Complementarity Modeling of a Ramsey-Type Equilibrium Problem with Heterogeneous Agents

We contribute to the field of Ramsey-type equilibrium models with heterogeneous agents. To this end, we state such a model in a time-continuous and time-discrete form, which in the latter case leads to a finite-dimensional mixed complementarity problem. We prove the existence of solutions of the latter problem using the theory of variational inequalities and present further properties of its solutions. Finally, we compute the growth dynamics in a calibrated model in which households differ with respect to their relative risk aversion, their discount factors, their initial wealth, and with respect to their interest rates on savings.