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On the completeness of complete markets

  • HERINGS, P. Jean-Jacques
  • ROHDE, Kirsten I.M.

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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number 2153.

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Handle: RePEc:cor:louvrp:2153
Note: In : Economic Theory, 37, 171-201, 2008
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  1. 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.
  2. Chattopadhyay, Subir & Gottardi, Piero, 1999. "Stochastic OLG Models, Market Structure, and Optimality," Journal of Economic Theory, Elsevier, vol. 89(1), pages 21-67, November.
  3. repec:tpr:qjecon:v:118:y:2003:i:4:p:1209-1248 is not listed on IDEAS
  4. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
  5. Drèze Jacques H. & Herings P. Jean-Jacques, 2003. "Sequentially complete Markets Remain Incomplete," Research Memorandum 058, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. P. Herings & Kirsten Rohde, 2006. "Time-inconsistent preferences in a general equilibrium model," Economic Theory, Springer, vol. 29(3), pages 591-619, November.
  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. George Loewenstein & Ted O'Donoghue & Matthew Rabin, 2003. "Projection Bias in Predicting Future Utility," The Quarterly Journal of Economics, Oxford University Press, vol. 118(4), pages 1209-1248.
  9. 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.
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