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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.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1399.

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Length: 12 pages
Date of creation: Feb 2003
Date of revision:
Handle: RePEc:cwl:cwldpp:1399

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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Permanent income hypothesis; Afriat's theorem; Law of demand; Consumer's surplus; Testable restrictions;

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Cited by:
  1. Daniel Friedman (University of California at Santa Cruz) József Sákovics (The University of Edinburgh), 2014. "Tractable Consumer Choice," ESE Discussion Papers 240, Edinburgh School of Economics, University of Edinburgh.
  2. 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.
  3. John Geanakoplos, 2013. "Afriat from MaxMin," Cowles Foundation Discussion Papers 1904, Cowles Foundation for Research in Economics, Yale University.
  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. John Geanakoplos, 2013. "Afriat from MaxMin," Levine's Working Paper Archive 786969000000000746, David K. Levine.
  6. John Geanakoplos, 2013. "Afriat from MaxMin," Economic Theory, Springer, vol. 54(3), pages 443-448, November.

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