Production theory needs generalizations so that it can incorporate broader class of production functions. A generalized Hotelling's lemma and a generalized Shephard's lemma in economic theory, which are established in virtue of nonsmooth analysis under the assumption of upper semicontinuity on production functions. Continuity of factor inputs with respect to a change of the factor prices is important in the cost minimization model. Locally Lipschitz strongly quasiconcave production functions are then introduced, which are shown to be a necessary and sufficient condition to have global stability and are reflexive in the cost minimization model. Finally, perturbations of the production models are examined for locally Lipshitz continuous production functions, and a new simple constraint qualification is considered for quasiconcave production functions.
Discussion Paper, Series A, No. 2007-195 Graduate School of Economics and Business Administration Hokkaido University Kita 9, Nishi 7, Kita-Ku Sapporo 060-0809 12/2007