n t s are not on ly a necessa ry but a s u f f i c i e n t 153 TABLE 5.12 Regress ion C o e f f i c i e n t s , Quadra t i c P r o f i t F u n c t i o n C o e f f i c i e n t s C a t t l e P r i c e ' Expec ted G a i n ' Crop P r i c e ' Labour P r i c e ' C a p i t a l P r i c e ' Beg inn ing Stock Constant C a t t l e 9989.8 ( 3 .4 ) * 14677.0 (-2.6) -2983.5 (-5.1) 0495.21 (-.14) 3542.2 ( .26) 4.4 (9.4) -304.93 (-1.7) Equat ion Inventory -14677.0 (2.6) 18339.0 (1.6) 4912.9 (4.3) 3014. 1 (.42) -7174.7 (-.26) 3. 1 (3.4) 361.76 (1.02) R 2 d.w. SEE .8384 1 .4 696.92 .6941 1 .5 1370.6 * t - s t a t i s t i c i n paren theses : z?~ Ho: a l l c o e f f i c i e n t s equa l to ze ro 136.38 d . f . x 2 ( • ° 5 ) Dec i s i on 11 19.68 Re jec t 154 c o n d i t i o n f o r gene r a t i ng p o s i t i v e output supp ly e l a s t i c i t i e s . F i n a l l y , the e s t ima ted c o e f f i c i e n t s f o r the beg inn ing s tock of c a t t l e v a r i a b l e are s t a t i s t i c a l l y s i g n i f i c a n t at the 5 pe r cen t l e v e l in both output e q u a t i o n s . The i n t e r c e p t term fo r the c a t t l e equa t ion i s s i g n i f i c a n t l y nega t i ve at the 95 percent con f i dence l e v e l , whereas f o r the end-o f-pe r i od i nven to r y equa t ion the i n t e r c e p t term i s s i g n i f i c a n t l y p o s i t i v e at on ly the 80 percent c o n f i d e n c e l e v e l . T h i s i n d i c a t e s that t e c h n i c a l change has been b i a s e d aga in s t c a t t l e p r o d u c t i o n but i n favor of end-of-p e r i o d i n v e n t o r i e s . The t e c h n i c a l b i a s aga in s t c a t t l e p r o d u c t i o n has been r e p o r t e d i n other s t u d i e s (McKay, Laurence , and V l a s t e r i n 1982). A d d i t i o n a l l y , these s t u d i e s have been ab le to demonstrate a b i a s in f avo r of c r op p r o d u c t i o n . However, data l i m i t a t i o n s p r o h i b i t e s t i m a t i n g the c rop equa t ion and t h e r e f o r e t h i s r e s u l t c o u l d not be t e s t e d . The t e c h n i c a l b i a s in f avo r of end-o f-pe r i od i n v e n t o r i e s i n d i c a t e s tha t t e c h n i c a l change has enab led farmers to ma in ta in l a r g e r c a t t l e i n v e n t o r i e s . T h i s has been ach i e ved p r i m a r i l y by t e c h n i c a l advancements that enab le farmers to e f f i c i e n t l y feed l a rge numbers of an ima l s . Moreso, t h i s r e s u l t i s c o n s i s t e n t wi th observed i n c r ea ses i n the aggregate herd over the p e r i o d of t h i s s t u d y . Summary measures of goodness of f i t e s t ima tes are a l s o r e p o r t e d in Tab le 5 .12. The equa t ions have R 2 measures of .8384 and .6941 fo r t o t a l c a t t l e supply and t o t a l end of p e r i o d i nven to ry demand r e s p e c t i v e l y . These s t a t i s t i c s 1 55 i n d i c a t e tha t the es t imated equa t ions e x p l a i n the v a r i a t i o n in output q u a n t i t i e s w e l l . The Durbin-Watson s t a t i s t i c ( fo r the t rans formed v a r i a b l e s ) i m p l i e s tha t a u t o c o r r e l a t i o n i s not a s e r i o u s p rob lem. F i n a l l y , a Ch i-squared t e s t s t a t i s t i c f o r the n u l l h y p o t h e s i s that a l l e s t ima ted c o e f f i c i e n t s are equa l to zero shows an easy r e j e c t i o n . Because on l y two net output equat ions can be e s t i m a t e d , many of the parameters of the no rma l i zed q u a d r a t i c v a r i a b l e p r o f i t f u n c t i o n are unknown. Consequen t l y , i t i s not p o s s i b l e to determine whether the p r o p e r t i e s of d u a l i t y are f u l l y s a t i s f i e d . However, the two es t imated equa t i ons can be eva lua ted to determine the c o n s i s t e n c y of t h e i r e s t ima ted c o e f f i c i e n t s wi th the d e s i r e d p r o p e r t i e s . Both equa t ions s a t i s f y the mono ton i c i t y requirement at each o b s e r v a t i o n . That i s , both equat ions p r e d i c t p o s i t i v e output r esponse . Fur thermore , both equa t ions s a t i s f y the necessary c o n d i t i o n fo r o b t a i n i n g a p o s i t i v e s e m i d e f i n i t e Hess ian mat r ix ( i . e . , own p r i c e c o e f f i c i e n t s are p o s i t i v e ) . From these r e s u l t s , i t i s assumed that the es t imated net output equa t ions p robab l y s a t i s f y the d u a l i t y p r o p e r t i e s and t h e r e f o r e r ep resen t the p r o f i t maximiz ing behav io r of cow-ca l f p r o d u c e r s . Us ing the formulas p resen ted in Se c t i on (4.4) of Chapter Fou r , e s t ima tes of the p a r t i a l e l a s t i c i t i e s of cho i ce are g i ven in Tab le 5.13. These es t imates are computed at the means of the exogenous v a r i a b l e s . In d e s c r i b i n g these e l a s t i c i t i e s , i t w i l l be conven ien t to once aga in d i v i d e the t a b l e i n t o sub-mat r i ces (here A, B, and C ) . TABLE 5.13 E l a s t i c i t i e s of Cho ice (Quadra t i c ) P r i c e s C a t t l e Invent . Crop C a t t l e .19 -.083 - .269 Invent . - .099 .037 16 Labour Cap. M a t e r i a l s .031 .043 .295 .067 -.03 - .10 Beg inn ing Stock 1 .8 47 157 In sub-matr ix A, the own e l a s t i c i t i e s of supp ly as we l l as c r o s s p r i c e e l a s t i c i t i e s fo r t o t a l c a t t l e supply and end-of-p e r i o d i n v e n t o r i e s are d i s p l a y e d . Own e l a s t i c i t i e s of supply are c o n s i s t e n t w i th a p r i o r i e x p e c t a t i o n s and are p o s i t i v e : however, both c a t t l e supp ly (.19) and i nven to r y (.037) e l a s t i c i t y e s t ima tes are l e s s than one i n d i c a t i n g an i n e l a s t i c response to p r i c e v a r i a t i o n s . •The i n e l a s t i c response fo r end-o f-pe r i od i n v e n t o r i e s i s c o n s i s t e n t ( a l though sma l l e r i n magnitude) wi th the es t imate ob t a i ned us ing the c r o s s - s e c t i o n a l t r a n s l o g model . However, the i n e l a s t i c c a t t l e supp ly response i s s i g n i f i c a n t l y lower than the one ob t a i ned us i ng the c r o s s - s e c t i o n a l t r a n s l o g mode l . The a l t e r n a t i v e o w n - e l a s t i c i t y e s t ima tes are compared in Tab le 5.14. What these r e s u l t s i n d i c a t e i s tha t under the genera l r e s t r i c t i o n of i n c r e a s i n g herd s i z e ( i . e . , c o n s t r a i n e d adjustment to op t ima l herd l e v e l s ) , the own e l a s t i c i t y of supply- f o r both c a t t l e supply and end of p e r i o d i n v e n t o r i e s i s r educed . These r e s u l t s p rov i de e m p i r i c a l ev idence to support the Le C h a t e l i e r p r i n c i p l e d i s c u s s e d in S e c t i o n (4.3) of Chapter F o u r . 7 I t i s worth n o t i n g tha t the magnitude of the t i m e - s e r i e s e s t ima ted e l a s t i c i t i e s support r e s u l t s p resen ted e a r l i e r that cow-cal f farmers respond r e l a t i v e l y l e s s to changes in expected c a t t l e p r i c e s than to changes in c u r r e n t c a t t l e p r i c e s . The es t ima ted c r o s s p r i c e e l a s t i c i t i e s g i ven in sub-mat r ix A of Tab le 5.13 are c o n s i s t e n t w i th a p r i o r i 158 TABLE 5.14 Summary of Own E l a s t i c i t y of Supply T r a n s l o g ( C r o s s - S e c t i o n a l ) Quad ra t i c (T ime-Ser ies ) C a t t l e Inventory 1 .43 .075 .19 .037 159 e x p e c t a t i o n s and i n d i c a t e a s u b s t i t u t e r e l a t i o n s h i p between c rops and c a t t l e supply (- .269) , between c a t t l e supply and end-o f-pe r i od i nven to r y (- .083) , and between end-o f-pe r i od i n ven to r y and c a t t l e supp ly (- .099 ) . However, the c r o s s p r i c e e l a s t i c i t y between c rops and end-o f-pe r i od i n v e n t o r i e s i s .16 which suggests a complementary r e l a t i o n s h i p between these two i n p u t s . T h i s r e s u l t i s o p p o s i t e to that genera ted in the c r o s s - s e c t i o n a l t r a n s l o g model . However, these r e s u l t s aga in demonstrate c o n s i d e r a b l e scope fo r changes in the exogeneous v a r i a b l e s to i n f l u e n c e the output compos i t i on on cow-cal f fa rms . These e m p i r i c a l f i n d i n g s i n d i c a t e tha t d u r i n g p e r i o d s when i n v e n t o r i e s of an ima ls are i n c r e a s i n g , an i n c r ea se in c rop p r i c e s r e s u l t s in a r e d u c t i o n in c a t t l e supp ly but causes an i n c r ea se in the number of an ima ls he ld in i n v e n t o r y . On the o the r hand, i f c a t t l e i n v e n t o r i e s are at an op t ima l l e v e l , an i n c r e a s e in c rop p r i c e s r e s u l t s in a r e d u c t i o n in both c a t t l e supp ly and end-o f-pe r i od i n v e n t o r i e s . Sub-matr ix B d e f i n e s the e l a s t i c i t y of output supp ly wi th r e s p e c t to input p r i c e s . The e l a s t i c i t y e s t ima tes fo r the m a t e r i a l s and s e r v i c e s v a r i a b l e are d e r i v e d from the es t ima ted equa t i on us ing the symmetry and homogenity r e s t r i c t i o n s . A one pe r cen t i n c r ease in the p r i c e of l abour w i l l decrease t o t a l c a t t l e supply by - .031% (which i s c o n s i s t e n t wi th r e s u l t s ob ta ined fo r the t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n ) but i n c r e a s e s end-o f-pe r i od i n v e n t o r i e s by .067%. A one pe rcen t i n c r ease in the p r i c e of c a p i t a l or m a t e r i a l s and s e r v i c e s w i l l i n c r ease t o t a l c a t t l e supply by .043% and .295% 160 r e s p e c t i v e l y but decrease end-o f-pe r i od i n v e n t o r i e s by - .03% and - .10% r e s p e c t i v e l y . F i n a l l y , sub-matr ix C shows the e l a s t i c i t y of output supply wi th respec t to beg inn ing i n v e n t o r i e s . Both es t ima tes are p o s i t i v e , i n d i c a t i n g tha t a one percent i n c r ease in the beg inn ing number of an imals w i l l i n c r ea se both c a t t l e supp ly by 1;8% and an imals h e l d in i nven to ry by .47% . The magnitude of these r e s u l t s aga in i n d i c a t e cow-cal f f a rmers ' p r e f e r e n c e s fo r c u r r e n t c a t t l e p r o d u c t i o n over f u tu r e c a t t l e p r o d u c t i o n . F o l l o w i n g procedures p r e v i o u s l y o u t l i n e d , the t o t a l e l a s t i c i t y of c a t t l e supp ly can be c a l c u l a t e d fo r the t ime-s e r i e s e s t i m a t e s . Tab le 5 .15 r e p o r t s the va lue of t h i s e l a s t i c i t y , es t imated at the means of the exogenous v a r i a b l e s , and fo r each o b s e r v a t i o n . These es t ima tes i n d i c a t e that i f e x p e c t a t i o n s are a l l owed to ad jus t to changes in c a t t l e p r i c e s output supp ly w i l l a lways dec r ease . That i s , cow-ca l f farmers w i l l a l t e r end-o f-pe r i od i n v e n t o r i e s and c a t t l e supply in response to chang ing c a t t l e p r i c e s and expected p r i c e s . However, there i s no ev idence to i n d i c a t e tha t t h i s tendency i s s u f f i c i e n t l y s t rong enough to decrease shor t run e l a s t i c i t i e s of supply to ze ro or l e s s . These r e s u l t s support ev idence p resen ted e a r l i e r and t h e r e f o r e , one can conc lude q u i t e s t r o n g l y that shor t run c a t t l e supp ly f u n c t i o n s are p o s i t i v e l y s l oped th roughout . However, i t i s worth n o t i n g tha t the t o t a l e l a s t i c i t y of c a t t l e supp ly i s i n e l a s t i c f o r non-opt imal l e v e l s of c a t t l e i n v e n t o r i e s but as c a t t l e i n v e n t o r i e s approach an op t ima l l e v e l , the e l a s t i c i t y of 161 TABLE 5.15 T o t a l E l a s t i c i t y of C a t t l e Supply T o t a l E l a s t i c i t y of Supply Means of Exogeneous V a r i a b l e s .16 1956 .095 1957 .073 1958 .102 1959 .121 1960 .083 1961 .104 1962 .084 1963 .103 1964 .080 1965 .067 1966 .071 1967 .078 1968 .071 1969 .105 1970 .134 1971 .101 1972 .102 1973 .128 1974 .071 1975 .037 1976 .036 1977 .046 1978 .103 1979 .151 1980 .082 1981 .057 1982 .058 162 c a t t l e supp ly i n c r e a s e s and in f a c t , becomes e l a s t i c . F i gu re 5.1 p rov i des a v i s u a l a c coun t i ng ( f o r i l l u s t r a t i o n on ly ) of the e f f e c t of changing p r i c e e x p e c t a t i o n s on the s lope of the c a t t l e supply f u n c t i o n f o r both the c r o s s - s e c t i o n a l and t ime-s e r i e s r e s u l t s . Curves A and B represen t the c r o s s - s e c t i o n a l r e s u l t s whereas C and D rep resen t the t i m e - s e r i e s r e s u l t s . A l l o w i n g p r i c e e x p e c t a t i o n s to ad ju s t to changes in cu r r en t p r i c e i n c r ea ses the s lope of the supp ly f u n c t i o n s (from B to A and from D to C) which dec reases the e l a s t i c i t y of c a t t l e supp ly in both c a s e s . To complete the e m p i r i c a l p r e s e n t a t i o n , Tab le 5.16 p r o v i d e s a summary of the t o t a l e l a s t i c i t y of supp ly es t imates genera ted in t h i s study and other e s t ima tes of these shor t run e l a s t i c i t i e s as r epo r t ed in past r e s e a r c h . Before c o n c l u d i n g t h i s c h a p t e r , i t i s a p p r o p r i a t e to o f f e r some e x p l a n a t i o n of why the re i s no ev idence of pe rve rse shor t run behav iour in the Canadian cow-cal f i n d u s t r y . Three f a c t o r s can be i d e n t i f i e d which may i n f l u e n c e t h i s behav iou r . F i r s t , in terms of North American c a t t l e s u p p l y , Canada i s a sma l l open economy wi th c a t t l e p r i c e s determined in the U.S. market . F a c t o r s e x t e r n a l to the Canadian market cause f l u c t u a t i o n s in c a t t l e p r i c e s . The cow-cal f farmer may or may not be aware of these f a c t o r s but e i the rway , t h i s i n c r eases the u n c e r t a i n t y of p r e d i c t i n g f u tu r e c a t t l e p r i c e s . The consequences of t h i s may be that the cow-cal f farmer responds r e l a t i v e l y more to changes in c u r r e n t c a t t l e p r i c e s than to expected p r i c e changes . Second, d e f i n i n g f l u c t u a t i o n s in p r i c e s and c a t t l e market ings as a c a t t l e c y c l e tends to imply 163 FIGURE 5.1 Supply F u n c t i o n s , C r o s s - S e c t i o n a l ve r sus T ime-Ser i es C a t t l e P r i c e C a t t l e Supply A - C r o s s - s e c t i o n a l B - C r o s s - s e c t i o n a l C - T ime-se r i e s D - T ime-se r i e s P r i c e e x p e c t a t i o n adjustment No adjustment P r i c e e x p e c t a t i o n adjustment No adjustment 1 64 TABLE 5.16 Summary of C a t t l e Supply E l a s t i c i t i e s E l a s t i c i t y wi th r espec t to the P r i c e o f : Feeder C a t t l e Non Feeder C a t t l e A l l C a t t l e T h i s Study A l l C a t t l e (Canada) T r a n s l o g ( c r o s s - s e c t i o n a l ) - - 1.41 Quad ra t i c ( t i m e - s e r i e s ) - - .16 Other S t ud i e s Osp ina & Shumway (U.S) - - - .45 Langemier & Thompson (U.S . ) feeder c a t t l e - .98 .30 non feeder c a t t l e 1.42 -1.24 a l l c a t t l e -1.06 George & K ing (U.S . ) a l l c a t t l e - - -.42 T r y f o s (Canada) - - - .009 Yver (Argent ina ) a l l c a t t l e ( shor t run) -1.61 a l l c a t t l e ( long run) 1.15 165 some r e g u l a r i t y to these v a r i a t i o n s . T h i s i s not the c a s e . I t i s not s u r p r i s i n g then tha t cow-cal f farmers do not respond to p r i c e changes as i f they were c l e a r l y d e f i n e d c y c l i c a l f l u c t u a t i o n s . Th i s f a c t o r would imply a p r e f e r ence fo r cu r r en t p r o d u c t i o n over f u tu r e p r o d u c t i o n . T h i r d , e m p i r i c a l ev idence i n d i c a t e s c o n s i d e r a b l e scope fo r output s u b s t i t u t i o n on cow-cal f fa rms. T h i s w i l l a l low cow-cal f farmers to a l t e r t h e i r output compos i t i on in response to changes in p r i c e s and expected p r i c e s . To conc lude t h i s d i s s e r t a t i o n , a summary of f i n d i n g s and c o n c l u s i o n s i s p resen ted in Chapter S i x . 166 FOOTNOTES TO CHAPTER FIVE 1 Asymptot i c t - r a t i o s are d e f i n e d as the r a t i o of the parameter e s t ima tes to t h e i r asympto t i c s t andard e r r o r s . 2 Us ing r a the r c o m p l i c a t e d n o n - l i n e a r t r a n s f o r m a t i o n s one can impose c o n v e x i t y on the model (Lau 1978). However, t h i s procedure imposes convex i t y at on l y one p o i n t ( i . e . , the p o i n t of expans ion) and i s r a t h e r c o s t l y c o m p u t a t i o n a l l y to pe r f o rm . 3 I would l i k e to thank Dr . Ken White f o r h i s a s s i s t a n c e in d e r i v i n g the s tandard e r r o r s f o r the e l a s t i c i t y e s t i m a t e s . 4 Canadian c a t t l e numbers reached a h igh of 15.6 m i l l i o n head in 1975. S t a t i s t i c s Canada, L i v e s t o c k and Animal P roduc ts S t a t i s t i c s 23-203, Ottawa, v a r i o u s i s s u e s . 5 Each v a r i a b l e i s t r ans fo rmed a c c o r d i n g to the f o l l o w i n g f o r m u l a : x t " K - i • V 6 The v a r i a b l e s were t rans fo rmed us ing a l t e r n a t i v e e s t ima tes f o r (5, however, except f o r 0 = 1 the Durbin-Watson t e s t i n d i c a t e d that f i r s t - o r d e r a u t o c o r r e l a t i o n remained. 7 In a d d i t i o n , the Le C h a t e l i e r P r i n c i p l e i m p l i e s r e s t r i c t i o n s on the c r o s s - p r i c e e l a s t i c i t i e s . However, because on l y two output equa t i ons are es t ima ted t h i s r e s t r i c t i o n can not be t e s t e d , see Diewert (1974) . 