Subject: Nonsmooth Methods in Mathematical Economics	Code: MO052	

Semester	 Hours: C+S+L	Type	 Section	
5	2+2+0	compulsory	Applied Mathematics	

Teaching Staff in Charge	Prof. MURESAN Marian, Ph.D., mmarian@math.ubbcluj.ro	
Aims	Getting to know several modern results on mathematical economy with
emphasis on  equilibria of economical problems	
Content	I.   Introduction to set-valued 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.  Two-persons games. Brouwer's fixed point theorem. Games in 
     normal form. Pareto optima. Conservative strategies. Cournot's 
     duopoly.  
V.   Nonlinear equations and inclusions. The Debreu-Gale-Nikaido theorem.
     Tangential condition. Viability theorem. Fixed point theorems.
     Equilibrium of a dynamic economy. Walras's equilibrium. Stakelberg
     equilibrium. Variational inequalities. Welfare theorems	
Selective References	1. AUBIN, L.-P., Optima and Equilibria, Springer, Berlin, 1998.
2. MURESAN, M., An introduction to Set-Valued Analysis, Cluj University Press, 1999.
3. MURESAN, M., Introducere in control optimal, Risoprint, Cluj-Napoca, 1999.
4. MURESAN, M., Analiza neneteda si aplicatii, Risoprint, Cluj-Napoca, 2001.
5. PETRUSEL, A., Multi-functii si aplicatii, Presa Universitara Clujeana, Cluj-Napoca, 2002	
Assessment	Written and spoken exam. 30% from the final mark is the activity at the seminar