Long run input use-input price relations and the cost function Hessian

Abstract

By definition, to compare alternative long run equilibria is to compare alternative points on the real input price frontier. It follows at once that one can never move between long run equilibria by changing just one input price; one must change at least two. And in some cases, indeed, such as the Wicksellian one, to change one price is ipso facto to change all the others in a determinate manner. Hence the Hessian of the cost function can – quite obviously – never represent the long run comparative statics of input price-input quantity relations with accuracy. More detailed investigation in fact shows the Hessian to be a hopeless guide to [dli/dwj], both qualitatively and quantitatively.