1. SylabUZ
2. Wydział Ekonomii i Zarządzania
3. semestr zimowy 2023/2024
4. Ekonomia - drugiego stopnia z tyt. magistra
5. Mathematical economics

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Mathematical economics - opis przedmiotu

Cel przedmiotu

The aim of the course is to provide in-depth knowledge in the field of creating economic models. Ability to recognize the causes and consequences of economic phenomena, analyze and interpret economic phenomena. In addition, shaping the ability to use the acquired knowledge in the process of solving problems related to mathematical modeling of micro- and macroeconomic phenomena.

Wymagania wstępne

Zapisz zmiany

Mathematics, microeconomics, macroeconomics

Zakres tematyczny

1. The space of goods and the relationship of consumer preferences. Continuity and convexity of preference relations.

2. Consumer preference field. Preferred baskets of goods - basic properties.

3. The utility function and its relationship with the relationship of consumer preferences - conditions of existence, basic properties and types of utility functions.

4. The influence of consumer prices and income on the choice of the preferred basket of goods. Formulation and solution of the consumer's decision problem (application of the Kuhn-Tucker theorem). Solution analysis.

5. Consumption demand function - basic properties and types of demand functions.

6. Competitive market of Arrow - Hurwicz. Market equilibrium prices. Walras' law.

7. Dynamic version of the Arrow - Hurwicz market. Basic price dynamics equation. Selected properties of price trajectories. Market stability criteria with continuous time.

8. Three examples of a competitive market. Determination of equilibrium prices and analysis of market stability.

9. Production space and production function. Basic properties and types of production functions.

10. Neoclassical theory of enterprise. An enterprise in conditions of perfect competition.

11. Leontief-Walras economy. Model description - basic assumptions. Conditions for the existence of a state of competitive equilibrium.

12. Theorem on the stability of competitive equilibrium in the Leontief-Walras economy with continuous time. Interpretation of stability conditions in L-E economy with discrete time.

13. Arrow-Debreu-McKenzie mathematical model of competitive economy. Model description and economic interpretation. Definition of competitive equilibrium.

14. Dynamic version of the A-D-Mc model. Theorem on the stability of competitive equilibrium.

Metody kształcenia

Conventional lectures with multimedia presentations, exercises using activating methods, solving tasks, case study, solving problems and tasks by students, discussion.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

1. Activity in class. Evaluation of students' preparation by solving selected tasks, problems and case studies.

2. Colloquium and exam with tasks of varying difficulty, closed and open questions.

The grade for the course consists of the grade for the exercises (50%) and the lecture exam (50%).

Literatura podstawowa

Yu K., Mathematical Economics, Springer, 2020.

Tarasov V. E., Mathematical Economics, MDPI AG, 2020.

Melkumian A., Mathematical Economics, Taylor & Francis Ltd, 2019.

Literatura uzupełniająca

Takayama Y., Mathematical Economics, Cambr. Univ. Press, Cambridge, 2006.

Uwagi

Zmodyfikowane przez mgr Łukasz Augustowski (ostatnia modyfikacja: 24-05-2023 01:08)