COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

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COWLES FOUNDATION DISCUSSION PAPER NO. 1399

The Strong Law of Demand

Donald J. Brown and Caterina Calsamiglia

February, 2003

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.

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

JEL Classification: D11, D12, D51