Factor Price Equalization : Geometrical Conditions

This paper presents a geometrical approach to the univalence problem for a system of cost functions. We present a natural (almost tautological) extension of a geometrical theorem due to McKenzie: our sufficient condition is related to the non-separability of two cones formed by convex combinations of the rows of the Jacobian matrix. This means that the cones spanned by the rows of Jacobian matrix (i.e., production coefficients) do not move wildly so that the two cones corresponding to the two end points (i.e., factor price vectors) cannot be separated by the hyperplane orthogonal to the vector of changes in factor prices. Unlike most ofthe previous propositions, our condition can naturally include as a special case such linear systems as having a non-singular matrix. We also give an alternative condition employing the concept of monotone functions. Dual to the above result is one more condition, which is shown to be closely connected with Kuhn's WARP-like requirement when the given functions are concave as well as homogeneous of degree one.

研究ノート (Note)