167 6. SUMMARY AND CONCLUSIONS The purpose of t h i s chapte r i s to p resen t a b r i e f summary of the d i s s e r t a t i o n and to r epo r t the p r i n c i p a l f i n d i n g s and c o n c l u s i o n s . The cow-ca l f farmer i s engaged in the pr imary a c t i v i t y of r ep roduc ing an imals and s e l l i n g the progeny . The b a s i c d e c i s i o n s f a c i n g the farmer are whether to s e l l an an imal now, feed to heav i e r weights be fo re s e l l i n g , or r e t a i n the an imal in the b reed ing herd fo r the purpose of p roduc ing new a n i m a l s . The d e c i s i o n to s e l l an an imal or to keep i t in the b r eed ing herd depends on p r e v a i l i n g and expected economic c o n d i t i o n s . These b a s i c p roduc t i on d e c i s i o n s can g i ve r i s e to an i n t e r e s t i n g economic c h a r a c t e r i s t i c whereby the e l a s t i c i t y of supp ly in the shor t run i s nega t i ve and g r a d u a l l y becomes p o s i t i v e over a long adjustment p e r i o d . Given an i n c r e a s e in the p r i c e of beef expected to p e r s i s t i n t o the f u t u r e , the c a t t l e producer w i l l f i n d i t p r o f i t a b l e to r e t a i n an ima l s in the herd tha t o therw ise may have been s o l d . For s t e e r s , t h i s i m p l i e s keep ing the an imal longer and f a t t e n i n g to h e a v i e r we igh t s . For h e i f e r s and cows, i t i m p l i e s e i t h e r f a t t e n i n g to heav i e r weights ( h e i f e r s ) or b reed ing the an imals to o b t a i n c a l v e s . In the aggregate and in the shor t run , t h i s i n d i c a t e s tha t the re w i l l be a decrease in the s l a u g h t e r of a l l a n i m a l s . In the long r un , the supp ly e l a s t i c i t i e s of beef w i l l be p o s i t i v e due to the i n c r ease in herd s i z e and average we igh t s . The aim of t h i s study was to deve lop a t h e o r e t i c a l p r o f i t max imiz ing model of a cow-cal f farm that e x p l a i n s t h i s 168 behav ior in the shor t run and to e m p i r i c a l l y es t imate shor t run supply response and investment behav ior of c a t t l e p r o d u c e r s . In d e v e l o p i n g the t h e o r e t i c a l model , the cow-ca l f farmer was assumed to have a predetermined s tock of an ima ls at the beg inn ing of each p e r i o d . Moreover , at any p o i n t in t ime , c u r r e n t beef and f a c t o r p r i c e s were known but next p e r i o d ' s beef p r i c e s were u n c e r t a i n . The farmer combines the i n i t i a l s tock of an ima ls wi th a v e c to r of v a r i a b l e inputs and , respond ing to an economic environment g i ven output p r i c e s , input p r i c e s , and h i s ex -p e c t a t i o n s about p r i c e next p e r i o d , the farmer determines the s tock of an ima ls r e t a i n e d at the end of the p e r i o d and the output supp ly d u r i n g the p e r i o d . End-o f-pe r iod s tocks are va lued at expec ted output p r i c e next p e r i o d and c u r r e n t output supp ly i s va lued at output p r i c e t h i s p e r i o d . T h i s s imple dynamic behav io r can be c h a r a c t e r i z e d us i ng a dua l v a r i a b l e p r o f i t f u n c t i o n where p r o f i t s are a f u n c t i o n of output p r i c e s , expected output p r i c e s , input p r i c e s , and predete rmined s tocks of a n i m a l s . By a p p l y i n g H o t e l l i n g ' s Lemma to the v a r i a b l e p r o f i t f u n c t i o n , the op t ima l q u a n t i t i e s of output s u p p l y , input demand, and end-o f-pe r i od i n v e n t o r i e s can be de te rm ined . These equa t i ons can be used to p o s t u l a t e an econometr i c mode l . Us ing the t h e o r e t i c a l model , a comparat i ve s t a t i c a n a l y s i s was c a r r i e d out to determine shor t run supp ly response of cow-ca l f f a rmers . In t h i s model , the s i gn of the shor t run e l a s t i c i t y of c a t t l e supply depends on three 169 f a c t o r s : i ) the t e c h n o l o g i c a l s t r u c t u r e of the i n d u s t r y ; i i ) the s u b s t i t u t i o n p o s s i b i l i t i e s between p r o d u c t i o n today and p r o d u c t i o n tomorrow; and i i i ) the s e n s i t i v i t y of f a rmers ' p r i c e e x p e c t a t i o n s wi th r espec t to changes in cu r r en t p r i c e . One can conc lude from t h i s r e s u l t tha t a shor t run nega t i ve supp ly e l a s t i c i t y in the cow-ca l f i n d u s t r y i s not a p r e d i c t i o n from economic t heo r y : r a the r the s i gn of the e l a s t i c i t y i s unknown and w i l l depend on p r i c e e x p e c t a t i o n s of p r o d u c e r s . The f i r s t stage in e s t i m a t i n g the system of ou tpu t , i n p u t , and end-o f-pe r i od i nven to r y equa t ions r e q u i r e d s p e c i f y i n g some e x p e c t a t i o n p rocess to be used in p r e d i c t i n g next p e r i o d ' s c a t t l e p r i c e s . A " q u a s i - r a t i o n a l " e x p e c t a t i o n p rocess was p o s i t e d to p r e d i c t e x a c t l y the p r i c e e x p e c t a t i o n s of cow-cal f p r o d u c e r s . T h i s e x p e c t a t i o n procedure was based on a t ime s e r i e s method whereby an a u t o r e g r e s s i v e i n t e g r a t e d moving average model was h ypo thes i z ed to represen t the e x p e c t a t i o n p r o c e s s . An ARIMA model was es t ima ted fo r each expected p r i c e v a r i a b l e in the model . The p r e d i c t i o n s genera ted by these es t ima ted models were combined w i th the main data base to complete the data requ i rements necessa ry fo r econometr ic e s t i m a t i o n . To es t imate the f u l l v a r i a b l e p r o f i t f u n c t i o n , the f o l l o w i n g i n fo rma t i on was r e q u i r e d : i ) the q u a n t i t y of d i f -f e r en t ou tputs produced by cow-ca l f farms and a s s o c i a t e d output p r i c e s ; i i ) the q u a n t i t y of d i f f e r e n t i npu ts used on farms and a s s o c i a t e d input p r i c e s ; i i ) the end-o f-pe r i od s tocks of c a t t l e and a s s o c i a t e d expected p r i c e s ; and iv ) the beg inn ing s tocks of c a t t l e . Two surveys conducted by 170 S t a t i s t i c s Canada (FES and NLS) were the pr imary sources fo r i n ven to r y and expend i tu re data on cow-cal f farms. The FES i s a c r o s s - s e c t i o n a l data s e r i e s whereas the NLS i s a t ime-s e r i e s data sample. Because of the c y c l i c a l nature of beef p r o d u c t i o n , the t i m e - s e r i e s data set a l l owed fo r e l a s t i c i t y measurements over the beef c y c l e which c o u l d be compared to the c r o s s - s e c t i o n a l r e s u l t s du r i ng a s i n g l e p e r i o d of the c y c l e . G e n e r a l l y , p r i c e s of farm inputs were ob ta ined from the main Cansim f i l e s of S t a t i s t i c s Canada and c a t t l e output p r i c e s were ob ta ined from market q u o t a t i o n s r epo r t ed in the L i v e s t o c k Market Review. It was d e c i d e d , f o r a t r a c t a b l e econometr ic s p e c i f i c a t i o n , to s p e c i f y three aggregate output v a r i a b l e s ( t o t a l c a t t l e supp ly s o l d o f f farms, end-o f-pe r i od i nven to ry demand, and t o t a l c r op s u p p l y ) , th ree aggregate input v a r i a b l e s ( l a b o u r , c a p i t a l , and m a t e r i a l s and s e r v i c e s ) , and one f i x e d f a c t o r r e p r e s e n t i n g the beg inn ing s tock of c a t t l e . The t r a n s c e n d e n t a l l o g a r i t h m i c f u n c t i o n a l form was p o s t u l a t e d fo r the m u l t i - o u t p u t , m u l t i - i n p u t v a r i a b l e p r o f i t f u n c t i o n . For econometr ic e s t i m a t i o n , H o t e l l i n g ' s Lemma was used to o b t a i n the revenue share equa t ions fo r each output and expend i tu re share equa t ions fo r each i n p u t . Z e l l n e r ' s SUR techn ique was employed (combined wi th the c r o s s - s e c t i o n a l data sample) to es t imate t h i s system of e q u a t i o n s . The es t ima ted c o e f f i c i e n t s were used to t e s t f o r s t r u c t u r e and to c a l c u l a t e e l a s t i c i t i e s of cho i c e fo r the cow-cal f i n d u s t r y . A l t e r n a t i v e e s t ima tes of the e l a s t i c i t i e s of cho i c e c o u l d then be genera ted us ing the t i m e - s e r i e s data sample. However, 171 a number of v a r i a b l e s r e q u i r e d to es t imate the f u l l p r o f i t f u n c t i o n were not a v a i l a b l e on a t i m e - s e r i e s b a s i s . S p e c i f i c a l l y , t h i s da ta set d i d not i n c l u d e i n fo rma t i on on t o t a l p r o f i t s , c r op p r o d u c t i o n , or the q u a n t i t i e s of i nputs used on cow-cal f f a rms . I t d i d i n c l u d e i n f o r m a t i o n on cu r r en t c a t t l e p r i c e s , expec ted c a t t l e p r i c e s , c r op p r i c e s , input p r i c e s fo r l a b o u r , c a p i t a l , and m a t e r i a l s and s e r v i c e s , and i n v e n t o r i e s of c a t t l e on cow-cal f fa rms. From the a v a i l a b l e t i m e - s e r i e s d a t a , net output supply equa t i ons were s p e c i f i e d fo r t o t a l c a t t l e output supply and t o t a l end-o f-pe r i od i nven to ry demand. I t i s un fo r tuna te tha t because the p r o f i t v a r i a b l e was absent from the d a t a , a t r a n s l o g f u n c t i o n a l form c o u l d . not be s p e c i f i e d fo r the v a r i a b l e p r o f i t f u n c t i o n . I n s t e a d , a no rma l i z ed q u a d r a t i c f u n c t i o n a l form was used . For the t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n c a s e , the e s t ima ted c o e f f i c i e n t s of the revenue and expend i tu re share equa t i ons were g e n e r a l l y s t a t i s t i c a l l y s i g n i f i c a n t w i th the share equa t ions p r o v i d i n g a good f i t to the d a t a . Fu r the rmore , s t a t i s t i c a l t e s t i n g i n d i c a t e d tha t the e s t ima ted v a r i a b l e p r o f i t f u n c t i o n s a t i s f i e d the r e q u i r e d d u a l i t y p r o p e r t i e s of symmetry, l i n e a r homogeneity in p r i c e s , and m o n o t o n i c i t y . Convex i t y of the Hess i an mat r ix was determined at each o b s e r v a t i o n by c a l c u l a t i n g the a s s o c i a t e d e i g e n v a l u e s . U n f o r t u n a t e l y , c o n v e x i t y f a i l e d because one e igenva lue was nega t i v e at each o b s e r v a t i o n . However, i t i s assumed that the t rue p r o f i t f u n c t i o n i s convex i n p r i c e s . Consequen t l y , one can conc lude tha t the es t imated share equa t ions have performed 1 72 we l l and tha t they adequate l y r ep resen t the p r o f i t maximiz ing behav io r of cow-cal f p r o d u c e r s . The es t imated c o e f f i c i e n t s of the revenue and expend i tu re share equa t i ons were used to t e s t f o r c e r t a i n c h a r a c t e r i s t i c s of the u n d e r l y i n g t r a n s f o r m a t i o n f u n c t i o n . I t was determined that the t e c h n o l o g i c a l s t r u c t u r e of cow-ca l f p roduc t i on in western Canada i s d e f i n e d by a non-homothet ic , non-homogeneous t r a n s f o r m a t i o n f u n c t i o n sub jec t to d e c r e a s i n g r e tu rns to s c a l e and j o i n t p r o d u c t i o n between c rops and c a t t l e . Other c h a r a c t e r i s t i c s of the cow-cal f i n d u s t r y were determined by c a l c u l a t i n g e l a s t i c i t i e s of c h o i c e . These e l a s t i c i t i e s conformed to a l l a p r i o r i e x p e c t a t i o n s wi th output supply f u n c t i o n s hav ing non-negat ive s l o p e s , d e r i v e d input demand f u n c t i o n s hav ing n o n - p o s i t i v e s l o p e s , and a s u b s t i t u t e r e l a t i o n s h i p p r e d i c t e d between c a t t l e supp ly and end-o f-pe r i od i n ven to r y demand. Own e l a s t i c i t i e s of supply f o r c a t t l e and c rops i n d i c a t e d an e l a s t i c response to changes in own p r i c e s whereas the own e l a s t i c i t y of end-o f-pe r i od i n v e n t o r i e s i n d i c a t e d an i n e l a s t i c response to changes in expected c a t t l e p r i c e s . These r e s u l t s imply tha t there i s no s i g n i f i c a n t output adjustment in an attempt to counte r the c a t t l e c y c l e . Rather changes in c a t t l e output are p o s i t i v e l y c o r r e l a t e d wi th p r i c e f l u c t u a t i o n s over the c a t t l e c y c l e . In o ther words, these r e s u l t s support the e x i s t e n c e of a c a t t l e c y c l e . In a d d i t i o n , c r o s s - p r i c e e l a s t i c i t i e s d e f i n e d a s u b s t i t u t e r e l a t i o n s h i p amongst a l l output c a t e g o r i e s . T h i s i n d i c a t e s s i g n i f i c a n t scope fo r changing the output 173 compos i t i on between c rops and c a t t l e on cow-cal f farms in western Canada. The own e l a s t i c i t i e s of input demand fo r l abour and m a t e r i a l s i m p l i e d an e l a s t i c demand for both i npu ts whereas the own e l a s t i c i t y of input demand for c a p i t a l i n d i c a t e d an i n e l a s t i c demand fo r t h i s i n p u t . T h i s i m p l i e s that the employment of c a p i t a l i nputs on farms i s more s t a b l e r e l a t i v e to the employment of labour and m a t e r i a l s i n p u t s . The c r o s s p r i c e e l a s t i c i t y between labour and c a p i t a l d e f i n e d these inputs as s u b s t i t u t e s . Moreover , fo r a g i ven set of r e l a t i v e p r i c e s , the s t r e n g t h of t h i s s u b s t i t u t i o n e f f e c t i m p l i e d that cow-cal f farms are s u b s t i t u t i n g away from labour and towards g rea te r c a p i t a l i z a t i o n . Other e l a s t i c i t y r e s u l t s suggested that in the p r o d u c t i o n of c a t t l e , both labour and m a t e r i a l s are used more i n t e n s i v e l y than c a p i t a l i n p u t s . C o n v e r s e l y , in the p r o d u c t i o n of c r o p s , the c a p i t a l input i s used more i n t e n s i v e l y than other i n p u t s . In the p r o d u c t i o n of each o u t p u t , i npu t s were c l a s s i f i e d as be ing s u p e r i o r , norma l , or i n f e r i o r . From t h i s c l a s s i f i c a t i o n , i t was conc luded that p o l i c i e s des igned to i n c r ea se farm p r i c e s of e i t h e r c a t t l e or c rops w i l l have q u i t e d i f f e r e n t e f f e c t s on r u r a l deve lopment . I n c r ea s i ng c r o p p r i c e s w i l l g i ve r i s e to s u b s t i t u t i o n away from labour which w i l l encourage i n c r ea sed m i g r a t i o n o f f farms and i n c r e a s i n g c a p i t a l i z a t i o n . Increased c a t t l e p r i c e s , on the o ther hand, w i l l r e s u l t in i n c r ea sed farm employment. To complete the e m p i r i c a l r e s u l t s f o r the t r a n s l o g v a r i a b l e p r o f i t f u n c t i o n , the t o t a l e l a s t i c i t y of c a t t l e 174 supply was c a l c u l a t e d . T h i s e l a s t i c i t y measure takes account not on ly of the e f f e c t of c a t t l e p r i c e f l u c t u a t i o n s , but a l s o the e f f e c t of changing e x p e c t a t i o n s of c a t t l e p r i c e s on c a t t l e s u p p l y . I t was determined tha t a c coun t i ng fo r adjustments in e x p e c t a t i o n s of c a t t l e , p r i c e s caused by changes in c u r r e n t c a t t l e p r i c e s w i l l a lways decrease the e l a s t i c i t y of c a t t l e s u p p l y . However, t h i s e f f e c t was not s t r ong enough to reduce the t o t a l e l a s t i c i t y of c a t t l e supply to ze ro or l e s s . The e l a s t i c i t i e s es t ima ted us ing the no rma l i zed q u a d r a t i c v a r i a b l e p r o f i t f u n c t i o n combined wi th the t i m e - s e r i e s data p r o v i d e d a l t e r n a t i v e measures (a l though g e n e r a l l y s i m i l a r ) to compare wi th the c r o s s - s e c t i o n a l r e s u l t s . Own supp ly e l a s t i c i t i e s were c o n s i s t e n t w i th a p r i o r i e x p e c t a t i o n s and were p o s i t i v e . However, both c a t t l e supp ly and i nven to r y es t ima tes were i n e l a s t i c and sma l l e r in magnitude than the co r r e spond ing c r o s s - s e c t i o n a l e l a s t i c i t i e s . The c r o s s p r i c e e l a s t i c i t i e s on the output s i de d e f i n e d (as expected) a s u b s t i t u t e r e l a t i o n s h i p between c rops and c a t t l e which aga in i m p l i e d that c o n s i d e r a b l e scope e x i s t s fo r chang ing the output compos i t i on between c rops and c a t t l e on cow-ca l f fa rms. F i n a l l y , the t o t a l e l a s t i c i t y of c a t t l e supply was c a l c u l a t e d fo r the t i m e - s e r i e s e s t i m a t e s . In c a l c u l a t i n g t h i s e l a s t i c i t y , i t was aga in determined that i f e x p e c t a t i o n s are a l l owed to ad jus t to changes in c a t t l e p r i c e s , output supp ly w i l l a lways d e c r e a s e . However, there i s no ev idence to i n d i c a t e tha t t h i s tendency was s i g n i f i c a n t l y s t rong enough to decrease shor t run e l a s t i c i t i e s of c a t t l e supp ly t o zero or 175 l e s s . T h e r e f o r e , o n e may c o n c l u d e t h a t a l t h o u g h n e g a t i v e s h o r t r u n s u p p l y e l a s t i c i t i e s a r e a t h e o r e t i c a l p o s s i b i l i t y i n t h e c o w - c a l f i n d u s t r y , e m p i r i c a l e v i d e n c e i n d i c a t e s t h a t t h e s h o r t r u n c a t t l e s u p p l y f u n c t i o n i n w e s t e r n C a n a d a i s p o s i t i v e l y s l o p e d t h r o u g h o u t . I t i s a p p r o p r i a t e t o c o m p l e t e a d i s s e r t a t i o n b y o f f e r i n g s o m e s u g g e s t i o n s f o r f u t u r e r e s e a r c h . T h e r e a r e t h r e e a r e a s w h i c h may o f f e r s o m e p o t e n t i a l f o r i n c r e a s i n g o u r u n d e r s t a n d i n g o f t h e t e c h n o l o g i c a l s t r u c t u r e o f c a t t l e p r o d u c t i o n a n d p r o v i d e a d d i t i o n a l i n f o r m a t i o n f o r p o l i c y d e t e r m i n a t i o n : 1) t h e e m p i r i c a l . i m p l i c a t i o n s o f u s i n g a l t e r n a t i v e p r i c e e x p e c t a t i o n p r o c e s s e s i n m o d e l l i n g t h e c o w -c a l f i n d u s t r y — s p e c i f i c a l l y , t h e e m p i r i c a l c o n s e q u e n c e s o f u s i n g c o n t i n u o u s a n d d i s c r e t e p r o c e s s e s f o r p r e d i c t i n g c a t t l e p r i c e s ; 2) m o d e l l i n g t h e i n p u t s i d e o f c o w - c a l f t e c h n o l o g y w i t h g r e a t e r p r e c i s i o n a n d t e s t i n g f o r s e p a r a b i l i t y — t h e F a r m E x p e n d i t u r e S u r v e y c a n p r o v i d e t h e d a t a n e c e s s a r y f o r t h i s e x a m i n a t i o n ; 3) s p e c i f y i n g a G o r m a n P o l a r F o r m t o r e p r e s e n t t h e v a r i a b l e p r o f i t f u n c t i o n - - t h i s w i l l i m p o s e e x a c t a g g r e g a t i o n o n t h e m o d e l a n d p r e s u m a b l y p r o v i d e m o r e a c c u r a t e e m p i r i c a l r e s u l t s . 176 BIBLIOGRAPHY A g r i c u l t u r e Canada, "Food and A g r i c u l t u r e Reg iona l Mode l : L i v e s t o c k , " Ottawa, Queen 's P r i n t e r , 1983. 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Shephard, R.W., Cost and P roduc t i on F u n c t i o n s , P r i n c e t o n , P r i n c e t o n U n i v e r s i t y P r e s s , 1953. Shumway, C . R . , " Supp l y , Demand, and Technology in a M u l t i p r o d u c t I ndus t r y : Texas F i e l d C r o p s " , American  J o u r n a l of A g r i c u l t u r a l Economics , 65, 1983, 748-760. S i d h u , S .S . and C A . Baanante, " E s t i m a t i n g Farm-Level Demand and Wheat Supply in the Ind ian Punjab Us ing a T r a n s l o g P r o f i t F u n c t i o n " , American J o u r n a l of A g r i c u l t u r a l  Economics , 63, 1981, 237-246. 