Risk Aversion and Uniqueness of Equilibrium in Economies with Two Goods and Arbitrary Endowments

We study the connection between risk aversion, the number of consumers, and the uniqueness of equilibrium. We consider an economy with two goods and impatience types, where each type has additive separable preferences with HARA Bernoulli utility function, . We show that if , the economy has a unique...

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Bibliographic Details
Published in:The B.E. journal of theoretical economics 2023-06, Vol.23 (2), p.679-696
Main Authors: Loi, Andrea, Matta, Stefano
Format: Article
Language:English
Subjects:
C62
Consumers
D51
D58
Descartes’ rule of signs
Equilibrium
excess demand function
Newton’s symmetric polynomials
polynomial approximation
Risk
risk aversion
Uniqueness
uniqueness of equilibrium
Utility functions
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Summary:We study the connection between risk aversion, the number of consumers, and the uniqueness of equilibrium. We consider an economy with two goods and impatience types, where each type has additive separable preferences with HARA Bernoulli utility function, . We show that if , the economy has a unique regular equilibrium. Moreover, the 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 = 3.
ISSN:1935-1704
2194-6124
1935-1704
DOI:10.1515/bejte-2021-0150