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UBC Theses and Dissertations

Approach to marginal analysis McLean, William Robert 1969

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AN APPROACH TO MARGINAL ANALYSIS WILLIAM ROBERT McLEAN B . S c . (mech. e n g . ) , UNIVERSITY OF MANITOBA, 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION i n t h e Depar tment o f BUSINESS ADMINISTRATION We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d , s t anda rd . THE UNIVERSITY OF BRIT ISH COLUMBIA O c t o b e r , 1969 In presenting th i s thes i s in pa r t i a l f u l f i lment o f the requirements fo r an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make i t f r ee l y ava i l ab le for reference and study. 1 fur ther agree tha permission for extensive copying of th i s thes i s for s cho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th i s thes i s f o r f i nanc ia l gain sha l l not be allowed without my wr i t ten permiss ion. Department of Business A d m i n i s t r a t i o n The Un ivers i ty of B r i t i s h Columbia Vancouver 8, Canada Date November 1, 1969 ABSTRACT T h i s t h e s i s d e v e l o p e d a p r a g m a t i c app r oach t o t h e o p t i m i z a t i o n o f b u s i n e s s d e c i s i o n s i n t h e c h l o r a l k a l i i n d u s t r y u t i l i z i n g b a s i c m a r g i n a l a n a l y s i s c o n c e p t s . I t a t t e m p t e d t o m e l d a c c o u n t i n g p r i n c i p l e s and t e c h n i q u e s w i t h economic c o n c e p t s f o r t h e pu rpo se o f e s t a b l i s h i n g a r a t i o n a l e and a w o r k a b l e m o d e l f o r g u i d i n g and e v a l u a t i n g e v e r y d a y b u s i n e s s d e c i s i o n s . The a p p r o a c h c o n c e n t r a t e d on s h o r t r u n d e c i s i o n mak i n g and d i d no t ge t i n v o l v e d w i t h c a p i t a l and o t h e r v a r i a b l e s w h i c h were f i x e d i n t h e s h o r t r u n . Many a t t e m p t s t o a p p l y m a r g i n a l a n a l y s i s t o t h e r e a l w o r l d have had o n l y l i m i t e d s u c c e s s . The c o n c e p t s as o u t l i n e d i n t h i s t h e s i s u s e d a p a r t i c u l a r e m p i r i c a l example t o c i r c u m v e n t some o f t h e i n h e r e n t d i f f i c u l t i e s a s s o c i a t e d w i t h m a r g i n a l a n a l y s i s . The emphas i s i n t h i s s t u d y was t o d e v e l o p a u s e f u l b u s i n e s s t o o l and no t t o f i t t h e o r e t i c a l economic c o n c e p t s i n t o t h e r e a l w o r l d . The s p e c i a l r e q u i r e m e n t s f o r t h i s mode l were a c a p i t a l i n t e n s i v e m u l t i p r o d u c t company w i t h a v e r t i c a l l y i n t e g r a t e d p r o d u c t i o n l i n e . Each p r o d u c t m a n u f a c t u r e d s h o u l d have two o u t l e t s ; a ) t o be u s e d as raw m a t e r i a l s t o upg rade t h e p r o d u c t b y f u r t h e r p r o c e s s i n g , o r b ) t o be s o l d i n t h e ma r ke t p l a c e . C o n s e q u e n t l y , t h e p r o d u c t l i n e s w i l l be d e v e l o p e d f r o m r e l a t i v e l y f ew raw m a t e r i a l s . T h i s i s t h e s i t u a t i o n i n most p e t r o c h e m i c a l and i n o r g a n i c c h e m i c a l p l a n t s , o i l r e f i n e r i e s , and c o u l d even be a p p l i e d t o e n t i r e i n d u s t r i e s such as f o r e s t p r o d u c t s , and p u l p and p a p e r . A l t h o u g h t h e c h l o r a l k a l i m o d e l ' s c o n s t r u c t i o n were d i s c u s s e d , t h e m o d e l i t s e l f was n o t i n c l u d e d i n t h e t h e s i s . The p a r t i c u l a r m o d e l u s e d was l a r g e and c o m p l e x , s p e c i a l l y a d a p t e d f o r t h e f i r m , and as a r e s u l t c o n t a i n e d c o n f i d e n t i a l i n f o r m a t i o n and r e l a t i o n s h i p s w h i c h were d i f f i c u l t t o d i s g u i s e . The e m p i r i c a l example a s s i s t e d i n t h e d e v e l o p -ment o f t h e e s s e n t i a l c o n c e p t s b u t d i d l i t t l e t o c o n t r i b u t e t o t h e p r o v i n g o f t h e h y p o t h e s i s . TABLE OF CONTENTS CHAPTER PAGE I . INTRODUCTION 1 Background S e t t i n g f or the Problem 2 Previous I n v e s t i g a t i o n s 4 Methodology and Sources of Data 4 L i m i t a t i o n s to the Study 5 Preview of Chapter Topics 6 I I . BASIC CONCEPTS 8 I n t r o d u c t i o n 8 The T r a d i t i o n a l Accounting Approach versus the Economic Approach 10 General 10 P r o f i t 10 Costs 12 Revenue 14 Marginal A n a l y s i s - Ratio n a l e and Assumptions . . . . 15 Framework of the Model 24 The Hypothesis , 28 I I I . THE EMPIRICAL SETTING 29 I n t r o d u c t i o n 29 S i g n i f i c a n c e of the E m p i r i c a l Framework 29 D e s c r i p t i o n of the E m p i r i c a l S e t t i n g 31 Background 31 D e s c r i p t i o n 31 Raw M a t e r i a l s 33 i i i CHAPTER PAGE Markets 34 Conclusion 36 IV. FITTING THE CONCEPTUAL FRAMEWORK TO THE FIRM 37 I n t r o d u c t i o n 37 Environment 37 Markets' 39 The Firm 41 Model St r u c t u r e and A n a l y s i s 44 Review of the Hypothesis 46 V. CONCLUSIONS 48 I n t r o d u c t i o n 48 R e i t e r a t i o n of Major Findings 48 Conclusions from Major Findings 51 Unsolved, Related Problems and Recommendations f o r Further Research 53 BIBLIOGRAPHY 55 APPENDIX 58 LIST OF FIGURES FIGURE PAGE 1. C h l o r a l k a l i P l a n t M a t e r i a l Balance 32 2. C h l o r a l k a l i Markets 40 CHAPTER I INTRODUCTION The advent of computer technology has developed an era of p r o f e s s i o n a l managers by expanding the in f o r m a t i o n h o r i z o n and h e l p i n g f i n d r e l e v e n t data f o r modern d e c i s i o n making techniques. P r i o r to t h i s e r a , the purveyors of most f i n a n c i a l i n f o r m a t i o n , the accountants, were not concerned w i t h i n f o r m a t i o n f o r d e c i s i o n making outside the f i n a n c i a l realm. Consequently many marketing and n o n - f i n a n c i a l type d e c i s i o n s were e i t h e r based on f i n a n c i a l input or made i n an i n t u i t i v e manner. On the other hand, economists have been concerned w i t h the development of economic theory without being completely s u c c e s s f u l i n applying these t h e o r i e s to management d e c i s i o n making. The o b j e c t i v e of t h i s paper i s to provide the business manager w i t h a b a s i s f o r making sounder d e c i s i o n s using more r e l e v e n t data. This has been accomplished i n a p a r t i c u l a r s i t u a t i o n by melding accounting techniques and economic concepts i n t o a workable model. B a s i c a l l y , the t h e s i s revolves around use of cost a n a l y s i s i n d e c i s i o n making f o r the o p t i m i z a t i o n of p r o f i t s . The approach has been to develop cost concepts i n a marginal a n a l y s i s framework, and i n so doing, touch upon many other r e l a t e d problems a s s o c i a t e d w i t h marginal a n a l y s i s . Demand and cost have been analyzed under s p e c i a l c o n d i t i o n s and c o n s t r a i n t s to provide an optimal way of choosing a marketing p l a n where p r o f i t i s the g o a l . Most s p a t i a l , d i s t r i b u t i o n a l , and l e g a l c o n s i d e r a t i o n s have been ignored as they do not a f f e c t the bas i c concepts and only add to the complexity of the a n a l y s i s . 2 I . BACKGROUND SETTING FOR THE PROBLEM The i n c r e a s i n g pace and complexity of business i n the modern world i s p l a c i n g increased d e c i s i o n making demands on today's manager. Technology and consumer demand have es c a l a t e d t h i s pace by mass production innovations and computer technology. With the r i s i n g costs of research and development, and the new competitive pressures, executives cannot a f f o r d i n c o r r e c t d e c i s i o n s . When business was slower and l e s s complex, our antiquated pen and q u i l l s t a t i s t i c a l record keeping and slow p a i n s t a k i n g a n a l y t i c a l techniques s u f f i c e d . I n a d d i t i o n , when mistakes were made, i t was u s u a l l y p o s s i b l e f o r the manager to r e a c t q u i c k l y and recover w i t h minimal damage. The emphasis on p r o f i t was d o l l a r s i n , l e s s d o l l a r s out, equals p r o f i t . - Consequently i f d o l l a r s out were analyzed and c o n t r o l l e d , and d o l l a r s i n were maximized, p r o f i t would be optimized. The era of computers made i t p o s s i b l e to add, s u b t r a c t , c o l l a t e and analyze w i t h p r e c i s i o n more q u i c k l y and i n greater d e t a i l . The a n a l y s i s was i n i t i a l l y only s u c c e s s f u l i n producing l a r g e volumes of r e p o r t s , most of which were poorly used, and many computer operators appeared to measure the success of t h e i r work by r e p o r t volume and l e n g t h . From an exposure to s e v e r a l computer o r i e n t e d companies, and t h e i r system's a n a l y s t s , f o r the past seven years, the author has deduced that most r e p o r t s are designed by computer t r a i n e d people and not by the operating managers. Consequently, many r e p o r t s c o n t a i n an abundance of i n c o r r e c t , u n r e l i a b l e , and u n s u i t a b l e i n f o r m a t i o n , and as such as o f t e n f i l e d unused by the people who make the d e c i s i o n s . There were examples of r e p o r t s produced weekly that contained i n f o r m a t i o n that was "nice to know" but served no u s e f u l purpose and once the r e l a t i o n s h i p s were "known" the remaining weekly r e p o r t s were redundant. Of a l l the departments i n a c o r p o r a t i o n , t h i s s i t u a t i o n a p p l i e s most s p e c i f i c a l l y to the marketing personnel, who presumably give o v e r a l l guidance to a company operating i n today's competitive market p l a c e . To the computer data bank, s o p h i s t i c a t e d l i n e a r programs, r i s k analyses, discounted cash flow, r e t u r n on investment, and other a n a l y t i c a l programs were added to lend credence to investment d e c i s i o n s . Nevertheless, executives were s t i l l wondering how to optimize  today's p r o f i t a b i l i t y i n the market place w i t h i n the c o n s t r a i n t s of the co r p o r a t i o n and the e x i s t i n g f a c i l i t i e s . These psuedo analyses and computer complications only seemed to d r i v e managers f u r t h e r towards an i n t u i t i v e approach. However, accountants and f i n a n c i a l a n a l y s t s using h i s t o r i c a l f i n a n c i a l s t a t i s t i c s were s t i l l able to evaluate performance, but unable to give guidance. Economic t h e o r i e s can suggest t h e o r e t i c a l concepts f o r p r o f i t o p t i m i z a t i o n . One concept o f t e n explored i n the l i t e r a t u r e i s marginal a n a l y s i s . T h i s technique determines the c o n d i t i o n f o r maximum economic p r o f i t by equating marginal revenues to marginal costs and s o l v i n g f o r the l e v e l of output. The many attempts a t marginal a n a l y s i s have made s u b s t a n t i a l c o n t r i b u t i o n s to the a n a l y t i c a l technique, but none have achieved a complete and workable methodology. The problems w i t h marginal a n a l y s i s were o f t e n a s s o c i a t e d w i t h miscellaneous input data; d e f i n i t i o n s and determination of marginal 4 revenues and marginal c o s t s , the i n t e r p r e t a t i o n of economic p r o f i t , and i t s r e l a t i o n s h i p to the p r o f i t and l o s s statement. Using s e c t i o n s of previous s t u d i e s and a pragmatic approach to marginal a n a l y s i s , t h i s t h e s i s has i n t e g r a t e d economic t h e o r i e s and accounting techniques i n t o a workable model to provide a meaningful approach to p r o f i t management and planning. The model has proposed a technique f o r generating and an a l y z i n g i n f o r m a t i o n to guide p r o f i t o p t i m i z a t i o n d e c i s i o n s i n the short run. As long run o p t i m i z a t i o n and e q u i l i b r i u m i s never l i k e l y to be achieved i n any f i r m or i n d u s t r y , the a n a l y s i s concentrated f o r p r a c t i c a l purposes on the short run only. I I . PREVIOUS INVESTIGATIONS Other i n v e s t i g a t i o n s have p r a g m a t i c a l l y u t i l i z e d the marginal a n a l y s i s concept. The major c o n t r i b u t o r to the development of a workable technique has been J . Johnson."'' His o f t e n quoted and almost c l a s s i c a l a n a l y s i s "Cost output v a r i a t i o n s i n a m u l t i p l e product f i r m " i s perhaps 2 the best known. Several other w r i t e r s who have updated the methodology such as Nancy Ruggles, J o e l Dean, B. P. Beckwith, plus Andrews, J . R. Nelson, and others have a l s o made s i g n i f i c a n t c o n t r i b u t i o n s to the approach. I I I . METHODOLOGY AND SOURCES OF DATA The general p l a n of a t t a c k has been to explore the concepts of a l t e r n a t e v a l u e , opportunity c o s t , costs i n general, and economic versus f i n a n c i a l p r o f i t s i n a c h l o r a l k a l i s i t u a t i o n a n a l y s i s . The p e c u l i a r i t y J . Johnston, " S t a t i s t i c a l Cost A n a l y s i s " , McGraw H i l l Book Company Inc., I960, o See B i b l i o g r a p h y . 5 of the empir ica l case under study enabled the model to circumvent some of the short comings and d i f f i c u l t i e s of e a r l i e r s tud ie s . Shortcomings and p e c u l i a r i t i e s have been discussed at length both conceptual ly and during the ana lys i s of the empir i ca l model. The next step was f i t t i n g those concepts into a marginal ana lys i s framework or opt imiz ing model. In add i t ion object ions to the a p p l i c a t i o n of marginal ana lys i s to dec i s ion making and the model were d i scussed. Overa l l concepts were supported by references to other studies and w r i t e r s , although the essence of the technique was found in the se l ec t i on of the empir i ca l model. A l l d e t a i l s and s t a t i s t i c a l information was suppl ied through the company being s tud ied. IV. LIMITATIONS TO THE STUDY Perhaps the most apparent l i m i t a t i o n of the study was the lack of supportive s t a t i s t i c a l data, however, a complete review of the model and output data demonstrated that th i s c o n f i d e n t i a l s t a t i s t i c a l information did not s u f f i c i e n t l y support or lend credence to the study to warrant i t s i n c l u s i o n . The complexity of the d e t a i l s i n the model only obscured the conceptual approach, which i s the theme of the the s i s . Unfortunate ly the study and tes t ing of only one empir i ca l example does not a l low a f u l l d e f i n i t i o n or support a l l requirements for a success fu l ana lys i s under var ious condi t ions and therefore a p p l i c a t i o n of the approach must be reserved. Many conclusions out of necess i ty w i l l be general in nature and as such subject to c r i t i c i s m and r e v i s i o n . 