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Duality in Production

In: Handbook of Production Economics

Author

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  • W. Erwin Diewert

    (University of British Columbia
    UNSW)

Abstract

The chapter 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 chapter 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 are explained.

Suggested Citation

  • W. Erwin Diewert, 2022. "Duality in Production," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 3, pages 57-168, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-3455-8_21
    DOI: 10.1007/978-981-10-3455-8_21
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    References listed on IDEAS

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    1. W. Erwin Diewert & Kevin J. Fox, 2016. "Sunk costs and the measurement of commercial property depreciation," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 49(4), pages 1340-1366, November.
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    26. W. Erwin Diewert & Kevin J. Fox, 2021. "The Difference Approach to Productivity Measurement and Exact Indicators," Springer Proceedings in Business and Economics, in: Christopher F. Parmeter & Robin C. Sickles (ed.), Advances in Efficiency and Productivity Analysis, pages 9-40, Springer.
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    30. Diewert, W.E., 1993. "Duality approaches to microeconomic theory," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 12, pages 535-599, Elsevier.
    31. Inklaar, Robert & Diewert, W. Erwin, 2016. "Measuring industry productivity and cross-country convergence," Journal of Econometrics, Elsevier, vol. 191(2), pages 426-433.
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    35. W. Diewert & Kevin Fox, 2010. "Malmquist and Törnqvist productivity indexes: returns to scale and technical progress with imperfect competition," Journal of Economics, Springer, vol. 101(1), pages 73-95, September.
    36. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    37. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
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    Cited by:

    1. Chihiro Shimizu & Erwin Diewert & Koji Nomura, 2024. "Estimating Flexible Functional Forms using Macroeconomic Data," Working Papers e206, Tokyo Center for Economic Research.
    2. Chao Chiung Ting, 2020. "Lucas Paradox, Declining Labor Share, Tendency of Rate of Profit to Fall of Karl Marx and Growth Theory of the Firm," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 12(9), pages 1-53, September.

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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; Variable profit functions; Properties of producer demand and supply functions; Shephard’s Lemma; Hotelling’s Lemma; Samuelson’s Lemma; Flexible functional forms; Estimation of technical progress; The valuation of public sector outputs; Modeling monopolistic behavior; Sunk costs;
    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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