Values of Perfectly Competitive Economies

Sergiu Hart

This chapter is devoted to the study of economic models with many agents, each of whom is relatively insignificant. These are referred to as perfectly competitive models. The basic economic concept for such models is the competitive (or Walrasian) equilibrium, which prescribes prices that make the total demand equal to the total supply, i.e., under which the "markets clear." The fact that each agent is negligible implies that he cannot singly affect the prices, and so he takes them as given when finding his optimal consumption - "demand." The chapter is organized as follows: Section 2 presents the basic model of an exchange economy with a continuum of agents, together with the definitions of the appropriate concepts. The Value Principle results are stated in Section 3. An informal (and hopefully instructive) proof of the Value Equivalence Theorem is provided in Section 4. Section 5 is devoted to additional material, generalizations, extensions and alternative approaches.

January, 2001
Published in: 
In R. J. Aumann & S. Hart (eds.) Handbook of Game Theory, with Economic Applications. (2002) Vol. III, Ch. 57, Elsevier/North-Holland