183 S i l b e r b e r g , E . , The S t r u c t u r e of Economics : A Mathemat i ca l  A n a l y s i s , New York , McGraw-H i l l , 1978. S t a t i s t i c s Canada, "Data C o l l e c t i o n and E s t i m a t i n g Procedures of the L i v e s t o c k E s t i m a t i n g U n i t " , Methodology Paper No. 3, A g r i c u l t u r e S t a t i s t i c s D i v i s i o n , 1982. T r y f o s , P., "Canad ian Supply F u n c t i o n s of L i v e s t o c k and Meat " , American J o u r n a l of A g r i c u l t u r a l Economics , 56, 1974, 107-113. V a r i a n , H . , Microeconomic A n a l y s i s , New York , W.W. Norton and C o . , 1978. Wales , T . J . , "On the F l e x i b i l i t y of F l e x i b l e F u n c t i o n a l Fo rms" , J o u r n a l of E conome t r i c s , 5, 1977, 183-193. Weaver, R .D . , " S p e c i f i c a t i o n and E s t i m a t i o n of C o n s i s t e n t Sets of Cho ice F u n c t i o n s " , in New D i r e c t i o n s i n Econometr ic  Mode l ing and Fo recas t ing in U.S. A g r i c u l t u r e , (ed) Rausser , G . C . , Amsterdam, N o r t h - H o l l a n d , 1982. Weaver, R .D . , " M u l t i p l e Input , M u l t i p l e Output P roduc t i on Cho ices and Technology in the U.S. Wheat R e g i o n " , American J o u r n a l of A g r i c u l t u r a l Economics , 65, 1983, 45-56. Whi te , K . J . , "A Genera l Computer Program fo r Econometr i c Methods-SHAZAM", E conomet r i c a , 46, 1978, 239-240. Woodland, A . D . , " S u b s t i t u t i o n of S t r u c t u r e s , Equipment and Labor in Canadian P r o d u c t i o n " , I n t e r n a t i o n a l Economic  Review, 16, 1975, 171-187. Woodland, A . D . , " M o d e l l i n g the P roduc t i on Sec tor of an Economy: A S e l e c t i v e Survey and A n a l y s i s " , D i s c u s s i o n Paper No. 21, Department of Economics , U n i v e r s i t y of B r i t i s h Co lumb ia , 1976. Woodland, A . D . , " E s t i m a t i o n of a V a r i a b l e P r o f i t and of P l ann ing P r i c e Func t i ons f o r Canadian M a n u f a c t u r i n g , 1947-70", Canadian J ou rna l of Economics , 10, 1977, 355-377. Woodland, A . D . , "On T e s t i n g Weak S e p a r a b i l i t y " , J o u r n a l of  E conomet r i c s , 8, 1978, 383-398. Y o t o p o u l o s , P .A . , L . J . Lau , and W.L. L im , "Microeconomic Output Supply and Fac to r Demand Func t i ons in the A g r i c u l t u r e of the P rov ince of Ta iwan " , American J ou rna l  of A g r i c u l t u r a l Economics , 58, 1976, 333-340. Yve r , R . E . , "The Investment Behav ior and the Supply Response of the C a t t l e Indus t ry in A r g e n t i n e " , Ph .D . d i s s e r t a t i o n , U n i v e r s i t y of C h i c a g o , 1974. MM APPENDIX A. Farm Expenditure Survey Questionnaire, 1981 SECTION A. OPERATING ARRANGEMENTS | Section R "]7To 1. Al July 1,1981, w u this firm being operated it: (i) tn individual of family holding (excluding partnerships and corporations)? (b) a partnership? (I) with a written agreement (ii) with no written agreement (a verbal partnership) (c) a corporation or company? (d) a community pasture or cooperative grazing association? (e) a llutterile colony? (0 other? Please specify (Co to Ovation 3) (Co to Qutttlon i) (Co to Out a bit 21 (Co to Qutttlon 3) (Co to Qutttlon 31 (Co to Qutttlon 3) (Co to Qutttlon 31 If a partnership, record name(s) and address(es) of partner(s). If one or more of the partners operate another farm entirely separate from this farm, DO NOT INCLUDE this other farm when completing thli questionnaire for the partnership farm. What are the names and addresses of the partners? Name Address (Co to Qutttlon 31 Name Address (Go to Qutttlon 3) Name Address (Go to Qutttlon 3) 3. Is the operator a hired manager? Yes | J I What U the name and address of the OWNER? No 11} ID (Go to Section B) Name Address 4 - S I 0 4 - 4 I 4 . I 185 SECTION B. AREA AND LOCATION OF FARM LAND OWNED, RENTED OR M A N A G E D Section R 120 This section deals with all the land you OPERATE at the present time including cropland, woodland, waste land, pasture land and summerfallow. • Include land you MANAGE FOR OTHERS and land you RENT FROM OTHERS as wetl as land you OWN. • Exclude land you RENT TO OTHERS. I. Is the headquarters of the holding situated within the boundaries of the segment? Yes No 12?' 121 2. Wfll the land area figures in this questionnaire be reported in acres? . . OR hectares? (X) one box • I2S 3. Of the total land area you operated July 1, 1981, how much did you: (a) Rent or lease from others? (b) Own and operate? • Exclude land rented to others . 4. Total land operated July 1,1981 (Sum 3a and 3b) 5. Of the total land reported above, what is the area of woodland? • Include woodlots,cut-over land, etc Total land Land operated operated inside segment at July 1,1981 it July 1,1981 0) (2) 126 123 NoneD NoneD 125 122 NoneD NoneD 127 124 129 NoneD 130 NoneD 6. At July 1, 1980 how much land did you operate? Include land rented or leased FROM others. Exclude land rented or leased TO others Total Land Operated at July 1,1980 131 NoneD i EDIT: Are the figures in Column (I) greater than or equal to the corresponding figures in Column (2)7 Yes D (Go to Section C) No D — - Make corrections with respondent. Continue 1 8 6 SECTION C. LAND USE Section R J20o[ JTj This section deals with land use for this year and last year. 1. Did you grow any wheat, oats, barley, rye, flaxseed, rapeseed or mustard seed last year OR are you growing any of these crops this year? Yes No 201 (Go to Part B) PART A: THE SEVEN GRAINS 2. Wheat: (a) Durum (b) Utility (c) Spring (red or white) . (d) Winter 3. Oats 4. Barley . . . 5. Rye (a) Fall (b) Spring . . , 6. Flaxseed 7. Rapeseed (canola) 8. Mustard seed . . . 9. Total seven grains (Sum 2 to 8) Total Land Operated at July 1,1980 to the nearest acre (hectare) Seeded 1980 (last year) 0) NoneD NoneD NoneD NoneD NoneD NoneD NoneD NoneD NoneD NoneD NoneD NoneD 202 203 204 20S lluvetfed 1980 206 207 208 lluveited 1980 209 210 "in" 212 213 Total Land Operated it July 1,1981 to the nearest acre (hectare) Seeded 1981 (this yea/) (2) NoneD 252 NoneD 2S3 NoneD 254 255 Remaining for harvest in 1981 NoneD NoneD 256 NoneD 257 NoneD 258 Remaliiinf for hsmstln 1981 NoneD 259 NoneD 260 261 NoneD NoneD 262 NoneD 263 COMMENTS: 4 - 1 I M - 4 I 4 . I 187 SECTION C. LAND USE (concluded) i Transfer the totals reported in question 9, Box 213 and Box 263 to their respective boxes in question 10 below. PART B. - OTHER LAND USE 10. Total seven grains (from Boxes 213 and 263) 11. Cqm (a) for grain (b) for fodder and ensilage 12. Other crops (Include mixed grains, sunflower seed, veg-etables, pulses, etc.) 13. Tame hay (area cut or to be cut for hay, ensilage or seed). • Exclude wfld hay 14. Summerfallow 15. Improved land for pasture or grazing (improved by seeding, draining, irrigating, fertilizing, or brush or weed control) 16. Other improved land (barnyards, lanes, home gardens, improved idle land, etc.) 17. Woodland • Include woodlots, cut-over land, etc 18.Other unimproved land (unimproved hayland, native pasture, sloughs, marshes, etc.) Exclude woodland 19. Total aO land (Sum 10 to 18). Total Land Operated at July 1,1980 to the nearest acre (hectare) Total Land Operated at July 1,1981 to the nearest acre (hectare) Seeded 1980 Oast year) (1) Seeded 1981 (this yew) (2) NoneD NoneD NoneD 214 NoneD 264 NoneD 215 NoneD 26S NoneD 216 None D 266 NoneD 217 NoneD 267 NoneD 218 NoneD 268 220 270 None D NoneD NoneD 223 NoneD 273 NoneD 224 NoneD 274 NoneD 22S NoneD 275 NoneD 222 NoneD 272 EDIT: 1. Does the figure in Box 272 equal the figure in Box 127 (Page 3)7 Yes • No D—*• Make corrections with respondent. Continue. 2. Does the figure in Box 274 equal the figure in Box 129 (Page 3)7 Yes O No O—»*• Make corrections with respondent. Continue. 3. Does the figure in Box 222 equal the figure in Box 272? Yes D (Go to Section D) No D—»» Ask respondent for reason and write It bdow? 1104-414.1 188 SECTION D. GRAINS FED (NON-COMMERCIAL) Section R 280 5 1. Did you feed any oats,barley or feed wheat to livestock during the 11-month period August 1,1980 to July 1,1981? • Include whole, chopped, rolled and crushed grain both with and without commercial supplements added. • Exclude - brand name commercially prepared feeds. — grains grown together I Report SEPARATELY all grains mixed together AFTER harvest Yes 2. How will your grains fed Figures be reported? No 2 8 1 J (Go to Section Ej Bushels • Tons of 2,000 lbs. Metric tonnes . . . 282 2 282 3 3. For the last eleven months, that is, between August 1,1980 and July 1,1981, please estimate the total amount of the following grains fed to livestock: (a) Oats fed (b) Barley Ted (c) Wheat fed (feed, utility or other). Amount fed between August 1,1980 and July 1,1981 on total land operated 283 NoneD 284 NoneD 285 NoneD COMMENTS: 4-1104-414.1 189 SECTION E. CATTLE A N D CALVES Section R 400 9 I. Since January 1,1981, hive you had, or do you have,cattle or calves on the land you operate? • Include - all animals on this holding, regardless of ownership. • Include - all animals OWNED BY YOU but pastured on a community pasture or public land. • Exclude - animals OWNED BY YOU but kept on a farm, ranch or feedlot operated by someone else. Yes No 401 2 (Co to Section Ft PART A. INVENTORY AT JULY 1,1981 2. BuDs, I year and over alnly for DAIRY purposes. mainly for BEEF purposes. 403 NoneD 3. Cows (all cows and heifers which have calved at least once) f (i)m  ( (b )  4. Heifers, 1 year and over (which have never calved) (a) raised for DAIRY herd replacement (b) raised for BEEF herd replacement.. . (c) raised for SLAUGHTER 5. Steers, 1 year and over . 6. Calves, under 1 year old 7. Total cattle and calves (Sum 2 to 6) 8. Does this figure (Enter Box 410) . Total Number it July 1.1981 404 NoneD 40S NoneD 406 NoneD 407 NoneD 402 NoneD 408 NoneD 409 NoneD 410 NoneD operated, plus all those kept on community pasture and on public land? f Y e s D -No D -•(Co to Question 9) -Make corrections, then to to Question 9. 9. Did you milk any cows YESTERDAY? Yes 9 No 431 (Go to Part B) (a) How many cows were milked YESTERDAY? account for all of the cattle and calves on the land Total Number 419 (b) How much milk did these cows produce YESTERDAY? (1 pound • 0.44 litre, 1 kilogram • 1 litre approx., 1 gallon • 4.S litres) Litres (1 day's production) 420 ^ J I 0 4 - 4 I 4 . I 190 SECTION E. CATTLE AND CALVES (concluded) PART B. CHANGE IN CATTLE AND CALF INVENTORIES FROM JUNE 3,1981 CENSUS TO JULY 1.1981. 10. Since the June 3,1981 Census of Agriculture, please report the number of: (a) Births, purchases, and transfers to the land you operate (between June 3, 1981 and July 1.1981) (b) Deaths, sales, slaughterings and transfers from the land you operate (between June 3,1981 and July 1,1981) Total Number 428 NoneD 429 NoneD PART C. CALVINGS AND DEATHS All questions below refer to 6 month periods 11. How many calves were born alive since January 1,1981, that is, during the past 6 months, on the land you operate? 12. How many cows and heifers are expected to calve before January 1,1982, that Is, during the next 6 months? 13. How many cattle (I year and over) have died, or have been destroyed, as a result of accident, in-jury or disease since January 1,1981? 14. How many calves (under I year) have died, or have been destroyed, as a result of accident, injury or disease since January 1,1981? 421 NoneD Total Number 424 NoneD 426 NoneD 427 NoneD COMMENTS: 4-1104.414.1 191 SECTION F. PIGS (concluded) PART B. CHANGE IN PIG INVENTORY FROM JUNE 3,1981 CENSUS TO JULY 1,1981 7. Since the June 3,1981 Census of Agriculture, please report the number of: a) Births, purchases and transfers to the land you operate (between June 3, 1981 and July 1.1981) b) Deaths, sales, slaughterings and transfers from the land you operate (between June 3,1981 and July 1,1981) Total Number 640 NoneD 641 NoneD PARTC. FARROWINGS, BIRTHS AND DEATHS All questions below refer to 3 month periods 8. How many sows and gilts farrowed during April, May and June 1981 on the land you operate? 9. How many pigs were bom alive during April, May and June 1981 on the land you operate? 10. How many pigs have died, or have been destroyed, as a result of accident, Injury or disease BEFORE weaning during April, May and June 1981? 11. How many pigs have died, or have been destroyed, as a result of accident, injury or disease AFTER weaning during April, May and June 1981? 12. How many sows and gilts are expected to farrow during July, August and September 1981? 13. How many sows and gilts are expected to farrow during October, November and December 1981? * Total Number ZSi— NoneD 635 NoneD 636 NoneD 637 NoneD 638 NoneD 639 NoneD 4-JI04-4I4.I SECTION F. PIGS Section R 600 9 I. Since April 1,1981, have you had, or do you have, pigs on the land you operate? • Include all pigs on this holding regardless of ownership. • Exclude pigs owned by you but kept on a farm operated by someone else. Yes No 601 PART A. INVENTORY AT JULY 1,1981 2. Boars 6 months and over for breeding . . 3. Sows for breeding and bred gilts (i) Under 45 pounds (20 kg) (ii) 45 to 130 pounds (20 to 60 kg). . (Ui) over 130 pounds (60 kg) 5. Total pigs (Sum 2 to 4) 4. All other pigs (Go to Section G) 6. Does this figure (Enter Box 610) account for all of the pigs on the land operated?. Total Number at July 1,1981 605 None • 606 NoneD 607 None • 608 None O 609 NoneD 610 NoneD Yes • «» (Go to Part B) No CD »*• Make corrections, then go to Part B COMMENTS: U 0 4 - 4 I 4 . 1 SECTION G . OTHER LIVESTOCK OR POULTRY Section R [300 l u I. At July 1.1981, do you have SHEEP and LAMBS, POULTRY or OTHER LIVESTOCK on the land you operate? • Include all livestock and poultry on this holding regardless of ownership. • Include all livestock OWNED BY YOU but pastured on a community pasture or public land. • Exclude livestock and poultry OWNED BY YOU but kept on a farm operated by someone else. Yes No 301 (Go to Section Hf PART A. SHEEP AND LAMBS 2. Sheep and Lambs PART B. POULTRY 3. HENS and PULLETS, 20 weeks of age and over, kept for laying 4. OTHER POULTRY (for example, broilers, turkeys, ducks, etc.) Total Number at July 1.1981 304 NoneD Total Number at July 1,1981 503 NoneD PLEASE SPECIFY Total Number at July 1.1981 OFFICE USE ONLY PART C. OTHER LIVESTOCK 5. Please list any OTHER LIVESTOCK (for example hones, goats, rabbits, etc.) • Exclude family pets. 504 None O PLEASE SPECIFY Total Number at July 1.1981 OFFICE USE ONLY SOS NoneD SECTION H. FARM BUSINESS EXPENSES (HI TO H17) Enter figure reported In Box 131, question 6, page 3 I N o n e ^ It the amount reported above greater than zero? Yes • (Below) No • (Co to Section K) The following sections deal with firm operating expenses that you had during the calendar year 1980. In cases where records are not kept on a calendar year basis, expenses should be reported for the most current fiscal year end. Calendar Year refers to the period January I to December 31. Fiscal Year re fen to any twelve month period which a business uses as its income tax year (for example, April I to March 31.) SECTION HI. RENTAL AND LEASING EXPENSES FOR AGRICULTURAL LAND OR BUILDINGS Section R 700 I. Did you have any cash rent, share rent or leasing expenses in 1980 for agricultural land or buildings rented or leased from others? • include - taxes paid by you on property rented from others. - community pasture or other grazing fees. Yes N o 701 2 (Go to Section H2) 2. In 1980, what was the amount of your: (a) Cash rent or leasing expenses? (b) Share rent or rent-ln-klnd (estimated dollar value)? 3. Total rental and leasing expenses (Sum 2a and 2b).. . Total expense in 1980 S 702 NoneD .00 703 NoneD .00 704 .00 EDIT: 1. Is box 126, page 3 equal to zero? If yes, please specify reason for rent or leasing expenses 4-SI04-414.1 S E C T I O N H 2 . O P E R A T I N G E X P E N S E S F O R M O T O R V E H I C L E S A N D F A R M M A C H I N E R Y Section R 710 9 1. Did you have any operating expenses for motor vehicles and farm machinery during 1980? • Indude farm business share of car. Yes No 7 n l I 2 | (Go to Section H3) 2. During 1980, what were your farm expenses for: (a) Fuel,oil and lubricants: report amount paid before any rebates are received from claims made to the federal or provincial governments (b) Repairs, maintenance, license, registration and insurance costs, (include parts, labour, tires, batteries, antifreeze, etc.) 3. Total expense (Sum 2a and 2b) Total Farm Business Expense in 1980 S 720 NoneD .00 721 NoneD .00 722 .00 COMMENTS: 4-3104-414.1 196 S E C T I O N H 3 . S E E D Section R 1. Did you have any expenses during 1980 for the purchase of seed and seedlings? N o |73l| | 2 | (Go to Section H4) Yes If seed treatment or cleaning costs were included in the purchase price, report total expense. 2. During 1980, what were your expenses for: (a) Wheat, oats, barley, rye, flaxseed, rapeseed and mustard seed? (b) Other seed? Please specify 3. Total seed expenses (Sum 2a and 2b) 4. What portion of the total cost for all seed was for seed bought from elevators, seed houses and seed dealers? • Exclude seed bought from other farmers Total expense in 1980 S 732 NoneD .00 733 None D .00 734 .00 NoneD 735 022 OR .001 A COMMENTS: 4-1I04-4I4.I 197 S E C T I O N H 4 . F E R T I L I Z E R Section R 7 4 0 [ j T 1. Did you htve iny expemei during 1980 Tor the purchase of fertilizer? Yes No 17411 | 2~) (Go to Section HS) 2. Fertilizer expenses. 3. What portion of the total expense figure for fertilizer was used or will be used in the production of wheat, oats, barley, rye, flaxseed, rapeseed and mustard seed? S E C T I O N H 5 . C H E M I C A L S ( P E S T I C I D E S ) Section R |7So[ | 9 | 1. Did you have any expenses during 1980 for chemicals to control all types of weeds, plants, Insects, rodents, etc.? No 751 £ ] (Go to Section H6) Yes If custom chemical application costs were included in the purchase price, report total expense. 2. Chemical expenses (Include herbicides, Insecticides, fungicides and other pesticides) 3. What portion of the total expense figure for chemicals was used or will be used in the production of wheat, oats, barley, rye, flaxseed, rapeseed and mustard seed? Total expense in 1980 S 752 .00 1 None • 753 024 — OR .00 1 4 - 1 1 0 4 - 4 1 4 . 1 198 S E C T I O N H 6 . F E E D A N D S U P P L E M E N T S Section R 770 1. In 1980, did you have any expanses Tor Teed and supplements? • Include cost of hay and straw used for feed. Y«[p No 771 (Go to Section H7) 2. In 1980, what were your total expenses for feed and supplements purchased from other farmers and from commercial channels? 3. What portion of the total cost of feed was for feed purchased through commercial channels? • Exclude feed bought from other farmers Total expense in 1980 S 772 .(XT 773 NoneD 1 m OR .00 1 % S E C T I O N H 7 . V E T E R I N A R Y A N D A.I. Section R |?8o| j 9 | 1. In 1980, did you have any expenses for veterinary services, medicines or A.I. fees? Yes No E l (Go to Section H8) 2. Total expenses for veterinary services, medicines and A.I. fees? Total expense in 1980 S 782 i .00 \ S E C T I O N H 8 . B U I L D I N G A N D F E N C E R E P A I R S Section R |790| j_9 I. Did you have any expenses during 1980 for repairs and maintenance of farm buildings and fences? • Include farm business share of expenses for repairs to the farm or any off-farm dwelling. • Exclude capital expenditures, that Is, new construction, renovations and additions. Yes No 791 2. What were your total expenses in 1980 for: (a) Repairs and maintenance to farm buildings? (b) Fencing? 3. Total expenses for repairs to farm buildings and fencing (Sum 2a and 2b) (Go to Section H9) Total expense in 1980 $ 792 None D .00 793 °~ NoneD .00 794 .00 4-1104-414.1 199 S E C T I O N H 9 . C O N T A I N E R S , T W I N E A N D W I R E Section R 800; ! T I. In 1980, did you have any expenset for small containers, baler twine, binder twine and baling wire? (Go to Section H10) Yes No 801 2. Total expenses for small containers, baler twine, binder twine and baling wire Total expense in 1980 $ 802 A .00* Section R 8lbl T T S E C T I O N H 1 0 . S M A L L T O O L S A N D M I S C E L L A N E O U S H A R D W A R E 1. In 1980, did you have expenses for small tools and miscellaneous hardware? • Include hand sprayers, dusters, fire extinguishers, grease guns, shovels, carpentry and other like tools, and all other equipment costing leu than $200 per item. • Exclude materials accounted for in Section H8 (BUILDING AND FENCE REPAIRS) Ye,[p No l8Ml .1 2J (ColoSectionlilll 2. Total expenses for small tools and miscellaneous hardware required for the farm business Total expense in 1980 $ 812 1 S E C T I O N H U . I N T E R E S T O N F A R M L O A N S , C R E D I T A N D M O R T G A G E S | Section R |820J ]~9~| . In 1980, did you have any farm business loans or mortgages? Ye,[p 2. What were your total interest expenses for these loans? No 821 ! 