Duesenberry Equilibrium and Heterogenous Agents

We define an inter-temporal Duesemberry Equilibrium where agents are rational agents that optimize their consumption and investment decisions with respect to the relative incomes of their peers (relative income hypothesis). We characterize these markets, provide existence and uniqueness when a sufficient weak condition is met, and develop some simple examples. We propose and solve a maximization problem by every agent to choose their optimal consumption and portfolios. The solution achieved maximize the relative well-being with respect to other members of society and A posteriori the optimization problem maximize the satisfaction on the relative magnitude of consumption in society. The theoretical framework used is a generalization of markets when the processes are Brownian Flows on Manifolds.