Disaggregation of excess demand functions in incomplete markets
The paper studies general equilibrium incomplete markets, where the number of consumer is \(N\), the number of goods is \(L\), and dimension of the space of admissible trades is \(K\). If \(K=L-1\), the market is complete. The market is incomplete if certain trades are not possible. Such situations arise naturally in the framework of risk-trading. The authors prove that, if \(N\geq K\), any non-vanishing analytic function satisfying the natural extension of the Walras law is, locally at least, the excess demand function of such a market. The technique of differential geometry due to \textit{R. Bryant, S. Chern, R. Garner, H. Goldschmidt} and \textit{P. Griffiths} [Exterior Differential Systems, Publ. MSRI 18 (1991; Zbl 0726.58002)] is extensively used in the proofs.
scientific article; zbMATH DE number 1330473