Curvature, Minimality and Uniqueness of Equilibrium (opens in new tab)

For a smooth pure exchange economy with fixed aggregate resources, we study two geometric conditions on the equilibrium manifold $E(r)$ endowed with the metric induced from its Euclidean ambient space. First, for arbitrary numbers of commodities and consumers, we prove that intrinsic flatness forces equilibrium prices to be locally constant. Together with Balasko's uniqueness--constancy criterion, this yields a necessary and sufficient condition...