1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2023/2024
4. Mathematics - drugiego stopnia z tyt. magistra
5. Mathematical Economics 2

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Mathematical Economics 2 - opis przedmiotu

Cel przedmiotu

The students get acquainted with the basic definitions and theorems of growth theory and dynamic systems in economics.

Wymagania wstępne

Zapisz zmiany

Mathematical Economics 1, Introduction to Optimization, Probability Theory.

Zakres tematyczny

Lecture

I. Growth models:

1. Harold Model, Solow-Swana Model, Frankel Model. (2 hours)
2. Ramsey Model. (2 hours)
3. Value function, Bellman equations. (2 hours)
4. Properties of the value function and the optimal policy. (2 hours)

II. Multisector growth models:

1. Ramsey model.(2 hours)
2. Consumption and saving problem. (2 hours)
3. Examples of optimal policies and optimal value functions. (4 hours)

III. Cycles and chaos in growth models:

1. Examples of chaos. (2 hours)
2. Existence of periodic orbits. (2 hours)

IV. Stochastic growth models:

1. Formulation of the problem. (2 hours)
2. Markov Decision Process. (4 hours)

V. Neoclassical Brock-Mirman model:

1. Bellman equations. (2 hours)
2. Existence of stationary distribution. (2 hours)

Class

I. Growth models:

1. Berge Maximum Theorem. (4 hours)
2. Ramsey Model. (2 hours)
3. The value function and Bellman equations. (2 hours)
4. Properties of the value function and the optimal policy. Analytical solution in Levhari-Mirman model. (2 hours)

II. Multisector growth models:

1. Ramsey model. Examples.(2 hours)
2. Consumption and investment problems. Examples of problems. Examples of problems. (2 hours)
3. Examples of optimal policies and value functions. (4 hours)

III. Cycles and chaos in growth models:

1. Examples of chaos. (2 hours)
2. Existence of periodic orbits. Examples. (2 hours)

IV. Stochastic growth models:

1. Formulation of problem. (2 hours)
2. Markov Decision Problem. Examples. (4 hours)

V. Test and summary: (4 hours).

Metody kształcenia

Conventional lecture; conversational lecture. Class -solving mathematical problems, the analysis of classic examples of games in economics and other applications.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

A positive evaluation of the class is a prerequisite for passing the exam. The evaluation of the course consists of the assessment of the class (40%) and the evaluation of the exam (60%). The prerequisite to passing the course is a positive evaluation of the exam.   

Literatura podstawowa

1. Le Van, C., Dana R-N, Dynamic Programming In Economics, Kluwer Acad. Dordrecht, 2003.
2. Bhattacharya R. Majumdar M., Random Dynamical Systems Theory and Applications, Cambridge Univ. Press, 2007.

Literatura uzupełniająca

1. Besanko, D., Braeutigam, R., Microeconomics. International student version. Wiley, 2011.

2. Browning, E.K., Zupan, M.A. Microeconomics: Theory and Applications 13th Edition, Wiley, 2020.

Uwagi

This course is also offered during the IV semester.

Zmodyfikowane przez dr Ewa Sylwestrzak-Maślanka (ostatnia modyfikacja: 10-04-2024 15:58)