On a Simple Equilibrium with Heterogeneous Quasi-Hyperbolic Discounting Agents

This article considers the long-run equilibrium distribution of an economy populated by heterogenous and present biased quasi-hyperbolic discounting agents. In a first configuration with logarithmic utility functions and Cobb-Douglas production technologies, this article establishes the existence and the uniqueness of the equilibrium: only one agent, determined by the highest value of a coefficient building from both the degree of present bias and the rate of discount, will have a positive long-run consumption and a positive long-run wealth. A second configuration with constant elasticities of substitution utilities and linear production technologies is then considered. This article similarly establishes the existence and the uniqueness of the equilibrium. There is generically a unique agent with the highest growth rate for his consumption and his wealth. This agent is determined by both preferences and technology parameters and may change following a technological shock.