Regular exchange economy

An exchange economy is regular when the derivative of its reduced aggregate excess demand has full rank at every equilibrium. For two goods and normalized prices $(p,1)$, this means $Z_p(p)\ne 0$ at every zero of first-good excess demand. Regular equilibria are locally isolated and persist smoothly under small parameter changes.

If zero is a regular value of the joint smooth aggregate excess demand $Z(p,t)$, almost every parameter gives a regular economy. The regular level set theorem makes the zero set a manifold. Its projection to parameter space fails to have full rank exactly where the derivative with respect to prices is singular; Sard theorem makes these exceptional parameter values a null set.