Modeling of Economical Processes (Modelarea proceselor economice)
Applied Mathematics, Modeling and Simulation
(Master Programs)
Professor Adrian Petruşel, Ph.D.
Contents
1) Mathematical models in economy: Arrow-Debreu model, consumer’s problem, maximal elements, Walras equilibrium, generalized game, Nash equilibrium, optimization problems;
2) Background in multivalued analysis: basic concepts, continuity, selection theorems, fixed point theorems;
3) KKM lemma and John von Neumann theorem;
4) Variational inequalities;
5) Optimal preferences, equilibrium points: existence, uniqueness and approximation.
Bibliography
1) C. D. Aliprantis, D. J. Brown, O. Burkinshaw: Existence and Optimality of Competitive Equilibria, Springer-Verlag, Berlin, 1990.
2) J. -P. Aubin: Optima and Equilibria, Springer, Berlin, 1993.
3) K. C. Border: Fixed Point Theorems with Applications to Economics and Game Theory, Cambridge Univ. Press, Cambridge, 1985.
4) A. Granas, J. Dugundji: Fixed Point Theory, Springer, Berlin, 2003.
5) G. Mot, A. Petrusel, G. Petrusel: Topics in Nonlinear Analysis and Applications to Mathematical Economics, House of the Book of Science, Cluj-Napoca, 2007.
6) R. Shone: An Introduction to Economic Dynamics, Cambridge Univ. Press, 2001.
7) B.S. Jensen: The Dynamic Systems of Basic Economic Growth Models, Kluwer Acad. Publ., 1994.
8) N. Schofield: Mathematical Models in Economics and Social Choice, Springer, 2004.
Assessment
The final grade is the weighted mean of the following three grades:
A. For the students from Applied Mathematics Master Program
40% Written Test (May 28, 2013)
30% 2 Written Reports (home works) - deadline May 15, 2012;
30% 2 Written Projects - deadline May 15, 2013:
i) to present a mathematical model in economics;
ii) to present a scientist working in the field of Mathematical Economics.
Successful passing of the exam is conditioned by the final grade that has to be at least 5.
B. For the students from Modeling and Simulation Master Program
60% 3 Written Reports (home works) - deadline May 15, 2012;
40% 2 Written Projects - deadline May 15, 2013:
i) to present a mathematical model in economics;
ii) to present a scientist working in the field of Mathematical Economics.
Successful passing of the exam is conditioned by the final grade that has to be at least 5.