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Small Income Effects: A Marshallian Theory of Consumer Surplus and Downward Sloping Demand

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  • Xavier Vives

Abstract

We formalize the Marshallian idea that when the proportion of income spent on any commodity is small then the income effects are small. If n is the number of goods, we show, under certain assumptions on preferences and prices, that the order of magnitude of the norm of the income derivative of demand is 1/√n. As a corollary we get that for the case of a single price change the percentage error in approximating the Hicksian Deadweight Loss by its Marshallian counterpart goes to zero at least at the rate 1/√n and that demand is downward sloping for n large enough.

Suggested Citation

  • Xavier Vives, 1987. "Small Income Effects: A Marshallian Theory of Consumer Surplus and Downward Sloping Demand," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 87-103.
  • Handle: RePEc:oup:restud:v:54:y:1987:i:1:p:87-103.
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    File URL: http://hdl.handle.net/10.2307/2297448
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    2. Edward Schlee, 2008. "Expected consumer’s surplus as an approximate welfare measure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(1), pages 127-155, January.
    3. Eilon Solan & Nicolas Vieille, 2006. "Equilibrium uniqueness with perfect complements," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 721-726, August.
    4. A. Dickson & R. Hartley, 2005. "The strategic Marshallian cross and bilateral oligopoly," The School of Economics Discussion Paper Series 0523, Economics, The University of Manchester.
    5. Terence C. Burnham, 2016. "Economics and evolutionary mismatch: humans in novel settings do not maximize," Journal of Bioeconomics, Springer, vol. 18(3), pages 195-209, October.
    6. Hayashi, Takashi, 2013. "Smallness of a commodity and partial equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 148(1), pages 279-305.
    7. Morimoto, Shuhei & Serizawa, Shigehiro, 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.
    8. John H. Nachbar, 1998. "The last word on Giffen goods?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 403-412.
    9. Ghosal, Sayantan, 2006. "Intertemporal coordination in two-period markets," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 11-35, December.
    10. Miyake, Mitsunobu, 2006. "On the applicability of Marshallian partial-equilibrium analysis," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 176-196, September.
    11. Klaus Ritzberger & Frank Milne, 2002. "Strategic pricing of equity issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 271-294.
    12. Dickson, Alex & Hartley, Roger, 2008. "The strategic Marshallian cross," Games and Economic Behavior, Elsevier, vol. 64(2), pages 514-532, November.
    13. repec:eee:jetheo:v:169:y:2017:i:c:p:641-665 is not listed on IDEAS
    14. Amir, Rabah & Evstigneev, Igor V., 2018. "A new look at the classical Bertrand duopoly," Games and Economic Behavior, Elsevier, vol. 109(C), pages 99-103.
    15. Junichi Minagawa & Thorsten Upmann, 2016. "Price Effects on Compound Commodities," CESifo Working Paper Series 6060, CESifo Group Munich.
    16. Hayashi, Takashi, 2008. "A note on small income effects," Journal of Economic Theory, Elsevier, vol. 139(1), pages 360-379, March.
    17. Jozsef Sakovics & Daniel Friedman, 2011. "The marginal utility of money: A modern Marshallian approach to consumer choice," ESE Discussion Papers 209, Edinburgh School of Economics, University of Edinburgh.
    18. Amir, Rabah & Erickson, Philip & Jin, Jim, 2017. "On the microeconomic foundations of linear demand for differentiated products," Journal of Economic Theory, Elsevier, vol. 169(C), pages 641-665.
    19. Hayashi, Takashi & Lombardi, Michele, 2017. "Implementation in partial equilibrium," Journal of Economic Theory, Elsevier, vol. 169(C), pages 13-34.
    20. Hayashi, Takashi, 2014. "Consumer surplus analysis under uncertainty: A general equilibrium perspective," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 154-164.
    21. Giuseppe Freni, 2001. "Sraffa's early contribution to competitive price theory," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 8(3), pages 363-390.
    22. Burkey, Mark L., 2010. "Geographic Access and Demand in the Market for Alcohol," The Review of Regional Studies, Southern Regional Science Association, vol. 40(2), pages 159-179.
    23. Michael Jerison & John K.-H. Quah, 2006. "Law of Demand," Discussion Papers 06-07, University at Albany, SUNY, Department of Economics.

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