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The Strong Law of Demand

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Abstract

We show that a demand function is derived from maximizing a quasilinear utility function subject to a budget constraint if and only if the demand function is cyclically monotone. On finite data sets consisting of pairs of market prices and consumption vectors, this result is equivalent to a solution of the Afriat inequalities where all the marginal utilities of income are equal. We explore the implications of these results for maximization of a random quasilinear utility function subject to a budget constraint and for representative agent general equilibrium models. The duality theory for cyclically monotone demand is developed using the Legendre-Fenchel transform. In this setting, a consumer's surplus is measured by the conjugate of her utility function.

Suggested Citation

  • Donald J. Brown & Caterina Calsamiglia, 2003. "The Strong Law of Demand," Cowles Foundation Discussion Papers 1399, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1399
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    Cited by:

    1. Ruediger Bachmann, 2006. "Testable Implications of Pareto Efficiency and Individualrationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 489-504, November.
    2. Donald J. Brown, 2014. "Approximate Solutions of the Walrasian Equilibrium Inequalities with Bounded Marginal Utilities of Income," Cowles Foundation Discussion Papers 1955, Cowles Foundation for Research in Economics, Yale University.
    3. John Geanakoplos, 2013. "Afriat from MaxMin," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 443-448, November.
    4. Donald J. Brown & Ravi Kannan, 2003. "Indeterminacy, Nonparametric Calibration and Counterfactual Equilibria," Cowles Foundation Discussion Papers 1426, Cowles Foundation for Research in Economics, Yale University.
    5. Donald J. Brown, 2014. "Approximate Solutions of the Walrasian Equilibrium Inequalities with Bounded Marginal Utilities of Income," Cowles Foundation Discussion Papers 1955R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2014.
    6. Daniel Friedman & József Sákovics, 2015. "Tractable consumer choice," Theory and Decision, Springer, vol. 79(2), pages 333-358, September.
    7. Bachmann, Ruediger, 2004. "Rationalizing allocation data--a nonparametric Walrasian theory when prices are absent or non-Walrasian," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 271-295, June.
    8. John Geanakoplos, 2013. "Afriat from MaxMin," Cowles Foundation Discussion Papers 1904, Cowles Foundation for Research in Economics, Yale University.
    9. Donald J. Brown & Caterina Calsamiglia, 2003. "Rationalizing and Curve-Fitting Demand Data with Quasilinear Utilities," Cowles Foundation Discussion Papers 1399R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2004.
    10. John Geanakoplos, 2013. "Afriat from MaxMin," Levine's Working Paper Archive 786969000000000746, David K. Levine.

    More about this item

    Keywords

    Permanent income hypothesis; Afriat's theorem; Law of demand; Consumer's surplus; Testable restrictions;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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