Testable Restrictions on the Equilibrium Manifold

It is shown that the property that the equilibrium manifold keeps the memory of the individual demand functions holds true if every individual demand function satisfies the following three properties: 1) It is a function of commodity prices and of consumer’s income; 2) Consumption belongs to the nonnegative orthant of the commodity space; 3) Walras law. Neither differentiability nor continuity are necessary. In addition, the demand functions do not have to be utility maximizing subject to budget constraints. Copyright Springer-Verlag Berlin/Heidelberg 2004Equilibrium manifold, Demand functions.,

Section: Introductionmentioning

confidence: 99%

The equilibrium manifold keeps the memory of individual demand functions

Balasko

2004

“…As Mas-Colell (1977a) showed, these results imply that any set of prices can be the equilibrium prices for some economy. This interpretation was challenged by Brown and Matzkin (1996), who showed that the restrictions of consumer demand that are generated by preference optimization are effectively translated into the equilibrium manifold of the economy. Brown and Matzkin (1996) showed that if individual endowments are observed, the aggregate behavior of the consumers satisfies restrictions that are derived from individual preference maximization.…”

mentioning

confidence: 99%

“…This interpretation was challenged by Brown and Matzkin (1996), who showed that the restrictions of consumer demand that are generated by preference optimization are effectively translated into the equilibrium manifold of the economy. Brown and Matzkin (1996) showed that if individual endowments are observed, the aggregate behavior of the consumers satisfies restrictions that are derived from individual preference maximization. 1 In an unpublished paper, Brown and Matzkin (1990) showed that given the equilibrium manifold of a pure exchange economy, one can identify the demand functions of all the consumers in the economy.…”

mentioning

confidence: 99%

Identification of consumers? preferences when their choices are unobservable

Matzkin

2005

Self Cite

We provide conditions under which the heterogenous, deterministic preferences of consumers in a pure exchange economy can be identified from the equilibrium manifold of the economy. We extend those conditions to consider exchange economies, with two commodities, where consumers' preferences are random. For the latter, we provide conditions under which consumers'heterogenous random preferences can be identified from the joint distribution of equilibrium prices and endowments. The results can be applied to infer consumers' preferences when their demands are unobservable.

“…Such a setting is considered in Brown and Matzkin [3], and Chiappori et al [5], (CEKP). The fact that z is defined as a function of prices and endowments has important implications on the structure of the aggregate excess demand function and the equilibrium manifold.…”

Section: Introductionmentioning

confidence: 99%

On the characterization of excess demand functions

Aloqeili¹

2005

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. Copyright Springer-Verlag Berlin/Heidelberg 2005Direct utility function, Indirect utility function, Excess demand function, Slutsky matrix.,