The Strong Law of Demand
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.
Brown, Donald J. and Calsamiglia, Caterina, "The Strong Law of Demand" (2003). Cowles Foundation Discussion Papers. 1666.