6 The subject of p r o f i t o p t i m i z a t i o n and planning i s complex by nature and t h i s approach i s no panacea to i t s s i m p l i f i c a t i o n . Only one economic theory has been e x p l o i t e d i n a very narrow sector of business. There have been many approximations and assumptions made, some of which can be overcome w i t h more complete and p r e c i s e data and some by a more elaborate computer s i m u l a t i o n . The a n a l y t i c a l technique i s only one of many for use as guides to p r o f i t o p t i m i z a t i o n , but t h i s approach can a l s o measure the p r o f i t impact of d e c i s i o n s before implementation. This p r o f i t o p t i m i z i n g concept a p p l i e s p r i m a r i l y to the marketing of a company's output; although p l a n t scheduling i s determined by the model, i t does not i n d i c a t e o p t i m i z a t i o n of maintenance schedules, purchasing, or p l a n t operation i n a l e a s t cost manner. Objectives of the c o r p o r a t i o n and various operating departments have not been i n c l u d e d , as p r o f i t optim-i z a t i o n was the primary o b j e c t i v e . T h e i r e x c l u s i o n from the a n a l y s i s i s not a serious l i m i t a t i o n because the impact on p r o f i t of these other o b j e c t i v e s can be determined separably i n the model. The d e s i r a b i l i t y of pursuing those o b j e c t i v e s can then be assessed i n terms of s a c r i f i c e d p r o f i t a b i l i t y versus the other b e n e f i t s accrued. V. PREVIEW OF CHAPTER TOPICS Chapter two explores the b a s i c concepts a s s o c i a t e d w i t h the model, touching upon the economic versus t r a d i t i o n a l accounting approaches to p r o f i t management. The t h e o r e t i c a l s t r u c t u r e of the model i s developed, supported, and readied f o r i n t e g r a t i o n w i t h the e m p i r i c a l example. A l l r e l a t i o n s h i p s between c r i t i c a l elements i n the model are analyzed and 7 assessed i n importance. From these r e l a t i o n s h i p s the d e f i n i t i o n s used i n the study are developed. I m p l i c a t i o n s of the r e l a t i o n s h i p s , d e f i n i t i o n s , and concepts are discussed and a hypothesis d e r i v e d . Chapter three the e m p i r i c a l s e t t i n g , describes c h a r a c t e r i s t i c s of the company, which are p e r t i n e n t to the issues being covered, such as corporate background and o b j e c t i v e s , product nature and assortment and market o p p o r t u n i t i e s . Chapter four i n t e g r a t e s the framework of the b a s i c concepts to the e m p i r i c a l s e t t i n g and analyzes the r e s u l t a n t . The hypothesis i s then rei n t r o d u c e d and a statement of s u b s t a n t i a t i o n or r e j e c t i o n made. Chapter f i v e , the l a s t chapter, contains a r e i t e r a t i o n of major f i n d i n g s and presents the conclusions drawn from them. Hopefully i t has a l s o touched upon the many unsolved r e l a t e d problems and made recommendations f o r f u r t h e r research. CHAPTER I I BASIC CONCEPTS I . INTRODUCTION I n dyanmic marketing s i t u a t i o n s , p r o f i t should be a determining guide f o r s e l e c t i n g from the v a r i o u s marketing p o l i c i e s , a strategy or program to achieve the corporate p r o f i t o b j e c t i v e . This chapter has e s t a b l i s h e d the b a s i c concepts f o r a methodology u t i l i z i n g p r o f i t to guide p r o f i t o p t i m i z i n g d e c i s i o n making. T r a d i t i o n a l l y accountants have been the record keepers of h i s t o r i c a l e x p l i c i t costs and revenues, p r o v i d i n g the only s t a t i s t i c s to guide the manager, but today the econo-mists are suggesting a l t e r n a t i v e approaches. "Although economists and accountants agree that company p r o f i t i s equal to income minus c o s t s , they sometimes d i f f e r as to which costs should be deducted i n computing p r o f i t " . P r i o r to a d i s c u s s i o n on the methodology f o r o p t i m i z i n g business p r o f i t s , the economists methods f o r c a l c u l a t i n g p r o f i t must be demonstrated to be r e a l i s t i c and d e s i r a b l e . This chapter, however, has not been an attempt to disprove or d i s c r e d i t the t r a d i t i o n a l techniques used by accountants, as they have obviously been used w i t h success around the w o r l d . John A Howard, Marketing Management, A n a l y s i s and Pl a n n i n g , (Revised E d i t i o n ; Homewood, I l l i n o i s : Richard D. I r w i n I n c . , 1963), p. 18. As p r o f i t i s equal to revenue minus c o s t s , a manager requires an intima t e knowledge of revenue and cost a n a l y s i s . Revenue i s g e n e r a l l y r e a d i l y determined, but costs can be much more e l u s i v e . Although many d i f f e r e n c e s e x i s t the accountants and the economists d e f i n i t i o n s and determination of revenue are o f t e n s u f f i c i e n t l y s i m i l a r to be used i n t e r -changeably i n t h i s a n a l y s i s . The accountant's approach to the determination of costs are pragmatic whereas the economists remain r a t h e r i d e a l i s t i c . One of the economists' t h e o r e t i c a l approaches f o r guiding p r o f i t o p t i m i z i n g d e c i s i o n s has been marginal a n a l y s i s . This means that a p r o f i t i s maximized whenever the business i s operated at a po i n t where the marginal costs equal the marginal revenue and the t o t a l cost curve i n t e r s e c t s the t o t a l revenue curve from below. When t h i s a n a l y t i c a l technique i s used, the c a l c u l a t i o n of marginal costs and revenues are u s u a l l y complex and d i f f i c u l t . Although the equating of marginal revenue to marginal cost i s an a b s t r a c t theory and u s u a l l y only used to help understand the r e a l w o r l d , i n t h i s t h e s i s i t does have pragmatic importance. However, before t u r n i n g to t h i s o p t i m i z a t i o n technique the inherent problems a s s o c i a t e d w i t h the uses of the economist's d e f i n i t i o n s of costs and revenues must be overcome or r a t i o n a l i z e d . One such d i f f i c u l t y has been the economist's i n s i s t e n c e on the use of opportunity costs at a l l times r a t h e r than h i s t o r i c a l e x p l i c i t c o s t s . The economist defines costs of production as the value of a l l foregone a l t e r n a t i v e products, which resources used i n i t s production could have o produced and not merely the sum of cash p a i d f o r these resources. Richard H. L e f t w i c h , The P r i c e System and Resource A l l o c a t i o n . (Revised E d i t i o n ; New York: H o l t , Rinehart and Winston, 1961), p. 136. 10 One of the hypotheses of t h i s t h e s i s i s that by c a r e f u l d e f i n i t i o n most of the inherent d i f f i c u l t i e s could be overcome and a meaningful marginal a n a l y s i s u s i n g the economist's d e f i n i t i o n could be developed to a s s i s t the manager i n t h i s p r o f i t a b l e management of h i s business. I I . THE TRADITIONAL ACCOUNTING APPROACH VERSUS THE ECONOMIC APPROACH General Accountants have been entrusted w i t h the recording of business r e s u l t s i n the most pragmatic and e f f i c i e n t manner a v a i l a b l e . Over the years they have developed techniques to record cash i n f l o w s and outflows and to compare these flows to other h i s t o r i c a l p a t t e r n s . Accountants have been t r a d i t i o n a l l y concerned w i t h costs estimates i n the f o l l o w i n g order of importance; f i n a n c i a l r e p o r t i n g and pl a n n i n g , managerial c o n t r o l and f i n a l l y d e c i s i o n making. I n comparison, the economists have been l a r g e l y confined to the educational and governmental i n s t i t u t i o n s and have been concerned w i t h the economic t h e o r i e s of p r i c e , demand and supply, and money. I n the business world today, the need f o r processed, analyzed, timel y i n f o r m a t i o n i s the source of much f r u s t r a t i o n . T h i s impediment i s i n p a r t a d i r e c t r e s u l t of the gap between the pragmatic accountants and the t h e o r e t i c a l economists. P r o f i t One obvious r i f t i s t h e i r c o n f l i c t over the concept of p r o f i t . The accountants have tended to use the concept of net p r o f i t which i s the 11 d i f f e r e n c e between o u t l a y costs and net revenue. To the economists, true p r o f i t must include i m p l i c i t and e x p l i c i t costs and revenues. As accountants u s u a l l y cannot define the e x p l i c i t costs and revenues p r e c i s e l y , they are of t e n ignored i n an a n a l y s i s . For d e c i s i o n making only costs and revenues a f f e c t e d by the d e c i s i o n should be included i n the a n a l y s i s . This i n c l u d e s both e x p l i c i t and i m p l i c i t c o s t s . Consequently f i x e d c o s t s ^ were r a r e l y i n c luded i n a short range d e c i s i o n making process and the p r o f i t c r i t e r i o n f o r s e l e c t i n g s t r a t e g i e s and programs were c o n t r i b u t i o n to p r o f i t or marginal p r o f i t . The process of d e c i s i o n making i s o f t e n r e l e g a t e d to the s e l e c t i o n of the most p r o f i t a b l e a l t e r n a t i v e . Often the a l t e r n a t i v e s could be adequately compared without determining the f u l l extent of the p r o f i t , p r o v i d i n g the d e c i s i o n maker was s a t i s f i e d that the same f i x e d p r o f i t s accrued to a l l a l t e r n a t i v e s under c o n s i d e r a t i o n . Thus, the s e l e c t i o n of the most p r o f i t a b l e a l t e r n a t i v e could be made by comparing v a r i a b l e p r o f i t s , marginal p r o f i t s and/or c o n t r i b u t i o n to p r o f i t o n l y . This concept has been developed more f u l l y i n the model. Generally the p r o f i t g a i n i s only an estimate, because f r e q u e n t l y there i s a problem of ass o c a t i n g the appropriate costs w i t h the b e n e f i t s or revenues accrued. Although the economists Fixed costs were used i n t h i s sense not only as defined by the accountants but a l s o as costs which were not a f f e c t e d by a p a r t i c u l a r d e c i s i o n . I n t h i s sense costs which are a f u n c t i o n of output could be c l a s s i f i e d as f i x e d , i f the a l t e r n a t i v e s being considered d i d not a f f e c t those costs nor the output. As the short run i s defined as a time span during which capacity does not change and the output i s o f t e n constant, i t could be st a t e d that f i x e d costs would r a r e l y be included i n short range d e c i s i o n making as the d e c i s i o n s being made r a r e l y a f f e c t them. 4 H i l l , Thomas M. and Gordon, Myron J . , Accounting a Managerial Approach Revised E d i t i o n ; R. D. I r w i n Inc. 1959 p. 324 " . . . f i x e d cost...may be defined as one which i s independent of the l e v e l of output". 12 approach i s conceptually the c o r r e c t one but p r a g m a t i c a l l y a d i f f i c u l t one, a model can be designed to overcome many of the o b s t a c l e s . Wherever p o s s i b l e costs have always been a s s o c i a t e d w i t h the accrued b e n e f i t s i n the determination of p r o f i t a b i l i t y . Costs For most marketing d e c i s i o n s , cost i n f o r m a t i o n must be c o l l e c t e d , c o l l a t e d , assembled, and c l a s s i f i e d on a s p e c i f i c b a s i s and only those cost items a f f e c t e d by the d e c i s i o n should be in c l u d e d . The task a t hand has been to e s t a b l i s h those concepts and combine the accountant's viewpoints w i t h the th e o r i e s of c o s t , and focus both on the marketing d e c i s i o n . Opportunity cost i s the e s s e n t i a l concept i n a l l cost a n a l y s i s f o r 5 d e c i s i o n making. Costs may be an a c t u a l expenditure, or they may be the p r i c e that the product or s e r v i c e would command i n the most productive a l t e r n a t i v e use. U t i l i z i n g the productive s e r v i c e s of anything f o r one purpose i s s a c r a f i c i n g the opportunity of using those s e r v i c e s f o r other purposes. The true cost of these s e r v i c e s then, i s the value of the most productive foregone opportunity. The production cost of any product could then be defined as the va l u e ^ of the most productive foregone a l t e r n a t i v e product plus a l l f u r t h e r i n c u r r e d processing c o s t s . Howard, op_. c i t . , p. 174. ^ L e f t w i c h , op_. c i t . , p. 136. Value can be defined as a net worth of products or s e r v i c e s to the economic system, i n the r e a l w o r ld s e l l i n g p r i c e s are o f t e n a reasonable measure of net worth to the system. Value i s measured i n terms of p r i c e i n the f r e e e n t e r p r i s e economy and the v a l u a t i o n process i s accomplished by consumers, themselves, as they spend t h e i r incomes. The d o l l a r values which they place on each of the va r i o u s goods depend upon how ur g e n t l y 13 Opportunity cost i s always the appropriate concept! Outlay c o s t s , however, o f t e n measure opportunity c o s t s , and can f r e q u e n t l y be a p p l i e d to the a n a l y s i s . They are e x p l i c i t costs and are measured by the t r a d i t i o n a l accounting approach. I m p l i c i t costs are an e s s e n t i a l part of the economists' concept of c o s t . For example, there i s an opportunity cost a s s o c i a t e d w i t h 8 self-owned self-employed resources. Since short run p r o f i t o p t i m i z a t i o n i s concerned only w i t h costs a f f e c t i n g d e c i s i o n s i n the short run, the opportunity costs of land, b u i l d i n g , manpower, and other resources have been excluded.^ - continued consumers, as a group, d e s i r e each r e l a t i v e to other goods, t h e i r w i l l i n g n e s s and a b i l i t y to back up d e s i r e w i t h d o l l a r s , and the s u p p l i e s of the goods a v a i l a b l e . For a true development of v a l u e , a l l foregone a l t e r n a t i v e s must have a proper t o t a l worth attached to them and the most productive a l t e r n a t i v e s e l e c t e d . This concept of value i s developed more f u l l y l a t e r i n the t h e s i s . Let i t s u f f i c e to say that i n t h i s e m p i r i c a l example many components of the t o t a l value of each a l t e r n a t i v e are s e l f c a n c e l l i n g when a l t e r n a t i v e s are compared to each other as only the a d d i t i o n a l or incremental value i s of importance to the d e c i s i o n . Incremental v a l u e , or worth, f o r the purpose of t h i s t h e s i s can then be defined i n terms of marginal p r o f i t . g There may be a problem w i t h the development of r e l e v e n t incremental cost data from accounting records which have been designed to provide average cost i n f o r m a t i o n . This problem could be overcome as evidenced f u r t h e r i n the paper. 9 The short run i s defined as the time p e r i o d where the f i r m i s unable to vary the q u a n t i t i e s of some resources used, such as land, b u i l d i n g s , heavy machinery, and top management. 14 Revenue Revenues, whose measurement i s plagued w i t h conceptual d i f f i c u l t i e s , are i n p r a c t i c e e a s i e r to determine. One d e f i n i t i o n of revenues which t y p i f i e s the accountants approach i s as f o l l o w s ; "Increases i n owners' equity r e s u l t i n g from the operation of the business are c a l l e d revenues,...". This i s the a c c r u a l concept f o r measuring income, and i t records events that change owners' equity i n a s p e c i f i e d time p e r i o d . Another accounting concept i s the r e a l i z a t i o n p r i n c i p l e which recognizes revenue not when goods or s e r v i c e s are exchanged but at the moment an exchange agreement i s reached. In essence revenue i s created when the sa l e i s made not when the goods are produced or d e l i v e r e d . The economists, on the other hand, are concerned w i t h the value of the flow of goods and s e r v i c e s from producer to consumer. To measure v a l u e , the economist o f t e n uses the concept of value added. In economics the manufacturing process i s regarded as c r e a t i n g value by producing products that can be s o l d and hence r e s u l t i n g i n revenues. I f i n v e n t o r i e s and p r i c e s remain r e l a t i v e l y constant, production equals sales and the revenues created by manufacturing can be considered to approximate the accountants a c c r u a l concept d e f i n i t i o n of revenue. In t h i s e m p i r i c a l example, the economists method c l o s e l y approximates the accountants approach and f o r the purposes of t h i s paper has been considered the same. H i l l and Gordon, op_. c i t . , p. 324. 