2 | (Go to Section HI 2) 3. What portion of your Interest expenses was for the purchase of real estate, farm vehicles, machin-ery, livestock, poultry, loans for building construction or renovation, o; land improvement? Total expense in 1980 S 822 .00' 824 ( „ „ .00 NoneD OR 026 % - 3 I M - 4 H . I 200 S E C T I O N H 1 2 . E L E C T R I C I T Y , T E L E P H O N E A N D H E A T I N G F U E L Section R Jjiloj | »"] t. Did you have my electricity, telephone or heating fuel expenses during 1980? • Include farm business share of house expenses. • Exclude installation costs. Yes 9 No 831 (Go to Section HI3) 2. What was the farm business share for: (a) Telephone expenses? (b) Electricity expenses? (c) Fuel expenses for heating, irrigation and grain drying? • Include natural gas, propane, heating oil, coal, wood • Exclude fuel expenses for motor vehicles and farm machinery already reported 3. Total telephone, electricity and hearing fuel expenses (Sum 2a to 2c) Fsrm business share of expenses in 1980 832 NoneD 00 833 NoneD .00 834 NoneD .00 83S .00 S E C T I O N H 1 3 . I N S U R A N C E P R E M I U M S [Section R J860 1. Did you have any property or crop insurance expenses during 1980? • Exclude - insurance on property rented to others. — insurance on motor vehicles and machinery reported earlier. - personal life insurance premiums. — unemployment insurance and liability insurance paid on behalf of employees. - Western Grain Stabilization Act (WGS A) levies. Y..J] No |86T 2 j (Go to Section H14) 2. During 1980, what were your total expenses for: (a) Crop and hait insurance? • Include insurance from government and nongovernment agencies (b) Farm business insurance? Include - fire, wind and other property insurance on alt farm build-ings, machinery and equipment — farm business share of insurance on the farm or on off-farm dwellings and contents - insurance on livestock and grain in storage 3. Total insurance premiums (Sum 2a and 2b) Total expense in 1980 S 863 NoneD .00 866 NoneD .00 86S .00 4 - S 1 0 4 - 4 I 4 . I 201 S E C T I O N H 1 4 . W A G E S , S E R V I C E S A N D S U P P L I E S F O R H I R E D L A B O U R Section R 1. Did you have any expenses for hired farm labour during 1980? • Exclude - paid labour for housework, custom work and contract work. - utilities, fuel and other items already claimed. Yes No 851 (Go to Section HIS/ T 2. What were your total cash wages for hired farm labour in 1980? • Include any contributions for Unemployment Insurance, Canada Pension Plan, Workmen's Com-Total expense In 1980 S 852 None • .00 3. Of the above cash wage expense, how much wu for your spouse S 853 None • .00 4. What is the estimated cash value of housing or lodging, food, fuel, transportation, utilities, etc. provided to hired farm labour during 1980? 854 None • .00 855 .00 COMMENTS: - J I 0 4 - 4 M . I 202 S E C T I O N H 1 5 . C U S T O M W O R K A N D M A C H I N E H I R E ! sect.o„R M \* The following section concentrates on operating expenses which are of a recurring nature such as stone picking, teed treatment and custom spreading of fertilizers. • Exclude - expenses where the benefits will be spread over many years, for example, dugouts, barns, clearing land, grain bins, etc. - seed, fertilizer and chemical materials, as well as custom work included in SECTIONS H3, H4 and H5. . Did you have any expenses in 1980 for. (a) Tilling, seeding, swathing, combining and grain drying . (b) Seed treatment and cleaning (c) Custom spreading of chemical fertilizer, spraying and dusting (d) Grain, livestock and feed trucking (e) Baling, chopping and feedlot cleaning (0 Renting or leasing of any machinery or equipment for farm purposes . (g) Other, please specify 2. Total custom work and machine hire expenses (Sum la to lg) , Total expense in 1980 S NoneQ .00 None D .00 None D .00 NoneD .00 NoneD .00 None D .00 NoneD .00 762 .00 Did the farm operator report any custom work and machine hire expenses for 19807 Yes • No I * Go to Section HI6 4-1104-414.1 203 S E C T I O N H 1 6 . M I S C E L L A N E O U S F A R M B U S I N E S S E X P E N S E S Section R 840 9 1. In 1980, did you have any expenses Tor accounting and consulting services, bank services, legal services, memberships (farm organiza-tions, unions, etc.), promotion, firm magazines, bulletins and technical journals? • Exclude interest charges on bank loans. Yes No 841 2 (Go to Section HI 7) 2. Total miscellaneous farm business expenses Total expense in 1980 S 842 t .00 \ S E C T I O N H 1 7 . O T H E R F A R M O P E R A T I N G E X P E N S E S f & ^ T A N D D E P R E C I A T I O N 870 1. During 1980, what were your expenses for: (a) Livestock and poultry purchases? . . . . Cb) Property taxes? (c) Depreciation or capital cost allowances? (d) Irrigation levies and taxes? (e) Other? Please specify Total expense in 1980 $ 871 NoneD .00 872 NoneD .00 873 NoneD .00 874 NoneD .00 875 NoneD .ooj COMMENTS: 4- J I04-4M. I 204 S E C T I O N I. R E C E I P T S F R O M C U S T O M W O R K A N D M A C H I N E R E N T A L Section R >!°L_i ?J 1. In 1980, did you have any cash receipts from custom work or from rental or leasing of your farm machinery to others? • Include custom feeding of cattle. • Exclude custom work done on an exchange basis, that is, where no money changes hands. Yes 7 No l9l ll I 21 /Go to Section J) 2. Total receipts from custom work and machine rental s ! 912 .00 ^ S E C T I O N J . T O T A L A G R I C U L T U R A L R E C E I P T S 1. What were your total agricultural receipts in 1980? • Include - sales of all agricultural products. - Box 703: landlord's share of products sold. - Box 912: custom work and machine hire receipts. - stabilization and deficiency payments. - CWB payments received in 1980. - cash advances for stored grain, patronage dividends and crop insurance , | Section R J900| | 9~j 2. What portion of the above total was for the sale of wheat, oats, barley, rye, flaxseed, rape seed and mustard seed? • Include Canadian Wheat Board payments received ln 1980 C C / ~ T | O k J K SASKATCHEWAN AND BRITISH COLUMBIA ONLY: FEDERAL/PROVINCIAL AGREEMENT O C V - I I W I N l \ . TO SHARE INFORMATION To avoid duplication of inquiries and lo reduce the costs of data collection, this survey is conducted under a joint agreement to collect and share information, as provided by Section 11 of the Statistics Act, with the Saskatchewan Department of Agriculture and the British Columbia Ministry of Agriculture. Are you willing to share this information with the agency/agencies in your province? (please check) Yes (O.K. to share Information) l??.2L_L?-4 No (not O.K. to share information) . . . MJJi 4 - 1 1 0 4 - 4 1 4 . 1 to o B. C r o s s - s e c t i o n a l Data By S o i l Zone Year 1981 1980 1979 1978 P r i c e s : cwt. S o i l Cows S t e e r s Steer He i£ers Hei f e r Zone C a l v e s C a l v e s 1 46.59 74.66 75.13 68.39 65.80 2 46.59 74.66 7 5.13 68.39 65.80 3 46.59 74.66 75. 13 68.39 ' 65.80 4 48. 52 76.58 75.64 72.36 66.53 5 45.84 75.82 72.92 69.91 60.05 6 48. 52 76.58 75.64 72.36 66.53 7 48.58 75.81 74.56 70.30 63.46 8 48.52 76.58 75.64 72.36 66.53 9 48.58 75.81 74.56 70.30 63.46 10 46.59 74.66 75. 13 68.39 65.80 1 1 45.84 75.82 72.92 69.91 60.05 12 48. 10 73.98 73.88 67.55 65. 16 1 3 48. 10 73.98 73.88 67.55 65. 16 14 48.10 73.98 73.88 67.55 65. 16 1 51 .27 79. 10 91 .90 72.93 80. 14 2 51 .27 79. 10 91 .90 72.93 80. 14 3 51 .27 79. 10 91 .90 72.93 80. 14 4 51 .77 82.01 94.01 75.86 84 .64 5 49.34 78.55 93.66 71 .48 79.26 6 51 .77 82.01 94.01 75.86 84.64 7 52.06 79. 18 92.26 73.08 81 .23 8 51 .77 82.01 94.01 75.86 84.64 9 52.06 79. 18 92.26 73.08 8 1 . 23 10 51 . 27 79. 10 91 .90 72.93 80. 1 4 1 1 49.34 78.55 93.66 71 .48 79.26 12 52.05 78.60 88.53 71.14 79.40 1 3 52.05 78.60 88.53 71.14 79.40 1 4 52.05 78.60 88.53 71.14 79.40 1 55.80 91 .08 108.65 88. 17 94.29 2 55.80 91 .08 108.65 88. 17 94.29 3 55.80 91 .08 108.65 88. 17 94.29 4 58.27 92.46 108.07 88.99 96.75 5 54.62 93.42 107.84 87.98 91.44 6 58.27 92.46 108.07 88.99 96.75 7 56.39 90.91 108.88 85.90 99.57 8 58. 27 92.46 108.07 88.99 96.75 9 56.39 90.91 108.88 85.90 99.57 10 55.80 91 .08 108.65 88. 17 94.29 1 1 54.62 93.42 107.84 87.98 91 .44 12 56.88 87.28 104.36 81 .26 92.80 13 56.88 87.28 104.36 81 .26 92.80 1 4 56.88 87.28 104.36 81 .26 92.80 1 38.73 65.35 75.07 56.86 65.30 2 38.73 65.35 75.07 56.86 65.30 3 38.73 65.35 75.07 56.86 65.30 4 40.27 66.53 82.06 58.86 72.35 5 38. 19 64.24 84.89 56.96 75.38 6 40.27 66.53 82.06 58.86 72.35 7 40.06 63.38 79.31 57. 17 70.48 8 40.27 66.53 82.06 58.86 72.35 9 40.06 63.38 79.31 57. 17 70.48 10 38.73 65.35 75.07 56.86 65.30 1 1 38. 19 64.24 84.89 56.96 75.38 12 39.93 60.48 74.05 53.72 64.68 13 39.93 60.48 74.05 53.72 64.68 14 39.93 60.48 74.05 53.72 64.68 B. C ross-sec t i ona l Data By S o i l Zone (continued) Year 1981 1980 1979 1978 P r i c e s : Indexes S o i l Bu i l d ing Fenc ing Machinery Operat ion Seed Zone Repairs 1 253.50 223.00 257.20 345.00 2 250.20 286.40 289.40 345.00 3 253.50 223.00 257.20 345.00 4 253.50 223.00 257.20 345.00 5 254. 10 247.60 271 .20 345.00 6 253.50 223.00 257.20 345.00 7 254. 10 247.60 271 .20 345.00 8 253.50 223.00 257.20 345.00 9 254.10 247.60 271.20 345.00 10 253.50 223.00 257.20 345.00 1 1 254.10 247.60 271 .20 345.00 12 243.70 276.70 273.90 345.00 13 243.70 276.70 273.90 345.00 14 243.70 276.70 273.90 345.00 1 236.60 217.00 213.80 300. 10 2 210.50 266.80 232.70 300.10 3 236.60 217.00 213.80 300. 10 4 236.60 '217.00 213.80 300. 10 5 238.20 226.00 222.30 300.10 6 236.60 217.00 213.80 300.10 7 238.20 226.00 222.30 300.10 8 236.60 217.00 21 3.80 300.10 9 238.20 226.00 222.30 300. 10 10 236.60 217.00 213.80 300.10 1 1 238.20 226.00 222.30 300. 10 12 228.30 246.90 223.30 300.10 13 228.30 246.90 223.30 300.10 1 4 228.30 246.90 223.30 300.10 1 231 .00 199.40 182.60 223.00 2 204.70 252.50 200.20 223.00 3 231.00 199.40 182.60 223.00 4 231.00 199.40 182.60 223.00 5 226.00 207.90 193.30 223.00 6 231.00 199.40 182.60 223.00 7 226.00 207.90 193.30 223.00 8 231.00 199.40 182.60 223.00 9 226.00 207.90 193.30 223.00 10 231.00 199.40 182.60 223.00 1 1 226.00 207.90 193.30 223.00 12 213.80 221.60 193.00 223.00 13 213.80 221.60 193.00 223.00 14 213.80 221.60 193.00 223.00 1 205.30 180.10 170.60 215.20 2 183.00 230.60 181.80 215.20 3 205.30 180. 10 170.60 215.20 4 205.30 180.10 170.60 215.20 5 197.40 191.20 181.60 215.20 6 205.30 180.10 170.60 215.20 7 197.40 191.20 181.60 215.20 8 205.30 180.10 170.60 215.20 9 197.40 191.20 181 .60 215.20 10 205.30 180.10 170.60 215.20 1 1 197.40 191.20 181.60 215.20 12 188.60 199.60 179.70 215.20 13 188.60 199.60 179.70 215.20 14 188.60 199.60 179.70 215.20 B. C r o s s - s e c t i o n a l Data By S o i l Zone (continued) Year 1981 Prices: Indexes 1980 1979 1978 S o i l F e r t i l i z e r P e s t i c i d e Twine Feed + Zone 366.60 359.90 Supplements 1 398.00 349.90 2 366.60 359.90 398.00 349.90 3 366.60 359.90 398.00 349.90 4 366.60 359.90 398.00 349.90 5 366.60 359.90 398.00 349.90 6 366.60 359.90 398.00 349.90 7 366.60 359.90 398.00 349.90 8 366.60 359.90 398.00 349.90 9 366.60 359.90 398.00 349.90 10 366.60 359.90 398.00 349.90 1 1 366.60 359.90 398.00 349.90 12 366.60 359.90 398.00 349.90 13 366.60 359.90 398.00 349.90 14 366.60 359.90 398.00 349.90 1 317.70 327.40 403.80 270.50 2 317.70 327.40 403.80 270.50 3 317.70 327.40 403.80 270.50 4 317.70 327.40 403.80 270.50 5 317.70 327.40 403.80 270.50 6 317.70 327.40 403.80 270.50 7 317.70 327.40 403.80 270.50 8 317.70 327.40 403.80 270.50 9 317.70 327.40 403.80 270.50 10 317.70 327.40 403.80 270.50 1 1 317.70 327.40 403.80 270.50 12 317.70 327.40 403.80 270.50 13 317.70 327.40 403.80 270.50 14 317.70 327.40 403.80 270.50 1 266.00 281.60 283.70 233.10 2 266.00 281.60 283.70 233.10 3 266.00 281.60 283.70 233. 10 4 266.00 281.60 283.70 233. 10 5 266.00 281.60 283.70 233. 10 6 266.00 281.60 283.70 233. 10 7 266.00 281.60 283.70 233.10 8 266.00 281.60 283.70 233. 10 9 266.00 281.60 283.70 233. 10 10 266.00 281.60 283.70 233. 10 1 1 266.00 281.60 283.70 233. 10 12 266.00 • 281.60 283.70 233. 10 13 266.00 281.60 283.70 233. 10 14 266.00 281.60 283.70 233.10 1 229.90 253.50 217.40 216.10 2 229.90 253.50 217.40 216.10 3 229.90 253.50 217.40 216.10 4 229.90 253.50 217.40 216.10 5 229.90 253.50 217.40 216.10 6 229.90 253.50 217.40 216.10 7 229.90 253.50 217.40 216.10 8 229.90 253.50 217.40 216.10 9 229.90 253.50 217.40 216.10 10 229.90 253.50 217.40 216.10 1 1 229.90 253.50 217.40 216.10 12 229.90 253.50 217.40 216.10 13 229.90 253.50 217.40 216.10 14 229.90 253.50 217.40 216.10 B. C r o s s - s e c t i o n a l Data By S o i l Zone (continued) Year 1981 1980 1979 1978 Pri c e s : Indexes S o i l Grain Oats Barley Wheat Zone Peed 1 359.90 314.50 387.20 408.70 2 356.10 331.20 362.00 367.80 3 359.90 314.50 387.20 408.70 4 359.90 314.50 387.20 408.70 5 495.50 469.80 574.50 483.20 6 359.90 314.50 387.20 408.70 7 495.50 469.80 574.50 483.20 8 359.90 314.50 387.20 408.70 9 495.50 469.80 574.50 483.20 10 359.90 314.50 387.20 408.70 1 1 495.50 469.80 574.50 483.20 1 2 427.90 426.30 424.50 439.50 13 427.90 426.30 424.50 439.50 1 4 427.90 426.30 424.50 439.50 1 263.80 225.90 282.90 305.90 2 273.10 , 243.30 272.20 286. 10 3 263.80 225.90 282.90 305.90 4 263.80 225.90 282.90 305.90 5 358.40 328.80 435.30 350.60 6 263.80 225.90 282.90 305.90 7 358.40 328.80 435.30 350.60 8 263.80 225.90 282.90 305.90 9 358.40 328.80 435.30 350.60 10 263.80 225.90 282.90 305.90 1 1 358.40 328.80 435.30 350.60 12 324.00 322.40 322.40 332.50 13 324.00 322.40 322.40 332.50 14 324.00 322.40 322.40 332.50 1 221.00 209.60 202.50 250.50 2 234.80 214.50 194.10 244.60 3 221.00 209.60 202.50 250.50 4 221.00 209.60 202.50 250.50 5 278.30 254.50 311.90 290.60 6 221.00 209.60 202.50 250.50 7 278.30 254.50 311.90 290.60 8 221.00 209.60 202.50 250.50 9 278.30 254.50 311.90 290.60 10 221.00 209.60 202.50 250.50 1 1 278.30 254.50 31 1.90 290.60 12 248.90 247.20 226.60 269.60 13 248.90 247.20 226.60 269.60 14 248.90 247.20 226.60 269.60 1 202.70 190. 10 201.90 221.20 2 214.60 195.80 194.20 225.30 3 202.70 190.10 201.90 221.20 4 202.70 190. 10 201.90 221.20 5 265.60 256.90 290.50 262.40 6 202.70 190.10 201.90 221.20 7 265.60 256.90 290.50 262.40 8 202.70 190.10 201.90 221 .20 9 265.60 256.90 290.50 262.40 10 202.70 190. 10 201.90 221.20 1 1 265.60 256.90 290.50 262.40 12 226.90 240.20 209.80 223.00 13 226.90 240.20 209.80 223.00 14 226.90 240.20 209.80 223.00 B. Cr o s s - s e c t i o n a l Data By S o i l Zone (continued) Year 1981 Prices: Indexes 1980 1979 1978 S o i l A r t i f i c i a l Small E l e c t r i c i t y Telephor Zone Inseminat ion Tools 1 187.40 232.40 211.50 147.90 2 187.40 204.10 242.90 147.90 3 187.40 232.40 211.50 147.90 4 187.40 232.40 211.50 147.90 5 187.40 225.50 188.80 147.90 6 187.40 232.40 211.50 147.90 7 187.40 225.50 188.80 147.90 8 187.40 232.40 211.50 147.90 9 187.40 225.50 188.80 147.90 10 187.40 232.40 211.50 147.90 1 1 187.40 225.50 188.80 147.90 12 187.40 213.90 267.90 147.90 13 187.40 213.90 267.90 147.90 1 4 187.40 2 13.90 267.90 147.90 1 220.10 219.20 175.00 141 .70 2 220. 1 0 176.90 204.30 141 .70 3 220. 10 219.20 175.00 141 .70 4 220.10 219.20 175.00 141 .70 5 220. 1 0 206.50 188.80 141 .70 6 220. 10 219.20 175.00 141.70 7 220. 10 206.50 188.80 141.70 8 220. 10 219.20 175.00 141 .70 9 220. 10 206.50 188.80 141.70 10 220.10 219.20 175.00 141.70 1 1 220.10 206.50 188.80 141.70 1 2 220. 1 0 195.60 267.90 141 .70 13 220.10 195.60 267.90 141.70 14 220. 10 195.60 267.90 141.70 1 212.00 194.60 180.00 141.20 2 212.00 160.90 186.70 141 .20 3 212.00 194.60 180.00 141.20 4 212.00 194.60 180.00 141.20 5 212.00 186.00 1 8 8.80 141.20 6 212.00 194.60 180.00 141.20 7 212.00 186.00 188.80 141 .20 8 212.00 194.60 180.00 141.20 9 212.00 186.00 188.80 141.20 10 212.00 194.60 180.00 141.20 1 1 212.00 186.00 188.80 141.20 12 212.00 181.30 267.90 141 .20 13 212.00 181 .30 267.90 141.20 14 212.00 181.30 267.90 141 .20 1 210.20 170.90 175.90 135.30 2 210.20 151.50 186.70 135.30 3 210.20 170.90 175.90 135.30 4 210.20 170.90 175.90 135.30 5 210.20 160.60 175.80 135.30 6 210.20 170.90 175.90 135.30 7 210.20 160.60 175.80 135.30 8 210.20 170.90 175.90 135.30 9 210.20 160.60 175.80 135.30 10 210.20 170.90 175.90 135.30 1 1 210.20 160.60 175.80 135.30 12 210.20 155.90 232.80 135.30 13 210.20 155.90 232.80 135.30 14 210.20 155.90 232.80 135.30 B. Cr o s s - s e c t i o n a l Data By S o i l Zone (continued) Year 1981 1980 1979 1978 Prices: Indexes S o i l Custom Dai l y Hired Property Interest Zone Work Labour Taxes 1 257.50 306.90 195.80 668.60 2 254.90 271 .00 202.40 668.60 3 257.50 306.90 195.80 668.60 4 257.50 306.90 195.80 668.60 5 246,60 318.20 202.00 668.60 6 257.50 306.90 195.80 668.60 7 246.60 318.20 202.00 668.60 8 257.50 306.90 195.80 668.60 9 246.60 318.20 202.00 668.60 10 257.50 306.90 195.80 668.60 1 1 246.60 318.20 202.00 668.60 12 236.10 343.00 204.10 668.60 13 236.10- 343.00 204. 10 668.60 1 4 236.10 343.00 204.10 668.60 1 230.40 289.50 172.20 471 .40 2 229.30 248.00 171 .50 471.40 3 230.40 289.50 172.20 471.40 4 230.40 289.50 172.20 471 .40 5 225.00 294.10 177.90 471.40 6 230.40 289.50 172.20 471 .40 7 225.00 294.10 177.90 471.40 8 230.40 289.50 172.20 471.40 9 225.00 294. 10 177.90 471 .40 10 230.40 289.50 172.20 471.40 1 1 225.00 294.10 177.90 471 .40 12 221.40 326.20 202.70 471.40 13 221 .40 326.20 202.70 471 .40 14 221.40 326.20 202.70 471 .40 1 203.40 253 . 10 152.50 398.30 2 198.50 236.70 147.60 398.30 3 203.40 253.10 152.50 398.30 4 203.40 253.10 152.50 398.30 5 197.60 269.90 156.20 398.30 6 203.40 253.10 152.50 398.30 7 197.60 269.90 156.20 398.30 8 203.40 253. 1 0 152.50 398.30 9 197.60 269.90 156.20 398.30 10 203.40 253. 10 152.50 398.30 1 1 197.60 269.90 156.20 398.30 12 200.00 299.40 184.80 398.30 13 200.00 299.40 184.80 398.30 14 200.00 299.40 184.80 398.30 1 181.60 238.60 152.50 278.60 2 177.70 223.30 226.90 278.60 3 181 .60 238.60 152.50 278.60 4 181.60 238.60 152.50 278.60 5 182.80 246. 10 143.50 278.60 6 181.60 238.60 152.50 278.60 7 182.80 246.10 143.50 278.60 8 181.60 238.60 152.50 278.60 9 182.80 246.10 143.50 278.60 10 181.60 238.60 152.50 278.60 1 1 182.80 246.10 143.50 278.60 12 181 .20 287.50 170.40 278.60 13 181.20 287.50 170.40 278.60 14 181.20 287.50 170.40 278.60 B. C r o s s - s e c t i o n a l D a t a By S o i l Z o n e ( c o n t i n u e d ) P r i c e s ; Y e a r S o i l F a r m Z o n e R e n t 1981 1 3 5 9 . 1 0 2 3 5 9 . 1 0 3 3 5 9 . 1 0 4 3 5 9 . 1 0 5 3 5 9 . 1 0 6 3 5 9 . 1 0 7 3 5 9 . 1 0 8 3 5 9 . 1 0 9 3 5 9 . 1 0 10 3 5 9 . 1 0 11 3 5 9 . 1 0 12 3 5 9 . 1 0 13 3 5 9 . 1 0 14 3 5 9 . 1 0 1980 1 2 7 9 . 3 0 2 2 7 9 . 3 0 3 2 7 9 . 3 0 4 2 7 9 . 3 0 5 2 7 9 . 3 0 6 2 7 9 . 3 0 7 2 7 9 . 3 0 8 2 7 9 . 3 0 9 2 7 9 . 3 0 10 2 7 9 . 3 0 11 2 7 9 . 3 0 12 2 7 9 . 3 0 13 2 7 9 . 3 0 14 2 7 9 . 3 0 1 9 7 9 1 2 4 2 . 6 0 2 2 4 2 . 6 0 3 2 4 2 . 6 0 4 2 4 2 . 6 0 5 2 4 2 . 6 0 6 2 4 2 . 6 0 7 2 4 2 . 6 0 8 2 4 2 . 6 0 9 2 4 2 . 6 0 10 2 4 2 . 6 0 11 2 4 2 . 6 0 12 2 4 2 . 6 0 13 2 4 2 . 6 0 14 2 4 2 . 6 0 1 9 7 8 1 2 3 6 . 1 0 2 2 3 6 . 1 0 3 2 3 6 . 1 0 4 2 3 6 . 1 0 5 2 3 6 . 1 0 6 2 3 6 . 1 0 7 2 3 6 . 1 0 8 2 3 6 . 1 0 9 2 3 6 . 1 0 10 2 3 6 . 1 0 11 2 3 6 . 1 0 12 2 3 6 . 1 0 13 2 3 6 . 1 0 14 2 3 6 . 1 0 C P I F e n c i n g ( 1 9 7 1 = 1 0 0 ) R e p a i r s 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 3 6 . 90 2 5 8 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 6 0 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 2 1 0 . 60 2 3 7 . 2 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 191 . 20 2 2 6 . 8 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 1 7 5 . 2 0 2 0 2 . 3 0 1 7 5 . 20 2 0 2 . 