Existence of competitive equilibrium when incomes may be zero |
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Authors: | H. Abraham D. R. Smart J. Whittaker |
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Affiliation: | (1) Department of Economics, University of Cape Town, 7700 Rondebosch, South Africa;(2) Department of Mathematics, University of Cape Town, 7700 Rondebosch, South Africa;(3) Economics Division, Staffordshire University, Leek Rd., ST4 2DF Stoke-on-Trent, England |
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Abstract: | Summary In a pure exchange economy, there exists a price vector which is a quasi-equilibrium (Debreu 1962), but this may not be a competitive equilibrium if some individuals' demand functions are discontinuous because their incomes may be zero. We show nonetheless, in a pure exchange economy with free disposal, that there is asequence of prices approaching the quasi-equilibrium along which total excess demands tend to a non-positive limit.Comments on earlier drafts from K. J. Arrow, D. Duffie, H. E. Scarf, and D. Schmeidler are gratefully acknowledged. |
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