15 I I I . MARGINAL.ANALYSIS - RATIONALE AND ASSUMPTIONS I t has been verified''"''' that the maximum p r o f i t i s earned when the marginal cost equals the marginal revenue f o r the volume produced and s o l d . 12 Accepting t h i s theory, s u i t a b l e measurement devices to determine input and f o r reading the output must be found. The marginal a n a l y s i s model became one of the bases f o r a p r o f i t o p t i m i z a t i o n model. Marginal revenue i s defined as the change i n t o t a l revenue r e s u l t i n g 13 from a one u n i t change i n s a l e s . For the purposes of t h i s model, i t was d e s i r a b l e to s i m p l i f y the concept of revenue and to use the concept of net revenue. Net revenue was defined as the s e l l i n g p r i c e l e s s the v a r i a b l e costs of d i s t r i b u t i o n allowances, commissions and containers but not sales f o r c e c o s t s , a d v e r t i s i n g or other marketing costs as these are defined as f i x e d costs i n the short run. The i m p l i c a t i o n of t h i s d e f i n i t i o n i s to define a l l markets, regardless of t h e i r p r o x i m i t y to the p l a n t , on an equal b a s i s f o r ease of comparison. The f u l l impact of t h i s reasoning w i l l become s e l f evident at a l a t e r stage. Although i n t h i s e m p i r i c a l example the f i r m w i l l not be operating under pure competition c o n d i t i o n s , i t w i l l be shown that i t i s r e a l i s t i c to c a l c u l a t e the marginal revenue of a market segment under terms of pure competition. That i s , the t o t a l market i n some cases can be defined as a George J . S t i g l e r , The Theory of P r i c e (Revised E d i t i o n ; New York: The MacMillan Company, 1952). 12 The author surmised, that w i t h c a r e f u l model development and d e f i n i t i o n , many of the t h e o r e t i c a l and pragmatic ob j e c t i o n s could be mastered. SEE N. Ruggles, Recent Developments i n the Theory of Marginal  Cost P r i c i n g (Review of Economic S t u d i e s , V o l . 17, 1949-50), pp. 107-126. J- JLef t w i c h , op_. c i t . , pp. 175-177. 16 f i n i t e number of blocks of business, where each block or segment i n p r a c t i c e approaches c o n d i t i o n s of pure competition w i t h i n c e r t a i n c o n s t r a i n t s . I f t h i s i s the case, the s e l l i n g p r i c e i n each block (or i n our case the net revenue per u n i t ) equals the marginal revenue. Marginal cost i s defined as the change i n t o t a l cost r e s u l t i n g from a one u n i t change i n o u t p u t . ^ Another but s i m i l a r d e f i n i t i o n i s that marginal cost i s the value of a d d i t i o n a l f a c t o r s used to produce the marginal u n i t . ^ However, the d e f i n i t i o n that i s c o n c e p t u a l l y c o r r e c t i n the short run and that best s u i t s the needs of business men t r y i n g to maximize t h e i r p r o f i t s i n the short run i s that marginal cost i s the increment i n v a r i a b l e 16 cost to produce a small number of a d d i t i o n a l u n i t s . Optimizing d e c i s i o n s i n the short run focuses d e c i s i o n makers a t t e n t i o n on the f i x e d versus v a r i a b l e cost d i s t i n c t i o n . As marginal costs are dependent on changes i n t o t a l c o s t s , f i x e d costs can be disregarded i n the p r o f i t o p t i m i z a t i o n 17 model. "Opportunity cost i s a c e n t r a l concept i n a l l cost a n a l y s i s f o r 18 d e c i s i o n making." "To use the productive s e r v i c e s of anything f o r one purpose i s to s a c r i f i c e the opportunity of using those s e r v i c e s f o r other purposes. The cost of these s e r v i c e s , then, i s the most productive 19 foregone opp o r t u n i t y . " "The o p p o r t u n i t y - o u t l a y cost d i s t i n c t i o n i s of 14 L e f t w i c h , op_. c i t . , pp. 148-150. Burnham Putnam Beckwith, Marginal-Cost Price-Output C o n t r o l , (New York: Columbia U n i v e r s i t y Press, 1955), p. 178. j-fobid. ,ap. 179 and p. 183. ^ g l b i d . , o p . 180. Howard,op. c i t . , p. 173. 1 9 I b i d . 20 1 7 great p r a c t i c a l importance,although i t s a p p l i c a t i o n i s complex." One prime purpose of t h i s chapter i s to suggest how marginal costs f o r a marginal a n a l y s i s can be c a l c u l a t e d under p a r t i c u l a r c o n d i t i o n s using opportunity c o s t s . The accountant's concept of out l a y costs i n some instances may be a measure of opportunity cost as may h i s concept of replacement c o s t . The development of appropriate marginal costs from average v a r i a b l e costs u s i n g the opportunity cost concept w i l l be developed i n d e t a i l l a t e r . V a r i a b l e costs i n the proposed model can be grouped i n t o three c l a s s i f i c a t i o n s , marketing, p l a n t processing and raw m a t e r i a l s . The m a j o r i t y of the marketing costs such as sal e s promotion, sales s t a f f and other marketing and a d m i n i s t r a t i v e expenses although v a r i a b l e i n nature are u s u a l l y f i x e d i n p r a c t i c e w i t h r e l a t i v e l y l i t t l e v a r i a t i o n over small changes i n output. For the purpose of t h i s model these costs w i l l be 21 defined as f i x e d although t h i s i s not a n e c e s s i t y . The v a r i a b l e marketing costs i n v o l v i n g d i s t r i b u t i o n c o s t s , allowances, commissions, and container costs w i l l be deducted from gross revenue per u n i t to determine net revenue. This has no e f f e c t on the o p t i m i z a t i o n model except to place a l l products f o r a l l customers i n a l l containers on e x a c t l y the same base, ( i . e . bulk 22 product F.O.B. p l a n t tanks). 20 I b i d . A l l s ales inducing costs can be considered f i x e d as the s e l l i n g e f f o r t to secure sales i s u s u a l l y constant i n the short run. Although some marketing costs a s s o c i a t e d w i t h the sale are f i x e d ( i . e . , a d m i n i s t r a t i o n ) the m a j o r i t y of sales r e s u l t i n g costs are v a r i a b l e . ^ This approach does ignore the f a c t that d i f f e r e n t marketing e f f o r t s are expended to s e l l d i f f e r e n t customers, i n d i f f e r e n t packages-and as such, w i l l a f f e c t the p r o f i t a b i l i t y and the marketing e f f e c t i v e n e s s . In t h i s e m p i r i c a l example, i t was not deemed important enough to j u s t i f y the e f f o r t 18 As many v a r i a b l e sales r e s u l t i n g expenses i n v o l v e resources t h a t are r e a d i l y a v a i l a b l e from s e v e r a l sources such as the la b o u r - s a l e s p o o l , common c a r r i e r s , container s u p p l i e r s , e t c e t e r a , i t can be assumed that the company's use of these f a c i l i t i e s and resources w i l l have no f u r t h e r e f f e c t on p r i c e s i n the short run; such that the outlay costs can be assumed to approximate the opportunity c o s t s . The accounting f u n c t i o n , i f operating on a standard v a r i a b l e cost b a s i s has already taken great pains to e s t a b l i s h c o s t s as v a r i a b l e , semi-v a r i a b l e , and f i x e d . Without f u r t h e r a n a l y s i s , these d i s t i n c t i o n s may be used to develop average v a r i a b l e p l a n t processing costs f o r the model. Depending on the business, many p l a n t processing costs c o n s i s t of commodity items, such as:'miscellaneous s u p p l i e r s , heat, l i g h t , power, steam, water, labour and others which i n most cases, the business i n question r a r e l y consumes a qu a n t i t y large enough to a f f e c t p r i c i n g to an extent that out-la y costs do not c l o s e l y approximate opportunity c o s t s . Consequently, these average o u t l a y costs which approximate the true opportunity costs can be used as a measure of marginal costs of p l a n t processing c o s t s . Should the s i z e of the purchases markedly a f f e c t p r i c e s , these items should be handled i n a manner s i m i l a r to that described i n the next paragraph f o r raw m a t e r i a l s . I n the o p i n i o n of the author, p r i c e s of the major raw m a t e r i a l s i n l a r ge c o r p o r a t i o n s do not r e f l e c t opportunity c o s t s , p a r t i c u l a r l y i f any of the m a t e r i a l s come from self-owned resources or f a c i l i t i e s . I f 22 continued -of c a t e g o r i z i n g marketing e f f o r t s by customer, by product. I f i t were d e s i r a b l e to do so, a l l marketing costs would become v a r i a b l e and would be apportioned a c c o r d i n g l y . The author f e e l s that t h i s would not a f f e c t the conceptual s o l u t i o n . 19 t h i s can be shown to be the case, another method must be developed to provide the opportunity costs f o r marginal analysis.23 Perhaps t h i s d i s p a r i t y between o u t l a y costs and opportunity costs can best be represented by a f r u i t cannery which owns i t s own orchards. Costs f o r the f r u i t c o n s i s t s of land, taxes, f e r t i l i z e r , i n s e c t i c i d e s e t c e t e r a , and " p i c k e r ' s " f e e s . These outlay costs w i l l represent an e n t i r e l y d i f f e r e n t f i g u r e s than the opportunity c o s t s . The accountants would suggest replacement cost as the r e a l i s t i c f i g u r e to represent opportunity c o s t . The economist, however, suggest that the opportunity cost of the f r u i t i s the value of foregone a l t e r n a t i v e products which resources used i n i t s production could have produced. This opens up a whole host of a l t e r n a t i v e s , vegetable farming, i n d u s t r i a l s i t e s , housing developments and others, but i n the short run these a l t e r n a t i v e s are not p r a c t i c a l . Therefore i t would appear that the opportunity cost of t h i s f r u i t does not n e c e s s a r i l y i n v o l v e these other a l t e r n a t i v e s as they do not a f f e c t short run d e c i s i o n s . I t i s suggested that i n the short run the opportunity cost i s the value f o r which the products produced a t that moment of time could draw i n an a l t e r n a t i v e market p l a c e , or end-use. I f t h i s i s the s i t u a t i o n , i t may be the p r i c e paid by another cannery or the p r i c e of the goods i n the supermarkets. I f a f i r m i s engaged i n a type of business where these a l t e r n a t i v e s are r e a d i l y a v a i l a b l e such that i t i s able to s e l l e i t h e r on the open market or to i t s own cannery, then i t becomes a r e l a t i v e l y easy task to e s t a b l i s h opportunity costs of the raw m a t e r i a l s fo r the cannery. I f the grower could s e l l f r u i t on the open market f o r a This i s the s i t u a t i o n where e i t h e r raw m a t e r i a l p r i c e s due to some p e c u l i a r i t y do not t r u l y represent the opportunity costs or where p r o f i t centers do not provide an adequate i n d i c a t i o n of opportunity c o s t s . Thes.e s i t u a t i o n s w i l l become more r e a d i l y apparent i n chapter three when the e m p i r i c a l example i s discussed. 20 higher p r i c e than the cannery, i t would do so; conversely i f the cannery could purchase a t a p r i c e below that of the grower i t would a l s o do so. This arrangement would continue u n t i l the p r i c e obtained by the grower equaled that p a i d by the cannery, at which time i t would make no d i f f e r e n c e as to where the f r u i t was purchased. I f the grower was forced to s e l l to the cannery a t lower than market p r i c e , t h i s would be a non-optimum s o l u t i o n and the t o t a l company would operate w i t h l e s s p r o f i t . The t r a n s f e r p r i c e i n t h i s non-optimum s o l u t i o n would be the higher market v a l u e , q u i c k l y p o i n t i n g out that the cannery i s the non-optimum p o r t i o n of the company. To summarize, i f o u t l a y costs f o r the major raw m a t e r i a l s are not the appropriate costs f o r optimal a n a l y s i s , the a l t e r n a t e value concept may provide an adequate technique f o r the determination of these c o s t s . I f any f i r m produces- products s o l d on the open market which a l s o are used as raw m a t e r i a l s f o r f u r t h e r p r o c e s s i n g , the appropriate raw m a t e r i a l cost f o r optimal a n a l y s i s i s the lowest a t t a i n a b l e net r e t u r n or highest unaccepted p r i c e on the open market. Opportunity cost now takes on an added dimension of being the maximum value which could have been created by the best a l t e r n a t i v e use of the marginal u n i t of output. That i s the hi g h e s t unaccepted p r i c e o f f e r f o r the marginal u n i t of output.24 A c o r a l l a r y i s that both reproduceable and non-reproduceable products have an opportunity c o s t . Using these concepts, i t w i l l be p o s s i b l e to develop a model i n 24 Beckwithy op. c i t p . 183. 21 which the optimum a n a l y s i s w i l l decide the p r o p o r t i o n and t r a n s f e r p r i c e s of the products used as raw m a t e r i a l s f o r f u r t h e r processing. This a n a l y s i s i s of course d i r e c t l y i n f l u e n c e d by the net returns obtainable f o r the up-graded products and the p r i c e of raw m a t e r i a l s able to be borne by the up-graded products. At t h i s p o i n t , i t i s necessary to cement the r e l a t i o n s h i p s between v a r i a b l e c o s t s , average v a r i a b l e c o s t s , opportunity c o s t s , and marginal costs which are used i n the marginal a n a l y s i s . The o p t i m i z a t i o n model under development a p p l i e s only to the short run and as i t turns out only over r e l a t i v e l y small changes i n output. However, J . Johnston i n h i s 25 e a r l i e r s tudies s t a t e s , "In g e n e r a l , average d i r e c t costs per u n i t of product w i l l be expected to remain constant over large ranges of output, s o l l o n g as the business continues to employ the same methods of pr o d u c t i o n , and that the t o t a l of such costs w i l l vary p r o p o r t i o n a t e l y w i t h t o t a l output". These r e l a t i o n s h i p s were found to hold i n the e m p i r i c a l example used f o r t h i s paper such that i t l e n t i t s e l f to l i n e a r programming a n a l y s i s . However, should average d i r e c t costs per u n i t not remain constant, a step f u n c t i o n could be used which held costs constant only over l i m i t e d ranges i n output. This would make the model discontinuous at those outputs where costs changed. J o e l Dean s i m i l a r l y commented and concluded that "...the most r e l i a b l e estimate of marginal cost which can 26 be made.... i s that i t i s constant.... regardless of the r a t e of output." These r e l a t i o n s h i p s i n t h i s paper's model apply only to the manufacturing 25 J . Johnston, S t a t i s t i c a l Cost A n a l y s i s , (McGraw H i l l Book Co. Inc., 1960), p. 13, from P.W.S. Andrews, Manufacturing Business, (New York: The MacMillan Company, 1949), p. 102. ^ J o e l Dean, Studies i n Business A d m i n i s t r a t i o n , V o l . 7, No. 1, 1936, " S t a t i s t i c a l Determination of Costs w i t h S p e c i a l Reference to Marginal Costs". 