= Parametric regularity of exchange equilibria
{title2=$D_{(p,t)}Z\ne0\text{ on }Z^{-1}(0)$}
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>.
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