Opuscula Math. 34, no. 4 (2014), 827-835
http://dx.doi.org/10.7494/OpMath.2014.34.4.827
Opuscula Mathematica
Necessary and sufficient conditions for a Pareto optimal allocation in a discontinuous Gale economic model
Anna Michalak
Marcin Studniarski
Abstract. In this paper we examine the concept of Pareto optimality in a simplified Gale economic model without assuming continuity of the utility functions. We apply some existing results on higher-order optimality conditions to get necessary and sufficient conditions for a locally Pareto optimal allocation.
Keywords: Gale model, discontinuous functions, generalized directional derivatives, higher-order conditions, Pareto optimality.
Mathematics Subject Classification: 91B50, 90C29, 49J52.
- Anna Michalak
- University of Łódź, Faculty of Economics and Sociology, Department of Econometrics, Rewolucji 1905 r. No. 41, 90-214 Łódź, Poland
- Marcin Studniarski
- University of Łódź, Faculty of Mathematics and Computer Science, Chair of Algorithms and Databases, S. Banacha No. 22, 90-238 Łódź, Poland
- Received: 2014-05-02.
- Revised: 2014-09-29.
- Accepted: 2014-09-29.