27 2 2 costs where the r e l a t i o n s h i p s h o l d t r u e . This i s not the case f o r a l l c o s t s , p a r t i c u l a r l y raw m a t e r i a l s and Howard o f f e r s t h i s cautionary note. 28 " L i m i t e d e m p i r i c a l evidence suggests that average v a r i a b l e cost may sometimes be roughly equal to marginal cost of cost theory w i t h i n narrow ranges of the l e v e l of output. The evidence i s strong enough to suggest the use of average v a r i a b l e cost as a workable approximation of marginal cost over the u s u a l range of production i n some s i t u a t i o n s , but by no means 29 a l l s i t u a t i o n s . " I n some cases the concept of incremental costs f o r a d d i t i o n a l u n i t s r a t h e r than marginal cost per u n i t i s more r e a d i l y 30 determined. Howard again cautions and suggests that the incremental cost concept be used w i t h care as some d e c i s i o n s i n v o l v i n g t h i s incremental increase i n v o l v e long term commitments, consequently some costs 31 o r d i n a r i l y defined as f i x e d become incremental. Beckwith, however, r a t i o n a l i z e d that average v a r i a b l e costs were i d e n t i c a l to incremental costs and could be used as a good approximation of marginal c o s t s . Another problem area could be the d i s t i n c t i o n between traceable and common costs as seen i n the e m p i r i c a l example where c a u s t i c , c h l o r i n e , s a l t and hydrogen were a l l products of the same e l e c t r o l y t i c c e l l . The d i f f i c u l t y was to meaningfully a l l o c a t e the common v a r i a b l e costs to each product, and e s t a b l i s h an acceptable b a s i s f o r s p l i t t i n g costs among products. I n t h i s case, s a l t and hydrogen were discarded by-products and c a u s t i c and c h l o r i n e s p l i t the production costs on a molecular b a s i s . This 27 For f u r t h e r s u b s t a n t i a t i o n and a summary of the e m p i r i c a l evidence see J . Johnson, Cost-output V a r i a t i o n s i n a M u l t i p l e Product Firm, the Manchester School of Economics and S o c i a l Studies XXI (1953) . 2 8 I b i d , pp. 140 - 153. 2 ^ Howard, op. c i t . , pp. 177 - 178. 31 Beckwith, op_. c i t . , p. 179, p. 180, p. 183. 23 32 was j u s t i f i a b l e because a l l excess products, that i s , products produced 33 but not s o l d , have an opportunity cost of zero. Since hydrogen and s a l t were excess by-products, i t was decided that c a u s t i c and c h l o r i n e should bear 100% of the c o s t s . Caustic and c h l o r i n e s p l i t both the processing and the raw m a t e r i a l costs on a molecular b a s i s as a l l costs i n c u r r e d 34 were f o r the prime purpose of s p l i t t i n g the s a l t molecule. 35 Howard suggests that the d i s t i n c t i o n between future and h i s t o r i c a l costs i s important but o f t e n ignored. I n p r a c t i c e h i s t o r i c a l costs were used even to make d e c i s i o n s i n v o l v i n g future c o s t s . The only s o l u t i o n a p p l i c a b l e to t h i s model was one of awareness, and to design the model w i t h the f l e x i b i l i t y to inco r p o r a t e cost estimates of future c o n d i t i o n s . Economic theory sets f o r t h two time periods; the short run a p p l i c a b l e when the scale of output (plant c a p a c i t y ) i s constant, but the r a t e of output can be changed, and the long run which a p p l i e s when the scale and r a t e can be changed. Although the model being developed could guide long run d e c i s i o n making, many of the cost s t r u c t u r e s and r e l a t i o n -ships were not a p p l i c a b l e to o p t i m i z i n g long run d e c i s i o n s . Consequently, 32 The concept of excess products having an opportunity cost of zero i s discussed i n greater d e t a i l l a t e r . Although one p l a u s i b l e concept i s f o r proceeds from the sale of by-products to be used to reduce production c o s t s , i t i s only a question of a s s o c i a t i n g costs w i t h b e n e f i t s . I f by-products cannot be s o l d , then the products which are s o l d must bear the production c o s t s . I f one u n i t o f these by-products i s so l d the revenue i s u s u a l l y c l a s s i f i e d as a c o n t r i b u t i o n to corporate p r o f i t r a t h e r than a cost r e d u c t i o n . This a r b i t r a r y s p l i t was made f o r convenience of ope r a t i o n i n the model but i s not conc e p t u a l l y r e q u i r e d because i f the costs are t r u l y j o i n t c o s t s , any b a s i s of cost a l l o c a t i o n i s a r b i t r a r y and of l i m i t e d value i n short run d e c i s i o n s . I n the short run, one product would be considered a main product and the other a by-product. The s p l i t was a l s o i r r e l e v e n t , as market p r i c e s and the a b i l i t y to s e l l the products determine the opportunity c o s t s . The b a s i c d e c i s i o n to e i t h e r s e l l s a l t or to convert i t i n t o c a u s t i c , c h l o r i n e , and hydrogen i s made i n t o t a l as the d e c i s i o n to make any one product a u t o m a t i c a l l y makes the d e c i s i o n to produce the others i n f i x e d p r o p o r t i o n s . Howard, op_. c i t . 24 the model w i l l be used p r i m a r i l y f o r short run p r o f i t o p t i m i z a t i o n where the c a p a c i t y i f f i x e d . Although no operations research t o o l s such as c o r r e l a t i o n a n a l y s i s and curve f i t t i n g techniques were used i n t h i s study to develop cost r e l a t i o n s h i p s , t h i s does not preclude t h e i r use i n other s t u d i e s . The measure f o r determining optimum c o n d i t i o n s i s c o n t r i b u t i o n to f i x e d costs and p r o f i t where the c o n t r i b u t i o n i s the d i f f e r e n c e between net revenues and opportunity c o s t s . When based upon opportunity costs t h i s number i s disregarded i n f i n a n c i a l r e p o r t i n g , f o r i t bears l i t t l e resemblance to ou t l a y c o s t s , the foundation of most f i n a n c i a l statements. Double checking the optimum c o n d i t i o n s described by the model v e r i f i e s the optimum c o n d i t i o n s i n t r a d i t i o n a l f i n a n c i a l terms. IV. FRAMEWORK OF THE MODEL A set of p r i n c i p l e s f o r e s t a b l i s h i n g the p r o f i t o p t i m i z i n g model must now be developed. Theory of marginal c o s t output c o n t r o l d i f f e r s from the optimum investment theory i n f i x e d c a p i t a l and may be p r a c t i c e d 36 w i t h or without optimum investment. " I t i s worth r e p e a t i n g a t t h i s p o i n t that the p r a c t i c a l a p p l i c a t i o n of any pr i c e - o u t p u t theory to s p e c i f i c cases can only be guided by p a r t i a l optimum a n a l y s i s . The theory of a general optimum i s u s e l e s s f o r p r a c t i c a l purposes, r e g a r d l e s s of how mathematically elegant i t may be, because i t does not t e l l us how i n d i v i d u a l p r i c e s and 37 outputs should be determined." Beckwith, OD. c i t . , pp. 226. 3 7 I b i d . 25 I n the model the company's p r i c e - s a l e s r e l a t i o n s h i p s f o r each product have been defined as a step f u n c t i o n , w i t h each step operating under terms of pure competition and r e p r e s e n t i n g the major business or market segment. Cost data and r e l a t i o n s h i p s have been b u i l t i n t o a production m a t r i x that has then been i n t e g r a t e d i n t o a marketing m a t r i x . P h y s i c a l q u a n t i t i e s of production and s a l e s were assumed to be equal so f i n i s h e d goods inventory remained constant. The model has then been programmed, using l i n e a r programs to seek the optimum c o n d i t i o n s , o c c u r r i n g where marginal costs equal net marginal revenues. The model was designed to supply markets on raw m a t e r i a l s i n descending order of p r o f i t a b i l i t y u n t i l MR —MC. The s o l u t i o n then became a s t r a i g h t forward l i n e a r program operating under the v a r i o u s c o n s t r a i n t s of c a p a c i t y , markets, p r i c e and product. The necessary input data c o n s i s t e d of process y i e l d s , production r e l a t i o n s h i p s , c a p a c i t i e s , p l a n t processing c o s t s , raw m a t e r i a l c o n s t r a i n t s and p r i c e s , market r e l a t i o n s h i p s i n c l u d i n g r e s a l e and exchange arrangements, market o p p o r t u n i t i e s and a l t e r n a t i v e s , and net returns f o r each product by market segment. A l l input data was completely f l e x i b l e and s u b s t i t u t a b l e a t any time to r e f l e c t new operating c o n d i t i o n s or to study the e f f e c t s of new a l t e r n a t i v e s or markets on p r o f i t and product a l l o c a t i o n s . The b a s i c s o l u t i o n f u r n i s h e d the f o l l o w i n g i n f o r m a t i o n w i t h i n the e s t a b l i s h e d c o n s t r a i n t s ; the optimum a l l o c a t i o n of products to markets, and production f a c i l i t i e s to supply these products; gross margin based on opportunity costs and i f programmed, on o u t l a y c o s t s ; and the marginal value 26 of resources, market o p p o r t u n i t i e s and p l a n t c a p a c i t i e s . E s s e n t i a l l y t h i s was the change i n p r o f i t r e s u l t i n g from an incremental increase i n the employment of a resource, market opportunity, or c a p a c i t y . These marginal values corresponded c l o s e l y to the concept of value of marginal product 38 f o r a p a r t i c u l a r resource. The a n a l y s i s provided opportunity costs f o r markets as w e l l as products by e s t a b l i s h i n g a product's value i n a l t e r n a t i v e markets or processes. This was d e s i r a b l e as opportunity costs vary w i t h the a l l o c a t i o n of product to markets or processes. For products, then, opportunity cost could a l s o be defined as the marginal value of the raw m a t e r i a l s plus a l l processing costs - which includ e a l l production costs and the p r o f i t gained from a one u n i t change i n market opportunity or 39 t p l a n t c a p a c i t y . I f the products were r e s t r i c t e d by production c a p a c i t y , the opportunity cost would therefore equal the net r e t u r n of the u n s a t i s f i e d market. Without a c a p a c i t y c o n s t r a i n t , the program would supply the market u n t i l MR-^MC unless i t became more p r o f i t a b l e to upgrade t h i s resource u n t i l another c o n s t r a i n t was reached. When excess products were not marketed nor upgraded, t h e i r marginal value would probably become negative and the opportunity cost 40 would be zero. The opportunity cost of zero could be q u i c k l y checked by i d e n t i f y i n g the a d d i t i o n a l p r o f i t of s e l l i n g surplus goods at below ou t l a y c o s t s . The opportunity cost of by-products normally would be zero and t h e i r sale o r d i n a r i l y r e s u l t e d i n a c o n t r i b u t i o n . G e n e r a l l y , excess products are by-products for most companies endeavour to produce only saleable products. 38 L e f t w i c h , _op. c i t . , pp. 284, f o r f u r t h e r <iiscussions. 39 The opportunity costs excluded a r e t u r n on the investments f a c i l i t i e s and other assets since these costs didnot a f f e c t short run rlfir i s i nns . 27 Markets a l s o have an opportunity cost equal to the net r e t u r n i n 41 the market place l e s s the marginal value f o r the market. The s i z e of the market's opportunity cost i s an i n d i c a t i o n of the p r o f i t importance, and the l i k e l i h o o d of a market being s u p p l i e d should i t s s i z e i n c r e a s e . I n many marketing s i t u a t i o n s i t i s expedient to produce and s e l l some markets which appear economically unsound. The reasons may be p o l i t i c a l or simply a volume consumer purchasing on an 100% requirements c o n t r a c t w i t h a s p e c i a l p r i c e . Unless otherwise i n s t r u c t e d the computer would p r e f e r a b l y supply higher net business f i r s t and ignore the volume c o n t r a c t . As these r e l a t i o n s h i p s are f o r c e d , the program has been devised to provide the costs of f o r c i n g a non-optimum s o l u t i o n , defined as l o s t p r o f i t a b i l i t y i n operating a non-optimum s o l u t i o n . The next chapter w i l l a l s o h i g h l i g h t some a d d i t i o n a l output which i s of i n t e r e s t but not a p p l i c a b l e to the concepts. Economic theory suggests that a l l a l t e r n a t i v e s should be evaluated i n a marginal cost-output a n a l y s i s , however, i n the short run where c a p a c i t i e s and a l t e r n a t i v e s are l i m i t e d , the number of v a r i a b l e a l t e r n a t i v e s are reduced to a f i n i t e number. C a r e f u l d e f i n i t i o n s and s e l e c t i o n of e m p i r i c a l examples can overcome the many t h e o r e t i c a l and p r a c t i c a l o b j e c t i o n s to marginal a n a l y s i s and provide a meaningful and u s e f u l a n a l y s i s . Although some o b j e c t i o n s may have been neglected i n the e m p i r i c a l example, none were ser i o u s enough to a f f e c t the c o r r e l a t i o n of the marginal a n a l y s i s r e s u l t s w i t h a f i n a n c i a l a n a l y s i s check. 40 Marginal value i s zero or negative because u s u a l l y excess products are a nuisance and i n c u r a cost to dispose of them. 41 Marginal value f o r a market i s a concept advanced to measure the marginal c o n t r i b u t i o n to p r o f i t of d i s c a r d i n g the l e a s t p r o f i t a b l e market i n favour of another. The opportunity cost of the new market i s equal to the market w i t h the lowest net revenue being d i s p l a c e d . This concept i s not an i n t e g r a l p a r t of the t h e s i s and i s mentioned f o r i n t e r e s t . 28 V. THE HYPOTHESIS Although there have been many approaches made to marginal a n a l y s i s , there are few that have developed a r a t i o n a l e f o r using common place accounting p r i n c i p l e s i n a marginal a n a l y s i s . To the best of the author's awareness l i t t l e s p e c i f i c work has been done on developing marginal costs f o r raw m a t e r i a l s w i t h a l t e r n a t i v e market v a l u e s . A c c o r d i n g l y , i t was hypothesized that economic and accounting concepts could be s u c c e s s f u l l y melded under p a r t i c u l a r circumstances to e x p l o i t advantages of the opportunity cost d o c t r i n e when attempting to use a marginal a n a l y s i s f o r o p t i m i z i n g p r o f i t s i n the short run. These p a r t i c u l a r circumstances i n v o l v e d a mul t i p r o d u c t f i r m manufacturing products which uses as raw m a t e r i a l s , products the f i r m i s already manufacturing and s e l l i n g from an e a r l i e r p rocessing stage. CHAPTER I I I 29 THE EMPIRICAL SETTING I . INTRODUCTION Although a true e m p i r i c a l approach r e l i e s upon p r a c t i c a l experience without reference to s c i e n t i f i c p r i n c i p l e s , an e m p i r i c a l example was chosen which could develop the b a s i c concepts i n order to prove or disprove the hypothesis. An e m p i r i c a l environment was a l s o r e q u i r e d f o r a pragmatic a p p l i c a t i o n of these t h e o r i e s . A c h l o r a l k a l i chemical p l a n t e m p i r i c a l s e t t i n g was chosen f o r i t s 1 s i m p l i c i t y to h i g h l i g h t the concepts more e x p l i c i t l y . As the concepts of opportunity c o s t i n g and marginal a n a l y s i s are simple i n theory and d e c e p t i v e l y complex i n a p p l i c a t i o n , t h i s e m p i r i c a l s e t t i n g was able to circumvent the l e s s important but conceptually complex areas of a p p l i c a t i o n . I n previous studies these areas o f t e n represented the primary source of d i f f i c u l t i e s and have l i m i t e d the development of a pragmatic marginal a n a l y s i s . I I . SIGNIFICANCE OF THE EMPIRICAL FRAMEWORK One of the most d e s i r a b l e c h a r a c t e r i s t i c s of t h i s e m p i r i c a l s e t t i n g was i t s extensive product range, which was v e r t i c a l l y i n t e g r a t e d and developed from r e l a t i v e l y few raw m a t e r i a l s . The v e r t i c a l i n t e g r a t i o n pro-v i d e d a product h i e r a r c h y which a s s i s t e d i n handling the d i f f i c u l t i e s a s s o c i a t e d w i t h the a l t e r n a t e value concept. The basis f o r the development of the marginal cost curve were meaningful opportunity cost values f o r 30 products and raw m a t e r i a l s , and a w e l l defined v a r i a b l e c o s t i n g system which co u l d be r e l a t e d to the volume of output. The product hierarchy a l s o helped develop the cost curves f o r raw m a t e r i a l s , and a s o p h i s t i c a t e d v a r i a b l e cost accounting system f a c i l i t a t e d the development of marginal costs f o r the balance. The marginal a n a l y s i s concept has had l i m i t e d success i n p r a c t i c a l a p p l i c a t i o n s . Some of the short-comings were a s s o c i a t e d w i t h demand curve d e f i n i t i o n and the d e r i v a t i o n of marginal revenues. In t h i s example the pr o x i m i t y of the p l a n t and i t s distance from competitors to markets i n s u l a t e d i t from the outside w o r l d , such that short range p r i c e changes were u s u a l l y a d i r e c t r e s u l t of a c o n d i t i o n change i n the l o c a l environment. The approach of the t h e s i s has not been to e s t a b l i s h new th e o r i e s on marginal a n a l y s i s or opportunity c o s t i n g , but only to develop a pragmatic approach to the a p p l i c a t i o n of these t h e o r i e s . In a d d i t i o n a primary o b j e c t i v e was to demonstrate how t r a d i t i o n a l accounting s t a t i s t i c s can supply much of the data r e q u i r e d f o r a marginal a n a l y s i s . The development of a r a t i o n a l e f o r melding accounting techniques and economic concepts i n t o a meaningful a n a l y s i s was b e l i e v e d to be a p r e r e q u i s i t e f o r the success of the a n a l y s i s . Information was f r e e l y a v a i l a b l e , and management co-operative i n developing accurate s t a t i s t i c s and meaningful r e l a t i o n s h i p s . The model was r e l a t i v e l y simple and was based on l i n e a r production r e l a t i o n s h i p s . I t s s i m p l i c i t y not only a f f o r d e d the greatest propensity to e s t a b l i s h a workable model but a l s o o f f e r e d a convenient apparatus f o r t e s t i n g other t h e o r i e s . 