Nonsmooth methods in mathematical economics 
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Teaching Staff in Charge 

Aims 
Getting to know several modern results on mathematical economy with
emphasis on equilibria of economical problems. 
Content 
I. Introduction to setvalued analysis. Multifunctions. Concepts
of measurability. Selections. II. Convex analysis. Convex functions. Separation theorems. Fenchel's theorem. Conjugate functions. Support functions. III. Nonsmooth analysis. Subdiferentials. Tangent and normal cones. Fermat's theorem. IV. Twopersons games. Brouwer's fixed point theorem. Games in normal form. Pareto optima. Conservative strategies. Cournot's duopoly. V. Nonlinear equations and inclusions. The DebreuGaleNikaido theorem. Tangential condition. Viability theorem. Fixed point theorems. Equilibrium of a dynamic economy. Walras's equilibrium. Stakelberg equilibrium. Variational inequalities. Welfare theorems. 
References 
1. AUBIN, L.P., Optima and Equilibria, Springer, Berlin, 1998.
2. MURESAN, M., An introduction to SetValued Analysis, Cluj University Press, 1999. 3. MURESAN, M., Introducere in control optimal, Risoprint, ClujNapoca, 1999. 4. MURESAN, M., Analiza neneteda si aplicatii, Risoprint, ClujNapoca, 2001. 5. PETRUSEL, A., Multifunctii si aplicatii, Presa Universitara Clujeana, ClujNapoca, 2002. 
Assessment 
Written and spoken exam. 30% from the final mark is the activity at the seminar. 