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Smallness of a commodity and partial equilibrium analysis

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  • Hayashi, Takashi

Abstract

Partial equilibrium analysis has a conceptual dilemma that its object should be negligibly small in order to be free from income effect but then the consumer does not care for it and the notion of willingness to pay for it does not make sense. In the setting of a continuum of commodities, we propose a limiting procedure which transforms the general many-commodity framework into a partial single-commodity framework. In the limit, willingness to pay for a commodity is established as a density notion and it is shown to be free from income effect. This pins down an exact relationship between general equilibrium analysis and partial equilibrium analysis.

Suggested Citation

  • Hayashi, Takashi, 2013. "Smallness of a commodity and partial equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 148(1), pages 279-305.
    • Handle: RePEc:eee:jetheo:v:148:y:2013:i:1:p:279-305
    DOI: 10.1016/j.jet.2012.12.017
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    References listed on IDEAS

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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, November.
    2. Hayashi, Takashi, 2008. "A note on small income effects," Journal of Economic Theory, Elsevier, vol. 139(1), pages 360-379, March.
    3. Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-832, July.
    4. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    5. Xavier Vives, 1987. "Small Income Effects: A Marshallian Theory of Consumer Surplus and Downward Sloping Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 87-103.
    6. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. , & ,, 2015. "Strategy-proofness and efficiency with non-quasi-linear preferences: a characterization of minimum price Walrasian rule," Theoretical Economics, Econometric Society, vol. 10(2), May.
    2. Hayashi, Takashi & Lombardi, Michele, 2017. "Implementation in partial equilibrium," Journal of Economic Theory, Elsevier, vol. 169(C), pages 13-34.
    3. Francesca Busetto & Giulio Codognato & Giorgia Pavan & Simone Tonin, 2023. "Cournotian duopolistic firms may be Walrasian: a case in the Gabszewicz and Vial model," Journal of Economics, Springer, vol. 140(2), pages 121-140, October.
    4. Tsuyoshi Sasaki, 2019. "Welfare evaluations and price indices with path dependency problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(1), pages 127-159, January.
    5. Hayashi, Takashi, 2014. "Consumer surplus analysis under uncertainty: A general equilibrium perspective," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 154-164.

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    Keywords

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    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D60 - Microeconomics - - Welfare Economics - - - General

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