Disaggregation of excess demand functions in incomplete markets. (English) Zbl 0958.91016
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 R. Bryant, S. Chern, R. Garner, H. Goldschmidt and P. Griffiths [Exterior Differential Systems, Publ. MSRI 18 (1991; Zbl 0726.58002)] is extensively used in the proofs.
Reviewer: George Osipenko (St.Peterburg)
MSC:
91B26 | Auctions, bargaining, bidding and selling, and other market models |
91B42 | Consumer behavior, demand theory |
91B50 | General equilibrium theory |
Keywords:
incomplete market; demand function; optimization problem; Cartan character; disaggregation problem; pressure flowCitations:
Zbl 0726.58002References:
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