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Minimality and uniqueness of equilibrium

Loi, Andrea and Matta, Stefano (2019): Minimality and uniqueness of equilibrium.

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Abstract

In this paper we propose the following conjecture: the equilibrium manifold E(r) ⊂ RLM−1, where L is the number of goods and M the number of consumers, is a minimal submanifold 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 for an arbitrary number of consumers and two goods under the assumption that the normal vector field of E(r) is constant outside a compact subset.

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