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A social welfare function characterizing competitive equilibria of incomplete financial markets

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  • Mario Tirelli
  • Sergio Turner

Abstract

A classic characterization of competitive equilibria views them as feasible allocations maximizing a weighted sum of utilities. It has been applied to establish fundamental properties of the equilibrium notion, such as existence, determinacy, and computability. However, it fails for economies with missing financial markets. We give such a characterization for economies with missing financial markets, by an amended social welfare function. Its parameters capture both the relative importance of households’ welfare–the classic weights–as well as the disagreements among them as to the value of the missing markets. As a by-product, we identify the dimension of the set of interior equilibrium allocations.

Suggested Citation

  • Mario Tirelli & Sergio Turner, 2008. "A social welfare function characterizing competitive equilibria of incomplete financial markets," Departmental Working Papers of Economics - University 'Roma Tre' 0093, Department of Economics - University Roma Tre.
  • Handle: RePEc:rtr:wpaper:0093
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    References listed on IDEAS

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    1. Mantel, Rolf R, 1971. "The Welfare Adjustment Process: Its Stability Properties," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 12(3), pages 415-430, October.
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    3. Atsushi Kajii & Antonio Villanacci & Alessandro Citanna, 1998. "Constrained suboptimality in incomplete markets: a general approach and two applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 495-521.
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    5. Joseph E. Stiglitz, 1982. "The Inefficiency of the Stock Market Equilibrium," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 241-261.
    6. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics,in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
    7. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
    8. Siconolfi, P & Villanacci, A, 1991. "Real Indeterminacy in Incomplete Financial Market Economies without Aggregate Risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(3), pages 265-276, July.
    9. Tirelli, Mario, 2008. "Constrained inefficiency in GEI: A geometric argument," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1197-1214, December.
    10. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
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    More about this item

    Keywords

    incomplete markets; social welfare function; manifold;

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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