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.

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

Loi, A.;Matta, S.
2021-01-01

Abstract

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.
2021
Entropy; Uniqueness of equilibrium; Price multiplicity; Equilibrium manifold; Minimal submanifold
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/327234
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