In this paper we consider the problem of stability of the competitive equilibrium. The market demand functions are sums of individual demand functions obtained directly by utility maximization. The rate of change of the price of each commodity is assumed to be proportional to the excess market...

Irving Fisher's Ph.D. thesis, submitted to Yale University in 1891, contains a fully articulated general equilibrium model presented with the broad scope and formal mathematical clarity associated with Walras and his successors. In addition, Fisher presents a remarkable hydraulic apparatus for...

The simplicial complex K(A) is defined to be the collection of simplices, and their proper subsimplices, representing maximal lattice free bodies of the form {x : Ax = b}, with A a fixed (n + 1) x n matrix. The topological space associated with K(A) is shown to be homeomorphic to R^{n}, and the...

Let A be a fixed integer matrix of size m by n and consider all b for which the body is full dimensional. We examine the set of shortest non-zero integral vectors with respect to the family of norms. We show that the number of such shortest vectors is polynomial in the bit size of A, for fixed...

The paper, prepared for a Roundtable on Major Economic Problems in the U.S. and the U.S.S.R., discusses some aspects of price theory ñ in particular, the theory of general equilibrium -ñ which may offer some theoretical insights about the economic problems to be encountered during the...