COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281 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 |