| Sumario: | The purpose of this paper is to characterize the class of utility and production functions whose associated demand functions are everywhere differentiable in the positive orthant of n-dimensional Euclidean space. To avoid tiresome repetition we shall refer to such functions as everywhere differentiable. The problem is an essential one, since in the usual comparative statics analysis one obtains a number of qualitative results whose derivation depends on the existence of certain derivatives. While it is true that as stated such results require only local differentiability about the equilibrium point, none the less since the price vector and other relevant quantities are taken as arbitrary points in the positive orthant of the appropriate space, in fact the validity of comparative statics analysis requires that the utility and production function employed admit of everywhere differentiable demand functions.
|
|---|