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Price-dependent consumption externalities and non-existence of equilibria

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  • Noguchi, Mitsunori
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    Abstract

    We construct a concrete example of an exchange economy which admits no equilibria in the presence of price-dependent consumption externalities. In our example, agents form a finite atomless measure space . A reference coalition of each agent t at a price system p is the subset C(t,p)[subset of]T consisting of those agents whose income falls into a certain income range associated with t. The interdependence of the taste of agent t operates through a reference consumption vector [eta], which represents the aggregated effect on t's taste of the various consumption choices made by all agents in C(t,p). We choose , the mean consumption bundle of all agents in C(t,p), where denotes the assignment of a commodity bundle to agent s and where the measure (1/([mu][C(t,p)]))[mu] may be interpreted as the relative frequencies of contact that t makes with other members in C(t,p). In light of the law of large numbers, the above [eta] can be viewed as the consumption trend of the agents in C(t,p), which influences the taste of t.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 45 (2009)
    Issue (Month): 3-4 (March)
    Pages: 205-211

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    Handle: RePEc:eee:mateco:v:45:y:2009:i:3-4:p:205-211

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    Web page: http://www.elsevier.com/locate/jmateco

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    Keywords: Interdependent preferences Measure space of agents Equilibrium;

    References

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    1. Pollak, Robert A, 1976. "Interdependent Preferences," American Economic Review, American Economic Association, American Economic Association, vol. 66(3), pages 309-20, June.
    2. SCHMEIDLER, David, . "Competitive equilibria in markets with a continuum of traders and incomplete preferences," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -62, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Pollak, Robert A, 1977. "Price Dependent Preferences," American Economic Review, American Economic Association, American Economic Association, vol. 67(2), pages 64-75, March.
    4. Bernard Cornet & Mihaela Topuzu, 2005. "Existence Of Equilibria For Economies With Externalities And A Measure Space Of Consumers," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 200505, University of Kansas, Department of Economics, revised Feb 2005.
    5. Pollak, Robert A, 1978. "Endogenous Tastes in Demand and Welfare Analysis," American Economic Review, American Economic Association, American Economic Association, vol. 68(2), pages 374-79, May.
    6. Noguchi, Mitsunori, 2005. "Interdependent preferences with a continuum of agents," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 41(6), pages 665-686, September.
    7. Greenberg, Joseph & Shitovitz, Benyamin & Wieczorek, Andrzej, 1979. "Existence of equilibria in atomless production economies with price dependent preferences," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 6(1), pages 31-41, March.
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    Cited by:
    1. Sebastián Cea-Echenique & Carlos Hervés-Beloso & Juan Pablo Torres-Martínez, 2012. "Endogenous Information: The Role of Sequential Trade and Financial Participation," Working Papers, University of Chile, Department of Economics wp361, University of Chile, Department of Economics.

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