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Risk in Production Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 5-1984 Risk in Production Mamadou Dian Diallo Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Economics Commons Recommended Citation Diallo, Mamadou Dian, "Risk in Production" (1984). All Graduate Theses and Dissertations. 4143. https://digitalcommons.usu.edu/etd/4143 This Dissertation is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. ii ACKNOWLEDGMENTS I wish to express my sincere gratitude to my major professor, Dr . Terrence F. Glover , who made this study possible. His constant encouragement , availability, care, and patience through this resarch are invaluable and unforgettable. I am deeply g r ateful to Dr. Basudeb Biswas for his friendship, encouragement and he l p through the year s at Utah State University. I wish to especially thank Dr. Cris Lewis, Head of the Economics Department , who was always available whenever I needed assistance and help at Utah Stat e University. I extend my appreciation and thanks to Dr. Bruce Godfrey and Dr . Robert Lamb, mem bers of my s upe rvisory comm it t ee for reviewing this wo r k. Financial assistance was pr ovided through the Utah Agricultural Experiment Station . I wish to express my appreciation to Janet Alderman for typing this dissertation. Mamadou Dian Diallo iii TABLE OF CONTENTS Page ACKNOWLEDGMENTS . ii LIST OF TABLES • v LIST OF FIGURES . vi ABSTRACT •••• vii Chapter I . INTRODUCTION . Problem Statement 3 Objectives 4 Literature Review 5" Optimization Models Under Risk. 7 Monte Carl o Programming • 15 Current Risk Studies by Use of Production Structures and Econometrics Models ••••.••••••.• 17 II. ~~ru~ING , ~ASURES, AND BEHAVIOR TOWARD RISK 20 Definiti on of Risk •••. 21 Risk Aversion . 21 Measure of Risk Aversion . 24 Measures of Risk. 27 The Theory of the Firm and Behavior Toward Risk • • • • • • • • • • • • 32 Review of the Mean Va r iance Approach to Assessing Risk and Its Limitations 43 The Two-Stage Decision Process and the Concept of Increasing Risk. • • • • • • 47 III. INCORPORATING RISK INTO PRODUCTION STRUCTURES 68 Incorporating Risk into Profit Functions . 69 Estimation of Output Supply , Fac t or Demand and Profit Functions ••••• 75 Stochastic Production Structure • • • 78 The Cobb- Do uglas Production Function. 79 The Quad ratic Production Function . 79 Stochastic Production Method ••••• 80 Advan tages , Limitations and Conclusions 88 i v TABLE OF CONTENTS (Cont . ) Page Chapter IV . ESTIMATION OF THE IMPACTS OF RISK IN UTAH RANCHING 91 Estimation Procedure. 96 Estimation Procedure for the Cobb- Douglas Production Function • • • • • • • • • 97 Estimation of the Quadratic Function. 100 Modeling Results •••• •• •• 101 Suggestions for Future Research 107 BIBLIOGRAPHY 109 VITA • • • • 114 v LIST OF TABLES Table Page 1 . Utah Ranch Operation Data ••. • ••••• 94 2. Cobb- Douglas Production Function Estimation for Cow- Calf Operation in Utah (Six Variables) . 102 3. Cobb- Douglas Production Function Estimation for Cow- Calf Operation in Utah (Five Variables) 103 vi LIST OF FIGURES Figure Page l. Concave utility function for a risk averse individual • • • 22 2. Convex utility function for a risk prone individual •• • • 25 3. Comparison between two probabilities distribution with the same mean and different variance. A is riskier than B. • • • • • 28 4. Density functions 31 5 . Distribution functions . 31 6 . Concave function 33 7. Convex func t ion • 33 8 . The tangency point (C) between the utility curve and the E- V frontier (AB) is the optimum 45 9 . The E- V frontier is the lows of tangency between the !so- Revenue curve and the !so- Variance curve . • . 46 10. Two-stage decision process. 49 !1. Elastic and inelastic supply-­ response to price change • ••• 52 vii ABSTRACT Risk in Production by Mamadou Dian Diallo , Doctor of Philosophy Utah State University, 1984 Major Professor: Dr. Terrence F. Glover Department: Economics Most production activities undertaken involve a certain degree of risk. Agricultural pr oduction is particularly risky since it is susceptible to the physical vagaries of nature a nd all economic and social variations. For most countries, agriculture is an important and vital sector whe r e production decisions a r e made under risk. Hence , decision making under risk requires careful analysis and represents an important area of study. The present r esearch has been directed to advance our knowledge about the consequences of risk, and the behavior t owa rd risk in the o rganization of production, particularly agricultural production. This ob j ective is ach i eved by a review of risk theory , duality and the use of applied economet rics in order to develop some empirical production structures capable of assessing the impacts of risk, particularly