HESSIAN DETERMINANTS OF COMPOSITE FUNCTIONS WITH APPLICATIONS FOR PRODUCTION FUNCTIONS IN ECONOMICS

Abstract

B.-Y. Chen [7] derived an explicit formula for the Hessian determinants of composite functions defined by f = F (h(1) (x(1)) + ... + h(n) (x(n))). In this paper, we introduce a new formula for the Hessian determinants of composite functions of the form f = F (h(1) (x(1)) x ... x h(n) (x(n))). Several applications of the new formula to the well-known Cobb-Douglas production functions in economics are also given.