The Strong Law of Demand
13 Pages Posted: 17 Feb 2003
Date Written: 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
Suggested Citation: Suggested Citation