31 I I I . DESCRIPTION OF THE EMPIRICAL SETTING Background From the e l e c t r o l y s i s of common ta b l e s a l t , the c h l o r a l k a l i p l a n t produced c h l o r i n e , m u r i a t i c a c i d , c a u s t i c soda, and calcium c h l o r i d e . C h l o r a l k a l i chemicals are heavy, low: cost products, and are u s u a l l y con-sumed i n large tonnages. As t r a n s p o r t a t i o n costs are a major f a c t o r , p l a n t s are l o c a t e d c l o s e to markets and raw m a t e r i a l s . This p l a n t i s s t a t i o n e d i n Western Canada on top of the great s a l t beds of A l b e r t a . I t i s a small p l a n t by i n d u s t r y standards b u i l t p r i m a r i l y to s e r v i c e one large petro-chemical complex and a bleached k r a f t paper m i l l . As a r e s u l t of l i m i t e d demand and being the only c h l o r a l k a l i p l a n t i n the v i c i n i t y , i t was necessary to expand v e r t i c a l l y i n t o chemistry which consumed c a u s t i c and c h l o r i n e as raw m a t e r i a l s . V e r t i c a l i n t e g r a t i o n was a defensive manoeuver to consume c h l o r i n e as f o r every pound of c a u s t i c , approximately one pound of c h l o r i n e i s produced. Upgrading c h l o r i n e i n t o m u r i a t i c a c i d i s p r e f e r r a b l e to v e n t i n g surplus c h l o r i n e i n t o the atmosphere. These upgraded products a l s o increase the p l a n t ' s f l e x i b i l i t y i n m a i n t a i n i n g the product balance as w e l l as c o n t r i b u t i n g to p r o f i t s . D e s c r i p t i o n This c h l o r a l k a l i p l a n t produces l e s s than one hundred tons per year of l i q u i d c h l o r i n e . The chemical u n i t consumes s a l t , water, and n a t u r a l gas, and produces bulk c h l o r i n e , c h l o r i n e c y l i n d e r s , c h l o r i n e tonners, 50% c a u s t i c , 73% c a u s t i c , 50% p u r i f i e d c a u s t i c , 73%. p u r i f i e d c a u s t i c , fused c a u s t i c , f l a k e 32 Figure I C h l o r a l k a l i P l a n t M a t e r i a l Balance Production Process 32 c a u s t i c , m u r i a t i c a c i d , calcium c h l o r i d e , s a l t , and s a l t - c a l c i u m c h l o r i d e mixtures. The process begins w i t h water being piped down to d i s o l v e s a l t beds. The r e s u l t a n t b r i n e i s then pumped to the surface and i m p u r i t i e s removed, (see Figure I ) . Treated bri n e i s pumped to e l e c t r o l y t i c c e l l s and decomposed by d i r e c t e l e c t r i c c u r r e n t . E l e c t r i c i t y i s produced at the p l a n t from n a t u r a l gas. There are three products produced i n the c e l l ; hydrogen, gaseous c h l o r i n e and 10% c a u s t i c soda. I n the c a u s t i c soda c i r c u i t the 10% s o l u t i o n i s evap-orated by steam heat to o b t a i n a 50% s o l u t i o n . This s o l u t i o n i s e i t h e r shipped i n tankcars or tanktrucks to customers, or a d d i t i o n a l l y processed by f u r t h e r evaporation to 73% or p u r i f i e d to remove s a l t and c h l o r a t e s . The 50% p u r i f i e d c a u s t i c can be s o l d d i r e c t l y or concentrated to 73% s t r e n g t h . A p o r t i o n of the 73% c a u s t i c i s concentrated to 100% and then drummed as a fused product or processed i n t o f l a k e c a u s t i c . Flake c a u s t i c can be shipped i n drums or bags. The s a l t from the c o n c e n t r a t i o n and p u r i f i c a t i o n process i s recovered i n a c e n t r i f u g e and-dissolved as b r i n e feed f o r the c e l l s or used as s a l e a b l e s a l t . In the c h l o r i n e c i r c u i t , gaseous c h l o r i n e i s cooled and d r i e d w i t h s u l p h u r i c a c i d and then compressed and l i q u i f i e d by r e f r i g e r a t i o n . L i q u i d c h l o r i n e i s then loaded i n t o tankcars, tonners, or c y l i n d e r s f o r s a l e to customers. The p o r t i o n of c h l o r i n e that cannot be l i q u i f i e d i s used to manufacture m u r i a t i c a c i d by burning i t w i t h hydrogen, c o o l i n g the gas and d i s s o l v i n g i t i n water to produce the 31-35%, st r e n g t h h y d r o c h l o r i c a c i d known as m u r i a t i c a c i d . A c i d i s s o l d or used i n manufacturing calcium 33 c h l o r i d e . Reacting lime rock and m u r i a t i c a c i d produces a 307o calcium c h l o r i d e s o l u t i o n which i s s o l d or upgraded i n t o s o l i d calcium c h l o r i d e . This v e r t i c a l product i n t e g r a t i o n , and i n t e r - r e l a t i o n of products i n the product h i e r a r c h y i s important i n e s t a b l i s h i n g opportunity costs and a l t e r n a t e values i n the model. Raw M a t e r i a l s The m a t e r i a l balance i n Figure I i l l u s t r a t e d that the raw m a t e r i a l s purchased by the company have an opportunity cost which i s d i f f e r e n t than the purchased cost of the raw m a t e r i a l s . Raw m a t e r i a l s owned or s e l f s u p p l i e d , such as gas and s a l t can be procured at a d e f i n a b l e purchase p r i c e or s o l d at comparable p r i c e s f o r the q u a n t i t i e s . For example gas i s burned to produce steam and e l e c t r i c i t y , but l i m i t e d generating c a p a c i t y has n e c e s s i t a t e d the purchase of e l e c t r i c i t y from the u t i l i t y company. However when the p l a n t i s shut down t h i s c a p a c i t y can supply the u t i l i t y company. Consequently, s e v e r a l a l t e r n a t i v e s can be s p e c i f i c a l l y d e f i n e d , and opportunity costs and a l t e r n a t e values can be a s c e r t a i n e d f o r s e l f -owned, c a p t i v e raw m a t e r i a l s . Other supplies used i n the process are consumeable m a t e r i a l s purchased on the open market from the best source of supply. Opportunity costs f o r these items were determined as discussed 1 i n chapter I I I , Since c a u s t i c and c h l o r i n e are produced i n f i x e d p r o p o r t i o n s , product f r e q u e n t l y i s purchased from or s o l d to other s u p p l i e r s i n order to m aintain the output balance w i t h demand. 1 see S e c t i o n I I I i n chapter I I . 34 Process supplies and maintenance m a t e r i a l s are bought on the open market and t h e i r costs recorded as true outlay costs i n the t r a d i t i o n a l accounting manner. In most cases purchases are so small that the market i s not a f f e c t e d i n any s i g n i f i c a n t way. Hence an assumption was drawn that these m a t e r i a l s and supplies were purchased under c o n d i t i o n s approaching those of pure competition. As such, opportunity costs and a l t e r n a t e values are determined by outlay c o s t s . Markets Most c h l o r a l k a l i chemicals are s o l d F.O.B. the s e l l e r ' s p l a n t , f r e i g h t e q u a l i z e d on the nearest competitive p o i n t , which i s u s u a l l y a competitor's p l a n t . Consequently, the marketing e f f o r t and d i s t r i b u t i o n costs are f i x e d costs to the company. Some products are s o l d on a d e l i v e r e d b a s i s and others through agents or d i s t r i b u t o r s . As the various d i s t r i b u t i o n methods and the packages do not have f i x e d d i s t r i b u t i o n c o s t s , revenues were comparable only i f the concept of net revenue was used. Net revenue was defined as the cash flow i n t o the company a f t e r a l l f r e i g h t , package c o s t s , allowances, d i s c o u n t s , e t c e t r a , were deducted. This f i g u r e was then f r e e of a l l v a r i a b l e marketing and d i s t r i b u t i o n costs and the a l t e r n a t i v e s open to the company were comparable on an equal b a s i s . This common basis was defined as bulk product i n the process storage tanks on p l a n t - s i t e . Apart from o c c a s i o n a l volume d i s c o u n t s , p r i c i n g i n the i n d u s t r y was w e l l d e f i n e d , and r a r e l y f o l l o w e d a short term demand and supply r e l a t i o n -s h i p . A customer's p r o x i m i t y to a p l a n t and economical modes of t r a n s p o r t a t i o n tend to a f f e c t the market p r i c e to a much greater extent. The major p o r t i o n 35 of production i s s o l d i n bulk, i n tankcars or tanktrucks to a r e l a t i v e l y few customers. This p r i c i n g s i t u a t i o n and s i z e of i n d i v i d u a l shipments has segmented the market i n t o a few w e l l defined compartments. I f a demand curve f o r each segment were drawn i t would e x h i b i t the shape of a stepped f u n c t i o n w i t h each step being smaller than the s i z e of the tankcar or tank-truck. In the long run, t r a n s p o r t a t i o n i n f l u e n c e s the expansion of new markets. The markets a v a i l a b l e to the c h l o r a l k a l i o p e r ation c o n s i s t s of one l a r g e , bleached, k r a f t m i l l , one large petrochemical company, approximately twenty-five miscellaneous bulk customers, and many small customers who purchase products i n smaller packages p r i m a r i l y through two d i s t r i b u t o r s . Most bulk accounts are s i t u a t e d i n A l b e r t a and a l l package accounts are l o c a t e d w i t h i n a 250 m i l e r a d i u s . This l i m i t e d market has f a c i l i t a t e d s p e c i f i c d e f i n i t i o n s of i t s s i z e and o p p o r t u n i t i e s . Competitive plants are l o c a t e d i n Eastern Canada, Manitoba, Saskat-2 chewan and B r i t i s h Columbia. The marketing radius of these operations has been l i m i t e d by d i s t r i b u t i o n economics and as such do not represent a c t i v e competition. The exception occurs where the marketing reaches of other p l a n t s overlap and then business i s secured or l o s t on f a c t o r s other than p r i c e . More r e c e n t l y another c h l o r a l k a l i p l a n t has been b u i l t i n A l b e r t a and i t w i l l d i r e c t l y compete w i t h t h i s one. I t would be of i n t e r e s t to l i n k t h i s competitive f a c t o r i n t o the marginal a n a l y s i s model to t e s t and develop new marketing s t r a t e g i e s i n a more dynamic model. IV. CONCLUSION 36 Long range supply and demand r e l a t i o n s h i p s have not entered i n t o the a n a l y s i s because the o b j e c t i v e has been to optimize the short run c o n t r i b u t i o n of t h i s p a r t i c u l a r f i r m and i t s own environment. The c h l o r a l k a l i e m p i r i c a l example has provided the necessary p r e r e q u i s i t e to i l l u s t r a t e a pragmatic approach to marginal a n a l y s i s . Although t h i s s i t u a t i o n has circumvented s e v e r a l d i f f i c u l t i e s , i t has provided the framework f o r the development of a concept f o r p r o f i t o p t i m i z i n g i n other s i t u a t i o n s . The next chapter has a p p l i e d the b a s i c concepts and i n t e g r a t e d them i n t o the e m p i r i c a l example f o r a n a l y s i s . CHAPTER IV 37 FITTING THE CONCEPTUAL FRAMEWORK TO THE FIRM I . INTRODUCTION Consistent w i t h the b a s i c concepts presented e a r l i e r , t h i s chapter has analyzed the fi r m ' s environment and markets as w e l l as the general c h a r a c t e r i s t i c s of the model i t s e l f . A f t e r o b j e c t i v e s had been reviewed and input data c a l c u l a t e d , the model's s t r u c t u r e and operation were examined. The output and c o l l e c t i v e r e s u l t s have been presented and the di s c r e p a n c i e s or d e v i a t i o n s h i g h l i g h t e d . This chapter has o u t l i n e d the d i f f e r e n c e s and s i m i l a r i t i e s between the model and the bas i c concepts. I I . ENVIRONMENT As discussed e a r l i e r , the markets of the c h l o r a l k a l i p l a n t do not represent a l i n e a r demand curve, but c o n s t i t u t e i n s t e a d blocks of business which represent r e l a t i v e l y f i x e d q u a n t i t i e s a t a given p r i c e f o r each b l o c k . I n p a r t , t h i s r e s u l t s from low cost items being s o l d to major consumers such as the pulp and paper i n d u s t r y , the a g r i c u l t u r a l i n d u s t r y and the chemical i n d u s t r y . For i n s t a n c e , one or two bleached k r a f t m i l l s u s u a l l y consume the m a j o r i t y of the output of any one p a r t i c u l a r c h l o r a l k a l i p l a n t . I n the e m p i r i c a l example, the l a r g e s t customer, a bleached k r a f t m i l l , was secured on an annual c o n t r a c t b a s i s . Of the remaining business, approximately eighty percent i s s o l d to e i g h t other customers. Although other new business does e x i s t , the opportunity i s represented by one or two f i r m s c u r r e n t l y being s u p p l i e d by the competitors, and by new fir m s 38 not yet i n p r o d u c t i o n . These market o p p o r t u n i t i e s could be secured a t the expense of the competitors. As the p r i c e of each market opportunity i s w e l l defined and g e n e r a l l y supported by a l l competitors, business could be switched from one s u p p l i e r to another by concentrating on non-p r i c e competitive f a c t o r s l i k e t e c h n i c a l s e r v i c e , d e l i v e r y , terms, a v a i l a b i l i t y of products, e t c e t e r a . This i s not to imply that p r i c e was never an important competitive f a c t o r . Competition stemmed from f i v e other c h l o r a l k a l i p l a n t s w i t h i n the marketing reach. These p l a n t s created competitive p r i c e l e v e l s but were f a r enough removed to d i m i n i s h the d a i l y competitive t h r e a t . There was o f t e n an element of cooperation between c h l o r l a k a l i producers who traded or purchased product to maintain t h e