The Second Welfare Theorem of Classical Welfare Economics
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The Second Welfare Theorem of Classical Welfare Economics
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2001-08
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Center for Economic Research, Department of Economics, University of Minnesota
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Working Paper
Abstract
We extend the Second Fundamental Theorem of Welfare Economics in several
directions.
For pure exchange economies, we drop all insatiability requirements on preferences.
For economies with production, we use a concept of directional optimality to
provide necessary and sufficient conditions for a given allocation to be competitive.
This enables us to show, for example, that not all consumers need to be
locally nonsatiated, if the economy is "connected." (An example due to Stanley
Reiter shows that such extra conditions are unavoidable.)
We use weak assumptions on feasibility sets, allowing, but not requiring,
short sales and a very general form of disposability. We do not require that
preferences be reflexive, transitive, total, or negatively transitive; and we replace
full continuity of preferences by a semicontinuity condition for strict preferences.
This provides decentralization results extending some of Arrow's original results
[1], as well as those in Arrow and Hahn [2, Theorem 4, pp. 93-94] Debreu
[6, Theorem 6.4, p. 95], [4, p. 281], and elsewhere.
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Discussion Paper
312
312
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Previously Published Citation
Hurwicz, L. and Richter, M.K., (2001), "The Second Welfare Theorem of Classical Welfare Economics", Discussion Paper No. 312, Center for Economic Research, Department of Economics, University of Minnesota.
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Hurwicz, Leonid; Richter, Marcel K.. (2001). The Second Welfare Theorem of Classical Welfare Economics. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/55879.
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