A consistent, reflexive duality framework of production: An application of quasi-concave conjugacy theory

Abstract

The duality theory of production, as pioneered by Hotelling, Shephard, Diewert, McFadden, and others, is essential to applied production analysis (for an excellent survey see Diewert, 1982, and McFadden, 1978). When confronting actual data, it is usually more convenient to examine the cost function (and its related concepts, the profit and indirect production functions) than the production function itself. For singleproduct firms, under appropriate conditions all economically relevant information about the purely technological relationships can be obtained by observing the optimizing behavior of economic agents and economic phenomena such as costs, input prices, and derived factor demands. While traditional analysis of the theory of the firm has concentrated on single-product firms, as argued in Bailey and Friedlander (1982) "most businesses produce many products, and many regulatory and antitrust issues involve only these enterprises." While the concepts of cost and cost functions still apply in the multiproduct setting (see Baumol, 1977, and Panzar and Willig, 1977),