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Zbl 1121.91061
Ekeland, Ivar; Djitté, Ngalla
An inverse problem in the economic theory of demand. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 23, No. 2, 269-281 (2006). ISSN 0294-1449

Summary: Given an exchange economy consisting of $k$ consumers, there is an associated collective demand function, which is the sum of the individual demand functions. It maps the price system $p$ to a goods bundle $x(p)$. Conversely, given a map $p\rightarrow x(p)$, it is natural to ask whether it is the collective demand function of a market economy. We answer that question in the case when $k$ is less than the number of goods $n$. The proof relies on finding convex solutions to a strongly nonlinear system of partial differential equations.

MSC 2000:: *91B42 Consumer behavior etc.
58A15 Exterior differential systems (Cartan theory)
91B16 Utility theory

Keywords: utility function; aggregate demand function; inverse problems; exterior differential systems; integral manifolds

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