3 0 213 B. Cross-sectional Data By Soil Zone (continued) Year 1981 1980 1979 1978 Soil Receipts: $ Custom Total Grains Zone Work Agr iculture 1 861196. 00 69004432 .00 30060768. 00 2 156959. 00 20046976 .00 4699093. 00 3 6714407. 00 377858992 .00 87652526. 00 4 15996818. 00 618422546 .00 243946834. 00 5 5988133. 00 370194156 .00 210853708. 00 6 858625. 00 100938891 .00 42479732. 00 7 2679761. 00 246416596 .00 134755782. 00 8 565223. 00 123855889 .00 40391130. 00 9 1929471 . 00 267709378 .00 115052900. 00 10 5196232. 00 554136776 .00 232451039. 00 1 1 3306930. 00 209836642 .00 114442414. 00 12 556710. 00 106690231 .00 56176697. 00 13 3412218. 00 227176263 .00 101855787. 00 14 940607. 00 53887773 .00 12984888. 00 1 228392. 00 49181057 .00 19341093. 00 2 478165. 00 20020827 .00 5491368. 00 3 4464154. 00 363462541 .00 68505901. 00 4 21873769. 00 568327306 .00 190862782. 00 5 2249517. 00 307794834 .00 174460432. 00 6 311003. 00 9330801 6 .00 28482517. 00 7 1708522. 00 272034984 .00 1 39815823. 00 8 363791 . 00 109769488 .00 42324153. 00 9 1449689. 00 218840603 .00 99173629. 00 10 3532707. 00 442647642 .00 155266500. 00 1 1 1300937. 00 225512181 .00 102887047. 00 12 1869534. 00 83623172 .00 36094375. 00 13 2210467. 00 164794614 .00 68398128. 00 14 1987664. 00 61819410 .00 12631950. 00 1 478165. 00 44434246 .00 10886191. 00 2 19548. 00 11060588 .00 1716811. 00 3 1521372. 00 281807485 .00 63100491. 00 4 25377328. 00 558740318 .00 151528553. 00 5 2273599. 00 251528614 .00 12299201 1 . 00 6 30048. 00 75285114 .00 16992149.00 7 2004649. 00 257857869 .00 129746041. 00 8 641867. 00 87258228 .00 30593476. 00 9 2787492. 00 209446613 .00 82432722. 00 10 2839443. 00 368325851 .00 120817725.00 1 1 560720. 00 197905775 .00 83106868. 00 12 226554. 00 60404321 .00 26600643. 00 13 979395. 00 172185857 .00 60624769.00 14 1201968. 00 45282841 .00 7133268. 00 1 360417. 00 21928690 .00 4902209. 00 2 385405. 00 10757768 .00 3465771 . 00 3 1770757. 00 208307390 .00 37808449. 00 4 14701805. 00 452241930 .00 106880854. 00 5 1099474. 00 204888786 .00 94347162. 00 6 281170. 00 67254294 .00 15084603. 00 7 1305357. 00 191627091 .00 106703979. 00 8 201647. 00 54131506 .00 20223020. 00 9 1695629. 00 156057169 .00 74038060. 00 10 1136646. 00 242170413 .00 67389682. 00 1 1 1982675. 00 146831925 .00 70633576. 00 12 180598. 00 46003016 .00 21600361. 00 13 1038577. 00 144626306 .00 46153713. 00 14 389870. 00 37081924 .00 5797794. 00 214 B. C r o s s - s e c t i o n a l D a t a By S o i l Z o n e ( c o n t i n u e d ) Y e a r 1981 E x p e n d i t u r e : 1 9 8 0 1 9 7 9 1 9 7 8 S o i l M i s c . Z o n e 1 4 4 3 3 8 0 . 00 2 1 6 2 1 8 6 . 00 3 2 7 8 3 1 4 0 . 00 4 5 2 3 2 3 0 1 . 00 5 1 4 7 7 9 2 8 . 00 6 5 5 0 6 1 2 . 00 7 1 2 7 6 5 1 6 . 00 8 6 2 6 6 0 6 . 00 9 1 1 8 5 8 8 6 . 00 10 2 8 3 4 2 7 8 . 00 1 1 1 0 0 1 7 2 9 . 00 12 4 2 5 4 2 4 . 00 1 3 1 5 4 7 5 0 7 . 00 14 3 3 8 4 6 7 . 00 1 3 8 0 5 0 9 . 00 2 1 3 9 4 4 1 . 00 3 1 9 6 2 9 3 1 . 00 4 3 9 9 5 0 6 8 . 00 5 1 2 1 3 8 0 8 . 00 6 4 2 6 6 6 0 . 00 7 1 5 2 6 5 3 2 . 00 8 4 2 8 4 0 8 . 00 9 1 0 0 5 1 7 4 . 00 10 2 2 9 6 7 4 1 . 00 1 1 1 3 3 3 7 1 5 . 00 12 3 0 6 4 7 6 . 00 1 3 7 0 1 2 0 9 . 00 1 4 2 6 2 2 7 7 . 00 1 2 5 5 2 3 4 . 00 2 1 1 6 3 1 3 . 00 3 1 6 7 4 3 2 4 . 00 4 4 0 9 6 0 6 7 . 00 5 1 2 2 7 3 7 4 . 00 6 4 0 0 9 8 7 . 00 7 1 0 8 4 5 5 2 . 00 8 5 0 9 6 8 4 . 00 9 1 0 3 1 0 9 0 . 00 10 1 8 6 3 6 6 4 . 00 1 1 8 8 3 8 2 7 . 00 12 2 6 4 4 3 0 . 00 1 3 1 0 6 0 8 6 3 . 00 14 1 8 3 8 3 8 . 00 1 3 4 3 8 1 5 . 00 2 1 5 6 6 6 5 . 00 3 1 5 1 5 3 5 5 . 00 4 3 0 9 9 6 0 0 . 00 5 9 2 3 1 8 3 . 00 6 3 6 5 9 7 3 . 00 7 1 2 9 7 2 3 0 . 00 8 4 1 8 6 5 1 . 00 9 7 7 5 0 0 4 . 00 10 1 6 6 0 0 7 5 . 00 11 8 6 1 7 9 5 . 0 0 12 3 5 2 2 0 3 . 00 13 9 7 9 4 8 6 . 00 14 2 0 8 1 1 4 . 00 $ H i r e d L a b o u r 1 3 0 5 8 3 1 . 0 0 1 0 5 9 2 8 4 . 0 0 1 4 6 5 0 9 9 4 . 0 0 2 4 5 1 3 4 2 6 . 0 0 9 6 6 7 2 8 6 . 0 0 4 2 4 4 3 5 4 . 0 0 7 0 7 7 2 3 5 . 0 0 3 7 7 3 6 0 0 . 0 0 1 0 6 8 4 2 6 1 . 0 0 1 5 3 2 5 9 7 3 . 0 0 8 0 6 5 0 3 9 . 0 0 2 8 7 3 7 8 6 . 0 0 7 0 9 9 4 0 5 . 0 0 1 9 8 6 0 0 4 . 0 0 1 3 7 8 8 2 1 . 0 0 1 1 7 0 6 4 5 . 0 0 1 0 6 4 6 4 0 2 . 0 0 2 3 1 2 8 1 5 8 . 0 0 7 6 1 4 0 9 7 . 0 0 3 8 6 0 8 5 2 . 0 0 8 7 3 8 5 3 8 . 0 0 4 6 9 2 3 8 3 . 0 0 8 3 9 0 7 9 3 . 0 0 1 4 4 9 4 2 4 1 . 0 0 5 8 7 9 0 8 2 . 0 0 2 4 9 5 5 3 5 . 0 0 3 4 7 5 0 5 6 . 0 0 2 2 7 8 0 2 4 . 0 0 8 3 7 3 6 8 . 0 0 3 8 3 4 8 2 . 0 0 5 6 1 8 4 4 9 . 0 0 2 1 2 6 1 6 2 9 . 0 0 5 5 1 7 3 9 6 . 0 0 2 6 3 1 0 5 6 . 0 0 6 2 9 8 0 1 9 . 0 0 2 7 2 3 0 2 9 . 0 0 6 5 3 6 7 0 1 . 0 0 8 5 6 9 8 7 5 . 0 0 4 3 0 8 8 1 7 . 0 0 1 3 7 9 4 6 9 . 0 0 3 3 1 7 4 6 6 . 0 0 1 5 3 1 3 5 0 . 0 0 7 1 3 6 5 3 . 0 0 3 4 1 1 0 6 . 0 0 6 9 0 8 2 1 7 . 0 0 2 0 1 6 9 4 3 2 . 0 0 5 0 9 4 3 1 9 . 0 0 2 7 0 4 2 6 0 . 0 0 5 4 7 4 5 5 6 . 0 0 1 3 3 0 6 9 9 . 0 0 4 9 9 7 7 0 9 . 0 0 5 0 0 5 0 7 6 . 0 0 3 5 9 6 0 3 3 . 0 0 8 8 3 8 1 1 . 0 0 4 4 7 7 8 2 3 . 0 0 1 5 1 3 9 9 9 . 0 0 F a m i l y L a b o u r 4 3 3 2 1 7 . 0 0 7 4 2 6 0 . 0 0 6 1 8 0 8 1 4 . 0 0 4 6 6 3 2 5 0 . 0 0 3 6 8 8 3 9 1 . 0 0 1 3 8 2 6 9 1 . 0 0 2 6 4 5 1 7 6 . 0 0 1 0 1 8 5 3 5 . 0 0 3 6 7 7 4 9 0 . 0 0 5 5 9 5 3 2 1 . 0 0 3 4 8 9 6 4 1 . 0 0 1 1 9 4 8 5 0 . 0 0 1 2 0 9 9 9 4 . 0 0 6 0 5 7 2 2 . 0 0 4 7 5 5 9 4 . 0 0 5 3 2 5 1 . 0 0 3 1 5 3 1 6 6 . 0 0 4 7 6 6 7 2 6 . 0 0 2 9 3 2 9 5 9 . 0 0 1 1 6 2 3 5 0 . 0 0 2 8 3 1 0 1 6 . 0 0 1 0 6 9 8 5 8 . 0 0 2 5 3 0 4 1 6 . 0 0 3 9 4 5 4 5 0 . 0 0 2 5 8 6 3 7 6 . 0 0 1 0 4 9 6 1 2 . 0 0 8 4 5 2 9 4 . 0 0 4 8 6 6 9 0 . 0 0 1 5 7 4 0 7 . 0 0 2 5 5 7 1 . 0 0 1 0 5 3 1 1 0 . 0 0 1 7 9 4 6 9 2 . 0 0 1 2 9 8 7 8 9 . 0 0 2 7 9 2 0 2 . 0 0 1 9 1 7 7 2 3 . 0 0 4 4 0 7 0 3 . 0 0 1 3 6 0 6 5 2 . 0 0 1 6 3 0 8 8 0 . 0 0 1 0 4 5 5 8 6 . 0 0 2 2 8 8 4 3 . 0 0 5 4 4 6 6 9 . 0 0 1 9 5 1 4 6 . 0 0 2 2 9 9 1 5 . 0 0 1 4 9 2 0 2 . 0 0 1 7 0 3 9 3 6 . 0 0 3 1 7 4 5 1 6 . 0 0 1 7 5 6 7 8 1 . 0 0 6 5 2 4 1 7 . 0 0 2 3 0 0 7 0 8 . 0 0 4 7 3 2 8 2 . 0 0 1 4 2 4 0 1 6 . 0 0 2 1 8 8 2 8 9 . 0 0 1 6 8 3 2 6 9 . 0 0 1 6 5 5 9 7 . 0 0 5 3 4 2 2 9 . 0 0 2 8 6 5 8 6 . 0 0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 Room + B o a r d 7 8 7 9 6 . 0 1 2 1 7 2 4 , 3 9 6 7 8 2 , 1 2 0 0 3 0 6 , 2 7 0 8 3 3 , 2 9 7 6 6 3 . 0 1 7 9 6 0 5 . 0 1 8 9 0 9 0 . 0 5 4 9 1 9 9 . 0 6 0 2 2 5 2 . 0 1 5 3 6 6 0 , 1 5 9 9 1 0 , 2 5 9 4 8 3 , 1 4 6 2 9 8 9 8 0 7 8 . 0 1 6 8 3 8 1 . 0 1 1 0 3 8 4 7 . 0 2 3 7 2 1 3 2 . 0 3 2 6 1 1 7 . 0 1 9 7 3 5 3 . 0 5 4 8 9 2 8 . 0 1 8 8 3 6 7 . 0 7 3 8 9 7 1 . 0 1 0 2 1 5 3 7 . 0 2 8 0 0 3 3 . 0 8 1 6 7 9 . 0 2 3 1 4 3 4 . 0 1 8 4 0 6 2 . 0 7 4 5 1 3 . 0 1 0 2 3 0 2 . 0 7 3 0 8 8 0 , 1 3 7 3 4 1 7 , 4 9 2 0 0 0 . 1 5 6 3 5 7 , 2 7 0 9 5 3 , 9 3 4 3 3 , 6 6 3 8 1 4 . 0 7 9 5 7 6 6 . 0 2 2 9 9 7 7 . 0 9 0 6 5 0 , 2 4 7 3 9 7 , 1 2 6 1 0 3 , 3 8 2 1 4 , 3 0 6 8 6 , 8 7 9 9 9 1 , 1 5 8 7 0 8 8 , 4 0 3 3 7 1 , 1 7 0 0 8 4 . 0 3 4 5 8 4 7 . 0 2 8 2 5 5 2 . 0 5 2 2 9 9 7 . 0 4 2 5 4 1 5 . 0 2 5 7 2 3 9 . 0 1 2 9 6 1 6 . 0 3 3 9 0 5 4 . 0 1 4 1 7 1 4 . 0 .0 ,0 .0 ,0 .0 ,0 . 0 . 0 .0 . 0 . 0 . 0 . 0 .0 B, Year 1981 Cross-sec t iona l Data By S o i l Zone (continued) Expendi ture : $ 1980 1979 1978 S o i l P es t i c i de Custom Feed + Zone 1075849. Work Supplements 1 00 1607579. 00 3463687 .00 2 120230. 00 697567. 00 994182 .00 3 5974791 . 00 81 1 5454. 00 19767462 .00 4 11313184. 00 15145941. 00 73785600 .00 5 7197874. 00 6890977. 00 22769111 .00 6 1292502. 00 2664105. 00 9473521 .00 7 5882897. 00 4255609. 00 16296504 .00 8 1700626. 00 2194402. 00 8155861 .00 9 7443529. 00 4261261. 00 9516930 .00 10 15202173. 00 15158327. 00 27397437 .00 1 1 5908766.00 3934396. 00 9925806 .00 12 3486102. 00 1646101 . 00 3156532 .00 13 8894202. 00 6063169. 00 12279585 .00 14 944390. 00 1108648. 00 3851327 .00 1 524546. 00 838755. 00 1994248 .00 2 49032. 00 521656. 00 790665 .00 3 4672776. 00 5268751. 00 24762689 .00 4 9262628. 00 11701593. 00 58438651 .00 5 4189690. 00 3798441. 00 16931331 .00 6 725477. 00 1527836. 00 7897040 .00 7 4341050. 00 4925397. 00 20380444 .00 8 1 169084. 00 994502. 00 6207869 .00 9 5567305. 00 5179575. 00 7911963 .00 10 10704360. 00 7734537. 00 19078980 .00 1 1 5127500. 00 3969964. 00 16994164 .00 1 2 2386046. .00 1649727. 00 5075033 .00 13 4434958. 00 3450473. 00 17954261 .00 14 712992. 00 1346659. 00 6463063 .00 1 399616. 00 865891. 00 1129487 .00 2 71712. 00 234374. 00 363548.00 3 4227998. 00 5081446. 00 22106413 .00 4 7023863, 00 10759995. 00 64857405 .00 5 3850644. 00 2853852. 00 10771106 .00 6 640434. 00 1365692. 00 5526133 .00 7 5390250. 00 3267434. 00 11570493 .00 8 726998. 00 1438961. 00 5395533 .00 9 4946248. 00 2447162. 00 6709134 .00 10 8007411. 00 5808227. 00 18114441 .00 1 1 4800323. 00 2639491. 00 7086903 .00 12 ' 2287752. 00 904997. 00 1651887 .00 13 5067768. 00 3384916. 00 9661447 .00 14 548233. 00 613733. 00 2663373 .00 1 277737. 00 785863. 00 826140 .00 2 240641. 00 222841. 00 267285 .00 3 3272177. 00 2955327. 00 15879192 .00 4 5117971 . 00 8299652. 00 43821748 .00 5 2870402. 00 3231379. 00 8258080 .00 6 438371 . 00 1277547. 00 5474762 .00 7 4419814. 00 2486168. 00 7135760 .00 8 456437. 00 565259. 00 2708170 .00 9 5065210. 00 2531154. 00 5128369 .00 10 5679775. 00 3081527. 00 12614860 .00 1 1 3904248. 00 2175529. 00 3967830 .00 12 1683073. 00 598945. 00 1535164 .00 13 4184923. 00 2840056. 00 88 1 1965 .00 14 518297. 00 590355. 00 2002284 .00 B. C ross-sec t i ona l Data By S o i l Zone (continued) Year 1981 Expendi ture : $ 1980 1979 1978 S o i l Vet + A r t i f i c i a l Interest on Telephone Zone Insemination Loans 1 580809. 00 8012127 .00 288825. 00 2 280534. 00 3340005 .00 1 33574 , 00 3 4090674. 00 34442391 .00 1355824. 00 4 5105883. 00 63170463 .00 1679451. 00 5 2218745. 00 35787448 .00 1334304. 00 6 579177. 00 7868979 .00 254452. 00 7 2010782. 00 20875797 .00 861661. 00 8 923140. 00 10159465 .00 407450. 00 9 1759961. 00 24292598 .00 792599. 00 10 4013219. 00 57522760 .00 1525427. 00 1 1 1647088. 00 20080649 .00 686671. 00 12 623658. 00 8061884 .00 248059. 00 13 1643325. 00 1692670 .00 633540. 00 14 498070. 00 470255 .00 324887. 00 1 341531. 00 6344059 .00 296253. 00 2 178746. 00 2973055 .00 120198. 00 3 3073768. 00 30047549 .00 1379298. 00 4 3876794. 00 57600252 .00 1702931 . 00 5 1594320. 00 24978997 .00 1154092. 00 6 621675. 00 4742134 .00 312984. 00 7 2191901 . 00 23133223 .00 1210221. 00 8 790850. 00 6229689 .00 446190. 00 9 1629934. 00 16578166 .00 865935. 00 10 3246921. 00 42382317 .00 1502702. 00 1 1 1855515. 00 17420689 .00 859665. 00 12 709174. 00 5904521 .00 298169. 00 13 1315864. 00 16385148 .00 607349. 00 14 539308. 00 4445575 .00 320357. 00 1 548274. 00 5262112 .00 242954. 00 2 74612. 00 1098254 .00 31288. 00 3 2975098. 00 17393725 .00 1215356. 00 4 4545861 . 00 40612507 .00 1609256. 00 5 1515004. 00 16934334 .00 1040745. 00 6 366184. 00 2920298 .00 196297. 00 7 2014192. 00 16190059 .00 915927. 00 8 541599. 00 5689553 .00 444247. 00 9 1710681. 00 14789414 .00 880408. 00 10 2821272. 00 24223384 .00 1323024. 00 1 1 2196796. 00 14099012 .00 773031 . 00 1 2 332549. 00 3852454 .00 204452. 00 1 3 1324132. 00 12149390 .00 558738. 00 14 347718. 00 , 2567016 .00 195711. 00 1 211422. 00 61381 1 .00 228306. 00 2 109720. 00 4911 16 .00 89081 . 00 3 1886474. 00 4410485 .00 935546. 00 4 3315453. 00 11526299 .00 1410204. 00 5 1084573. 00 3359640 .00 819645. 00 6 398136. 00 912735 .00 216784. 00 7 1261172. 00 2822993 .00 738610. 00 8 325233. 00 1674767 .00 320720. 00 9 1108873. 00 2677789 .00 588091. 00 10 1900751. 00 6693003 .00 1005271. 00 1 1 1266626. 00 1582533 .00 689164. 00 12 280704. 00 997370 .00 172167. 00 13 986510. 00 3033420 .00 553704. 00 14 325623. 00 1001047 .00 225225.00 2 1 7 B. C ross-sec t i ona l Data By S o i l Zone (continued) Expendi ture : Year 1981 $ 1980 1979 1978 S o i l E l e c t r i c i t y Fuel Insurance Zone 1 708371. 00 401072. 00 1 103706. 00 2 227792. 00 160525. 00 159692. 00 3 3883668. 00 2292300. 00 6102282. 00 4 4165063. 00 3218239. 00 10846184. 00 5 2746130. 00 1517827. 00 7747274. 00 6 576393. 00 599205. 00 1998436. 00 7 2077997. 00 902674. 00 6106082. 00 8 958584. 00 548098. 00 2831962. 00 9 1923441 . 00 877424. 00 4193868. 00 10 3711765. 00 2705718. 00 9505185. 00 1 1 1717002. 00 669830. 00 5784475. 00 12 859146. 00 324567. 00 1735575. 00 13 1984133. 00 694852. 00 4078125. 00 1 4 856537. 00 202950. 00 859805. 00 1 605697. 00 485177. 00 756468. 00 2 179429. 00 180451. 00 233717. 00 3 3863978. 00 3005743. 00 4372277. 00 4 4628779. 00 4188200. 00 8532114. 00 5 2628199. 00 1857003. 00 5773325. 00 6 613870. 00 573119. 00 1542297. 00 7 2554128. 00 1875679. 00 5982657. 00 8 997624. 00 584666. 00 2264338. 00 9 1882771 . 00 1703860. 00 3539361. 00 10 3278702. 00 2709449. 00 6909279. 00 1 1 2229450. 00 1340910. 00 5342597. 00 1 2 1009122. 00 390726. 00 1388918. 00 13 1877526. 00 520608. 00 2613256. 00 1 4 1012448. 00 284627. 00 845690. 00 1 512764. 00 292450. 00 627102. 00 2 53395. 00 55020. 00 68834. 00 3 3382126. 00 2457590. 00 3476782. 00 4 3757057. 00 3273086. 00 6633640. 00 5 2396389. 00 1770687. 00 5084049. 00 6 405046. 00 437729. 00 987233. 00 7 2476526. 00 1 463551 . 00 6004582. 00 8 868739. 00 535918. 00 1280702. 00 9 2178373. 00 1329108. 00 3584736. 00 10 3070968. 00 2233483. 00 4853653. 00 1 1 2133703. 00 1433053. 00 3817821. 00 12 831314. 00 350459. 00 1118121. 00 13 2079444. 00 735224. 00 2818127. 00 14 742208. 00 206997. 00 394035. 00 1 546391. 00 341981 . 00 448709. 00 2 140637. 00 9551 1 . 00 170459. 00 3 2433042. 00 1678674. 00 2627636. 00 4 3880673. 00 2722565. 00 4945778. 00 5 2046965. 00 1374054. 00 4720179. 00 6 532088. 00 381960. 00 1068055. 00 7 2090850. 00 1189058. 00 5129566. 00 8 643927. 00 321 161 . 00 1067497. 00 9 1729119.00 782592. 00 2838098. 00 10 2658040. 00 1759703. 00 3828526. 00 1 1 1834995. 00 1055985. 00 4017323. 00 12 794976.00 279257. 00 1072921. 00 13 2193042. 00 604783. 00 2956014. 00 14 770571 . 00 307702. 00 460082. 00 218 B. C ross-sec t i ona l Data By S o i l Zone (continued) Year 1981 1980 1979 1978 S o i l Expendi ture : $ Property Deprec ia t ion Bu i ld ing Zone Tax Repairs 1 844611. 00 9404018. 00 891819.00 2 176571. 00 2100143. 00 164059. 00 3 5482938. 00 63807431. 00 5280290. 00 4 7833695. 00 80115253. 00 7906551. 00 5 9890461. 00 62240864. 00 2824674. 00 6 1210469. 00 14325780. 00 774101. 00 7 5312501. 00 50329652. 00 2315565. 00 8 1878389. 00 19965125. 00 1389963. 00 9 4762849. 00 36493448. 00 2453299. 00 10 8046915. 00 82233441. 00 5455804. 00 1 1 5659376. 00 36614591. 00 1979636. 00 1 2 2469792. 00 14772700. 00 952967. 00 1 3 5136627. 00 29195733. 00 2264886. 00 1 4 1395154. 00 8701976. 00 497675. 00 1 681380. 00 9461013. 00 619209. 00 2 187802. 00 2386745. 00 196324. 00 3 4441520. 00 65470742. 00 4531329. 00 4 6655388. 00 ' 73875804. 00 6469924. 00 5 8516039. 00 54720894. 00 2864026. 00 6 1952538. 00 14100925. 00 748786. 00 7 6234212. 00 48503163. 00 2360119. 00 8 1856521. 00 18871472. 00 883780. 00 9 4392774. 00 37236810. 00 2068957. 00 10 6656018. 00 71267927. 00 3732038. 00 1 1 5618518. 00 40722480. 00 2328207. 00 12 2171314. 00 13919459. 00 1005960. 00 1 3 4141422. 00 26690584. 00 1876444. 00 1 4 1112679. 00 10958829. 00 781732. 00 1 545796. 00 10853578. 00 465070. 00 2 116780. 00 1294554. 00 66505. 00 3 3698704. 00 52476355. 00 3965410. 00 4 7091463. 00 59189042. 00 6013242. 00 5 7126074. 00 49940628. 00 2573873. 00 6 1097438. 00 8928490. 00 522093. 00 7 5669892. 00 50116086. 00 2451967. 00 8 1110563. 00 17428486. 00 768030. 00 9 4098901. 00 37652794. 00 2227948. 00 10 5138630. 00 58289337. 00 4466204. 00 1 1 4546930. 00 36160541. 00 2168989. 00 12 1666974. 00 9197278. 00 725770. 00 1 3 3782190. 00 25848705. 00 1776189. 00 1 4 857879. 00 6465004. 00 564120. 00 1 340326. 00 4150089. 00 457737. 00 2 197961. 00 1849368. 00 250118. 00 3 3219789. 00 38761244. 00 2825116. 00 4 5664297. 00 57744467. 00 3987440. 00 5 6183670. 00 43680584. 00 2284152. 00 6 1437642. 00 12968795. 00 862852. 00 7 6286317. 00 41906773. 00 2461868. 00 8 1043297. 00 11910413. 00 564507. 00 9 3733705. 00 26632151. 00 1656865. 00 10 4303791. 00 35984272. 00 4030321.00 1 1 4550774. 00 28805626.00 1767566. 00 12 1477306. 00 7945392. 00 712647. 00 13 3606715. 00 20768491. 00 1914019. 00 14 1039502. 00 5809655. 00 676916. 00 2 1 9 B. C ross-sec t i ona l Data By S o i l Zone (continued) Year 1981 1980 1979 1978 Expendi ture : $ S o i l Rental Machinery Seed Zone 1 2347930. 00 1 1629733 .00 1 1 48700 . 0 2 465432. 00 3960682 .00 514625 .00 3 1 1713816. 00 54469821 .00 5440749 .00 4 22732692. 00 55066901 .00 4523363 .00 5 13839929. 00 44677252 .00 2284540 .00 6 2719929. 00 9609172 .00 633015 .00 7' 11639316. 00 36295873 .00 2383136 .00 8 4350344. 00 14530497 .00 597873 .00 9 9387737. 00 33353259 .00 4566410 .00 10 23799645. 00 69539964 .00 6675581 .00 1 1 8569584. 00 32513981 .00 3670806 .00 12 3640208. 00 14626929 .00 1706099 .00 13 7290640. 00 31692508 .00 4912247 .00 14 2032495. 00 12217437 .00 1157480 .00 1 1336184. 00 7679156 .00 618540 .00 2 362542. 00 2901372 .00 192249 .00 3 12690743. 00 40678179 .00 4206984 .00 4 26577998. 00 50318434 .00 5228461 .00 5 16600326. 00 36666662 .00 2167987 .00 6 2001858. 00 7728612 .00 717305 .00 7 15309897. 00 35442041 .00 3563111 .00 8 4263367. 00 13379886 .00 546233 .00 9 .9667148. 00 29027273 .00 3692527 .00 10 16025937. 00 51907738 .00 5088342 .00 1 1 9368233. 00 30130893 .00 3533218 .00 12 3541224. 00 12784197 .00 1660840 .00 13 6785140. 00 20831451 .00 4431883 .00 1 4 1521068. 00 1 0700942 .00 917594 .00 1 479605. 00 7445386 .00 722602 .00 2 339303. 00 1480204 .00 171023 .00 3 8865101. 00 31877822 .00 4039767 .00 4 19772871 . 00 40033928 .00 3954920 .00 5 9513101. 00 28530972 .00 1 393377 .00 6 1635130. 00 5754439 .00 505943 .00 7 12453306. 00 28735014 .00 2167864 .00 8 3101739. 00 8260422 .00 536389 .00 9 8740839. 00 27279265 .00 3263364 .00 10 12742865. 00 36548830 .00 3842261 .00 1 1 5231367. 00 22294831 .00 2978549 .00 12 1753542. 00 7841970 .00 1304156 .00 13 8679488. 00 17656406 .00 3242914 .00 14 1563871. 00 7089774 .00 633643 .00 1 373922. 00 5117505 .00 453639 .00 2 491837. 00 2236662 .00 177927 .00 3 6997168. 00 23809977 .00 3124300 .00 4 15023742. 00 34701066 .00 3566643 .00 5 8960997. 00 25436049 .00 1094443 .00 6 1927452. 00 6497354 .00 591631 .00 7 8762352. 00 24775190 .00 1977139 .00 8 1704573. 00 6838602 .00 377817 .00 9 6427456. 00 22574849 .00 2607439 .00 10 10256784.00 30629209 .00 3528819 .00 1 1 5992353. 00 22591510 .00 2708063 .00 12 1942862. 00 7015729 .00 1105228 .00 13 7041289. 00 18552040 .00 2975987 .00 14 1258924. 