Equilibria of Heterogeneous Economies with a Continuum of Agents

The dynamic heterogeneous economies studied are described by a collection of heterogenous indi- viduals, their individual states and an aggregate state, such that the individuals' actions are given by the policy obtained from an optimization program and the aggregate law of motion is given by the aggregation of the individuals' actions. These economies have been used in computer simula- tions, however the analytical information about the equilibria of such economies is scarce and the classical approach of Stokey and Lucas with Prescott (1989) does not apply. This paper denes the relevant concepts of equilibria and proves the existence of such equilibria using the Schauder Fixed Point Theorem. In order to apply Schauder's theorem, a metric for the space of operators between measures is provided, and the compactness of a specic operator is proved. Moreover, the existence of a steady state for the aggregate state of the system is obtained through the Schauder-Tychonov Theorem. The results are related to models available in the literature.