Abstract
We study the existence of solutions to a nonlinear functional differential system that describes the equilibrium of a dynamic stochastic economy with heterogeneous agents facing borowing constraints. Our model is a generalization of the one studied in Scheinkman and Weiss [3] to display the effect of borrowing constraints in aggregate economic activity, and the mathematical techniques that we developp can be useful to deal with more complex models.The system has aspects of a free boundary value problem in which there are different equations for different domains, with the domains themselves and their boundary determined by the solutions. It also has some of the characteristics of hyperbolic systems that one would obtain by differentiating Hamilton-Jacobi equations. These aspects combine to require, at least apparently, a very specific new approach to the existence problem. One payoff of this technique is that the existence proof is also an algorithm for computation.
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