Stochastic Dynamic Duality: Theory and Empirical Applicability

This paper explores duality relationships for a broad class of stochastic dynamic production problems. Assuming that the decision maker maximizes the expected present value of profit, it is shown that product supply, negative factor demand, and negative quasifixed factor acquisition equations cannot be directly obtained by partial differentiation of the indirect profit function if price expectations have a Markovian structure. Consequently, empirical application of duality to many stochastic dynamic problems is quite complex and may be more difficult than a primal approach to the problem.

[1]  Larry G. Epstein.  Duality Theory and Functional Forms for Dynamic Factor Demands , 1981 .

[2]  Ronald A. Howard,et al.  Dynamic Programming and Markov Processes , 1960 .

[3]  T. Kako.  The estimation of the transcendental logarithmic function and the decomposition analysis of derived demand for factor inputs : the case of rice production in Japan , 1978 .

[4]  S. S. Sidhu,et al.  Estimating Farm-Level Input Demand and Wheat Supply in the Indian Punjab Using a Translog Profit Function , 1981 .

[5]  Hans P. Binswanger,et al.  A Cost Function Approach to the Measurement of Elasticities of Factor Demand and Elasticities of Substitution , 1974 .

[6]  C. Willis,et al.  Estimation of Substitution Possibilities between Water and Other Production Inputs , 1982 .

[7]  R. Just,et al.  Economic Welfare Evaluations for Producers under Uncertainty , 1983 .

[8]  R. Weaver.  Multiple Input, Multiple Output Production Choices and Technology in the U.S. Wheat Region , 1983 .

[9]  Ramón López.  Analysis of a Small Open Economy: The Case of Energy Prices in Canada , 1982 .

[10]  S. Ray.  A Translog Cost Function Analysis of U.S. Agriculture, 1939–77 , 1982 .

[11]  R. Pope.  Expected Profit, Price Change, and Risk Aversion , 1982 .

[12]  D. Young.  RELEVANCE OF DUALITY THEORY TO THE PRACTICING AGRICULTURAL ECONOMIST: DISCUSSION , 1982 .

[13]  D. Heien.  The Structure of Food Demand: Interrelatedness and Duality , 1982 .

[14]  Michael D. Intriligator,et al.  Frontiers of Quantitative Economics. , 1972 .

[15]  Le Thanh Nghiep.  The Structure and Changes of Technology in Prewar Japanese Agriculture: Reply , 1979 .

[16]  Ramón López.  The Structure of Production and the Derived Demand for Inputs in Canadian Agriculture , 1980 .

[17]  David Easley,et al.  Characterization of optimal plans for stochastic dynamic programs , 1982 .

[18]  R. López.  APPLICATIONS OF DUALITY THEORY TO AGRICULTURE , 1982 .

[19]  L. Lau,et al.  Microeconomic Output Supply and Factor Demand Functions in the Agriculture of the Province of Taiwan , 1976 .

[20]  Lawrence J. Lau,et al.  Profit, Supply, and Factor Demand Functions , 1972 .

[21]  C. R. Taylor,et al.  TECHSIM: A Regional Field Crop and National Livestock Econometric Simulation Model , 1983 .

[22]  R. Pope.  The Generalized Envelope Theorem and Price Uncertainty , 1980 .

[23]  R. Bellman.  Dynamic programming. , 1957, Science.

[24]  R. Chambers.  Duality, the Output Effect, and Applied Comparative Statics , 1982 .

[25]  R. Pope.  To Dual or Not to Dual , 1982 .