We study the connection between risk aversion, the number of consumers, and the uniqueness of equilibrium. We consider an economy with two goods and I impatience types, where each type has additive separable prefer- 𝛾 ( a )1−𝛾 ences with HARA Bernoulli utility function, uH(x) := 1−𝛾 b + 𝛾 x . We show (] that if 𝛾 ∈ 1, I , the economy has a unique regular equilibrium. Moreover, the I−1 methods used, including Newton’s symmetric polynomials and Descartes’ rule of signs, enable us to offer new sufficient conditions for uniqueness in a closed-form expression that highlight the role played by endowments, patience, and specific HARA parameters. Finally, we derive new necessary and sufficient conditions that ensure uniqueness for the particular case of CRRA Bernoulli utility functions with 𝛾 = 3.

Risk aversion and uniqueness of equilibrium in economies with two goods and arbitrary endowments

Matta, Stefano
Co-primo
2022-01-01

Abstract

We study the connection between risk aversion, the number of consumers, and the uniqueness of equilibrium. We consider an economy with two goods and I impatience types, where each type has additive separable prefer- 𝛾 ( a )1−𝛾 ences with HARA Bernoulli utility function, uH(x) := 1−𝛾 b + 𝛾 x . We show (] that if 𝛾 ∈ 1, I , the economy has a unique regular equilibrium. Moreover, the I−1 methods used, including Newton’s symmetric polynomials and Descartes’ rule of signs, enable us to offer new sufficient conditions for uniqueness in a closed-form expression that highlight the role played by endowments, patience, and specific HARA parameters. Finally, we derive new necessary and sufficient conditions that ensure uniqueness for the particular case of CRRA Bernoulli utility functions with 𝛾 = 3.
Uniqueness of equilibrium; excess demand function; risk aversion; polynomial approximation; Descartes’ rule of signs; Newton’s symmetric polynomials.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/346153
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