Finiteness and comparative statics
Mukul Majumdar · 2009
Only later, from Gerard Debreu, did I realize that “almost always” the number of possible equilibria would be finite. Paul A. Samuelson Consider an economy that has an equilibrium x such that in any neighborhood of x, there are infinitely many other equilibria. In this situation the explanation of equilibrium is essentially indeterminate, at least near x. Moreover the economic system … is unstable in the sense that arbitrarily small perturbations from x to a neighboring equilibrium induce no tendency for the state of the economy to return to x. It is therefore highly desirable to have an economy … for which the set of equilibria is discrete.