Center for Economic Research, Department of Economics, University of Minnesota
We extend the Second Fundamental Theorem of Welfare Economics in several
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
, 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.
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.
Hurwicz, Leonid; Richter, Marcel K..
The Second Welfare Theorem of Classical Welfare Economics.
Center for Economic Research, Department of Economics, University of Minnesota.
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