Fuss M., McFadden D.L. (еd.) Production Economics: A Dual Approach to Theory and Applications. Volume I. The Theory of Production

North-Holland, Amsterdam, 1978. — 482 pages — ISBN: 0-444-85012-0Volume 1 develops the theory of production from the standpoint of economic observables - prices, demands, supplies, cost, and profit-utilizing duality to relate this approach to the underlying production technology. The papers of Part I set out models of production and basic duality theorems, and discuss theoretical applications of these models.
In Chapter 1.1, McFadden provides an introduction to cost, revenue, and profit functions. The first twelve sections of his chapter provide a detailed description of properties of production and cost functions, duality, the geometry of cost functions, and the comparative statics of the firm using cost functions. The remainder of the chapter introduces the concept of the restricted profit function-of which cost, revenue, and total profit functions are special cases-and utilizes the mathematical theory of convex conjugate and polar reciprocal forms to deduce the properties implied for the restricted profit function by various properties on the technology, and vice versa. Of particular interest are Tables 1, 3, and 4 listing dual properties; Tables 2 and 5 listing composition rules for concave functions which can be used to construct functional forms or deduce theorems on production structure; and Tables 6 and 7 summarizing the duality mappings holding for restricted profit functions.
In Chapter 1.2, Hanoch shows how formal duality theory can be used to generate new functional forms for cost and production functions. This chapter explores the use and implications of structural assumptions on technology, cost, and profit in the specification of functional forms.
In Chapter 1.3, Lau applies the restricted profit function to a variety of theoretical production problems. Using the classical theory of Legendre transformations, he develops a convenient formal calculus for working with derivatives of dual production and profit functions. Lau establishes the implications for the profit function of various homotheticity and separability properties, and develops a number of specific functional forms. He considers the formulation in terms of the profit function of measures of the elasticity of technical substitution and rates of technical change. Finally, he explores the structure of production in multiple-output firms and its implications.
Part II concentrates on the development of functional forms for econometric analysis, and the interaction of functional and stochastic specification. In Chapter II. 1, Fuss, McFadden, and Mundlak set out the criteria that might be used to choose among functional forms, and use these criteria to compare many of the econometric forms appearing in the literature. The issue of stochastic specification is surveyed in the context of an extended example.
In Chapter II.2, McFadden outlines a general procedure for generating linear-in-parameters functional forms, and establishes conditions under which an arbitrary restricted profit function can be approximated to the second order by a specified approximating form.
In Chapter II.3, Hanoch applies the concepts of symmetric duality and polar production functions to develop specific functional forms for the study of substitutability in multiple-factor production functions.
In Chapter II.4, Fuss and McFadden develop a nested generalized Leontief functional form for the econometric representation of an ex ante-ex post production structure, and suggest methods for the analysis of technological flexibility within this structure.