Minimal entropy and uniqueness of price equilibria in a pure exchange economy

We introduce uncertainty into a pure exchange economy and establish a connection between Shannon’s differential entropy and uniqueness of price equilibria. The following conjecture is proposed under the assumption of a uniform probability distribution: entropy is minimal if and only if the price is...

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Bibliographic Details
Published in:Journal of mathematical economics 2021-12, Vol.97, p.102555, Article 102555
Main Authors: Loi, Andrea, Matta, Stefano
Format: Article
Language:English
Subjects:
Arbitrariness
Consumers
Entropy
Entropy (Information theory)
Equilibrium
Equilibrium manifold
Minimal submanifold
Nonlinear equations
Price multiplicity
Prices
Probability
Uncertainty
Uniqueness
Uniqueness of equilibrium
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Summary:We introduce uncertainty into a pure exchange economy and establish a connection between Shannon’s differential entropy and uniqueness of price equilibria. The following conjecture is proposed under the assumption of a uniform probability distribution: entropy is minimal if and only if the price is unique for every economy. We show the validity of this conjecture for an arbitrary number of goods and two consumers and, under certain conditions, for an arbitrary number of consumers and two goods.
ISSN:0304-4068
1873-1538
DOI:10.1016/j.jmateco.2021.102555