The Principle of Two-stage Maximization in Price Theory

One of the most important methodological contributions made by Sir John R. Hicks’s classic work on Value and Capital (1946 ed, p. 312-13) is the ‘Composite-Good Theorem’, which states that a group of commodities with fixed relative prices can be treated analytically as an ordinary individual commodity. It is on the basis of this theorem that Hicks was able to reduce the general multicommodity model to a two-dimensional indifference curves diagram where all but one of the commodities are lumped into a single composite good. To prove this theorem Hicks applies (in an appendix) advanced-calculus techniques which became the usual tools for analyses of this kind. The purpose of this paper is to show how the composite good theorem and some of its important applications in the theory of the firm can be derived alternatively by a principle which can be called ‘Two-Stage Maximization’ (in short tsm). ¹ The advantage of this approach is both in its mathematical simplicity and in its intuitive appeal.