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The complete removal of individual uncertainty: multiple optimal choices and random exchange economies

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Author Info

  • Yeneng Sun

    ()
    (Department of Mathematics, National University of Singapore, Singapore 119260, SINGAPORE)

Abstract

The aim of this paper is to develop some measure-theoretic methods for the study of large economic systems with individual-specific randomness and multiple optimal actions. In particular, for a suitably formulated continuum of correspondences, an exact version of the law of large numbers in distribution is characterized in terms of almost independence, which leads to several other versions of the law of large numbers in terms of integration of correspondences. Widespread correlation due to multiple optimal actions is also shown to be removable via a redistribution. These results allow the complete removal of individual risks or uncertainty in economic models where non-unique best choices are inevitable. Applications are illustrated through establishing stochastic consistency in general equilibrium models with idiosyncratic shocks in endowments and preferences. In particular, the existence of "global" solutions preserving microscopic independence structure is shown in terms of competitive equilibria for the cases of divisible and indivisible goods as well as in terms of core for a case with indivisible goods where a competitive equilibrium may not exist. An important feature of the idealized equilibrium models considered here is that standard results on measure-theoretic economies are now directly applicable to the case of random economies. Some asymptotic interpretation of the results are also discussed. It is also pointed out that the usual unit interval [0,1] can be used as an index set in our setting, provided that it is endowed together with some sample space a suitable larger measure structure.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 14 (1999)
Issue (Month): 3 ()
Pages: 507-544

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Handle: RePEc:spr:joecth:v:14:y:1999:i:3:p:507-544

Note: Received: September 14, 1998; revised version: January 6, 1999
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Related research

Keywords: Individual uncertainty; Removal of widespread correlations; General equilibrium models with idiosyncratic shocks.;

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Cited by:
  1. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.
  2. M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2011. "On Large Games with a Bio-Social Typology," Economics Working Paper Archive 585, The Johns Hopkins University,Department of Economics.

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