On the characterization of excess demand functions

Summary.

In this paper, we give the necessary and sufficient conditions that characterize the individual excess demand function when it depends smoothly on prices and endowments. A given function is an excess demand function if and only if it satisfies, in addition to Walras’ law and zero homogeneity in prices, a set of first order partial differential equations, its substitution matrix is symmetric and negative semidefinite. Moreover, we show that these conditions are equivalent to the symmetry and negative semidefiniteness of Slutsky matrix, Walras’ law and zero homogeneity of Marshallian demand functions.