00 7664000 .00 745151 .00 220 B. C ross-sec t i ona l Data By S o i l Zone (continued) Expendi ture : $ Year S o i l Fencing Zone Repairs 1981 1 527412.00 2 196614.00 3 3728656.00 4 2444183.00 5 2330619.00 6 458409.00 7 1377066.00 8 907886.00 9 1821189.00 10 3705807.00 11 1765525.00 12 485036.00 13 1197332.00 14 486797.00 1980 1 378899.00 2 125401.00 3 2968528.00 4 2388589.00 5 2063117.00 6 660644.00 7 1586456.00 8 889599.00 9 1207505.00 10 3758887.00 11 1212891.00 12 562376.00 13 1025385.00 14 587705.00 1979 1 253964.00 2 27204.00 3 2604099.00 4 2298418.00 5 1610484.00 6 467513.00 7 1322442.00 8 990720.00 9 1390158.00 10 2973527.00 11 1347174.00 12 399192.00 13 748957.00 14 513465.00 1978 1 290455.00 2 104656.00 3 2067523.00 4 2211783.00 5 1709433.00 6 517867.00 7 1424005.00 8 540709.00 9 1113805.00 10 2505078.00 11 1218230.00 12 436692.00 13 870294.00 14 540510.00 Twine + Wi re 396087.00 99933.00 1842548.00 1351417.00 997619.00 189291.00 823146.00 255660.00 1021408.00 1422058.00 900222.00 357162.00 931080.00 403534.00 346845.00 125158.00 1856414.00 1668076.00 1345151.00 255066.00 1235600.00 325001.00 1064476.00 1 478389.00 1 146714.00 458419.00 808605.00 382968.00 247992.00 38084.00 1628234.00 1479584.00 1136218.00 219785.00 1045935.00 264666.00 1 205464.00 1650951.00 1096802.00 247922.00 831049.00 279647.00 187252.00 73497.00 1094196.00 1330471.00 931264.00 292859.00 692418.00 205766.00 905951.00 1 184119.00 870863.00 253422.00 766312.00 220822.00 Hardware 634740.00 151301.00 3762318.00 00 00 00 ,00 00 3750614 2921449 595253 2009052 954933 1655078.00 3746062.00 1514295 668013 1692670 470255 701435 267023 3019576 3995113 2338613 690515 2491761 954035 1556174 3137159 1729529 624482 1104541 493317 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 368886.00 59141.00 2777170.00 3509112.00 2159882.00 471 100.00 21 31926.00 781110.00 1835759.00 2552728.00 1301576.00 445777.00 930861.00 433496.00 344976.00 114444.00 2158975.00 2322071.00 1727931.00 489983.00 1707562.00 608737.00 1293068.00 2131257.00 1 153705.00 340333.00 959935.00 411809.00 221 B. C ross-sec t i ona l Data By S o i l Zone (continued) Year 1981 1980 1979 1978 Expendi ture : $ S o i l Zone F e r t i l i z e r I r r i g a t i o n Other 1 4552104.00 0.0 144072.00 2 823422.00 0.0 11376.00 3 23615482.00 27782.00 210692.00 4 33679644.00 1894672.00 407911.00 5 6068933.00 164295.00 177847.00 6 2571543.00 253963.00 93979.00 7 7728924.00 120329.00 219181 .00 8 1400715.00 10528.00 44801.00 9 17264488.00 13202.00 69135.00 10 46615041.00 0.0 155284.00 1 1 8700811.00 166.00 282052.00 12 8488230.00 0.0 27848.00 13 17697486.00 0.0 275676.00 14 3384426.00 0.0 9946.00 1 2670252.00 17976.00 51595.00 2 650134.00 302.00 30427.00 3 19908746.00 15312.00 261059.00 4 28489907.00 1825600.00 378766.00 5 4861713.00 478884.00 191131.00 6 1403622.00 261382.00 78881.00 7 9484002.00 1 1 1256.00 511022.00 8 1545929.00 19000.00 117086.00 9 14996368.00 0.0 44235.00 10 29293798.00 1000.00 166338.00 1 1 9063718.00 37394.00 288839.00 12 6333442.00 0.0 93980.00 13 13222369.00 0.0 262306.00 1 4 2546440.00 0.0 35378.00 1 2847228.00 0.0 82809.00 2 458543.00 0.0 99864.00 3 17600494.00 87724.00 886962.00 4 27527427.00 1709615.00 671589.00 5 3791746.00 405621.00 119792.00 6 1221637.00 288143.00 11648.00 7 10639665.00 21849.00 189591.00 8 1685671.00 10505.00 142827.00 9 13853248.00 0.0 312403.00 10 22436217.00 1164.00 302792.00 1 1 8387632.00 54586.00 349827.00 12 5074812.00 11026.00 214407.00 13 13125254.00 5077.00 336670.00 14 1726562.00 5304.00 11513.00 1 1222735.00 0.0 9496.00 2 1201406.00 248.00 232449.00 3 12956492.00 0.0 1844156.00 4 22321693.00 1504437.00 1169044.00 5 2252895.00 90627.00 289189.00 6 1057444.00 222387.00 378963.00 7 7041243.00 46082.00 1268367.00 8 834009.00 0.0 260854.00 9 10403566.00 10.00 864482.00 10 15906005.00 0.0 760206.00 1 1 6506594.00 60902.00 641835.00 12 3368362.00 0.0 143366.00 13 12252735.00 7282.00 600265.00 14 1795427.00 14095.00 68453.00 222 B. C ross-sec t i ona l Data By S o i l Zone (continued) Year 1981 1980 1979 1978 S o i l Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 1 3 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 Acres : To ta l of 7 Grains 366516.00 61813.00 1128662.00 2036666.00 1939235.00 371369.00 1534546.00 721953.00 1361581.00 2599305.00 1310021.00 541365.00 1050914.00 205689.00 303664.00 58561.00 1 148531.00 2276044.00 1954909.00 373166.00 1876436.00 . 696805.00 1299791.00 2155027.00 1615616.00 516540.00 839094.00 160447.00 205029.00 27970.00 986992.00 1960517.00 1781996.00 247220, 1916560, 639581, 1354552, 1813940, 1340634, 389251, 00 00 00 00 00 00 00 913779.00 154242.00 198269.00 37802.00 940820.00 1998755.00 1821287.00 247210.00 1842131.00 635609.00 1285825.00 1809310.00 1306365.00 399543.00 919077.00 133307.00 Tame Hay 246379.00 86079.00 890095, 361252. 281699. 49199, 192683.00 1 1 3725.00 392292.00 609789.00 180547, 127898, 287454, 214659, 178011, 74973, 902697.00 378104.00 306079.00 76022.00 391560.00 1 4 1 356.00 302216.00 516909.00 235453, 158073, 311528, 184584, 193343, 29575, 883254, 483148, 00 ,00 ,00 ,00 00 00 ,00 00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 334786.00 00 00 00 00 ,00 00 53166, 297157, 130085, 437657, 598017, 234042, 104549.00 259084.00 157903.00 199467.00 28481.00 846848, 495001, 331717, 56893, 284896.00 129418.00 435042.00 544089.00 234027.00 98638.00 272869.00 153249.00 ,00 00 ,00 00 Rented Land 428117. 138157. 1356160. 1922621. 4075988. 00 00 00 00 00 1290770.00 1257266. 3247162. 1997421. 1848443. 763202. 377094. 784954. 1208652. 415210, 67474, 1355732, 2788536, 3822595, 2106745, 1693780, 2310534, 2261031, 2421534, 897107. 443380, 697142, 1216744, 250868, 94351, 1474954, 2836234, 3503472, 1508371, 1 47281 1 , 3377117, 2403749.00 2849089.00 81 1406, 249966, 813751, 1051217, 298725, 84833, 1585269, 1936623, 3200173, 2124811, 1458498, 2507702, 1663632. 2015509. 783637.00 269535.00 748389.00 1356211.00 00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00.00 00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 ,00 00 ,00 00 00 223 B. ( Year 1981 1980 1979 1978 -sec t i ona l Data By S o i l Zone (continued) Ac res : S o i l Other Summer A l l Crops Zone Crops Fal low 1 5013.00 73738.00 691648.00 2 3396.0.0 10059.00 161348.00 3 12228.00 102417.00 2133404.00 4 18834.00 705764.00 3122516.00 5 35107.00 1597981.00 3854023.00 6 1 1774.00 316856.00 749199.00 7 26859.00 1071744.00 2825833.00 8 31690.00 529902.00 1397272.00 9 42523.00 433763.00 2230160.00 10 67140.00 611109.00 3887344.00 1 1 23141 .00 703899.00 2217609.00 1 2 10287.00 178490.00 858041.00 13 87378.00 156996.00 1582744.00 14 15569.00 74862.00 510781.00 1 10807.00 57206.00 549690.00 2 4480.00 6693.00 1 44708.00 3 19744.00 108511.00 2180308.00 4 33773.00 809748.00 3524075.00 5 26704.00 1637048.00 3927799.00 6 4444.00 306214.00 768878.00 7 32401.00 1384961.00 3694295.00 8 29586.00 564682.00 1432681.00 9 62777.00 451951.00 2128709.00 10 44689.00 560383.00 3283519.00 1 1 22435.00 932225.00 2819239.00 12 10093.00 171383.00 858191.00 13 61879.00 142059.00 1391321.00 14 24282.00 71792.00 441106.00 1 1646.00 77324.00 477364.00 2 1092.00 13203.00 71841 .00 3 32718.00 135548.00 2041902.00 4 48425.00 931985.00 3431954.00 5 6050.00 1588606.00 3711799.00 6 12141 .00 211905.00 527150.00 7 11403.00 1463123.00 3692061.00 8 10027.00 478093.00 1260198.00 9 37250.00 590999.00 2428242.00 10 60088.00 577315.00 3052205.00 1 1 13856.00 813314.00 2408464.00 12 15190.00 161591.00 672909.00 13 56267.00 248425.00 1 488020.00 1 4 24590.00 63880.00 400617.00 1 4350.00 66600.00 468687.00 2 898.00 13912.00 81095.00 3 36816.00 162901.00 1991682.00 4 30185.00 877233.00 3410528.00 5 2846.00 1571502.00 3728125.00 6 10605.00 210597.00 528165.00 7 5469.00 1439288.00 3575820.00 8 13026.00 496514.00 1278349.00 9 38500.00 617265.00 2376654.00 10 65682.00 554771.00 2976714.00 1 1 11997.00 803564.00 2359698.00 12 7670.00 162834.00 670665.00 13 50951 .00 259652.00 1510064.00 14 21157.00 90484.00 398449.00 224 B. C r o s s - s e c t i o n a l D a t a By S o i l Z o n e ( c o n t i n u e d ) Y e a r 1981 1980 1 9 7 9 1978 A c r e s : S o i l I m p r o v e d O t h e r Z o n e P a s t u r e L a n d 1 1 3 0 8 5 0 . 0 0 6 3 9 8 9 9 . 0 0 2 3 9 4 1 5 . 0 0 2 4 4 0 3 7 . 0 0 3 8 0 9 5 6 2 . 0 0 1 5 6 1 3 6 8 . 0 0 4 3 5 5 0 5 9 . 0 0 31 1 6 6 5 0 . 0 0 5 2 8 4 9 4 7 . 0 0 4 7 9 2 6 4 8 . 0 0 6 7 3 8 2 5 . 0 0 1 8 6 1 7 4 9 . 0 0 7 2 1 3 6 3 7 . 0 0 1 2 1 4 0 0 0 . 0 0 8 3 3 4 7 8 . 0 0 3 3 9 9 9 3 6 . 0 0 9 2 1 7 5 9 5 . 0 0 2 2 3 2 2 0 6 . 0 0 10 4 3 2 3 3 4 . 0 0 2 6 4 3 9 8 8 . 0 0 1 1 8 4 2 4 0 . 0 0 9 8 8 9 1 9 . 0 0 12 6 6 2 3 2 . 0 0 5 0 4 4 7 9 . 0 0 13 1 4 9 3 3 5 . 0 0 9 3 8 7 8 7 . 0 0 14 7 5 3 0 5 . 0 0 1 6 0 3 7 4 3 . 0 0 1 9 1 1 2 3 . 0 0 6 1 0 7 2 2 . 0 0 2 4 6 2 1 2 . 0 0 1 9 8 5 7 5 . 0 0 3 7 3 1 7 0 9 . 0 0 1 7 6 9 5 2 7 . 0 0 4 4 3 3 3 3 8 . 0 0 3 6 0 4 2 4 1 . 0 0 5 3 1 1 8 2 8 . 0 0 4 5 6 1 5 9 6 . 0 0 6 1 1 9 2 7 0 . 0 0 2 8 8 3 5 2 3 . 0 0 7 1 9 5 6 8 0 . 0 0 1 7 7 9 2 4 9 . 0 0 8 3 2 6 1 7 7 . 0 0 2 3 0 1 0 7 2 . 0 0 9 2 1 0 3 2 5 . 0 0 2 5 6 3 9 2 0 . 0 0 10 4 4 4 8 3 4 . 0 0 3141 1 0 5 . 0 0 1 1 1 0 5 0 3 1 . 0 0 1 2 3 2 3 2 4 . 0 0 12 6 1 7 3 1 . 0 0 4 9 7 1 3 2 . 0 0 13 1 3 4 5 9 8 . 0 0 9 6 6 2 6 9 . 0 0 14 6 7 8 3 8 . 0 0 1 6 5 2 1 8 7 . 0 0 1 8 3 0 5 0 . 0 0 5 2 1 6 2 1 . 0 0 2 3 9 0 0 9 . 0 0 1 1 9 4 6 7 . 0 0 3 6 2 2 8 6 3 . 0 0 1 8 9 9 7 3 4 . 0 0 4 3 5 5 4 8 7 . 0 0 3 7 8 4 7 7 0 . 0 0 5 2 3 9 7 2 6 . 0 0 4 5 9 8 8 4 5 . 0 0 6 1 3 5 5 4 4 . 0 0 21 1 2 1 4 0 . 0 0 7 2 1 2 1 8 8 . 0 0 1 4 5 1 6 2 8 . 0 0 8 3 9 6 5 2 . 0 0 3 1 7 1 7 8 5 . 0 0 9 2 0 9 7 9 6 . 0 0 2 6 9 8 6 3 9 . 0 0 10 3 5 9 9 5 6 . 0 0 3 7 0 3 6 4 8 . 0 0 1 1 1 0 5 6 9 2 . 0 0 1 2 2 9 2 2 4 . 0 0 12 4 5 8 0 3 . 0 0 3 8 2 0 8 0 . 0 0 13 9 9 6 7 7 . 0 0 1 0 4 6 6 6 0 . 0 0 14 3 9 0 9 8 . 0 0 1 4 2 6 3 1 1 . 0 0 1 8 2 2 9 2 . 0 0 5 4 2 5 1 2 . 0 0 2 2 6 8 7 4 . 0 0 1 6 4 3 5 5 . 0 0 3 6 1 6 7 8 5 . 0 0 1 7 9 0 3 1 7 . 0 0 4 3 6 1 3 7 7 . 0 0 3 2 9 9 5 0 9 . 0 0 5 2 4 2 1 6 9 . 0 0 4 4 1 4 0 4 8 . 0 0 6 1 3 5 9 4 5 . 0 0 3 0 1 7 7 8 6 . 0 0 7 2 1 2 2 6 2 . 0 0 1 5 5 4 2 0 0 . 0 0 8 3 7 1 6 9 . 0 0 2 5 0 8 6 8 4 . 0 0 9 1 9 7 9 6 6 . 0 0 1 9 6 0 8 1 0 . 0 0 10 3 4 1 9 0 5 . 0 0 2 7 3 0 6 2 4 . 0 0 1 1 1 0 1 2 8 1 . 0 0 1 1 7 8 4 6 6 . 0 0 12 4 4 7 0 5 . 0 0 4 1 7 5 1 3 . 0 0 13 9 8 6 2 9 . 0 0 1 1 0 0 4 6 2 . 0 0 14 4 0 7 6 5 . 0 0 1 6 5 6 4 6 0 . 0 0 T o t a l L a n d 1 4 6 2 3 9 8 . 0 0 4 4 4 8 0 1 . 0 0 4 5 0 4 3 0 4 . 0 0 6 5 9 4 2 6 7 . 0 0 8 9 3 1 6 4 2 . 0 0 2 6 8 4 7 7 4 . 0 0 4 2 5 3 4 7 0 . 0 0 4 8 3 0 6 8 9 . 0 0 4 6 7 9 9 2 1 . 0 0 6 9 6 3 6 1 7 . 0 0 3 3 0 0 7 4 4 . 0 0 1 4 2 8 7 1 8 . 0 0 2 6 7 0 8 3 3 . 0 0 2 1 8 9 8 2 0 . 0 0 1 2 5 1 5 8 8 . 0 0 3 8 9 4 9 6 . 0 0 4 6 8 1 6 2 6 . 0 0 7 5 6 0 7 4 3 . 0 0 8 8 0 1 4 0 3 . 0 0 3 7 7 1 6 7 9 . 0 0 5 6 6 9 6 6 0 . 0 0 4 0 5 9 9 7 3 . 0 0 4 9 0 3 6 8 1 . 0 0 6 8 6 9 1 0 8 . 0 0 4 1 5 6 9 7 6 . 0 0 1 4 1 7 2 6 0 . 0 0 2 4 9 2 2 9 1 . 0 0 2 1 6 1 1 5 5 . 0 0 1 0 8 1 7 1 6 . 0 0 2 3 0 3 1 8 . 0 0 4 5 6 4 4 7 5 . 0 0 7 5 7 0 2 7 5 . 0 0 8 5 5 0 1 8 5 . 0 0 2 7 7 4 7 7 4 . 0 0 5 3 5 6 7 5 6 . 0 0 4 4 7 5 6 9 3 . 0 0 5 3 3 5 9 4 3 . 0 0 7 1 1 5 6 3 2 . 0 0 3 7 4 3 2 5 7 . 0 0 1 0 9 9 9 4 1 . 0 0 2 6 3 4 2 4 8 . 0 0 1 8 6 6 0 2 7 . 0 0 1 0 0 9 4 9 8 . 0 0 3 3 8 0 6 1 . 0 0 4 1 8 3 8 1 3 . 0 0 6 6 6 7 7 2 2 . 0 0 8 4 6 3 7 8 6 . 0 0 3 7 7 4 3 9 8 . 0 0 5 3 0 5 4 9 8 . 0 0 3 6 9 8 5 9 2 . 0 0 4 6 7 0 3 7 3 . 0 0 6 0 2 1 5 6 0 . 0 0 3 7 9 5 1 8 2 . 0 0 1 0 8 8 9 3 9 . 0 0 2 7 3 6 5 0 0 . 0 0 2 1 7 3 9 4 5 . 0 0 B. C r o s s - s e c t i o n a l D a t a B y S o i l Z o n e ( c o n t i n u e d ) Ye ,ar 1981 1 9 8 0 1 9 7 9 1 9 7 8 S o i l Z o n e Q u a n t i t y : bu. W h e a t F e d O a t s F e d B a r l e y F e d 1 1 6 6 9 8 . 0 0 1 2 4 5 9 1 1 . 0 0 7 6 3 2 0 9 . 0 0 2 5 0 0 0 . 0 0 3 5 6 1 6 1 . 0 0 1 8 7 4 8 6 . 0 0 3 3 5 4 3 6 0 . 0 0 7 0 8 1 0 0 3 . 0 0 1 0 4 3 9 8 1 1 . 0 0 4 3 6 9 3 2 5 . 0 0 4 0 3 8 4 3 4 . 0 0 1 7 1 3 8 2 5 3 . 0 0 5 1 4 7 2 0 5 . 0 0 3 7 8 0 7 0 0 . 0 0 3 6 5 9 5 4 9 . 0 0 6 1 1 5 0 4 . 0 0 5 3 9 5 4 9 . 0 0 1 3 1 0 7 0 3 . 0 0 7 1 9 4 5 7 8 . 0 0 4 5 6 1 3 4 5 . 0 0 4 0 3 3 2 5 2 . 0 0 8 9 0 0 1 5 . 0 0 2 1 4 3 6 7 2 . 0 0 1 5 2 3 8 8 1 . 0 0 9 1 2 4 4 4 3 . 0 0 5 0 3 8 8 0 4 . 0 0 5 1 3 8 1 7 9 . 0 0 10 1 2 6 9 5 4 . 0 0 9 5 8 1 1 5 1 . 0 0 1 4 3 9 2 6 7 8 . 0 0 1 1 1 7 6 3 9 3 . 0 0 5 5 6 6 2 9 0 . 0 0 3 1 8 2 0 6 3 . 0 0 1 2 3 1 4 9 5 . 0 0 2 2 6 7 1 9 7 . 0 0 1 7 1 2 5 6 5 . 0 0 1 3 2 1 2 5 0 8 . 0 0 4 2 3 6 2 5 8 . 0 0 3 6 9 3 0 2 1 . 0 0 14 6 2 1 4 7 . 0 0 1 1 4 3 0 0 4 . 0 0 8 4 3 6 0 4 . 0 0 1 7 8 0 0 . 0 0 7 1 2 7 3 7 . 0 0 9 2 6 4 8 5 . 0 0 2 8 2 4 5 . 0 0 3 1 5 3 1 0 . 0 0 1 7 0 2 0 2 . 0 0 3 3 0 5 4 4 1 . 0 0 7 1 4 8 3 0 8 . 0 0 1 1 9 7 6 5 3 7 . 0 0 4 5 2 3 8 1 1 . 0 0 4 1 5 6 5 2 0 . 0 0 1 8 8 3 3 4 0 5 . 0 0 5 3 2 2 1 3 8 . 0 0 3 6 1 3 5 0 6 . 0 0 2 6 6 0 4 8 2 . 0 0 6 9 9 4 0 9 . 0 0 9 4 7 4 0 5 . 0 0 1 4 9 1 5 5 5 . 0 0 7 6 4 3 0 5 7 . 0 0 6 3 1 2 5 0 5 . 0 0 5 1 7 4 2 7 5 . 0 0 8 1 4 3 9 4 3 . 0 0 2 1 3 8 2 1 5 . 0 0 1 0 9 5 4 5 6 . 0 0 9 1 6 5 2 6 1 . 0 0 5 7 6 1 0 5 7 . 0 0 5 0 7 9 7 4 7 . 0 0 10 5 4 7 7 0 9 . 0 0 1 1 0 8 5 4 9 5 . 0 0 1 0 4 6 8 8 4 8 . 0 0 1 1 3 7 5 3 3 2 . 0 0 6 0 7 2 4 8 6 . 0 0 3 5 9 3 4 8 2 . 0 0 12 2 0 6 3 8 . 0 0 2 3 1 3 2 7 2 . 0 0 2 1 7 1 9 9 6 . 0 0 13 1 9 5 4 6 3 . 0 0 3 2 3 5 5 5 1 . 0 0 3 8 9 0 8 8 0 . 0 0 1 4 1 6 6 3 1 1 . 0 0 7 1 2 7 9 3 . 0 0 9 0 2 9 1 2 . 0 0 1 1 2 2 0 7 . 0 0 7 7 7 5 7 8 . 0 0 1 1 4 1 2 5 6 . 0 0 2 1 1 0 2 . 0 0 1 3 1 5 1 6 . 0 0 1 0 6 1 9 6 . 0 0 3 7 8 6 4 0 6 . 0 0 6 7 1 7 4 6 6 . 0 0 1 2 5 4 8 1 0 1 . 0 0 4 7 2 9 5 3 1 . 0 0 8 6 6 3 2 4 9 . 0 0 3 1 8 2 7 7 5 7 . 0 0 5 3 6 3 6 6 5 . 0 0 3 4 9 3 1 3 8 . 0 0 2 5 0 5 0 9 3 . 0 0 6 4 5 5 9 6 . 0 0 7 6 6 0 5 1 . 0 0 1 0 2 5 0 8 6 . 0 0 7 6 5 3 1 7 7 . 0 0 5 0 3 9 4 9 3 . 0 0 5 5 8 9 7 0 3 . 0 0 8 4 4 5 1 9 0 . 0 0 2 2 2 4 1 3 0 . 0 0 1 0 6 0 9 5 8 . 0 0 9 2 1 2 3 9 7 . 0 0 7 0 8 1 4 9 5 . 0 0 4 6 7 5 3 9 5 . 0 0 10 2 9 7 1 3 5 . 0 0 1 0 9 0 3 6 8 3 . 0 0 8 6 0 0 2 9 9 . 0 0 1 1 4 4 8 2 3 3 . 0 0 7 3 9 9 8 8 2 . 0 0 4 1 0 1 3 8 5 . 0 0 1 2 5 5 6 7 8 . 0 0 1 7 0 9 4 1 4 . 0 0 1 4 0 2 6 2 9 . 0 0 1 3 3 1 6 8 6 6 . 0 0 4 7 9 0 8 6 7 . 0 0 3 5 3 6 5 1 8 . 0 0 14 1 9 8 7 5 4 . 0 0 1 4 3 3 0 8 8 . 0 0 1 0 7 0 4 4 0 . 0 0 1 0 . 0 8 1 6 1 9 0 . 0 0 5 5 7 8 4 5 . 0 0 2 5 0 0 0 . 0 0 1 9 1 1 5 9 . 0 0 6 3 3 4 3 5 . 0 0 3 1 0 9 1 7 7 . 0 0 4 9 1 9 1 0 8 . 0 0 8 2 5 4 3 0 4 . 0 0 4 3 2 6 8 2 3 , 0 0 3 6 6 0 5 3 8 . 0 0 1 6 1 1 2 8 4 8 . 0 0 5 2 0 0 9 5 4 . 0 0 3 1 7 2 0 3 2 . 0 0 1 5 9 0 1 8 0 . 0 0 6 1 6 6 1 3 . 0 0 8 3 7 4 9 7 . 0 0 1 5 1 2 7 1 8 . 0 0 7 1 2 3 8 7 4 . 0 0 4 5 0 8 7 0 0 . 0 0 3 4 6 8 5 7 0 . 0 0 8 5 4 7 0 3 . 0 0 1 1 4 3 5 1 5 . 0 0 9 7 7 3 8 4 . 0 0 9 7 0 2 1 9 . 0 0 3 8 4 2 9 2 7 . 0 0 3 6 3 6 0 6 5 . 0 0 10 1 7 4 2 7 5 . 0 0 8 3 0 9 8 0 4 . 0 0 6 1 1 1 9 5 6 . 0 0 1 1 4 3 6 9 7 . 0 0 6 0 2 1 3 7 9 . 0 0 1 6 3 2 9 9 1 . 0 0 12 3 5 1 6 1 . 0 0 1 4 3 5 6 3 7 . 0 0 8 7 3 6 0 1 . 0 0 13 1 0 1 5 5 5 . 0 0 4 9 3 0 4 4 7 . 0 0 2 8 9 1 2 7 9 . 0 0 14 1 0 0 2 8 0 . 0 0 1 1 5 1 2 2 2 . 0 0 5 9 2 2 3 1 . 0 0 B. ( Year 1981 1980 1979 1978 -sec t i ona l Data By S o i l Zone (continued) S o i l Quant i t y : Head Calves Beef Replacement Zone Born Cows Hei fe rs 1 68906.00 78740.00 11886.00 2 20916.00 24848.00 4797.00 3 330090.00 375585.00 67594.00 4 325742.00 357753.00 59345.00 5 272700.00 299056.00 36520.00 6 65276.00 69926.00 13221.00 7 132479.00 153619.00 25360.00 8 1 14822.00 122615.00 15164.00 9 165736.00 185753.00 25293.00 10 309558.00 352425.00 47438.00 1 1 137818.00 154327.00 20856.00 12 63729.00 69864.00 10208.00 13 135035.00 151788.00 26980.00 14 91473.00 101810.00 24405.00 1 51923.00 57246.00 14172.00 2 19902.00 22382.00 5386.00 3 331554.00 369101.00 65633.00 4 306492.00 343525.00 57300.00 5 261451.00 286365.00 41692.00 6 101077.00 108394.00 20445.00 ' 7 188946.00 517091.00 39245.00 8 90296.00 105411.00 15967.00 9 192338.00 212577.00 34668.00 10 307069.00 328066.00 56623.00 1 1 169293.00 188051.00 33356.00 12 62726.00 70162.00 12114.00 13 128730.00 145105.00 23237.00 14 86969.00 99762.00 15164.00 1 56211.00 64789.00 10268.00 2 7835.00 9269.00 3413.00 3 331456.00 369122.00 60687.00 4 331345.00 356713.00 66066.00 5 241312.00 268980.00 42587.00 6 72132.00 80021.00 12719.00 7 168493.00 185766.00 33887.00 8 116324.00 126472.00 23647.00 9 190642.00 221094.00 41228.00 10 297564.00 322718.00 51644.00 1 1 155874.00 178381.00 31475.00 1 2 48475.00 54240.00 6820.00 13 tr 126565.00 139657.00 27489.00 14 62018.00 73590.00 13775.00 1 45-1 33.00 50768.00 13809.00 2 14505.00 15188.00 3448.00 3 306890.00 345208.00 93897.00 4 320727.00 360773.00 98130.00 5 278438.00 307327.00 53782.00 6 78052.00 87797.00 23881.00 7 185045.00 204244.00 35743.00 8 85822.00 96538.00 26258.00 9 164573.00 181648.00 31788.00 10 259152.00 291510.00 79291.00 1 1 163552.00 180521.00 31591.00 12 47173.00 52356.00 14921.00 13 134147.00 148887.00 42433.00 14 88071.00 97748.00 27858.00 B. Y e a r 1981 C r o s s - s e c t i o n a l D a t a By S o i l Z o n e ( c o n t i n u e d ) 1 9 8 0 1 9 7 9 1 9 7 8 S o i l Z o n e 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 Q u a n t i t y : H e a d S t e e r s 7 9 7 0 . 0 0 4 5 0 7 . 0 0 8 2 6 3 1 . 0 0 1 4 6 5 4 0 . 0 0 4 3 6 8 1 . 0 0 2 6 8 8 3 . 0 0 3 9 9 6 0 . 0 0 1 5 5 0 2 . 0 0 3 9 1 4 9 . 0 0 6 2 8 8 7 . 0 0 4 2 4 2 0 . 0 0 1 7 4 5 6 . 0 0 3 9 5 6 9 . 0 0 1 6 9 6 1 . 0 0 7 0 6 9 . 0 0 2 6 3 4 . 0 0 1 0 6 1 3 9 . 0 0 1 3 4 3 1 3 . 0 0 3 0 4 0 1 . 0 0 1 6 0 0 7 . 0 0 2 9 2 3 0 . 0 0 1 6 7 0 9 . 0 0 3 2 8 0 4 . 0 0 7 5 8 0 4 . 0 0 3 8 1 4 3 . 0 0 1 6 5 0 3 . 0 0 3 4 3 6 0 . 0 0 1 1 8 2 0 . 0 0 1 3 3 2 7 . 0 0 2 8 9 9 . 0 0 7 6 9 8 9 . 0 0 1 4 2 4 1 1 . 0 0 3 3 3 2 0 . 0 0 1 4 6 0 2 . 0 0 2 8 8 5 9 . 0 0 1 3 6 8 5 . 0 0 3 9 7 6 5 . 0 0 7 4 8 2 0 . 0 0 3 4 8 9 4 . 0 0 9 7 2 9 . 0 0 3 7 7 6 7 . 0 0 1 4 4 2 4 . 0 0 1 7 0 1 6 . 0 0 3 0 0 7 . 0 0 1 1 5 6 4 5 . 0 0 1 2 0 8 5 9 . 0 0 4 0 8 7 4 . 0 0 2 9 4 1 2 . 0 0 2 7 1 6 5 . 0 0 3 2 3 4 0 . 0 0 2 4 1 5 9 . 0 0 9 7 6 5 6 . 0 0 2 4 0 0 9 . 0 0 1 5 9 6 9 . 0 0 4 5 4 1 1 . 0 0 2 9 8 1 3 . 0 0 S l a u g h t e r H e i f e r s 1 7 6 6 . 0 0 1 9 9 6 . 0 0 4 7 0 0 1 . 0 0 6 4 9 8 8 . 0 0 1 7 3 7 3 . 0 0 1 2 1 3 4 . 0 0 1 7 2 7 5 . 0 0 1 4 1 7 6 . 0 0 2 8 6 2 1 . 0 0 6 2 0 8 9 . 0 0 1 7 3 1 3 . 0 0 9 7 8 4 . 0 0 2 2 7 4 9 . 0 0 7 9 6 7 . 0 0 2 4 3 4 . 0 0 4 7 6 . 0 0 5 1 7 2 7 . 0 0 6 8 0 2 3 . 0 0 7 0 6 4 . 0 0 5 4 7 0 . 0 0 1 3 2 5 6 . 0 0 7 3 7 0 . 0 0 1 2 9 0 5 . 0 0 6 2 5 5 4 . 0 0 1 1 5 7 8 . 0 0 5 6 4 8 . 0 0 2 0 2 0 3 . 0 0 3 8 7 7 . 0 0 2 4 0 8 . 0 0 3 3 2 . 0 0 3 6 9 6 8 . 0 0 5 2 7 1 1 . 0 0 1 8 5 8 4 . 0 0 3 7 1 9 . 0 0 1 2 7 8 5 . 0 0 4 7 4 9 . 0 0 1 0 1 6 0 . 0 0 3 9 2 3 4 . 0 0 9 1 5 6 . 0 0 3 6 8 3 . 0 0 1 5 4 1 9 . 0 0 4 0 6 1 . 0 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 1978 I n c l u d e d i n R e p l a c e m e n t H e i f e r s C a l v e s 00 00 00 ,00 ,00 6 6 4 5 3 , 2 1 0 6 6 , 3 2 7 4 6 9 , 3 1 3 3 2 8 , 2 5 7 0 6 5 , 6 1 5 0 4 . 0 0 1 3 0 2 6 1 . 0 0 1 12251 . 0 0 1 6 2 3 2 3 . 0 0 2 9 7 9 4 3 . 0 0 1 3 5 4 1 1 . 0 0 6 2 6 0 3 . 0 0 1 3 2 5 3 4 . 0 0 9 0 0 3 9 . 0 0 4 8 5 2 1 . 0 0 1 9 4 6 7 . 0 0 3 2 8 7 7 3 . 0 0 3 0 9 2 9 6 . 0 0 2 6 3 5 5 8 . 0 0 9 9 6 0 9 . 0 0 1 9 0 5 2 6 . 0 0 9 6 3 5 8 . 0 0 1 9 1 0 9 6 . 0 0 3 0 1 5 4 0 . 0 0 1 6 5 0 4 5 . 0 0 6 4 1 1 2 . 0 0 1 3 2 0 6 6 . 0 0 8 9 5 8 8 . 0 0 5 2 4 7 5 . 0 0 7 6 5 0 . 0 0 3 3 3 9 2 4 . 0 0 3 1 8 2 5 9 . 0 0 2 4 3 4 4 0 . 0 0 7 2 3 2 4 . 0 0 1 6 3 3 4 2 . 0 0 1 0 8 5 0 9 . 0 0 1 9 2 5 4 0 . 0 0 2 9 8 2 7 2 . 0 0 1 5 7 0 4 8 . 0 0 4 9 7 9 7 . 0 0 1 2 5 4 7 4 . 0 0 6 2 6 5 9 . 0 0 4 5 6 4 0 . 0 0 1 3 4 2 6 . 0 0 3 1 0 3 4 2 . 0 0 3 2 4 3 3 5 . 0 0 2 0 9 9 0 4 . 0 0 7 8 9 3 0 . 0 0 1 3 8 8 8 6 . 0 0 8 6 7 8 8 . 0 0 1 2 4 0 6 6 . 0 0 2 6 2 0 6 7 . 0 0 1 2 3 2 9 6 . 0 0 4 5 0 7 9 . 0 0 1 2 8 1 9 2 . 0 0 8 4 1 6 1 . 0 0 227 C a t t l e + C a l v e s 1 7 0 7 9 4 . 0 0 5 8 6 8 4 . 0 0 9 2 6 5 4 6 . 0 0 9 7 4 9 6 2 . 0 0 6 6 9 1 8 4 . 0 0 1 8 8 1 1 7 . 0 0 3 7 6 8 8 7 . 0 0 2 8 7 5 8 1 . 0 0 4 5 2 6 4 7 . 0 0 8 4 8 4 1 7 . 0 0 3 8 0 4 7 4 . 0 0 1 7 4 4 8 6 . 0 0 3 8 3 2 8 9 . 0 0 2 4 7 3 6 2 . 0 0 1 3 2 0 2 2 . 0 0 5 7 4 7 2 . 0 0 9 4 4 2 5 6 . 0 0 9 4 3 6 7 3 . 0 0 6 4 3 0 8 9 . 0 0 2 5 6 1 4 5 . 0 0 5 0 7 0 5 5 . 0 0 2 4 7 1 6 3 . 0 0 4 9 7 8 6 0 . 0 0 8 5 1 3 4 4 . 0 0 4 4 5 8 7 3 . 0 0 1 7 5 6 3 1 . 0 0 3 6 6 0 4 6 . 0 0 2 2 9 5 8 7 . 0 0 1 4 6 6 0 6 . 0 0 2 4 5 6 9 . 0 0 9 0 8 2 5 9 . 0 0 9 6 9 4 5 2 . 0 0 6 2 0 3 2 1 . 0 0 1 8 9 1 1 5 . 0 0 4 3 9 2 9 9 . 0 0 2 8 4 1 3 7 . 0 0 5 1 8 6 7 1 . 0 0 8 0 7 9 0 9 . 0 0 4 2 2 1 6 5 . 0 0 1 2 8 2 4 3 . 0 0 3 5 7 6 5 2 . 0 0 1 7 2 4 0 9 . 0 0 9 1 4 3 1 . 0 0 3 0 5 5 2 . 0 0 7 2 7 4 0 2 . 0 0 9 7 3 9 1 8 . 0 0 4 4 3 2 3 5 . 0 0 1 7 1 2 7 1 . 0 0 3 9 8 1 8 9 . 0 0 1 5 1 0 7 7 . 0 0 3 8 5 0 1 7 . 0 0 5 9 8 2 8 4 . 0 0 3 4 7 4 3 8 . 0 0 1 0 6 4 1 3 . 0 0 3 3 1 7 3 2 . 0 0 1 7 2 0 3 0 . 