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On the completeness of complete markets

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  • P. Herings

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  • Kirsten Rohde

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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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Suggested Citation

  • P. Herings & Kirsten Rohde, 2008. "On the completeness of complete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(2), pages 171-201, November.
  • Handle: RePEc:spr:joecth:v:37:y:2008:i:2:p:171-201
    DOI: 10.1007/s00199-007-0291-y
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    References listed on IDEAS

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    1. P. Herings & Kirsten Rohde, 2006. "Time-inconsistent preferences in a general equilibrium model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 591-619, November.
    2. R. A. Pollak, 1968. "Consistent Planning," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 201-208.
    3. 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.
    4. 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.
    5. 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.
    6. Chattopadhyay, Subir & Gottardi, Piero, 1999. "Stochastic OLG Models, Market Structure, and Optimality," Journal of Economic Theory, Elsevier, vol. 89(1), pages 21-67, 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. Drèze, Jacques H. & Herings, P. Jean-Jacques, 2008. "Sequentially complete markets remain incomplete," Economics Letters, Elsevier, vol. 100(3), pages 445-447, September.
    9. Haller, Hans, 1990. "Non-market reopening, time-consistent plans and the structure of intertemporal preferences," Economics Letters, Elsevier, vol. 32(1), pages 1-5, January.
    10. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
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    Cited by:

    1. Tommaso Gabrieli & Sayantan Ghosal, 2013. "Non-existence of competitive equilibria with dynamically inconsistent preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 299-313, January.
    2. Dziewulski, Paweł, 2015. "Efficiency of competitive equilibria in economies with time-dependent preferences," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 311-325.
    3. repec:eee:matsoc:v:87:y:2017:i:c:p:40-54 is not listed on IDEAS
    4. Peeters R.J.A.P. & Méder Z.Z. & Flesch J., 2014. "Naiveté and sophistication in dynamic inconsistency," Research Memorandum 005, Maastricht University, Graduate School of Business and Economics (GSBE).

    More about this item

    Keywords

    Time-inconsistency; Competitive equilibrium; Market completeness; Allocational equivalence; D51; D61; D91;

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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