Density of Transversal Intersection

Abstract

Comparative statics requires that to a path in the space of economic parameters starting at an economy E and to a given equilibrium p of E there corresponds a uniquely determined path of equilibria starting at p . If p is not essential , there need not be any such path of equilibria . But even if p is the unique equilibrium of E and therefore essential , comparative statics in any arbitrarily small neighborhood of E will be impossible if E can be approximated by economies with an infinite number of equilibria . For example an economy like in figure 5 on p.82 can be approximated in any reasonable topology by economies like in figure 4 . Therefore comparative statics requires to rule out economies like in figure 5 in addition to those economies which have non-essential equilibria . What then are we left with ?