0 0 228 C. T ime-Ser i es Data Year P r i c e s and Expected P r i c e s S tee r * Expected Expected Expected S teer H e i f e r H e i f e r Cow Cow 1956 16.10 15.77 12.10 11.91 10.40 9.99 1957 16.85 17.34 1 2.87 13.36 1 1 .40 12.06 1958 21 .90 23.72 18.93 20.53 15.84 16.97 1959 23.08 21 .57 19.32 17.61 16.55 15.19 1960 19.90 18.10 16.71 1 5.80 14.87 14.05 1961 20.50 22.01 16.68 17.46 15.05 15.71 1962 24.20 25.52 20.25 21 .34 16.60 17.05 1963 23.25 21 .38 20.47 1 9.46 16.55 15.98 1964 20.70 20.01 17.83 1 6.97 14.75 14.17 1965 21 .95 23.49 18.33 19.28 13.90 1 4.26 1966 24.90 25.64 20.30 20.74 17.95 19.61 1967 26.40 25.86 22.00 21 .92 18.50 17.23 1968 26.40 25.81 22.50 22. 1 4 18.45 18.24 1969 31 .25 33.27 26. 45 27.49 21 .70 22.80 1970 32.40 30.96 27.05 26.04 22.20 21 .20 1971 33.80 33.93 27.80 27.85 22.20 22.02 1972 37.84 38.98 32.32 33.46 25.85 27.07 1973 49.89 53.35 43.15 45.06 33.91 35.29 1974 42.64 34.82 35.78 30.29 26.06 20.54 1975 36.84 37.28 30.77 31 .48 21 .30 22.53 1976 36.62 38.83 31 .97 33.84 22.91 25. 16 1977 40.54 42.27 34.52 34.93 24.99 25.11 1978 66.53 75.89 58.86 65.45 40.27 44.63 1979 92.46 93.05 88.99 90.75 58.27 58.80 1980 82.01 67.35 75.86 62.80 51 .77 43. 14 1981 76.58 78.44 72.36 75.26 48.52 49.77 1982 74.64 81 .37 69. 14 77.20 46.39 51.35 * C a t t l e p r i c e s in u n i t s cwt. C. T ime-Ser ies Data ( con t . ) Year P r i c e s and Expected P r i c e s Expected G ra i n I n t e r e s t Labour C a l f C a l f Index C . P . I . Rate Index 1956 10. 40 9. 99 98. 80 68. 50 5. 04 48. 90 1957 1 1 . 40 12. 06 92. 40 70. 70 5. 58 51 . 90 1958 15. 84 16. 97 94. 90 72. 60 5. 27 54. 10 1959 16. 55 15. 19 97. 70 73. 40 5. 62 56. 50 1960 14. 87 14. 05 102. 80 74. 30 5. 75 58. 30 1961 15. 05 15. 71 118. 50 75. 30 5. 60 59. 60 1962 16. 60 17. 05 124. 90 75. 90- 5. 71 60. 90 1963 16. 55 15. 98 121 . 40 77. 20 5. 75 62. 40 1964 14. 75 14. 17 122. 30 78. 60 5. 75 65. 30 1965 13. 90 14. 26 120. 90 80. 50 5. 77 69. 70 1966 17. 95 19. 61 125. 80 83. 50 6. 00 76. 80 1967 18. 50 17. 23 123. 30 86. 50 5. 92 83. 50 1968 18. 45 18. 24 110. 50 90. 00 6. 92 88. 30 1969 21 . 70 22. 80 98. 90 94. 10 7. 96 92. 70 1970 22. 20 21 . 20 99. 80 97. 20 8. 17 94. 90 1971 22. 20 22. 02 100. 00 100. 00 6. 48 100. 00 1972 25. 85 27. 07 117. 10 104. 80 6. 00 108. 50 1973 33. 91 35. 29 223. 00 112. 70 7. 65 1 24. 10 1974 26. 06 20. 54 311. 40 1 25. 00 10. 75 1 48. 10 1975 21 . 30 22. 53 298. 40 138. 50 9. 42 176. 30 1976 22. 91 25. 16 245. 30 148. 90 10. 04 203. 40 1977 24. 99 25. 1 1 213. 00 160. 80 8. 50 225. 80 1978 40. 27 44. 63 229. 90 175. 20 9. 58 239. 90 1 979 58. 27 58. 80 285. 60 191 . 20 12. 90 254. 10 1980 51 . 77 43. 14 357. 60 210. 60 14. 25 272. 30 1981 48. 52 49. 77 377. 00 236. 90 19. 29 291 . 10 1982 46. 39 51 . 35 325. 30 262. 50 15. 81 309. 90 C. T ime-Ser ies Data ( con t . ) Year P r i c e s C a t t l e I n v e n to r i e s (,000) C a p i t a l M a t e r i a l s End-o f-Fe r i od Index Index S teer Hei f e r Cow C a l f 1 956 63. 40 74. 30 749. 8 1615. 8 1 530 .3 537. 7 1 957 67. 50 75. 50 838. 4 1667. 0 1 602 .0 569. 5 1958 71 . 30 76. 80 659. 8 1773. 0 1633 .0 520. 7 1959 74. 60 78. 80 614. 0 1852. 0 1 720 .0 520. 5 1960 76. 40 80. 50 668. 2 1911. 0 1776 .3 538. 8 1961 78. 50 81 . 80 791 . 6 2016. 8 1921 .4 586. 4 1962 79. 70 88. 50 737. 0 2037. 0 1989 .0 581 . 0 1963 81 . 80 87. 80 795. 0 21 52. 0 2105 .0 665. 0 1964 83. 50 87. 40 945. 0 2292. 0 2333 .0 778. 0 1965 84. 50 87. 40 943. 0 2399. 0 2528 .0 806. 0 1966 86. 80 91 . 00 995. 1 2377. 9 2517 .4 735. 8 1967 89. 60 94. 90 950. 0 2305. 0 2514 .0 771 . 0 1968 93. 20 96. 20 939. 0 2236. 0 2444 .0 721 . 0 1969 95. 10 98. 70 921 . 0 2197. 0 2428 .0 708. 0 1970 97. 30 97. 60 984. 0 2363. 0 2597 .0 836. 0 1971 100. 00 100. 00 980. 0 2555. 9 2866 .4 901 . 4 1 972 1 03. 60 103. 10 1039. 0 2706. 0 3047 .0 1024. 0 1 973 1 07. 90 109. 60 1038. 0 2883. 0 3341 .0 1023. 0 1974 121. 10 121 . 10 1277. 0 3073. 0 3658 .0 1 1 22. 0 1 975 1 40. 30 136. 50 1428. 0 31 35. 0 3747 .0 1 164. 0 1976 1 53. 10 150. 10 1410. 0 3027. 0 3362 .0 1261. 0 1 977 1 64. 80 161. 10 1 199. 0 2862. 0 3265 .0 1119. 0 1978 1 76. 50 172. 70 1119. 0 2677. 5 3017 .0 1060. 0 1979 193. 90 190. 10 1096. 0 2626. 0 2964 .0 1043. 0 1980 221 . 90 207. 50 998. 0 2733. 5 301 3 .0 1025. 0 1981 260. 70 244. 60 988. 0 2796. 0 2937 .0 1024. 0 1982 287. 60 268. 40 998. 0 2683. 0 2845 .0 1009. 0 C. T ime-Ser i es Data ( con t . Year C a t t l e I n ven to r i e s (, B eg inn ing-o f-Pe r i od S teer H e i f e r Cow 1956 669. 0 1490. 0 1 345. 0 1957 749. 8 1615. 8 1 530. 3 1958 838. 4 1667. 0 1 602. 0 1959 659. 8 1773. 0 1 633. 0 1960 614. 0 1852. 0 1720. 0 1961 668. 2 1911. 0 1776. 3 1962 791 . 6 2016. 8 1 921 . 4 1 963 737. 0 2037. 0 1989. 0 1964 795. 0 2152. 0 2105. 0 1965 945. 0 2292. 0 2333. 0 1 966 943. 0 2399. 0 2528. 0 1 967 995. 1 2377. 9 2517. 4 1 968 950. 0 2305. 0 2514. 0 1969 939. 0 2236. 0 2444. 0 1 970 921 . 0 2197. 0 2428. 0 1 971 984. 0 2363. 0 2597. 0 1 972 980. 0 2555. 9 2866. 4 1973 1039. 0 2706. 0 3047. 0 1974 1038. 0 2883. 0 3341 . 0 1975 1 277. 0 3073. 0 3658. 0 1976 1428. 0 3135. 0 3747. 0 1 977 1410. 0 3027. 0 3362. 0 1978 1 199. 0 2862. 0 3265. 0 1979 1119. 0 2677. 5 3017. 0 1980 1096. 0 2626. 0 2964. 0 1 981 998. 0 2733. 5 3013. 0 1 982 988. 0 2796. 0 2937. 0 Quant i t y Ca l ves Gra in C a l f Born Index 494. 0 21 48. 6 86.3 537. 7 2351 . 0 47.8 569. 5 2375. 9 51.3 520. 7 2322. 0 55.0 520. 5 2401 . 4 67.3 538. 8 2500. 5 22.9 586. 4 2509. 0 87.4 581 . 0 2616. 0 109.3 665. 0 2775. 0 80.5 778. 0 3001 . 0 95. 1 806. 0 2921 . 0 124.9 735. 8 2830. 0 80.2 771 . 0 2725. 0 102.2 721 . 0 2714. 0 105.9 708. 0 2851 . 0 55.7 836. 0 3149. 0 100.0 901 . 4 3462. 0 84. 1 1024. 0 3626. 0 94.6 1023. 0 3837. 0 74.6 1 122. 0 3889. 0 111.1 1 164. 0 3518. 0 151.2 1 261 . 0 3553. 0 134.3 1119. 0 3357. 0 131.4 1060. 0 3213. 0 97.0 1043. 0 3239. 0 123.0 1025. 0 3239. 0 172.8 1024. 0 3170. 0 183.8 D. Reg ress ion Resu l t s us ing Cobb-Douglas and T r a n s l o g F u n c t i o n a l Forms: Almon Lag P r i c e P r e d i c t i o n s The r e s u l t s ob ta ined from econometr ic e s t i m a t i o n of the m u l t i - o u t p u t , m u l t i - i n p u t v a r i a b l e p r o f i t f u n c t i o n assuming tha t f a rmers ' e x p e c t a t i o n s of c a t t l e p r i c e s can be r ep resen ted e x a c t l y by the p r e d i c t i o n s of an Almon l ag (Almon 1965) e x p e c t a t i o n p rocess a re r epo r t ed in t h i s append ix . T h i s expec t a t i on p rocess d e f i n e s expected p r i c e as the p r e d i c t i o n of a po l ynomia l d i s t r i b u t e d l ag model of annual own p r i c e s p r i o r to the c u r r e n t y ea r . T h i s p r e d i c t i o n model can be w r i t t e n a s : (D.1) n ^ 1 = a + l=Q V t - i The r e l a t i o n s h i p between expected p r i c e s ^ p ^ + 1 ^ a n < ^ P a s t p r i c e s (P f c ) can be d e s c r i b e d by a f i n i t e l a g of n p e r i o d s wi th l agged weights (W )^ c o n s t r a i n e d to l i e on a po l ynomia l of degree q : q k W = E B, i , n> q . k=0 k Equa t i on (D.1) i s used to generate an expected p r i c e f o r each an ima l c a t e g o r y . Data used to es t imate the po l ynomia l are based on annual o b s e r v a t i o n s of p r i c e s from 1946 to 1983, f o r f i v e a u c t i o n markets in western Canada as d e s c r i b e d in Chapter F o u r . In order to generate the best f i t to the d a t a , a l t e r n a t i v e s p e c i f i c a t i o n s of the model were a t tempted . The degree of the po l ynomia l was v a r i e d from one to four and the l eng th of the l ag was v a r i e d from two to f i v e y e a r s . The f i n a l model was s e l e c t e d on the b a s i s of R 2 -va lues and t-stat is t ics for the estimated coefficients . A po l ynomia l of degree three w i th a l a g l eng th of f i v e p rov ided the best f i t to the d a t a . In Tab le D . I , the es t imated c o e f f i c i e n t s fo r each animal ca tegory fo r the Ca lga ry market are r e p o r t e d . The econometr ic r e s u l t s f o r the o ther market a reas are s i m i l a r . An example of expected p r i c e s genera ted by the s t ee r equa t ion i s r epo r t ed in Tab le D .2 . T h i s t a b l e i l l u s t r a t e s tha t p r e d i c t e d p r i c e s f o l l ow a c t u a l p r i c e s and are dampened w i t h i n one p e r i o d . T h i s i s i m p l i e d by the l a rge e s t ima ted c o e f f i c i e n t s in the f i r s t year as compared to o the r coef f i c i e n t s . The p r i c e s p r e d i c t e d fo r each an imal ca tegory were t rans formed i n t o expected ga in v a r i a b l e s as d e s c r i b e d in Chapter Four . These expected ga in v a r i a b l e s were combined wi th the main data base to a l low econometr ic e s t i m a t i o n of the mode l . The Cobb-Douglas f u n c t i o n a l form was p o s t u l a t e d as an i n i t i a l s p e c i f i c a t i o n of the m u l t i - o u t p u t , m u l t i - i n p u t v a r i a b l e p r o f i t f u n c t i o n model . T h i s f u n c t i o n a l form fo r the t h r ee-ou tpu t , t h r e e - i n p u t , o n e - f i x e d - f a c t o r case can be w r i t t e n a s : ( D ' 2 ) n = a P a l P 6 " 2 P a 3 P a 4 P a 5 P a 6 Ab^ n 6 1 n 6 2 n 6 3 Jl Fl 2 3 4 5 6  Dx D 2 D 3 , where a l l v a r i a b l e s are as p r e v i o u s l y d e f i n e d (Table 4.3) except that i s genera ted us i ng an Almon l ag e x p e c t a t i o n p r o c e s s . It i s i n t e r e s t i n g to note that fo r input p r i c e s , the 234 TABLE D.1 Es t imated P r i c e P r e d i c t i o n Equa t ions us ing a Po lynomia l D i s t r i b u t e d Lag Time Pe r i od S teer Ca l ves Cows H e i f e r s t .988 1 .09 1 .05 .941 (. 164)* ( . 173) ( . 163) (.167) t-1 -.174 -.327 -.173 -.124 (.181) ( .206) ( . 180) ( .184) t-2 -.207 -.192 - .196 -.192 (.081 ) ( .084) (.091) (.091) t-3 .242 .386 .229 .224 (.191) ( .228) ( .190) ( .200) t-4 .530 .298 .346 .610 ( .250) ( .256) (.240) ( .280) Sum Of Lagged C o e f f i c i e n t s 1.38 1.26 1.26 1.46 r 2 .9108 .8766 . .8656 .8926 Degree of Po l ynomia l 3 3 3 3 Durbin-Watson 1.98 1.86 2.04 2.09 * s tandard e r r o r in paren theses TABLE D.2 Example of P r e d i c t e d P r i c e s , S teer Equat ion Year Observed P r e d i c t e d C a l c u l a t e d Va lue Va lue E r r o r 1960 22.62 18.50 4.110 1 961 20.16 20.82 -0.662 1962 20.75 17.11 3.638 1963 23.45 19.62 3.833 1964 22.65 25.74 -.3090 1965 20.40 24.49 -4.098 1966 21 .40 20.69 0.707 1967 24.70 23.21 1 .494 1968 26.40 27.99 -1.598 1969 26.75 27.93 -1.177 1970 31 .50 26.34 5. 1 56 1971 33.20 31 .96 1 .242 1972 33.55 34.90 -1.354 1973 38.60 34.96 3.642 1974 48.98 40.88 8. 104 1975 42.03 53. 12 -11.088 1976 34.25 44.39 -10.137 1977 35.44 37. 17 -1.728 1978 38.77 46.33 -7.564 1979 65.35 54.85 10.503 1980 91 .08 74.72 16.360 1981 79. 10 91.01 -11.910 1982 74.66 70.63 4.029 1983 73.26 71 .22 2.039 236 c o n v e x i t y c o n d i t i o n s are s a t i s f i e d in Equa t ion (D.2) i f the mono ton i c i t y c o n d i t i o n s are s a t i s f i e d . M o n o t o n i c i t y r e q u i r e s tha t &j < 0, j = 4 , 5 , 6 , and t h i s r e s t r i c t i o n a l s o ensures that c o n v e x i t y i s s a t i s f i e d . T h i s can be demonstrated by examining the second order d e r i v a t i v e s of Equat ion (D.2) w i th respec t to input p r i c e s : n_ „ = -a. (a.-l)P.II j = 4,5,6. Convex i t y r e q u i r e s n = = > 0 fo r a l l j . T h i s c o n d i t i o n i s j i s a t i s f i e d i f fi.. < 0 fo r a l l j . For output p r i c e s however, the s a t i s f a c t i o n of the mono ton i c i t y c o n d i t i o n s ( i . e . , > 0, i=1 ,2 ,3 ) i s not s u f f i c i e n t to ensure tha t convex i t y i s s a t i s f i e d . T h i s can be demonstrated by examining the second order d e r i v a t i v e of Equa t ion (D.2) wi th r e spec t to output p r i c e s : np ± P ± - a ± ( 0 ^ - 1 ) ^ 1 1 i = 1,2,3. A g a i n , convex i t y r e q u i r e s tha t n_ _ > o but t h i s c o n d i t i o n i s s a t i s f i e d on ly i f fii > 1, fo r a l l i . Consequen t l y , the s a t i s f a c t i o n of the mono ton i c i t y c o n d i t i o n s are necessary but not s u f f i c i e n t to ensure convex i t y in output p r i c e s . Keeping in mind tha t the ' s are d e f i n e d as the share of revenue from output i i n t o t a l p r o f i t , t h i s r e s t r i c t i o n i n d i c a t e s tha t in order to s a t i s f y c o n v e x i t y in output p r i c e s , the revenue r e c e i v e d fo r each output i must be g r ea t e r than the t o t a l p r o f i t r e c e i v e d by the farm. Casua l o b s e r v a t i o n of the sample data used in t h i s study r e v e a l s that the c o n v e x i t y c o n d i t i o n s would not be s a t i s f i e d f o r the mu l t i -ou tpu t Cobb-Douglas p r o f i t f u n c t i o n . Fu r the rmore , r e g r e s s i o n r e s u l t s f o r Equa t ion (D.2) supported 237 t h i s c o n c l u s i o n . To c i rcumvent t h i s prob lem, i t was dec i ded to ma in ta in a Cobb-Douglas s p e c i f i c a t i o n on the input s i de but to generate an aggregate output p r i c e index us ing a t r a n s l o g f u n c t i o n a l form (Fuss 1977). The t r a n s l o g f u n c t i o n does not r e q u i r e r e s t r i c t i o n s on the revenue shares in order to s a t i s f y c o n v e x i t y . The t r a n s l o g p r i c e index can be w r i t t e n a s : (D.3) 3 3 3 lnP T = InB + 2 B InP + JjE Z B . InP InP , I o ± = 1 i i ± = l k = 1 i j i j where P j i s the aggregate p r i c e index and a l l o ther v a r i a b l e s are as p r e v i o u s l y d e f i n e d . App l y i ng H o t e l l i n g ' s Lemma to Equa t ion (D .3 ) , the revenue share equa t i ons can be d e f i n e d a s : ( D . 4 ) . S i = B i + E B i k l n V + e i i = X ' 2 ' 3 ' k=l where i s output i ' s revenue share in t o t a l revenue and e A i s a random e r r o r term. Econometr ic e s t i m a t i o n of Equa t ion ( D . 4 ) w i l l generate e s t ima tes of a l l c o e f f i c i e n t s in Equat ion (D.3) except the i n t e r c e p t te rm, InBo. Consequen t l y , the aggregate p r i c e index (InPj.) i s d e f i n e d on l y up to a cons tan t s c a l i n g f a c t o r . Dummy v a r i a b l e s are added to the i n t e r c e p t term in Equa t ion ( D . 4 ) to account fo r the c r o s s - s e c t i o n a l , t ime-s e r i e s da ta used in e s t i m a t i n g the share e q u a t i o n s . Fu r the rmore , p r i o r to e s t i m a t i o n , symmetry and the adding-up c o n s t r a i n t s are imposed on the model . E s t ima tes of the parameters of the th ree revenue share equa t ions d e r i v e d us ing Z e l l n e r ' s (SUR) r e g r e s s i o n procedure are r epo r t ed in Tab le D .3 . F i v e i t e r a t i o n s were r e q u i r e d fo r convergence . Own output p r i c e c o e f f i c i e n t s are p o s i t i v e and s t a t i s t i c a l l y s i g n i f i c a n t at the 5 percent l e v e l which i s a necessary c o n d i t i o n fo r c o n v e x i t y . Fur thermore , a l l remain ing p r i c e c o e f f i c i e n t s are s t a t i s t i c a l l y s i g n i f i c a n t at the 5 percent l e v e l . Convex i t y c o n d i t i o n s are checked by computing the e i genva lues of the Hess ian mat r ix of the p r i c e index f u n c t i o n . These va lues were determined at the means of the endogeneous v a r i a b l e s and e q u a l l e d .332, .102 , and .001 . T h e r e f o r e , the Hess ian mat r ix of the p r i c e index f u n c t i o n i s convex. Measures of output s u b s t i t u t i o n , h o l d i n g t o t a l output c o n s t a n t , can be genera ted us i ng the es t imated c o e f f i c i e n t s in Tab le D .3 . In Tab le D.4 the output supply and c ro s s p r i c e e l a s t i c i t i e s are p r e s e n t e d . T h i s t ab l e i n d i c a t e s tha t own output supply e l a s t i c i t i e s are p o s i t i v e and i n e l a s t i c . In a d d i t i o n , the e s t ima ted c r o s s p r i c e e l a s t i c i t i e s suggest a s u b s t i t u t e r e l a t i o n s h i p between output p a i r s . Us ing the es t imated c o e f f i c i e n t s in Tab le D .3 , an aggregate p r i c e index can now be generated through Equa t ion (D .3 ) . T h i s index can be used to r ewr i t e Equa t ion (D.2) as a s i n g l e output no rma l i zed Cobb-Douglas p r o f i t f u n c t i o n : II - a if if if A"5 „Ji „ « „ «3 , where p r i c e and p r o f i t v a r i a b l e s are norma l i zed by Pj . A p p l y i n g H o t e l l i n g ' s lemma to Equat ion (D .5 ) , the d e r i v e d input demand equa t ions can be d e f i n e d a s : , TABLE D.3 Regress ion R e s u l t s : T r a n s l o g P r i c e Index Share P r i c e s Dummy V a r i a b l e s C a t t l e Inven. * Crops C o n s t . 1981 1980 1979 R 2 C a t t l e .421 -.230 -.191 .595 .056 .0001 --.056 .513 (5 .4 ) * * (6.5) (3.3) (6.4) (3.6) ( .006) (3.3) Inven. -.23 .325 -.095 .652 • -.037 .014 .023 .556 (6.5) (6.6) (2.2) (10. ) (1.9) (.81) (1.0) Crops -.191 -.095 .286 • -.247 -.019 -.014 .033 I n v e n t o r i e s t - s t a t i s t i c s in parentheses TABLE D.4 Output Supply and C ross P r i c e E l a s t i c i t i e s Ho ld i ng T o t a l Output Constant , Mean of the Exogeneous V a r i a b l e s , 1981 Quan t i t y C a t t l e I n v e n t o r i e s Crops P r i c e s C a t t l e I n v e n t o r l e s ,623 , 1 27 ,827 - .200 .147 -.062 Crops -.424 -.020 .889 (D.6) x = -<*.,n/j? j = 4,5,6, where X i s the jt-h input q u a n t i t y , j E f f i c i e n t parameter e s t ima tes of Equa t ion (D.5) can be genera ted by s imu l t aneous l y e s t i m a t i n g Equa t ion (D.5) and (D.6) w i th symmetry r e s t r i c t i o n s imposed. These es t imated parameters are d e r i v e d us ing Z e l l n e r ' s (SUR) r e g r e s s i o n p rocedure and are e x h i b i t e d in Tab le D .5 . Own input p r i c e c o e f f i c i e n t s are nega t i ve and s t a t i s t i c a l l y s i g n i f i c a n t at the 5 pe rcen t l e v e l , i n d i c a t i n g that mono ton i c i t y and convex i t y are s a t i s f i e d . These es t imated c o e f f i c i e n t s can be used to compute measures of own p r i c e e l a s t i c i t i e s , c r o s s p r i c e e l a s t i c i t i e s , and e l a s t i c i t i e s w i th respec t to the f i x e d f a c t o r . These va lues are r epo r t ed in Tab le D .6 . With r espec t to own p r i c e s , , aggregate output supp ly e l a s t i c i t y i s p o s i t i v e and i n e l a s t i c whereas input demand e l a s t i c i t i e s are nega t i ve and e l a s t i c . The c r o s s e l a s t i c i t y measurements i n d i c a t e a complementary r e l a t i o n s h i p between a l l input p a i r s . T h i s r e s u l t i s imposed by the Cobb-Douglas f u n c t i o n a l form. To complete the p r e s e n t a t i o n of the Cobb-Douglas r e s u l t s , own p r i c e and c r o s s p r i c e e l a s t i c i t i e s fo r the output component are r e p o r t e d in Tab le D .7 . These e l a s t i c i t i e s now account f o r the a d d i t i o n a l e f f e c t of changes in aggregate output on the supply of i n d i v i d u a l o u t p u t s . These r e s u l t s i n d i c a t e tha t output supp ly e l a s t i c i t i e s a re p o s i t i v e but l a r g e r in magnitude than the co r r e spond ing " o u t p u t - c o n s t a n t " e l a s t i c i t i e s r epo r t ed in Tab le D.4. In 241 TABLE D.5 J o i n t E s t i m a t i o n : Norma l ized Cobb-Douglas P r o f i t Func t i on and Net Input Demand Equa t ions V a r i a b l e Parameter P r o f i t Func t i on Es t imated C o e f f i c i e n t s Constant Labour C a p i t a l M a t e r i a l s Begin ing I n ven to r i e s 1981 = 1 1980 = 1 1979 = 1 Net Input Equa t i ons Labour C a p i t a l Mater i a l s l na a. 1 a 2 a 3 a 2 a 3 2.46 (7.4) - .059 (16.8) - .055 (16.8) -.114 (12.6) 1 .06 (39.28) .237 (3.9) . 