Introduction

In this chapter we have two objectives. First, we need to determine the properties that consumer demand functions must possess when they are generated on the basis of the consumer maximizing a preference function satisfying the conditions discussed in Chapter 1. Second, we need to devise procedures for actually retrieving information about consumer preferences in the form of the money-metric from the aforesaid demand functions. Unfortunately, the analytic tools required to achieve this second objective receive scant attention in most modern economics texts. In particular, we need to make clear the relationship between the marginal utility of money expenditure and the mathematical concepts of (a) the Lagrange multiplier and (b) the integrating factor. The significance of these three variables (which, in fact, are conceptually identical) is that they provide the crucial linkage that will enable us to derive the money-metric from consumer demands. In the parlance of the mathematician, we shall need to determine an integrating factor in order to form an expression from which the demand functions can be integrated to create a utility function and, more specifically, the money-metric function. For this reason it is important that we examine the roles of these variables in rather basic terms. This approach has the added advantage that it will enable us to easily identify some of the difficulties into which consumer surplus theorists and index-number theorists have fallen in the past.