Disaggregation of excess demand functions in incomplete markets

We are interested in general equilibrium incomplete markets, where the number of consumers is N, the number of goods is L, and the dimension of the space of admissible trades is K (the case of complete markets being then K=(L−1)). We prove that, if N≥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.ou