Chapter 12 Duality approaches to microeconomic theory

This chapter develops the duality between cost and production functions. The chapter derives the regularity conditions that a cost function C must have and shows how a production function is constructed from a given cost function. The chapter considers the duality between a (direct) production function F and the corresponding indirect production function G. Under certain regularity conditions, G can also completely describe the technology, and thus there is a duality between direct and indirect production functions. The duality theorems have two interpretations: one in the producer context and the other in the consumer context. The chapter discusses a variety of other duality theoremsthat is, other methods for equivalently describing tastes or technology, either locally or globally, in the one-output, N-inputs context. The mathematical theorems presented in the chapter appear to be only theoretical results devoid of practical applications. However, this is not the case. The chapter also surveys some of the applications of the duality theorems developed earlier. These applications fall in two main categories: (1) the measurement of technology or preferences and (2) the derivation of comparative statics results.