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Price-dependent consumption externalities and non-existence of equilibria

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  • Noguchi, Mitsunori

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.

Suggested Citation

  • Noguchi, Mitsunori, 2009. "Price-dependent consumption externalities and non-existence of equilibria," Journal of Mathematical Economics, Elsevier, vol. 45(3-4), pages 205-211, March.
  • Handle: RePEc:eee:mateco:v:45:y:2009:i:3-4:p:205-211
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    References listed on IDEAS

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    1. Pollak, Robert A, 1977. "Price Dependent Preferences," American Economic Review, American Economic Association, vol. 67(2), pages 64-75, March.
    2. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-585, October.
    3. Noguchi, Mitsunori, 2005. "Interdependent preferences with a continuum of agents," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 665-686, September.
    4. Pollak, Robert A, 1978. "Endogenous Tastes in Demand and Welfare Analysis," American Economic Review, American Economic Association, vol. 68(2), pages 374-379, May.
    5. H. Leibenstein, 1950. "Bandwagon, Snob, and Veblen Effects in the Theory of Consumers' Demand," The Quarterly Journal of Economics, Oxford University Press, vol. 64(2), pages 183-207.
    6. Bernard Cornet & Mihaela Topuzu, 2005. "Existence of equilibria for economies with externalities and a measure space of consumers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 397-421, August.
    7. Pollak, Robert A, 1976. "Interdependent Preferences," American Economic Review, American Economic Association, vol. 66(3), pages 309-320, June.
    8. Greenberg, Joseph & Shitovitz, Benyamin & Wieczorek, Andrzej, 1979. "Existence of equilibria in atomless production economies with price dependent preferences," Journal of Mathematical Economics, 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 wp361, University of Chile, Department of Economics.

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