Yoshihiro Tanaka In this study we discuss the use of the simplex method to solve allocation problems whose flow matrices are doubly stochastic. Although these problems can be solved via a 0-1 integer programming method, H.W. Kuhn [4] suggested the use of linear programming in addition to the Hungarian method. Specifically, we use the Birkhoff’s theorem to … Read more
The Kuhn-Tucker conditions have been used to derive many significant results in economics. However, thus far, their derivation has been a little bit troublesome. The author directly derives the Kuhn-Tucker conditions by applying a corollary of Farkas’s lemma under the Mangasarian-Fromovitz constraint qualification. CitationDiscussion Paper Series A, No. 2011-234, Graduate School of Economics and Business … Read more
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 … Read more
This paper is devoted to optimality conditions for nonsmooth quasiconcave programming. Arrow and Enthoven (1961) formulate several economic problems into quasiconcave programming, and give a sufficient condition for smooth quasiconcave programming in their epoch-making and comprehensive paper. In this paper, generalized necessary and sufficient conditions for nonsmooth quasiconcave programming have been derived in terms of … Read more