i r production balance. P r i c e competition was g e n e r a l l y h e l d to a minimum w i t h most products s o l d a t the p u b l i s h e d l i s t p r i c e . P r i c i n g , however, does tend to be r a t h e r geographical i n nature, and new p r i c e l e v e l s were customarily e s t a b l i s h e d by one of the l a r g e producer's a c t i n g as p r i c e l e a d e r . Other s u p p l i e r s e i t h e r followed or the p r i c e change withdrawn as a d i s p r o p o r t i o n a t e amount of business would be placed w i t h the most competitive s u p p l i e r . Other p r i c e zones commonly followed a p r i c e lead which maintained the p r i c e d i f f e r e n t i a l caused by geographic or other f a c t o r s . P r i c e l e v e l s i n the c h l o r a l k a l i i n d u s t r y were i n f l u e n c e d as much by manufacturing costs as by market c o n d i t i o n s . This i n f o r m a t i o n on p r i c e s and f a c t o r s i n f l u e n c i n g p r i c e tended to prevent o p p o r t u n i s t i c p r i c i n g and lend a degree of p r i c i n g s t a b i l i t y . P r i c e s t a b i l i t y has important i m p l i c a t i o n s on the marginal 39 a n a l y s i s because only production r a t e s were changed to achieve optimum c o n d i t i o n s . Growth i n the c h l o r a l k a l i business i s steady w i t h l i t t l e seasonal v a r i a t i o n . The m a j o r i t y of the c h l o r a l k a l i products are s o l d i n tankcar 1 q u a n t i t i e s which represent 100 - 200,000 l b s . o f product per shipment. This package i n i t s e l f creates b l o c k s of business such that the demand curve f o r the c h l o r a l k a l i p l a n t could be described as a step demand. I n t h i s e m p i r i c a l example approximately 500 shipments per year supplied a l l customers. Since the volume of t h i s business was to two or three major customers, the remaining purchasers were e a s i l y defined i n f i n i t e steps, each step being a m u l t i p l e of the bas i c s i z e shipment. I I I . MARKETS The c h l o r a l k a l i i n d u s t r y i n Western Canada could be defined i n economic terms as an unorganized c o l l u s i v e o l i g o p o l y w i t h independent a c t i o n . Industry p r i c i n g could p a r t i a l l y be explained by a kinked demand curve, whereas each company's p r i c e s t r u c t u r e can be represented by the step demand curve. Each block of business could be represented as a p r i c e competition model where marginal revenue equals the p r i c e and not p r i c e minus p r i c e d i v i d e d by e l a s t i c i t y . Consequently, the marginal revenue curve was e a s i l y determined. (See f i g u r e two). The concept of net revenue was reint r o d u c e d to help s i m p l i f y the model. Net revenue represented the cash flow i n t o the company from the sale of i t s products. As net revenues d i d not in c l u d e d i s t r i b u t o r c o s t s , 1 For example, 110,000 l b s . f o r c h l o r i n e and 140,000 l b s . f o r c a u s t i c soda were common s i z e shipments i n Western Canada. 40 net returns #1 net returns M.R. market s i z e by customer #4 #2 #3 #5,6, 7,8, 9. #10 q u a n t i t y a d d i t i o n a l o p p o r t u n i t i e s marginal revenue curve q u a n t i t y Figure I I Markets 40 allowances, or d i s c o u n t s , a l l blocks of business, r e g a r d l e s s of l o c a t i o n or s a l e s o u t l e t were placed on an equal b a s i s . Consequently marginal revenue would be the net marginal revenue curve and would be on the same b a s i s f o r a l l blocks of business. Markets a v a i l a b l e to t h i s p l a n t were w e l l defined f o r the short run, namely one major pulp and paper m i l l , four b u l k c h l o r i n e , three 73% c a u s t i c , and s i c t e e n 50% c a u s t i c soda accounts r e p r e s e n t i n g 90% of the bulk business. As these were the major o p p o r t u n i t i e s open to the p l a n t , and as a 100% share of business a t these accounts was a v a i l a b l e i t was r e l a t i v e l y easy to define the demand curve f o r the products. A s i m i l a r e x e r c i s e was done f o r a l l products to a l l customers. Since the m a j o r i t y of c h l o r a l k a l i products are s o l d FOB s e l l e r ' s p l a n t , f r e i g h t e q u a l i z e d against the nearest competitive supply p o i n t , 2 o u t l i n i n g the a d d i t i o n a l o p p o r t u n i t i e s was f a c i l i t a t e d . (See f i g u r e two). . Opportunity a n a l y s i s a l s o suggests that a l l avenues and o p p o r t u n i t i e s be defined and evaluated. The a p p l i c a t i o n of t h i s concept could be a formidable and u n r e a l i s t i c task but the s i g n i f i c a n t a l t e r n a t i v e s a f f e c t i n g a d e c i s i o n can o f t e n be defined and evaluated more e a s i l y . The deductions from gross revenue f o r the c a l c u l a t i o n of net revenue and net marginal revenue have p r e v i o u s l y been d e f i n e d . However, i f costs were not d i r e c t l y a s s o c i a t e d w i t h a market op p o r t u n i t y , they were averaged over a l l o p p o r t u n i t i e s . For example; tankcar r e n t a l charges were averaged over a l l shipments by tankcars, even though some customers t r a d i t i o n a l l y 2 Using the concept of net revenue and net marginal revenue the opportunity was defined as the s e l l i n g p r i c e l e s s the normal deductions l e s s any e q u a l i z e d f r e i g h t . I t i s perhaps obvious, but the p o s i t i v e e v a l u a t i o n of an opportunity by the model d i d not a u t o m a t i c a l l y assure that the business would be sought as other competitive f a c t o r s w i l l i n f l u e n c e the d e c i s i o n . I t 41 detained tankcars longer than o t h e r s . Marketing costs remained r e l a t i v e l y constant as the s i z e of the sales force d i d not change w i t h volume and many other marketing costs were borne by the d i s t r i b u t o r s . Sales promotion and a d v e r t i s i n g was l i m i t e d w i t h expenditures remaining f a i r l y constant. S i m i l a r l y , other miscellaneous marketing costs did not vary w i t h output and could be considered as f i x e d . This a n a l y s i s j u s t i f i e d e x c luding marketing costs from the a n a l y s i s of the e m p i r i c a l example. Due to p e c u l i a r i t i e s of the market and company, non-optimum c o n d i t i o n s were o f t e n s u p p l i e d a t the expense of an optimum operating c o n d i t i o n . The cost of f o r c i n g t h i s non-optimum s o l u t i o n could be determined and was defined as the l o s s i n p r o f i t r e s u l t i n g from the d e v i a t i o n . Many examples of t h i s c o n d i t i o n s could be c i t e d , but many were e i t h e r p e c u l i a r 3 to the s i t u a t i o n or a loophole i n the model. IV. THE FIRM U t i l i z i n g the aforementioned concepts, marginal cost input data has been developed f o r the model . They were d i v i d e d i n t o the marginal costs of v a r i a b l e process s u p p l i e s and marginal costs of major raw m a t e r i a l s attempting to s u c c e s s f u l l y meld the-accountant's concepts w i t h economic t h e o r i e s . Costs defined by the accountants as f i x e d i n the short run have been excluded from the a n a l y s i s as they d i d not a f f e c t short run o p t i m i z i n g d e c i s i o n s . C e r t a i n minor consumable s u p p l i e s which vary w i t h output must be included i n the a n a l y s i s as a component of the cost f u n c t i o n . The task was to f i n d a s u i t a b l e measure f o r the opportunity costs of these items. For 3 One loophole forced the model to supply 100% of the pulp and paper company's business whereas the optimum s o l u t i o n was to supply other smaller higher net r e t u r n o p p o r t u n i t i e s . U n f o r t u n a t e l y the pulp and paper contact was for t o t a l requirements. 42 4 many of these items the accountant s concept of out lay costs were used because the company produced c h l o r a l k a l i products, not consumable goods. The small volume of these suppl ies , are probably purchased under condit ions approaching pure competit ion and the p l a n t ' s requirement does not a f f e c t the general market p r i c e . Opportunity costs are not neces sa r i l y marginal cos t s , but are o f ten represented as average v a r i a b l e cos t s . P r i o r documentation v e r i f i e d that under most condit ions average va r i ab le costs c l o s e l y approximate marginal costs for small changes in output.^ For process suppl ies and miscel laneous items the average va r i ab le costs approximate the i r true marginal cos t s . In f a c t , i t appears that due to the nature of the purchases and the quant i t i e s i nvo lved , the assumption appears v a l i d over large v a r i a t i o n s i n output. A requirement of th i s ana ly s i s was that c e r t a i n products manufactured for sa le were a l so raw mater ia l s for other products and processes. Th i s . p r e - r e q u i s i t e was necessary to e s t ab l i sh the marginal costs of primary raw mater i a l s . Raw mater ia l s are va r i ab le costs which must be costed at the value of foregone a l t e r n a t i v e products with which the resources used i n i t s product ion could have produced. I t i s reasonable to assume that resource a l l o c a t i o n i s we l l balanced to the extent that the resource p r i c i n g r e f l e c t s 7 the value of the foregone a l t e r n a t i v e products . 4 This i s a v a l i d concept as a l im i ted opportunity for these serv ices i n an a l t e r n a t i v e use ex i s t s and they represent a small po r t i on of t o t a l co s t s . Consequently, the assumption has been made that serv ice costs approx-imate the true opportunity costs and could be used to s imp l i fy the ana l y s i s , g See chapter two and J . Johnston, c>£. c i t . Process suppl ies and miscel laneous items inc lude the va r i ab le components ofalmost a l l items other than major raw mater i a l s , such as main-tenance mater i a l s , process reagents, c a t a l y s t s , hourly paid labour, steam, l i g h t , power (other than c e l l current) and minor raw mater ia l s (e lectrodes, water treatment chemicals, e t c e t e r a ) . 43 E s t a b l i s h i n g marginal costs of raw m a t e r i a l s was not e a s i l y accomplished f o r many products and raw m a t e r i a l s were derived from s e l f employed resources. The o b j e c t i v e was to determine the marginal costs by d e f i n i n g the opportunity cost f o r raw m a t e r i a l s as the value of products produced a t a s p e c i f i e d moment i n an a l t e r n a t i v e market place or end-use. For example, c h l o r i n e i s s o l d to f i v e bulk customers and many 150 pound and tonner container customers and i s a l s o up-graded i n t o HCL or m u r i a t i c a c i d . The c h l o r i n e raw m a t e r i a l cost to the HCL u n i t would be equal to the net r e t u r n s a v a i l a b l e i n the next most p r o f i t a b l e market or end-use. I t i s the value which other customers pay to secure the resource f o r another purpose. T h i s a l t e r n a t i v e value or opportunity cost concept could be a p p l i e d to each resource w i t h the o p t i o n of s e l l i n g the product or of g using i t was a raw m a t e r i a l f o r f u r t h e r processing. Consequently, the opportunity costs of the output are a l s o the marginal costs of the resource, and the marginal costs f o r raw m a t e r i a l s are r e a d i l y d e f i n a b l e . Marginal costs change w i t h the a l l o c a t i o n of product to a l t e r n a t e o p p o r t u n i t i e s as o p p o r t u n i t i e s are e i t h e r secured or re l e a s e d i n accordance w i t h the model's optimum s o l u t i o n . 7 This statement could be disputed on a t h e o r e t i c a l b a s i s , but there were no contrary i n d i c a t i o n s i n the e m p i r i c a l example. (See d i s c u s s i o n on value i n Chapter I I p. 12.). ^ Using Figure I i t could be seen that t h i s method e s t a b l i s h e d opportunity costs f o r a l l raw m a t e r i a l s except lime rock, hydrogen and raw b r i n e . B r i n e , however, could be manufactured from s a l e a b l e s a l t and t h i s value used to determining the opportunity c o s t . I n t h i s example, raw b r i n e could not be s o l d as such, so the opportunity cost was zero, and the c e l l b r i n e had a value equal to the v a r i a b l e c o s t s to t r e a t raw b r i n e . Hydrogen a l s o had no a l t e r n a t i v e market and i t s opportunity cost was zero. Outlay costs were used f o r lime rock which was purchased i n small q u a n t i t i e s a t p r i c e s e q u i v a l e n t to other u s e r s . ^ T h i s assumes the r e l a t i o n s h i p between average v a r i a b l e costs and marginal costs set f o r t h i n J . Johnston, c>p_. c i t . I n s e v e r a l cases t h i s r e l a t i o n s h i p u s i n g the opportunity costs concept can be proven by i n s p e c t i o n of the model. 44 V. MODEL STRUCTURE AND ANALYSIS Another p r e - r e q u i s i t e f o r t h i s a n a l y s i s r e q u i r e d d e f i n a b l e and obtainable v a r i a b l e c o s t s f o r each stage of the production process. The t r u l y v a r i a b l e cost components of s u p p l i e s and process cost were e s t a b l i s h e d by the accountant's t r a d i t i o n a l standard v a r i a b l e c o s t i n g technique. Each production process was defined u s i n g marginal costs i n a mathematical r e l a t i o n s h i p and each market opportunity defined i n terms of marginal revenues and volume p o t e n t i a l s i n order to develop the p r o f i t equation to be optimized. A l l production and market c o n s t r a i n t s were defined and q u a n t i f i e d before the f u n c t i o n which used l i n e a r programming techniques was optimized. This was i n s t i t u t e d by developing a product -resource a l l o c a t i o n operating the p l a n t as c l o s e to MRjS. MC^ as p o s s i b l e . E s s e n t i a l l y the model i s composed of two m a t r i c e s ; the production m a t r i x c o n t a i n i n g process y i e l d s , r e l a t i o n s h i p s , c a p a c i t i e s , costs and c o n s t r a i n t s , and the market m a t r i x d e s c r i b i n g market o p p o r t u n i t i e s i n terms of net p r i c e s or r e t u r n s , volume, r e l a t i o n s h i p s and c o n s t r a i n t s . The model was v e r i f i e d by applying o u t l a y costs and market p r i c e s to check the e f f e c t on p r o f i t margin of optimum s o l u t i o n s under d i f f e r e n t c o n d i t i o n s . Thus optimum s o l u t i o n s were expressed as a p r o f i t and l o s s statement which was the essence of the e x e r c i s e . The output of the model although i n c i d e n t a l to the t h e s i s provided the f o l l o w i n g i n f o r m a t i o n : 45 a) the optimum a l l o c a t i o n of products to markets and the optimum production f a c i l i t i e s to supply these products. b) the gross margin at t h i s optimum a l l o c a t i o n . c) the marginal value of market o p p o r t u n i t i e s and p l a n t c a p a c i t i e s . Marginal v a l u e was described as the increase i n p r o f i t r e s u l t i n g from an increase i n the market opportunity or p l a n t c a p a c i t y by one u n i t . d) opportunity costs of a market or product o p p o r t u n i t y . This gave the minimum p r o f i t a b l e net r e t u r n f o r a product to cover v a r i a b l e manufacturing costs i n c l u d i n g the marginal value of i t s raw m a t e r i a l s . e) the c o s t s of f o r c i n g a non-optimum s o l u t i o n . These were the increased costs or reduced p r o f i t i n c u r r e d by f o r c i n g a non-optimum market or production a c t i v i t y . f) other items such as c o n t r i b u t i o n s to gross margin of i n d i v i d u a l products or markets, s e n s i t i v i t y of gross margin and optimum a l l o c a t i o n to c o s t s , net r e t u r n s , and other input data. T h i s was the p o i n t where the s o l u t i o n d r a s t i c a l l y changed w i t h only small changes i n i n p u t . Another item was the range over which incremental values and optimum s o l u t i o n s are v a l i d . As the opportunity of a market changes, the marginal value of the market a p p l i e s only as long as the b a s i c s o l u t i o n does not change. The range over which t h i s marginal value a p p l i e s was found by r i g h t hand side ranging. I t was a l s o p o s s i b l e to determine the e f f e c t on t o t a l p r o f i t s of s e v e r a l simultaneous changes; to develop p r o f i t centers and t r a n s f e r p r i c e s , and many other b i t s of i n f o r m a t i o n which help d e c i s i o n making. Most of the model's a d d i t i o n a l b e n e f i t s focuses on data s u i t a b l e f o r marketing d e c i s i o n s . 