4 - Optimality and price equilibrium
Published online by Cambridge University Press: 05 January 2013
Summary
Introduction
In this chapter we have as initial data a production set Y, a collection of preference relations ≳1,…, ≳n and a commodity vector ω ᄐ Rℓ. After defining the notion of attainable allocation, we introduce the concepts of optimality in the sense of Pareto and of price equilibrium. This chapter is devoted to the study of the interrelationships of these two concepts. Under general continuity hypotheses, Section 4.2 gathers basic definitions and the well-known facts for the convex preferences case. Under smoothness, but not convexity, assumptions, Sections 4.3 and 4.4 deal, respectively, with local first- and second-order theory, and Section 4.5 contains some results on approximate global supportability of optima by prices. Finally, Section 4.6 investigates the simplest facts about the topological and manifold structure of the set of optimal allocations.
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- Information
- The Theory of General Economic EquilibriumA Differentiable Approach, pp. 114 - 165Publisher: Cambridge University PressPrint publication year: 1985