Chapter III.2 - Hicks' Aggregation Theorem and the Existence of a Real Value-Added Function

Abstract

This chapter focuses on Hicks' Aggregation Theorem and the existence of a real value-added function. The received theory of consumer demand, which deals with the case of a decision-making unit which maximizes a utility function subject to a budget constraint, treats commodities as well-defined and distinct. It turns out that the use of aggregates in the theory of consumer demand can be justified, provided that all price changes within an aggregate are proportional. This result is known as Hicks' Aggregation Theorem. The chapter discusses the problem of minimizing the cost of producing one unit of nominal value-added, and develops a duality theorem between the resulting cost function and the value-added function. It also discusses duality between direct and conditional indirect utility functions. The chapter describes the use of aggregate commodities in consumer demand studies could be justified without making any restrictive assumptions on the functional form of the micro utility function if the prices of the micro commodities within a group varied in strict proportion. The replacement of real output by deflated value-added in production function studies could be justified without making any restrictive assumptions on the functional form of the micro production (or transformation) function, provided that prices of outputs and intermediate inputs varied in strict proportion.