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On the Completeness of Complete Markets

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  • Herings,P. Jean-Jacques
  • Rohde,Kirsten I.M.

    (METEOR)

Abstract

We reconsider the allocational invariance of equilibria to different formulations of market completeness. We identify the so-far neglected assumption of sophisticated behavior as crucial to this result. The paper studies three market structures. First, the Arrow-Debreu setting is considered. Second, sequentially complete markets are analyzed, where goods on the spot markets and all contingent one-period ahead commodities can be traded in every state. Finally, complete markets are analyzed, where all possible contingent commodities can be traded at every state. Preferences may be time-consistent or time-inconsistent. A distinction is made between naïve and sophisticated behavior. For economies with time-inconsistent preferences, Arrow-Debreu equilibria are not related to either sequentially complete equilibria or complete equilibria. It does hold that every equilibrium consumption that can be attained in sequentially complete markets, can also be attained in complete markets. An example shows that the converse is not true for naïve economies. Finally, when preferences are restricted to be time-consistent and households are sophisticated, the three market structures yield the same equilibrium consumption. Surprisingly, for naïve households, this result is not true, even when preferences are time-consistent.

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Bibliographic Info

Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 053.

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Date of creation: 2004
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Handle: RePEc:unm:umamet:2004053

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Keywords: microeconomics ;

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References

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  1. George Loewenstein & Ted O'Donoghue & Matthew Rabin, 2001. "Projection Bias in Predicting Future Utility," General Economics and Teaching 0012003, EconWPA.
  2. Erzo G. J. Luttmer & Thomas Mariotti, 2003. "Subjective Discounting in an Exchange Economy," Journal of Political Economy, University of Chicago Press, vol. 111(5), pages 959-989, October.
  3. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
  4. Drèze, Jacques H. & Herings, P. Jean-Jacques, 2008. "Sequentially complete markets remain incomplete," Economics Letters, Elsevier, vol. 100(3), pages 445-447, September.
  5. Donaldson, John B. & Selden, Larry, 1981. "Arrow-Debreu preferences and the reopening of contingent claims markets," Economics Letters, Elsevier, vol. 8(3), pages 209-216.
  6. Subir Chattopadhyay & Piero Gottardi, 1999. "Stochastic OLG Models, Market Structure, and Optimality," Working Papers 99-12, Brown University, Department of Economics.
  7. Hellwig, Martin F., 1983. "A note on the implementation of rational expectations equilibria," Economics Letters, Elsevier, vol. 11(1-2), pages 1-8.
  8. Herings,Jean-Jacques & Rohde,Kirsten I.M., 2004. "Time-inconsistent Preferences in a General Equilibrium Model," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
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Cited by:
  1. Gabrieli, Tommaso & Ghosal, Sayantan, 2009. "Non-Existence of Competitive Equilibria with Dynamically Inconsistent Preferences," The Warwick Economics Research Paper Series (TWERPS) 900, University of Warwick, Department of Economics.

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