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.
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