increasing risk, on pr oducer's behavior. The concep t of increasing risk as incorporated into production structures is then applied to a livestock example in Utah. A stochastic prod uction function for ranch viii operations in Utah is estimated in order to derive information about the impacts of increasing risk on the output and input choices of ranchers. The results of the estimation and tests suggest that ranchers in Utah produce with inflexible production technology and a r e s ubject to significant production risk. Any policy affecting the use of inputs such as feed and pasture may exacerbate the risk condition which the ranchers face, since c hoices to employ alternative input combination to modify the condition of r isk are limited. (122 pages) CHAPTER I I NTRODUC TION Production in al l sec t o r s of the economy such as ag ricultu re , industry , se rvices , has always been subject t o risk. Risk and unce r tainty are causes of worries, f rus trations and insecurity for many people . Today, mo r e tha n ever, individuals and society are always looking for better wa ys to reduce insecurity and imp r ove decision­ making under risk. In modern societies , huge investment projec t s and produc tion decisions requiring risk assessment and risk-benefit tradeoffs a r e undertaken everyday. As a result, the insurance indus try is continuously growing and becoming an important necessity of economic development. Agricultu r a l production, energy produc tion (nuclear, hydro, and coal), education and health, strategic a rms lim~tations a nd genetic engineering are a few examples where expected benefits must be weighed agains t uncerta in and possibly severe losses. Hence, judgment under r isk and un ce rta inty constitutes an importa nt a r ea of s tudy. I n the ag ric ultural sector, whi ch is the main concern of this study, farming and ranching involves a g reat deal of risk since these enterprises are not only business activities but a lso ways of life . As a business activity, that i s a syst em of production, distribution and exchange , it is susceptible to all social and economic unce rtainties which any o ther similar econom ic acti vity, s uch as mining or industry, is called upon to face. As a mode of living, it has been r eckoned wi t h all the personal uncertainties arising from death o r impairment of health of the farmer or rancher thr ough sickness and accident and also 2 from the inability of agricultu r al laborers to sell or effectively employ their labor power. On top of all these, agriculture is especially susceptible to the physical variations of nature since it requires, as distinguished from most other majo r forms of business enterprises , extensive , direct and continuous contact with the forces of nature. Major operations have to be carried on in the open and the operator must be prepared to deal with various adverse elements like drought , flood , frost , hail, s t orm , earthquake, fire etc. All these hazards can make agriculture a very risky enterprise. The risk elements faced by agricultural pr oducers are generally classified into p roduction and price risk. L. Production risk is the risk which affects output and which arises because of variations in the combination of iputs to produce output. Production ri sk is also caused by variations in weathe r, prevalence of pest and disease , natural causes, such as fire, earthquake and drought, as well as varia tions in the application of t echnology in pr oduction. 2. Price risk is the risk which affects the price the producer r eceives for the goods he produces or the inputs he plans to purchase. Price variability may be gene r ated by supply variability or demand variability. For the market as a whole, price and production variability are intimately connected : variations in ou tput lead to variations in prices. These variations affect the farmer's income, his purchasing power and his level of satisfaction (utility). There is another form of risk which reflects the combined effects of production (or t echnol ogical risk) and price risk. This is the 3 concept of profit risk (Epstein, 1978). Net returns may be quite variable and this va riabilit y can be produced from a combination of risky factors . Problem Statement During the past decades , economists and econometricians have realized more and more the importance of the ris k factor in under­ standing the behavior of producers and have developed formal models to analyze the consequences of risk. There have been numerous studies in the litera ture concerning the problem of incorporating price risk into the behavi o r of a competitive firm. However , in spite of these efforts and the importance of varia tion in production, o ur understanding of r isk in production remains r a ther limited.
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