Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
MME1010	Modeling of Economical Processes	

Section	Sem.	Hours: C+S+L	Category	Type	
Applied Mathematics	2	2+1+0	speciality	optional	
Modeling and Simulation  - in English	4	2+1+0	speciality	compulsory	
Optimization of Computational Models	4	2+1+0	speciality	optional	

Teaching Staff in Charge	Prof. PETRUSEL Adrian Olimpiu, Ph.D., petrusel@math.ubbcluj.ro	
Aims	The goal of this course is to provide students with some models and problems of mathematical economics. After completing the course, the students will have basic concepts and tools of mathematical economics and they should be able to analyse and diagnose the behavior of some actual economical process.	
Content	Course 1. Arrow-Debreu model. 
Seminar 1. The functionals D, Delta, Rho and H (exercises and examples)
Course 2. The concept of generalized game and abstract economy.
Seminar 2. Hausdorff-Pompeiu metric (exercises and properties) 
Course 3. Continuity concepts for multivalued operators. 
Seminar 3. Examples and exercises in connection to the continuity of multivalued operators. 
Course 4. Selection results for multivalued operators. The continuous case. 
Seminar 4. Lipschitz-type multivalued operators. Basic properties. 
Course 5. Topological fixed point theorems for multivalued operators. 
Seminar 5. Examples and counterexamples for topological fixed point theorems. References: [4]-pages 533-540, [6]-pages 99-104.
Course 6. Properties of the fixed point set. 
Seminar 6. Middle Term Written Test
Course 7. KKM lemma.
Seminar 7. Examples and exercises, particular cases of KKM lemma. 
Course 8. Applications of KKM lemma to variational inequalities and game theory.
Seminar 8. Caristi&#8217;s theorem. Applications and extensions. 
Course 9. Stability results for the KKM set.
Seminar 9. (Report): Maximal elements. 
Course 10. Coincidence theorems and applications to Nash equilibrium points. 
Seminar 10 Coincidence theorems for singlevalued and multivalued operators. 
Course 11. Strict fixed point theorems.
Seminar 11 Strict fixed point theorems. 
Course 12. Existence results for equilibrium points. 
Seminar 12. Existence for Walras-type equilibrium. 
Course 13. The excess-demand multifunction.  
Seminar 13. Equilibrium price for the excess-demand multifunction. 
Course 14. New research directions in mathematical economics. 
Seminar 14. Models of written tests. Presentation of the grades obtained during the semester evaluation.
	
Bibliography	1)  G. Mot, A. Petrusel, G. Petrusel: Topics in Nonlinear Analysis and Applications to Mathematical Economics, House of the Book of Science, Cluj-Napoca, 2007. 
2)  J.P. Aubin: Optima and Eqilibria, Springer, Berlin, 1993. 
3)  G.X.Z. Yuan: KKM Theory and Applications in Nonlinear Analysis, Marcel Dekker, New York, 1999. 
4)  K. Border: Fixed Point Theorems with Applications to Economic and Game Theory, Cambridge University Press, London, 1985. 
5)  J. Dugundji, A. Granas.: Fixed Point Theory,.  Springer-Verlag, Berlin, 2003.
	
Assessment	The final grade is the weighted mean of the following three grades. 
The final grade = 50% Final Written Test + 25% Middle Term Written Test + 25% Report.  Successful passing of the exam is conditioned by the final grade that has to be at least 5. 
All university official rules with respect to students&#8217; attendance of academic activities, as well as to cheating and plagiarism, are valid and enforced.