# Geodesics on the equilibrium manifold

*Andrea Loi* and
*Stefano Matta*

*Journal of Mathematical Economics*, 2008, vol. 44, issue 12, 1379-1384

**Abstract:**
We show the existence of a Riemannian metric on the equilibrium manifold such that a minimal geodesic connecting two (sufficiently close) regular equilibria intersects the set of critical equilibria in a finite number of points. This metric represents a solution to the following problem: given two (sufficiently close) regular equilibria, find the shortest path connecting them which encounters the set of critical equilibria in a finite number of points. Furthermore, this metric can be constructed in such a way to agree, outside an arbitrary small neighborhood of the set of critical equilibria, to any given metric with economic meaning.

**Keywords:** Equilibrium; manifold; Regular; equilibria; Catastrophes; Riemannian; metric; Geodesics; Income; redistribution (search for similar items in EconPapers)

**Date:** 2008

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:mateco:v:44:y:2008:i:12:p:1379-1384

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