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Testing for optimality in the absence of convexity

In: Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research

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  • Herbert E. Scarf

Abstract

The modern treatment of the fundamental theorems of welfare economics was developed by two of the masters of our trade: Kenneth J. Arrow (1951) and Gerard Debreu (1951). The contrast between their presentation and that offered by a distinguished predecessor — Abba Lerner — is a striking illustration of the emergence of a new line of argumentation in economic theory. The index to Lerner’s book, The economics of control (1944), contains not a single reference to convex sets nor to the separating hyper-plane theorem: The basic mathematical tools used by Arrow and Debreu to demonstrate the relationship between prices and Pareto optimality.

Suggested Citation

  • Herbert E. Scarf, 2008. "Testing for optimality in the absence of convexity," Palgrave Macmillan Books, in: Zaifu Yang (ed.), Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, chapter 6, pages 131-148, Palgrave Macmillan.
    • Handle: RePEc:pal:palchp:978-1-137-02441-1_6
    DOI: 10.1057/9781137024411_6
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