46 The net r e s u l t of the a n a l y s i s i s o l a t e d the l e a s t p r o f i t a b l e and most p r o f i t a b l e markets suggesting where a marketing e f f o r t should concentrate. I t a l s o i n d i c a t e d markets and production u n i t s which had an abnormally large impact on p r o f i t a b i l i t y and pointed out the misconception of the dependance of the business on one la r g e customer. The a n a l y s i s i n s t i t u t e d r e - e v a l u a t i o n of the marketing s t r a t e g y and an i n v e s t i g a t i o n i n t o p r i c i n g p o l i c y . V I . REVIEW OF THE HYPOTHESIS I n one p a r t i c u l a r c h l o r a l k a l i p l a n t , accounting techniques and p r i n c i p l e s were s e l e c t i v e l y used to develop s e v e r a l economic t h e o r i e s i n t o a pragmatic model f o r more e f f e c t i v e d e c i s i o n making i n the p r o f i t -able management of the f i r m . Although some economic t h e o r i e s were l o o s e l y a p p l i e d , and the e m p i r i c a l example d i d avoid s p e c i f i c conceptual and pragmatic d i f f i c u l t i e s , the a n a l y s i s f u r n i s h e d an inf o r m a t i o n base for making sounder d e c i s i o n s . The c h l o r a l k a l i p l a n t was s e l e c t e d f o r i t s i n t e g r a t e d product l i n e and i s o l a t e d markets. However, the author has a p p l i e d the concept to other companies and b e l i e v e s i t i s v a l i d f o r other i n d u s t r i e s . The procedure must be c a r e f u l l y a p p l i e d i n the more d i v e r s i f i e d areas because the a l t e r n a t e values become v a s t l y more complex w i t h wider product ranges, markets, and many producing p o i n t s . The hypothesis s t a t e s that under p a r t i c u l a r c o n d i t i o n s a combination of economic concepts and accounting p r i n c i p l e s could e x p l o i t advantages of the opportunity cost d o c t r i n e u s i n g a marginal a n a l y s i s f or o p t i m i z i n g p r o f i t s i n the short run. These circumstances i n v o l v e a multiproduct f i r m manufacturing products which use as raw m a t e r i a l s , products the f i r m i s manufacturing and s e l l i n g from an e a r l i e r processing stage. W i t h i n the l i m i t e d context of the hypothesis, economic concepts and accounting p r i n c i p l e s were used to develop a p r o f i t o p t i m i z a t i o n model u s i n g the opportunity cost d o c t r i n e i n i t s e n t i r e t y . The model although s p e c i f i c to the e m p i r i c a l example, provided i n f o r m a t i o n f o r o p t i m i z a t i o n and s u c c e s s f u l l y a p p l i e d the concept f o r sound d e c i s i o n making. This statement p a r t i a l l y represents a management value judgement f o r the a n a l y s i s only h i g h l i g h t e d non-optimum operating c o n d i t i o n s . A l s o management was made aware of s e n s i t i v e areas and c o n d i t i o n s which could have r e s u l t e d i n unnecessary marketing t a c t i c s pursuing an erroneous marketing s t r a t e g y . I n concluding, the hypothesis has been accepted w i t h r e s e r v a t i o n s and the concept shown to be s u f f i c i e n t l y workable to be a p p l i e d to more complex s i t u a t i o n s . 48 CHAPTER V CONCLUSIONS I . INTRODUCTION Conclusions are the l a s t p a r t of a chain of reasoning i n a discourse and by d e f i n i t i o n a place where opinions formed during the i n v e s t i g a t i o n could a l s o be presented. A c c o r d i n g l y , t h i s chapter has presented a b f i f summary of f i n d i n g s before the conclusions are drawn. This discourse has o f f e r e d a p r a c t i c a l approach to p r o f i t o p t i m i z a t i o n using recognized t h e o r i e s of accounting and economics. This approach, how-ever, i s a p p l i c a b l e to only c e r t a i n s i t u a t i o n s which are p a r t l y c i r c u m s t a n t i a l and p a r t l y due to managements philosophy and the corporate's o b j e c t i v e s . P r o f i t o p t i m i z a t i o n i n the short run was p a r t i c u l a r l y conducive to v e r t i c a l i n t e g r a t e d m ultiproduct firms where short term p r o f i t maximization was a primary o b j e c t i v e . This t h e s i s has ignored other corporate o b j e c t i v e s except i n t h e i r r e l a t i o n to the short term p r o f i t o b j e c t i v e s . I I . REITERATION OF MAJOR FINDINGS The o p t i m i z a t i o n technique, through s e l e c t i o n of the e m p i r i c a l model, overcame many of the indigenous problems to marginal a n a l y s i s . The success-f u l a p p l i c a t i o n of t h i s technique has shown that a business could be managed using a l t e r n a t e values which do riot r e l a t e to outlay or accounting c o s t s . Thus, major f i n d i n g s could be separated i n t o pragmatic and conceptual f i n d i n g s . 49 Pragmatic f i n d i n g s concern the a p p l i c a t i o n of economic and accounting ideology to marginal a n a l y s i s or p r o f i t o p t i m i z a t i o n . Although i d e a l i s t i c i n nature, marginal a n a l y s i s and a l t e r n a t e values provided meaningful g u i d e l i n e s f o r the short run o p t i m i z a t i o n of p r o f i t s . Most input i n f o r m a t i o n was devel-oped from t r a d i t i o n a l accounting technique concerned w i t h f i n a n c i a l c o n t r o l . Although these d i d not blend smoothly w i t h the economic concepts, they d i d provide a p o r t i o n of the req u i r e d bank of in f o r m a t i o n . With the accountant's data b*se, economic i d e a l i s m and marginal a n a l y s i s concepts were formulated i n t o a workable mechanism f o r p r o f i t o p t i m i z a t i o n . E v o l v i n g unique marginal revenues and marginal costs overcame many of the d i f f i c u l t i e s a s s o c i a t e d w i t h other s t u d i e s . The two most s i g n i f i c a n t break-throughs were the concept of net marginal revenues f o r each block of business and the a p p l i c a t i o n of opportunity cost and a l t e r n a t e values to marginal a n a l y s i s . The economic d e f i n i t i o n s of opportunity cost and a l t e r n a t e values a p p l i e d i n a l o c a l i z e d short term environment s i m p l i f i e d t h e i r d e f i n i t i o n s and determination. Thus opportunity costs and a l t e r n a t e values were a v a i l a b l e i n many s i t u a t i o n s , but the ease of t h e i r determination depended l a r g e l y on the e m p i r i c a l example. The establishment of marginal costs u s i n g opportunity cost and a l t e r n a t e value concepts as defined by the economists p r o f i t equation r e s u l t e d i n costs being a s c e r t a i n e d and i n f l u e n c e d more by the product demand r e l a t i o n s h i p s than by the costs recorded i n the f i n a n c i a l c o n t r o l system. I f t h i s o b servation were v a l i d , i t would be impossible to s u c c e s s f u l l y meld accounting p r i n c i p l e s and concepts w i t h economic t h e o r i e s i n p r o f i t o p t i m i z a t i o n models. 50 Some unexpected i n f o r m a t i o n and important a n c i l l a r y data were f u r n i s h e d by the model and a greater comprehension of marginal c o s t s , a l t e r n a t e v a l u e s , and opportunity costs were a t t a i n e d . Values f o r s p e c i a l c o n d i t i o n s were defined. For i n s t a n c e ; at best, the opportunity cost of excess products are zero. The production cost of each product manufactured i n one production step i s d i r e c t l y p r o p o r t i o n a l to the demand or a l t e r n a t e value of that product. The marginal value of resources, market o p p o r t u n i t i e s , and c a p a c i t i e s are examples of the a n c i l l a r y data which could provide u s e f u l s t a t i s t i c s f o r assessing the impact of d e c i s i o n s and p r o v i d i n g g u i d e l i n e s f o r f u t u r e a c t i o n plans. An i n f o r m a t i o n base, p r e f e r a b l e to the accountant's s t a t i s t i c a l r ecords, was e s t a b l i s h e d f o r e s t i m a t i n g the impact of new or non-optimum de c i s i o n s on p r o f i t i n the short run. The conceptual and p o s s i b l y i d e o l o g i c a l f i n d i n g s were a d i r e c t r e s u l t of the attempt to meld accounting techniques w i t h economic theory. I t was suggested that costs a s s o c i a t e d w i t h p r o f i t o p t i m i z a t i o n are markedly d i f f e r e n t than those recorded by the accountants. For p r o f i t o p t i m i z a t i o n models i t would appear that only a l t e r n a t e values and opportunity costs w i t h only outlay cost c o n s t r a i n t s should be used i n the model. Opportunity costs and not recorded outlay costs are the appropriate concept f o r any p r o f i t o p t i m i z a t i o n technique i n v o l v i n g the marketing of the company's products. I t was observed that some product costs w i t h f i x e d production r e l a t i o n s h i p s were dependent on demand r e l a t i o n s h i p s f o r the f i n a l product 51 r a t h e r than on raw m a t e r i a l or process c o s t s . I f t h i s f i n d i n g was v a l i d , a f u n c t i o n r e l a t i n g product demand and production r e l a t i o n s h i p s to cost could be developed, d i f f e r e n t i a t e d and solved f o r l e a s t cost r e l a t i o n s h i p s . I I I . CONCLUSIONS FROM MAJOR FINDINGS For purposes of p r o f i t o p t i m i z a t i o n i t was undesirable to combine accounting techniques w i t h economic t h e o r i e s , but some data contained i n the record keeping system could be s u c c e s s f u l l y a p p l i e d i f c a r e f u l l y s e l e c t e d . The a p p l i c a t i o n of a l t e r n a t e values and opportunity cost concepts to marginal a n a l y s i s p r o f i t o p t i m i z a t i o n d i d l e a d to a u s e f u l a n a l y s i s i n t h i s e m p i r i c a l example, w i t h the p o s s i b i l i t y of a p p l i c a t i o n to many other companies. C r i t i c i s m could be d i r e c t e d to a d m i n i s t e r i n g the "Black Box" approach and i g n o r i n g the e f f e c t of changes i n o p p o r t u n i t i e s and a c t i o n s on i t s environment, namely the i n d u s t r y or economy. I f a major change i n the company's modus operandi a f f e c t s the environment, or v i c e v e r s a , these r e l a t i o n s h i p s could then be s t u d i e d independently of the i n t e r n a l segment of the "Black Box". The r e s u l t a n t change i n the company's o p p o r t u n i t i e s could then be re-analyzed f o r the optimum s o l u t i o n . I t i s o f t e n s t a t e d that p r o f i t management and planning r e q u i r e d i f -f e r e n t techniques and i n f o r m a t i o n than cost c o n t r o l and no accounting system should be used f o r p r o f i t management and planning. In some companies, these techniques c l o s e l y approximate one another, but i n the e m p i r i c a l example the •*"The "Black Box" technique i s o l a t e s a complex p o r t i o n of a system and analyzes the part measuring only inputs arid outputs from the t o t a l system or v i c e v e r s a . The t o t a l system could a l s o be examined i g n o r i n g the s e c t i o n i n the black box except f o r i t s inputs and outputs to the system. 52 accounting technique could only cost c o n t r o l and could not p r o f i t manage the company a f f a i r s . Although t h i s p r o f i t o p t i m i z a t i o n technique has been a p p l i e d s u c c e s s f u l l y and has l e a d to d e c i s i o n s i n c r e a s i n g gross p r o f i t a b i l i t y l i k e a l l operations research t o o l s , i t only provided i n f o r m a t i o n and suggested courses of a c t i o n , and d i d not replace the d e c i s i o n maker. Costs, as defined i n the economic p r o f i t equation change w i t h the o p p o r t u n i t i e s a v a i l a b l e to the company, and t h e r e f o r e i n a multiproduct company w i t h i n t e r - r e l a t e d product l i n e s , v a r i a b l e costs were as meaningless as f i x e d costs f o r short run p r o f i t o p t i m i z a t i o n . Outlay costs f o r i n d i v -i d u a l raw m a t e r i a l s a f f e c t e d the a n a l y s i s only by c o n s t r a i n i n g a t o t a l v a r i a b l e cost o u t l a y on the company as an e n t i t y , beyond which i t was more economical to c l o s e the p l a n t . The extent of t h i s c o n c l u s i o n w i l l vary w i t h each company according to a v a i l a b l e o p p o r t u n i t i e s and the degree of product i n t e r - r e l a t i o n . For companies w i t h l i m i t e d i d e a l i s t i c a l t e r n a t i v e s and product l i n e s which are not i n t e r - r e l a t e d , the t r a d i t i o n a l accounting approach to p r o f i t c o n t r o l and management would s u f f i c e . The hypothesis s t a t e d that "Economic concepts and accounting p r i n -c i p l e s can be s u c c e s s f u l l y melded under p a r t i c u l a r circumstances to e x p l o i t advantages of the opportunity cost d o c t r i n e when attempting to optimize p r o f i t s i n the short run. These p a r t i c u l a r circumstances i n v o l v e a m u l t i -product f i r m manufacturing products which used as raw m a t e r i a l s , products the f i r m i s already manufacturing and s e l l i n g from an e a r l i e r processing stage." This hypothesis must be r e j e c t e d because the b a s i c premise of combining economic concepts and accounting p r i n c i p l e s was undesirable and 53 i n c o r r e c t f o r p r o f i t o p t i m i z a t i o n . Accounting p r i n c i p l e s guide management and planning through the a n a l y s i s and c o n t r o l of h i s t o r i c a l cost i n f o r m a t i o n and a l t e r n a t i v e s . I n some s i t u a t i o n s these i n t e r p r e t a t i o n s s a t i s f a c t o r i l y measure o p p o r t u n i t i e s and t h e i r costs to give acceptable r e s u l t s . On the other hand, the balance of the hypothesis could be unequivocably accepted since the opportunity cost d o c t r i n e was s u c c e s s f u l l y e x p l o i t e d u s i n g the economic theory of marginal a n a l y s i s to optimize p r o f i t s under the c o n d i t i o n s s t a t e d . The true measure of the success of t h i s t h e s i s was i n the a n c i l l a r y problems and s o l u t i o n s gained by t h i s a n a l y t i c a l approach. IV. UNSOLVED RELATED PROBLEMS AND RECOMMENDATIONS FOR FURTHER RESEARCH The e n t i r e a n a l y t i c a l procedure has ignored the impact on long range s t r a t e g y . This i s due to a d i f f e r e n t dimension of c a p i t a l expenditures, changing c a p a c i t y and the p o s s i b i l i t y of a d i f f e r e n t demand curve or product l i n e , and f u r t h e r research should r e l a t e the e f f e c t of many models w i t h v a r i o u s parameters s i m u l a t i n g a long term e f f e c t . In a d d i t i o n the company's environment, the i n d u s t r y and economy has l a r g e l y been overlooked. I t should be p o s s i b l e to expand t h i s technique to the i n d u s t r y or world economic l e v e l s to achieve a s i m i l a r short run o p t i m i z a t i o n s o l u t i o n . The concept of the "Black Box" would be appropriate i f a p p l i e d i n reverse. Further scope f o r a n a l y s i s of the other output from these models mentioned i n Chapters two and four i s a v a i l a b l e . This data, the model, and 54 other operations research techniques may well be the forerunner of a new data base and simulation program for the profitable direction of a company or industry. This type of information system is an urgent requirement for business managers who like their predecessors s t i l l continue to conduct their business by intuition. BIBLIOGRAPHY BIBLIOGRAPHY 56 Alde r s o n , Wroe, and Green, Paul E. Planning and Problem S o l v i n g i n Marketing. Homewood I l l i n o i s : R ichard D. I r w i n Inc., 1964. A l l e n , R.G.D. Mathematical A n a l y s i s f o r Economists. New York: MacMillan and Co., 1938. Anthony, Robert N. Management Accounting. Revised Ed. Richard D. I r w i n Inc., 1960. Beckwith, Burnham Putnam. Marginal-Cost Price-Output C o n t r o l . New York: Columbia U n i v e r s i t y P r ess, 1955. Boulding, Kenneth E. Economic A n a l y s i s . Volume One Microeconomics, 4th ed. Harper and Row P u b l i s h e r s , 1966. Cassady, Ralph J r . "The Time Element and Demand A n a l y s i s " , Theory i n  Marketing. E d i t e d by W. Alderson and R. Cox. Homewood I l l i n o i s : R i chard D. I r w i n Inc., 1960. C a s s e l s , John M. "On the Law of V a r i a b l e P r o p o r t i o n s " , E x p l o r a t i o n s i n Economics. New York: McGraw H i l l Book Co. Inc., 1936. C u l l i t o n , James W. The Management of Marketing Costs. Boston: Graduate School of Business A d m i n i s t r a t i o n , Harvard U n i v e r s i t y , 1948. Davidson, Raplh K., Smith, Vernon L., and Wiley, Jay W. Economics: An A n a l y t i c a l Approach. Revised e d i t i o n . Richard D. I r w i n Inc., 1962. Dean, J o e l . Managerial Economics. P r e n t i c e - H a l l I nc., 1951. Dean, J o e l . S t a t i s t i c a l Determination of Costs w i t h S p e c i a l Reference to  Marginal Costs. Studies i n Business A d m i n i s t r a t i o n , V o l . 