Endowments, patience types, and uniqueness in two-good HARA utility economies

TL;DR

This paper explores how endowments and patience types influence the uniqueness of equilibrium in a two-good economy with HARA utility functions, providing conditions that guarantee equilibrium uniqueness across all utility parameters.

Contribution

It establishes sufficient conditions linking endowments, patience types, and HARA utility parameters to ensure equilibrium uniqueness in a two-good economy.

Findings

Provides conditions for equilibrium uniqueness for all HARA utility parameters.

Extends previous results on equilibrium uniqueness in pure exchange economies.

Analyzes the impact of patience types and endowments on economic stability.

Abstract

This paper establishes a link between endowments, patience types, and the parameters of the HARA Bernoulli utility function that ensure equilibrium uniqueness in an economy with two goods and two impatience types with additive separable preferences. We provide sufficient conditions that guarantee uniqueness of equilibrium for any possible value of $\gamma$ in the HARA utility function $\frac{\gamma}{1-\gamma}\left(b+\frac{a}{\gamma}x\right)^{1-\gamma}$. The analysis contributes to the literature on uniqueness in pure exchange economies with two-goods and two agent types and extends the result in [4].