151 (2.6) -.041 (.686) - .059 (13.3) -.055 (16.8) -.114 (12.6) TABLE D.6 Own Price E l a s t i t i c i e s , Cross Price E las t i t i ces , and E l a s t i t i c i e s With Respect To the Fixed Factor: Cobb-Douglas Profit Function Quantity Price Aggregate Beginning Output Labour Capital Materials Inventories Aggregate Output .228 -.059 -.055 - . 1 1 4 1 .02 Labour 1 .228 -1.059 -.055 - . 1 1 4 1 .02 Capi tal 1 .228 -.059 -1 .055 - . 1 1 4 1 .02 Mater ials 1 .228 -.059 -.055 - 1 . 1 1 4 1 .02 TABLE D.7 Total Supply E l a s t i c i t i e s : Output Component Output Prices Cattle Inventories Crops C a t t l e —^97 ^7084 -.386 Inventories -.049 .263 .018 Crops -.753 .054 .927 243 a d d i t i o n , a c coun t i ng fo r changes in aggregate output has a l t e r e d the apparent r e l a t i o n s h i p between i n v e n t o r i e s and c rops from s u b s t i t u t e s to complements. The r e s u l t s ob ta ined us ing a Cobb-Douglas s p e c i f i c a t i o n were s a t i s f a c t o r y . However, because of the r e s t r i c t i o n s imposed a p r i o r i by t h i s f u n c t i o n a l form, i t i s i n f e r i o r to models which a l low g rea t e r f l e x i b i l i t y of s t r u c t u r e . To ache i ve t h i s f l e x i b i l i t y , a t r a n s l o g f u n c t i o n a l form i s s p e c i f i e d to r ep resen t the m u l t i - o u t p u t , m u l t i - i n p u t v a r i a b l e p r o f i t f u n c t i o n model . The procedure fo l l owed in e s t i m a t i n g t h i s model i s i d e n t i c a l to that d e s c r i b e d in Chapter Fou r . The es t ima ted parameters are r epo r t ed in Tab le D.8. These c o e f f i c i e n t s are q u i t e s i m i l a r to those r epo r t ed in Chapter F i v e which are based on the assumpt ion of ARIMA p r i c e e x p e c t a t i o n s . It i s worth no t i ng however, that the c o e f f i c i e n t s r epo r t ed in Tab le D.8 g e n e r a l l y have lower t-s t a t i s t i c s than the co r r e spond ing es t ima tes in Chapter F i v e . F i n a l l y , own p r i c e and c r o s s p r i c e e l a s t i c i t i e s fo r cow-c a l f p r o d u c t i o n , which are computed sub jec t to the Almon l a g e x p e c t a t i o n p r o c e s s , a re p resen ted in Tab le D . 9 . A g a i n , these e s t ima tes are g e n e r a l l y q u i t e s i m i l a r to those r epo r t ed in Tab le 5.6 in Chapter F i v e . Table D.8 Estimated Parameters, Translog Profit Function; Almon Lag Price Expectations Share Prices Dummy Variables Cattle Inventories Crops Labour Capital Materials Stock Constant 1981 1980 1979 R2 Cattle .849 -.246 -.328 -.074 .077 -.279 .037 .761 .144 .002 -.145 .6947 (8.2)* (7.7) (5.2) (4.3) (4.9) (5.9) (5.3) (6.1) (6.9) (.19) (6.9) Inventories -.246 .299 -.105 .012 -.011 .051 -.036 1.09 -.046 .016 .031 .6395 (7.7) (7.0) (2.3) (2.3) (2.1) (4.3) (3.4) (8.1) (2.7) (1.0) (1.4) Crops -.328 -.105 .320 .013 -.038 .139 .01 -.578 -.046 -.009 .055 .4554 (5.2) (2.3) (4.8) (1.3) (3.8) (5.9) (.88) (3.7) (2.1) (.56) (2.1) Labour -.074 .012 .013 .021 -.007 .035 -.002 -.092 -.018 .002 .02 .6081 (4.3) (2.3) (1.3) (2.6) (1.4) (2.1) (1.7) (3.7) (4.7) (1.4) (5.8) Capital .077 -.011 -.038 -.007 -.017 -.003 .002 .054 .016 -.003 -.012 .5174 (4.9) (2.1) (3.8) (1.4) (2.9) (.29) (1.5) (2.5) (4.5) (2.4) (3.8) Materials -.279 .051 .139 .035 -.003 .057 -.011 -.235 -.05 -.004 .051 * t-statistics in parentheses 245 TABLE D.9 P r i c e E l a s t i t i c e s , C ross P r i c e E l a s t i t i c e s T r a n s l o g P r o f i t F u n c t i o n , Mean of Exogeneous V a r i a b l e s 1981, Almon P r i c e E x p e c t a t i o n s Quan t i t y P r i c e s C a t t l e I n v e n t o r i e s Crops Labour C a p i t a l M a t e r i a l s C a t t l e 1 , .380 - .028 -.604 -.211 .154 -.710 I n v e n t o r i e s i .023 .094 - .046 -.022 -.041 .015 Crops -1 , .760 - .167 1 .290 .044 -.274 .851 Labour 2, .160 .280 - . 1 52 -1.530 . 143 -.893 C a p i t a l -3, .220 1 .080 1 .960 .291 -.211 .068 M a t e r i a l s 4. .110 -.111 -1 .680 - .509 .019 -1 .830 246 E. E s t ima ted Parameters : ARIMA Models The es t ima ted c o e f f i c i e n t s fo r the ARIMA(2,1,0) model for each an imal ca tegory in each market l o c a t i o n ( i . e . , Edmonton, Reg ina , Saska toon , and Winnipeg) are r epo r t ed in t h i s append ix . The ARIMA(2,1,0) s p e c i f i c a t i o n can be w r i t t e n a s : AP. . = ch.AP. + cp-.AP. + e. j = 1 , . . . , * » , i j t Ij ijt-1 2j ijt-2 i j t where A i n d i c a t e s f i r s t d i f f e r e n c e s , P = i s the p r i c e s e r i e s of the i t h an imal ca tegory in ' j the j t h market l o c a t i o n , $ •+$ < 1 , j = 1 . . . 4 , i s a necessary c o n d i t i o n fo r 1J 2j s t a t i o n a r i t y , and e j j i s a random e r r o r term. The es t ima ted c o e f f i c i e n t s for each ARIMA(2,1,0) model a re r epo r t ed in Tab le E . 1 . Except f o r the parameters in the h e i f e r equa t ion fo r Reg ina , a l l e s t imated c o e f f i c i e n t s are s t a t i s t i c a l l y s i g n i f i c a n t at e i t h e r the 10 percent or 5 pe rcen t l e v e l of s i g n i f i c a n c e . Moreso, a t the 95 percent c o n f i d e n c e l e v e l the necessary c o n d i t i o n fo r s t a t i o n a r i t y $ i + $ 2 < 1 i s s a t i s f i e d in each es t ima ted e q u a t i o n . If the ARIMA models are c o r r e c t l y s p e c i f i e d , the r e s i d u a l s shou ld have independent and i d e n t i c a l normal d i s t r i b u t i o n s . T h i s c o n d i t i o n can be e va lua t ed by examining the p l o t s of the a u t o c o r r e l a t i o n f u n c t i o n of the r e s i d u a l s fo r each equa t i on and check ing the s t a t i s t i c a l s i g n i f i c a n c e of each o b s e r v a t i o n . Tab le E.2 reproduces the a u t o c o r r e l a t i o n 247 function for each equation along with 95 percent confidence intervals for each observation, which are denoted by the symbol on both sides of the vert ical axis. The large confidence intervals indicate that each observation is s t a t i s t i c a l l y insignificantly different from zero. TABLE E.l Estimated Parameters: ARIMA(2,1,0) Market Locat ion Edmonton Regina Saskatoon Winnipeg Animal Est imated Coef f i c i e n t s Category »i S t ee r s .4027** - .3856** .0171 S . E . (.165) ( . 1632) ( .232) Ca l ves .4333** - .5040** -.0707 S . E . ( . 1602) ( . 1631 ) ( .228) Cows .3747** - .3814** -.0066 S . E . (.1661) ( .1659) (.235) Hei f e r s .2731* - .2856* -.0125 S . E . (.1734) ( .1727) ( .245) S t ee r s .2508* - .2865* -.0357 S . E . (.172) (.170) ( .242) Ca l ves .4972** - . 5361* * - .0389 S . E . (.1615) (.1698) ( .234) Cows .2955** - .3272** -.0317 S . E . ( .1702) (.1689) ( .239) Hei f e r s . 1 565 -.2181 -.0616 S . E . (.177) (.175) ( .249) S t ee r s .3313** - .3289** .0024 S . E . (.1691 ) (.1668) ( .238) Ca l ves .4757** - .5400* * -.0643 S . E . ( .1579) ( .1628) ( .227) Cows .3146** - .3450** -.0304 S . E . (.170) (.1693) ( .239) Hei f e r s .2823* - .2753* .007 S . E . (.1744) ( .1730) ( .224) S t ee r s .3680** - . 3553* * .0127 S . E . (.1677) (.1665) ( .236) Ca l v e s .2402* - .3787** -.1385 S . E . (.170) (.1738) ( .243) Cows .3282** - .3608** -.0326 S . E . (.1684) (.1681) ( .238) Hei f e r s .3508** - .3206** .0302 S . E . (. 1714) (.1706) ( .242) * s i g n i f i c a n t at the * * s i g n i f i c a n t at the 10 percent l e v e l of s i g n i f i c a n c e 5 percent l e v e l of s i g n i f i c a n c e TABLE E.2 249 Plots of the /Autocorrelation Function of the Residuals Edmonton Market S t ee r s Ca l ves PLOT OF AUTOCORRELATIONS PLOT OF AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 -1.0 -0.6 -0.6 -0.4 -0 2 0.0 0.2 0. LAO LAO t -0.0T2 • I XXI • 1 -0.032 4 I XI * 2 -0.126 • xxxi • 2 -0.153 4 XXXXI 4 3 0.0S3 IX • 3 0.044 4 IX 4 4 -0.223 XXXXXXI • 4 -0.157 4 XXXXI * 3 -0.003 I • 5 -0.114 • XXXI * 6 0. 180 4 ixxxx 6 0. 136 4 IXXX 7 -0.036 4 XI 7 0.060 4 • IX 4 6 0.052 • IX 4 8 -0.029 4 XI 9 0.007 I • 9 0.028 4 IX • 10 0.020 I • 10 0. 1 14 • IXXX • 11 0.009 I • 11 -0.033 4 XI 4 12 O.OSI IX fr 12 0.053 4 IX 4 13 -0.048 4 XI 4 13 0.001 4 1 4 14 -0.020 * XI • 14 -0.073 4 XXI 4 IS -0.038 * XI • IS -0.016 4 1 fr 16 -0.019 * i 4 16 -0.006 4 I 4 17 -0.034 • XI • 17 -0.108 4 XXXI 4 18 -0.003 • I • 18 0.085 4 IXX 4 19 -0.074 • XXI • 19 -0.089 4 XXI 4 20 0.063 • IXX 4 20 0.019 4 I 21 0.011 * I . • 21 0.073 4 IXX 22 0.001 * I 4 22 0.047 4 IX 23 0.033 • IX 4 23 •0.O99 • XXI 24 -0.104 * xxxi • 24 -0.091 4 XXI 23 -0.133 * XXXI 4 23 0.032 4 IX 26 -0.047 * XI 4 26 -0.137 4 XXXI 27 -0. 126 4 XXXI 4 27 -0.099 4 XXI 28 0.215 * IXXXXX • 28 0. 192 4 IXXXXX 29 -0.026 • XI 4 29 -0.103 4 XXXI 30 •0.063 XXI 4 30 -0.026 4 XI Cows PLOT OF AUTOCORRELATIONS -1.0 -0.8 -0.6 -0 . 4 - 0.2 0.0 0.2 0.' LAG 1 -0. 040 • I XI 4 2 -0. 144 • XXXXI • 3 0. 039 IX • 4 -0. 201 4 XXXXXI 4 9 -0. 141 4 XXXXI 4 6 0. 202 4 ixxxxx 4 7 0. 038 4 IX * 8 -0. O i l • I 4 9 -0. 008 • I 4 10 0. 092 4 ixx • 11 -0. 058 4 XI 4 12 0. 097 4 IXX 4 13 -0. 008 4 I 4 14 -0 129 4 XXXI 4 IS 0. 058 4 IX 4 16 -0. 051 • XI • IT -o 094 • XXI * 18 0 081 • IXX 4 19 -0 054 4 XI 4 20 0 032 4 IX 4 21 -0 003 • I 4 22 0 147 4 ixxxx 4 23 -0 103 4 XXXI 4 34 -0 130 4 XXXI 4 35 -0 035 4 XI • 26 -0 148 • XXXXI • 27 -0 086 4 XXI 4 28 0 222 4 IXXXXXX 4 29 -0 029 4 XI 30 -0 026 4 XI Hei f e r s PLOT OF AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 -0 2 0.0 0.2 0 LAG 1 -0.069 4 XXI 4 2 -0.086 • XXI 4 3 -0.056 4 XI • 4 -0.179 4 XXXXI 4 5 -0.07 1 4 XXI 4 6 0. 182 4 IXXXXX 4 7 -0.023 4 XI fr a 0.030 4 IX 4 9 0.021 4 IX • 10 0.029 4 IX fr 11 -0.002 • 1 fr 12 0.054 4 IX fr 13 -0.023 4 XI • 14 -0.077 4 XXI fr IS -0.021 4 XI • 16 -0.013 4 1 fr 17 -O.TJIJ 4 I fr 18 -0.030 4 XI fr 19 -0.036 4 XI 4 20 0.054 4 IX • 2 1 0.012 4 I fr 22 0.035 4 IX • 23 -0.035 • XI fr 34 -0.091 4 XXI • 23 -0.076 XXI fr 26 -0.079 4 XXI • 27 -0.086 • XXI fr 28 0.236 4 IXXXXXX • 29 -0.031 4 XI 30 -0.021 4 XI TABLE E.2 (cont.) Plots of the Autocorrelation Function of the Residuals Saskatoon Market Steers Calves PLOT OF AUTOCORRELATIONS PLOT OF AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 -1.0 -0.8 -0.6 -0.4 • 0.2 0.0 0.2 0.4 LAC LAG 1 -0.033 • I XI • 1 -0.033 4 I XI • 3 -0.140 4 XXXXI 4 2 -0. 190 4 XXXXXI • 3 0.083 4 IXX 4 3 0. 123 4 IXXX • 4 -0.268 • XXXXXXXI 4 4 -0.206 4 XXXXXI S 0.021 4 IX . 5 -0.O63 4 XXI • 6 0. 176 • 1XXXX 4 6 0. 1 16 4 IXXX * 7 -0.034 4 XI 4 7 0.076 4 IXX • S 0.073 • IXX 4 8 -0.073 4 XXI • 9 -O.OIS 4 I * 9 0.063 4 I XX • 10 0.016 4 I • 10 0.063 4 I XX • 11 0.005 4 I • 11 -0.032 4 XI 12 0.043 • IX 4 12 0.033 , • IX • 13 -0.035 4 XI 4 13 0.011 4 I • 14 -0.034 XI 4 14 -0.068 4 XXI • 13 -0.031 * XI 4 13 -0.027 4 XI • 16 -0.031 XI 4 16 0.006 4 I • 17 -0.007 4 I 4 17 -0.092 4 xxt • 18 -0.043 • XI 4 18 0.053 4 IX • 19 -0.035 4 XI 4 19 -0.031 4 xt • 20 O.OSO • IX 4 20 0.023 • IX • 21 -0.021 4 XI 4 21 0.044 4 IX * 22 0.026 4 IX . 22 0.022 4 IX 23 0.036 • IX 4 23 -0.069 4 xxt • 24 -0.142 4 XXXXI 4 24 -0.131 4 XXXXI • 33 -0.038 4 XI 4 25 0.092 4 I XX • 26 -0.119 4 XXXI 4 26 -0.173 4 XXXXI • 27 •0.094 4 XXI 4 27 -0.086 4 XXI 28 0. 183 4 IXXXXX 4 28 0. 148 4 IXXXX 39 0.002 4 1 4 29 -0.043 4 XI SO •0.068 4 XXI 4 30 -0.027 4 XI • Cows PLOT OF AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 LAO CORR. 4- 4 4 4 4 4 -4 I 1 -O.OSO 4 XI 4 2 -0.131 4 XXXI 4 3 0.027 4 IX • 4 -0.240 • XXXXXXI • 3 -0.091 4 XXI 6 0. 191 4 IXXXXX 4 7 0.033 4 IX 4 a 0.002 4 I 4 9 0.001 4 I 4 to 0.034 4 IX 4 11 0.006 4 I 4 12 0.034 4 IX 4 13 -0.003 4 I 4 14 -0.103 4 XXXI 4 IS 0.055 4 IX 4 16 -0.039 4 XI 4 17 -0.065 4 XXI 4 18 0.017 4 I 4 19 -0.022 4 XI 4 20 0.037 4 IX 4 21 -0.038 4 XI 4 22 0. ISO 4 ixxxxx 4 23 -0.078 4 XXI 4 24 -0.133 • XXXI 4 23 •0.038 4 XI 4 26 -0.160 4 XXXXI 4 27 -0.065 4 XXI 4 28 O. 188 . IXXXXX 4 29 -0.034 4 XI 4 30 0.008 4 I 4 Hei fers PLOT OF AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 • -0.2 0.0 0.2 0. LAO 1 -0.042 4 I XI 4 2 -0.116 4 XXXI 4 3 0.046 4 IX • 4 -0.263. •XXXXXXXI 4 3 -0.O49 4 XI 4 6 0. 161 . 4 IXXXX • 7 -0.021 4 XI * 8 0.058 4 IX 4 9 -0.016 4 1 4 10 0.040 4 IX 4 11 -0.009 4 I 4 12 0.047 4 IX 4 13 -0.011 4 I 4 14 -0.075 4 XXI 4 15 -0.025 4 XI 4 16 0.022 4 IX 4 17 -0.063 4 XXI 4 18 0.008 • I 4 19 0.012 4 1 4 20 -0.014 4 1 4 21 0.028 4 IX 4 22 0.052 4 IX • 23 -o.oao 4 xxt • 24 -0.089 4 XXI 4 25 -0.035 4 XI 4 26 -0.147 4 XXXXI * 27 -O.0S7 4 XI 28 0. 193 • IXXXXX 29 -0.022 4 XI 30 -0.013 4 1 251 TABLE E.2 (cont.) Plots of the Autocorrelation Function of the Residuals Regina Market Steers Calves PLOT OF AUTOCORRELATIONS PLOT OF AUTOCORRELATIONS -1.0 .-0.8 -0.6 -0.4 -0. 3 0.0 0.3 0.4 -1.0 -0.8 -0.6 -0.4 LAO LAO 1 -0.057 • 1 XI • 1 -0.083 2 -0. 113 * XXXI • 2 -0.066 • 3 0.031 • IX • 3 -0.031 • 4 -0.276 •XXXXXXXI • 4 -0.117 9 0.072 • IXX • 5 -0.001 • 6 0. 124 • IXXX • 6 0.053 • 7 0.007 • I • 7 0. 108 * 6 0.055 • IX • 8 -0.088 • 9 -0.009 • I • 9 0.062 4 10 0.006 • 1 4 10 0.035 4 11 -0.020 • XI • 1 1 0.018 * 12 0.054 IX • 12 0.000 4 13 -0.036 XI • 13 0.010 14 -0.036 • XI • 14 -0.061 IS -0.033 • XI • 15 -0.021 • 16 -0.013 I • 16 -0.015 • 17 -0.030 • XI • 17 -0.065 • 18 -0.032 • XI • 18 0.047 19 -0.035 • XI 4 19 -0.068 * 20 0.044 • IX • 20 0.049 4 21 -0.005 I • 21 0.012 • 22 0.013 • I 4 22 0.022 • 23 0.051 • IX • 23 -0.042 • 24 -0. 138 • xxxi 24 -0.170 • 2S •0.063 XXI 25 0. 101 • 26 -0.101 4 XXXI • 26 -0.227 27 -0. 11S 4 XXXI • 27 -0.025 28 0.305 • IXXXXX • 28 0.071 • 29 -0.013 4 I 39 0.017 • 30 •0.054 4 XI 30 -0.043 -0.2 0.0 0.3 0.4 I XXI XXI XI XXXI I IX IXXX xxt IXX IX I I I xxt XI I XXI IX XXI IX I IX XI XXXXI IXXX XXXXXXI XI IXX I XI Cows PLOT OF AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 -0.3 0.0 0.2 0.4 LAG CORR. • • • • • » 1 -0.056 4 1 XI 4 2 -0.098 4 XXI 4 3 -0.020 • XI • 4 -0.219 4 XXXXXI 4 5 -0.055 4 XI 4 6 0. 108 4 IXXX 4 7 0.061 4 IXX 4 6 0.010 4 1 4 9 -0.022 4 XI 4 10 0.058 4 IX 4 11 0.007 4 I 4 12 0.050 4 IX 4 13 0.013 4 I 4 14 -0.139 4 XXXI 4 IS 0.036 4 IX 4 16 -0.027 4 XI 4 17 -0.076 4 XXI 4 18 0.040 4 IX 4 19 -0.039 4 XI 4 30 0.056 4> IX 4 21 •0.024 4 XI • 32 0. 116 4 IXXX 4 23 -0.005 4 I 4 24 -0.184 4 XXXXXI 4 35 -0.031 4 XI 4 26 -0.128 4 XXXI 4 27 -0.133 4 XXXI 4 28 0.255 4 IXXXXXX 4 29 -0.034 4 XI 4 30 0.005 4 I 4 Heifers PLOT OF AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 -0. 2 0.0 0.3 0 .4 LAG 1 -0.044 4 I XI 4 2 -0. 103 4 XXXI 4 3 0.000 4 I • 4 •0.394 •XXXXXXXI 4 3 -0.011 4 1 6 0. 141 • IXXXX 7 0.004 4 1 8 0.047 4 IX 9 -0.036 4 XI to 0.062 4 IXX 11 -0.010 4 I 13 0.036 4 IX 13 -0.014 4 I 14 -0.051 • XI 15 -0.022 4 XI 16 -0.027 4 XI 17 -0.029 4 XI 18 -0.018 4 1 19 -0.028 4 XI 20 0.069 * IXX 21 0.014 4 1 22 0.042 4 IX 23 0.002 4 1 24 -0.137 4 XXXI 25 -0.044 4 X! 4 26 •0.086 4 XXI 4 27 -0.093 4 XXI 4 28 0. 187 4 IXXXXX 4 29 -0.009 4 I • 30 -0.044 4 XI 4 TABLE E.2 (cont.) 252 Plots of the /Autocorrelation Function of the Residuals Winnipeg Market Steers Calves PLOT OF AUTOCORRELATIONS PLOT OF AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 LAG LAG 1 -0.050 • I XI * 1 -0.034 • 1 XI • 2 -0.151 4 XXXXI • 2 -0.114 4 XXXI 3 0.082 4 IXX • 3 -0.047 4 XI • 4 -0.220 4 XXXXXXI 4 -0.171 4 XXXXI 4 S -0.070 4 XXI 5 -0.144 4 XXXXI 4 6 0.216 4 IXXXXX 4 6 0. 137 4 IXXX 4 7 -0.013 4 I 4 7 0.031 4 IX 4 8 0.045 • IX 4 a 0.029 4 IX 4 a -0.019 • I • 9 -0.032 4 XI 4 10 0.044 4 IX • 10 0.110 4 IXXX * 11 0.017 4 I 4 11 0.005 4 1 4 12 0.030 4 IX 4 12 0.021 4 IX * 13 -0.022 4 XI 4 13 0.013 4 1 4 14 -0.032 • XI 4 14 -0.058 4 XI 4 15 -0.023 4 XI 4 IS -0.032 • XI 4 16 -0.035 4 XI 4 16 -0.040 4 XI 4 17 -0.022 4 XI 4 17 -0.033 4 XI * 18 -0.023 4 XI 4 18 0.019 4 1 » 19 -0.031 4 XI 4 19 -0.053 4 XI 4 20 0.034 4 IX 4 20 0.011 4 1 • 21 -0.032 4 XI 4 21 0.099 4 IXX 4 22 0.083 • IXX 4 22 0.033 4 IX 4 23 -0.002 • 1 4 23 -0.019 4 1 4 24 -O. 140 * XXXI 4 24 -0.079 4 XXI • 25 -0.023 XI 4 29 -0.046 • XI • 26 -0.108 XXXI 4 26 -0.059 4 XI * 27 -0.136 * xxxi 4 27 -0. 170 4 XXXXI 4 28 0. 193 IXXXXX 4 28 0. 170 4 IXXXX 4 29 -0.019 • I . 4 29 -0.002 4 1 4 30 -0.061 • XXI 4 30 -0.035 4 XI 4 Cows PLOT OF AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 LAO fl 1 -0.036 4 1 XI 4 2 -0. 113 4 XXXI 4 3 -0.009 4 I 4 4 -0.163 4 XXXXI 4 3 -0. 113 4 XXXI 4 6 0. 165 4 IXXXX 4 7 0.056 4 IX • 8 -0.016 4 I 4 9 -0.011 4 I 4 10 0.068 • IXX 4 « 1 0.003 4 I 4 12 0.054 4 IX 4 13 0.004 4 I 4 14 -0.109 4 XXXI • 15 0.037 4 IX 4 16 -0.033 4 XI * 17 -0.093 • XXI 18 0.054 4 IX • 19 -0.059 4 XI 4 20 0.043 IX *. 21 -0.008 4 I 4 22 0. 146 4 IXXXX 4 23 -0.062 4 XXI 4 24 •0.126 4 XXXI 4 23 -0.053 4 XI 4 26 -0.139 4 xxxi 4 27 -0.107 4 XXXI 4 28 0.222 4 IXXXXXX 4 29 -0.039 4 XI 4 30 -0.009 4 I 4 Heifers PLOT OF AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0 LAG 1 -0.058 4 I XI • 2 -0.110 4 xxxi 4 3 0.007 4 I 4 4 -0.197 * XXXXXI 4 3 -O.095 4 XXI 4 6 0. 193 4 IXXXXX 4 7 -0.021 4 XI 4 8 0.066 4 IXX 4 9 -0.033 4 XI 4 10 0.040 ' 4 IX * 11 0.015 * I 12 0.034 4 IX 4 13 -0.025 4 XI * 14 -0.022 4 XI 4 13 -0.036 4 XI 4 16 -0.028 • XI 4 17 -0.031 + XI 4 18 -0.011 • I 4 19 -0.041 4 XI 4 20 0.061 4 IXX 4 21 0.021 4 IX 4 22 0.046 4 IX • 23 -0.033 • XI 24 -0.103 4 XXXI 4 25 -0.051 4 XI • 26 -0. 109 4 XXXI 4 27 -0.096 4 XXI 4 28 0.213 4 IXXXXX • 29 -0.036 4 XI 30 -0.020 4 XI F. P r i ce P r e d i c t i o n s : ARIMA Models Y e a r S o i l S t e e r Z o n e 1981 1 7 7 . 4 9 2 7 7 . 4 9 3 7 7 . 4 9 4 7 8 . 4 4 5 7 9 . 4 0 6 7 8 . 4 4 7 7 8 . 5 5 8 7 8 . 4 4 9 7 8 . 5 5 10 7 7 . 4 9 11 7 9 . 4 0 12 7 5 . 3 6 13 7 5 . 3 6 14 7 5 . 3 6 1980 1 6 4 . 3 5 2 6 4 . 3 5 3 6 4 . 3 5 4 6 7 . 3 5 5 6 6 . 4 6 6 6 7 . 3 5 7 6 6 . 2 4 8 6 7 . 3 5 9 6 6 . 2 4 10 6 4 . 3 5 11 6 6 . 4 6 12 6 5 . 8 8 13 6 5 . 8 8 14 6 5 . 8 8 1979 1 9 1 . 1 9 2 9 1 . 1 9 3 9 1 . 1 9 4 9 3 . 0 5 5 9 3 . 3 9 6 9 3 . 0 5 7 9 1 . 8 2 8 9 3 . 0 5 9 9 1 . 8 2 10 9 1 . 1 9 11 9 3 . 3 9 12 8 9 . 2 1 13 8 9 . 2 1 14 8 9 . 2 1 1978 1 7 4 . 7 7 2 7 4 . 7 7 3 7 4 . 7 7 4 7 5 . 8 9 5 7 0 . 0 4 6 7 5 . 8 9 7 7 0 . 9 1 8 7 5 . 8 9 9 7 0 . 9 1 10 7 4 . 7 7 11 7 0 . 0 4 12 6 7 . 7 3 13 6 7 . 7 3 14 6 7 . 7 3 C a l f H e i f e r Cow 7 6 . 3 1 71 . 5 0 4 6 . 5 6 7 6 . 3 1 71 . 5 0 4 6 . 5 6 7 6 . 3 1 7 1 . 5 0 4 6 . 5 6 7 4 . 2 0 7 5 . 2 6 4 9 . 7 7 7 0 . 2 1 7 3 . 2 6 4 6 . 5 3 7 4 . 2 0 7 5 . 2 6 4 9 . 7 7 7 5 . 12 7 3 . 0 4 4 8 . 9 8 7 4 . 2 0 7 5 . 2 6 4 9 . 7 7 7 5 . 12 7 3 . 0 4 4 8 . 9 8 7 6 . 3 1 71 . 5 0 4 6 . 5 6 7 0 . 2 1 7 3 . 2 6 4 6 . 5 3 7 6 . 3 6 6 9 . 5 3 4 8 . 5 5 7 6 . 3 6 6 9 . 5 3 4 8 . 5 5 7 6 . 3 6 6 9 . 5 3 4 8 . 5 5 6 7 . 7 2 5 9 . 8 3 4 3 . 0 6 6 7 . 7 2 5 9 . 8 3 4 3 . 0 6 6 7 . 7 2 5 9 . 8 3 4 3 . 0 6 71 . 3 9 6 2 . 8 0 4 3 . 14 7 4 . 3 1 6 2 . 13 4 2 . 4 0 71 . 3 9 6 2 . 8 0 4 3 . 1 4 6 8 . 3 4 61 . 5 5 4 5 . 0 6 71 . 3 9 6 2 . 8 0 4 3 . 14 6 8 . 3 4 6 1 . 5 5 4 5 . 0 6 6 7 . 7 2 5 9 . 8 3 4 3 . 0 6 7 4 . 3 1 6 2 . 1 3 4 2 . 4 0 6 8 . 1 1 5 8 . 7 6 4 4 . 3 5 6 8 . 1 1 5 8 . 7 6 4 4 . 3 5 6 8 . 1 1 5 8 . 7 6 4 4 . 3 5 1 0 6 . 3 1 9 0 . 17 5 6 . 19 1 0 6 . 3 1 9 0 . 17 5 6 . 19 1 0 6 . 3 1 9 0 . 17 5 6 . 19 9 9 . 8 1 9 0 . 7 5 5 8 . 8 0 9 6 . 9 7 8 7 . 6 2 5 4 . 6 2 9 9 . 8 1 9 0 . 7 5 5 8 . 8 0 1 0 2 . 2 9 8 7 . 2 3 5 5 . 8 4 9 9 . 8 1 9 0 . 7 5 5 8 . 8 0 1 0 2 . 2 9 8 7 . 2 3 5 5 . 8 4 1 0 6 . 3 1 9 0 . 1 7 5 6 . 19 9 6 . 9 7 8 7 . 6 2 5 4 . 6 2 1 0 6 . 4 4 8 3 . 7 4 5 7 . 0 9 1 0 6 . 4 4 8 3 . 7 4 5 7 . 0 9 1 0 6 . 4 4 8 3 . 7 4 5 7 . 0 9 8 6 . 8 2 6 2 . 15 4 3 . 8 2 8 6 . 8 2 6 2 . 15 4 3 . 8 2 8 6 . 8 2 6 2 . 15 4 3 . 8 2 9 8 . 3 2 6 5 . 4 4 4 4 . 6 3 1 0 1 . 8 0 6 0 . 3 6 41 . 8 8 9 8 . 3 2 6 5 . 4 4 4 4 . 6 3 9 4 . 8 6 6 3 . 5 0 4 4 . 5 8 9 8 . 3 2 6 5 . 4 4 4 4 . 6 3 9 4 . 8 6 6 3 . 5 0 4 4 . 5 8 8 6 . 8 2 6 2 . 15 4 3 . 8 2 1 0 1 . 8 0 6 0 . 3 6 41 . 8 8 6 4 . 7 0 6 0 . 5 7 4 4 . 0 1 6 4 . 7 0 6 0 . 5 7 4 4 . 0 1 6 4 . 7 0 6 0 . 5 7 4 4 . 0 1 

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