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Duality in Production

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  • Diewert, Erwin

Abstract

The paper reviews the application of duality theory in production theory. Duality theory turns out to be a useful tool for two reasons: (i) it leads to relatively easy characterizations of the properties of systems of producer derived demand functions for inputs and producer supply functions for outputs and (ii) it facilitates the generation of flexible functional forms for producer demand and supply functions that can be estimated using econometrics. The paper focuses on describing the properties of five functional forms that have been used in the production literature: (i) the Constant Elasticity of Substitution (CES), (ii) the Generalized Leontief, (iii) the translog, (iv) the Normalized Quadratic and (v) the Konüs Byushgens Fisher functional forms. The applications of GDP functions and joint cost functions to various areas of applied economics is explained.

Suggested Citation

  • Diewert, Erwin, 2018. "Duality in Production," Microeconomics.ca working papers erwin_diewert-2018-2, Vancouver School of Economics, revised 06 Feb 2018.
  • Handle: RePEc:ubc:pmicro:erwin_diewert-2018-2
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    More about this item

    Keywords

    Production theory; duality theory; cost functions; production functions; joint cost functions; national product functions; GDP functions;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing

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