In this paper we propose the following conjecture: the equilibrium manifold E(r) 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.
Minimality and uniqueness of equilibrium
Loi Andrea;Matta Stefano
2018-01-01
Abstract
In this paper we propose the following conjecture: the equilibrium manifold E(r) 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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