7, No. 1, 1936. E a r l e y , James S. "Marginal P o l i c i e s of E x c e l l e n t l y Managed Companies", American Economic Review, XLVI, 1956. E a r l e y , James S. "Recent Developments i n Cost Accounting and the Marginal Analysis", J o u r n a l of P o l i t i c a l Economy, L X I I I , 1955. H i l l , Thomas M., Gordon, Myron J . Accounting: A Management Approach. Revised e d i t i o n . Richard D. I r w i n Inc., 1959. Howard, John A. Marketing Management: A n a l y s i s and Planning. Revised e d i t i o n . Homewood I l l i n o i s : Richard D. I r w i n Inc., 1963. 57 Johnston, J . "Cost Output V a r i a t i o n s i n a M u l t i p l e Product Firm", The  Manchester School of Economic and S o c i a l S t u d i e s . XXI, 1953. Johnston, J . S t a t i s t i c a l Cost A n a l y s i s . McGraw-Hill Book Co. Inc., 1960. L e f t w i c h , R.H. The P r i c e System and Resource A l l o c a t i o n . 3rd ed. H o l t , R i n e h a r t , Winston, 1966. Liebhapky, H.H. The Nature of P r i c e Theory. The Dorsey Press Inc., 1963. Chapter 17 "Basic Concepts of Li n e a r Programming". M i l l s , Edwin S. P r i c e , Output and Inventory P o l i c y . "A Study i n the Economics of the Firm and Industry". John Wiley and Sons Inc., 1962. Nelson, James R. Marginal Cost P r i c i n g i n P r a c t i c e . P r e n t i c e H a l l Inc., 1964. Ruggles, Nancy. "Recent Developments i n the Theory of Marginal Cost P r i c i n g " , Review of Economic S t u d i e s . V o l . 17, 1949-1950, pp. 107-126. Spencer, M.H. and Siegelman, L. Managerial Economics: D e c i s i o n Making and Forward Planning. Revised e d i t i o n . Homewood I l l i n o i s : Richard D. I r w i n I n c., 1964. S t i g l e r , George J . "The Kinky Ol i g o p o l y Demand Curve and R i g i d P r i c e s " , J o u r n a l of P o l i t i c a l Economy, LV, 1947. S t i g l e r , George J . The Theory of P r i c e . Revised e d i t i o n . New York: The MacMillan Co., 1952. "The Marginal Revenue Curve Under P r i c e D i s c r i m i n a t i o n " , American Economic Review. XXXI, Dec. 1941, pp. 794-802. APPENDIX APPENDIX THE CHLORALKALI MODEL In a c a p i t a l i n t e n s i v e i n d u s t r y such as c h l o r a l k a l i where v a r i a b l e costs represent a small p r o p o r t i o n of the s e l l i n g p r i c e , the cost information as provided by a standard cost accounting system d i d not provide the required i n f o r m a t i o n f o r guiding the company d e c i s i o n makers. The best a l t e r n a t i v e at the time was to develop costs based upon a l t e r n a t e value or opportunity c o s t s . Thus the cost of securing an a l t e r n a t i v e was equal to the net r e t u r n of the best a l t e r n a t i v e . To give guidance i n s e t t i n g the production r a t e s , production mix, and the best a l l o c a t i o n of products to markets, the concept of marginal analy-s i s was introduced to determine maximum p r o f i t c o n d i t i o n s . Often the c o n d i t i o n s f o r maximum p r o f i t could not be immediately im-plemented due to other f a c t o r s which could not be included i n the l i n e a r program model. For example, the impact of a change i n the c h l o r a l k a l i d i v i s i o n s p o l i c y or marketing philosophy on the o v e r a l l c o r p o r a t i o n was d i f f i c u l t to measure and many d e c i s -ions were made w i t h i n the c o n s t r a i n t s of o v e r a l l corporate p o l i c y . The l i n e a r program as developed f o r the c o r p o r a t i o n was r e l a t i v e l y s t r a i g h t forward i n c o n s t r u c t i o n but large i n s i z e w i t h 144 v a r i a b l e s i n the program. Many of the v a r i a b l e s were used to define r e l a t i o n s h i p s and c o n d i t i o n s more p r e c i s e l y and 60 have l i t t l e s i g n i f i c a n c e to the model i t s e l f . To i l l u s t r a t e the basic c o n s t r u c t i o n , a s i m p l i f i e d model has been developed. Out of nec e s s i t y the p r e c i s e q u a n t i t i e s and r e l a t i o n s h i p s have been changed to avoid the r e l e a s e of c o n f i d e n t i a l information. I. SIMPLIFIED MODEL eoAJsrea/Ajrs { X, V> x, -7.1 -0.3 63.0 60.0 DC. fiocoee. cwac/ry WKWH *7SO +2.7S CEU. CMlO&HOE POOL M 7bAJ ± 0 -ho H03 CSLL CAosnC Pooc K» TOAi ± o +/0L, BULK. CMLO&A)£ POOL. ro TON) * o -AO Ho SO*A OAOsr/C fiooC /yffo/O £ o -AO +/.0 ChU>&/fO£ 0PPd4T0Riri6S m ro/O ±280 -AO £4</sr/£ ofiPoewM/nes /» TON <z30Q -AO A l g e b r a i c Representation +2.75 X, -1.0 X +1.03 X 2 -1.1 X, +1.06 X, 1.0 X„ +1.0 X '3 2 "4 1.0 X 75.0 <• 0 ± 0 +1.0 X ±0 •1.0 X, "£28.0 •1.0 X 5 £30.0 MAXIMIZE PROFIT = -7.2 X, -0.3 X„ -5.1 X_ +63.0 X. +60.0 X c 1 2 3 4 5 Imput Requirements a) Process y i e l d s and production r e l a t i o n s h i p s b) P l a n t c a p a c i t i e s c) V a r i a b l e operating costs d) Market c o n s t r a i n t s e) Market r e l a t i o n s h i p s f ) Net returns f o r each product by market The values of the f i r s t three items changed i n f r e q u e n t l y and c o n s t i t u t e d the b a s i c production matrix. These were only updated whenever p l a n t changes occurred. The marketing items would change from time to time. The imput was completely f l e x -i b l e . Any of the market data, y i e l d s , c a p a c i t i e s or costs could be r e v i s e d or deleted and the new markets or f a c i l i t i e s added to study t h e i r e f f e c t on p r o f i t and on optimum a l l o c a t i o n of products and f a c i l i t i e s . Output Information a) optimum a l l o c a t i o n of products to market and optimum a l l o c a t i o n of production f a c i l i t i e s to supply these products. b) gross margin as determined by the accountants v a r i a b l e c o s t i n g system. c) opportunity cost of a market opportunity or product. d) marginal value of market o p p o r t u n i t i e s and p l a n t c a p a c i t i e s . e) cost of f o r c i n g . 62 The model could also be programmed to provide the f o l l o w i n g : a) c o n t r i b u t i o n to gross margin of i n d i v i d u a l products or markets ( p a r a l l e l s t u d i e s or parametric programming) b) s e n s i t i v i t y of gross margin and optimum a l l o c a t i o n to c o s t s , net returns and other input data, (cost ranging and s e n s i t i v i t y a n a l y s i s ) c) range over which marginal costs are v a l i d , ( r i g h t hand si d e ranging) d) e f f e c t on p r o f i t and a l l o c a t i o n of a simultaneous change i n s e v e r a l c o s t s , net returns or market c o n s t r a i n t s . I I APPLICATION OF THE MODEL ' Product A l l o c a t i o n to Markets: c a u s t i c / c h l o r i n e pro-d u c t i o n r a t e f i x e d . In t h i s small c h l o r a l k a l i p l a n t there were over 100 major product - market r e l a t i o n s h i p s and each of the f i f t e e n major pro-ducts had d i f f e r e n t marketing reaches. As a l l products were d e r r i v e d from s a l t , the r e l a t i o n s h i p s were i n t e r r e l a t e d . Other than i n t u i t i o n there was l i t t l e to guide management i n determin-ing the optimum a l l o c a t i o n of products to markets. Without be-labouring the p o i n t , nor being involved w i t h p r e c i s e r e l a t i o n s h i p s , i t could be shown that the model suggested a d i f f e r e n t course of a c t i o n than v a r i a b l e cost a n a l y s i s . eg: C h l o r i n e can be s o l d or used to manufacture m u r i a t i c a c i d which i n t u r n can be s o l d or reacted w i t h limestone to produce calcium c h l o r i d e . CL2 + H 2 - * - 2 H C L HCL + C a C 0 3 CaCI^ C h l o r i n e : net r e t u r n of l a s t ton s u p p l i e d $60, next ton of opportunity at $60 HCL: Cai marginal revenue $60/ton v a r i a b l e cost $ 8/ton c o n t r i b u t i o n $52/ton marginal cost $60/ton m^ r. - m.c. $ 0 marginal revenue $3l/ton v a r i a b l e cost $ 5/ton c o n t r i b u t i o n $26/ton marginal cost $31/ton m.r. - m.c. $ 0 marginal revenue $68/ton v a r i a b l e cost $29/ton c o n t r i b u t i o n $39/ton marginal costs $55/ton m.r. - m.c. $13/ton : per day:. c h l o r i n e 50 tons HCL 25 tons CaCI^ 10 tons 64 Rank by a) C o n t r i b u t i o n / t o n b) Contribution/day c) M.R. - M.C./ton 1. C h l o r i n e $52 1. C h l o r i n e $2600 1. CaCI^ $13 2. CaCL 2 $39 2. HCL $ 975 2. HCL $ 0 3. HCL $26 . 3. CaCI^ $260 3. C h l o r i n e $ 0 A n a l y s i s by c o n t r i b u t i o n suggested that the company concentrate on c h l o r i n e . A n a l y s i s by the model however suggested that the great e s t p r o f i t improvement would come from concentrate ing on calcium c h l o r i d e and that e i t h e r p r i c e s of t h i s product could be lowered to increase volume or the marketing reach extend" ed u n t i l the marginal revenue equaled the marginal cost of $55/ton or u n t i l c a p a c i t y l i m i t e d . Should c a p a c i t y l i m i t s a l e s an ex-pansion should be evaluated using net returns between the l a s t accepted and $55/ton. I f lower p r i c e s f o r c h l o r i n e or m u r i a t i c a c i d are accepted, calcium c h l o r i d e becomes a l l the more a t t r a c t -i v e . E s t a b l i s h i n g production r a t e and Balancing Sales w i t h  P r o d u c t i o n ; One problem o f t e n encountered by managers of c h l o r a l k a l i p l a n t s was the d e c i s i o n to purchase product and reduce output, or to maintain output and seek new short term markets i n order to maintain the c h l o r i n e / c a u s t i c s a l e s / p r o d u c t i o n balance. For example: I f 737o c a u s t i c were i n short supply and could be s o l d at the lowest net r e t u r n of $57/ton, what would be the c o r r e c t d e c i s i o n i f c a u s t i c could be purchased at $60/ton. 65 One s o l u t i o n was to produce s u f f i c i e n t c a u s t i c to meet t h i s r e -quirement. However as 1.0 l b . c h l o r i n e was produced f o r every 1.1 l b . of c a u s t i c , c h l o r i n e would be s u r p l u s . The dumping of surplus product i n new markets on a sporadic b a s i s was un-d e s i r e a b l e from a competitive standpoint as other c h l o r a l k a l i producers would r e t a l i a t e and destroy the s t a b i l i t y of the market. The f i r s t observation i s that c a u s t i c purchased at $60 and s o l d f o r $57 i s u n p r o f i t a b l e , however as a 1007o c o n t r a c t i s i n v o l v e d , the purchased m a t e r i a l a c t u a l l y maintains supply to a $65 market and a p r o f i t i s made on the r e s a l e , ( i . e : $57 - 60 + 65 - 60 = $2/ton) There are of course other a l t e r n a t i v e s to operate at a production l e v e l where c a u s t i c production equals s a l e s . C h l o r i n e would then be upgraded i n t o other products and higher inventory l e v e l s of c h l o r i n e based products would be maintained u n t i l s ales and production were balanced. This meant the development of other markets f o r c h l o r i n e based products i n an o r d e r l y f a s h i o n . Which markets, at what p r i c e s , w i t h what products, then became the d e c i s i o n . Obviously the most p r o f i t a b l e ones, and management must decide whether the pursue bulk c h l o r i n e , c h l o r i n e tonners, c h l o r i n e c y l i n d e r s , m u r i a t i c a c i d , calcium c h l o r i d e , lump, f l a k e , g r a n u l a r , s p e c i a l f i n e s or l i q u i d markets and determine the acceptable net returns f o r each and the optimum a l l o c a t i o n of product to market. (The optimum a l l o c a t i o n could change w i t h every new piece of business.) On the other hand 66 i t may have been more p r o f i t a b l e and e a s i e r to reduce sales of c a u s t i c based products and s e l e c t i v e l y market these products. And there would be an equal number of a l t e r n a t i v e s to the marketing of c a u s t i c and c a u s t i c based products. Managements s o l u t i o n to t h i s problem i n the past was to take the e a s i e s t course of a c t i o n . There was i n i t i a l l y a push i n the sal e s department to s e l l the surplus products. I f t h i s f a i l e d , a f t e r i n v e n t o r i e s had increased, surplus product was o f f e r e d to competitors. I f a s a l e couldn't be arranged, production was reduced to br i n g c h l o r i n e i n t o balance and the shortage was purchased. C a r e f u l planning and years of management experience u s u a l l y avoided a c r i s i s and the company continued to make a p r o f i t . P r i c e s were e s t a b l i s h e d at a l e v e l the market would bear and new c a p a c i t i e s f o r any product evaluated on i t s own merits. Without using the model, the a n a l y s i s was l a r g e l y i n t u i t i v e as the c o s t i n g system maintained by the company d i d not provide the necessary guidance. The large number of a l t e r n a t i v e s to be considered lend themselves to computer a n a l y s i s and make manual a n a l y s i s i m p r a c t i c a l . Using the model, however, the e f f e c t of each change or a n t i c i p a t e d change could e a s i l y be assessed, the new optimum c o n d i t i o n determined, and p o s i t i v e a c t i o n taken. 67 Other: There are many a p p l i c a t i o n s f o r the model which ranged from assessing the p r o f i t impact of; changes i n the market s i z e and composition, p r i c e changes, l o s s of a major customer, a nonopt-imum d e c i s i o n s , an i n o p e r a t i v e production u n i t , a s t r i k e or act of god, and any proposed d e c i s i o n s . One other major a p p l i c a t i o n of the model was to evaluate s e v e r a l expansion a l t e r n a t i v e s and determine the c o r r e c t s i z i n g of each u n i t . 

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