Testing for optimality in the absence of convexity

Herbert Scarf

Chapter 6 in Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, 2008, pp 131-148 from Palgrave Macmillan

Abstract: 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.

Keywords: Convex Hull; Lattice Point; Integer Program; Convex Body; Large Firm (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:pal:palchp:978-1-137-02441-1_6

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DOI: 10.1057/9781137024411_6

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