Duality in Production

Walter Diewert

Chapter 3 in Handbook of Production Economics, 2022, pp 57-168 from Springer

Abstract: 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.

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; C02; C32; C43; D24; D42; D92; E01; E22; F11; H44; L51; M40; O47 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/978-981-10-3455-8_21

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