Mathematics for Economists

2024/2025

Учебный год

ENG

Обучение ведется на английском языке

3

Кредиты

Кто читает:

Отдел сопровождения учебного процесса в магистратуре

Статус:

Курс по выбору

Когда читается:

2-й курс, 3 модуль

Course Syllabus

Abstract

The course has been designed to convey to the students how mathematics can be used in the modern micro and macro economic analysis. Emphasis is placed on the model-building techniques, methods of solution and economic interpretations. Topics studied comprise the following: methods of optimization, dynamic pro-gramming, optimal control theory.

Learning Objectives

• The objective of the course is to equip the students with some of the theoretical foundations of the modern mathematics and what is more important with the analytical methods of solving problems posed by the micro and macro analysis.

Expected Learning Outcomes

• Apply Lagrange method as well as analysis of Bellman’s equations to macroeconomics
• Apply methods of linear algebra to economic issues
• Apply multidimensional calculus, optimization to economic problems
• Apply the theorems that provide sufficiency conditions in the problems of optimization
• Handle first-order DE and linear DE of higher order with the constant coefficients
• Solve problems of calculus of variations as well as optimal control theory
• Solve elementary ordinary differential equations and understand the dynamics induced by a system of equations
• Understand the balancing of intertemporal trade-offs via the Euler equation and the recursive formulation of the problems via Bellman's equation
• Solve problems of calculus of variations and optimal control theory, and interpret the multiplier function as a reflection of incentives

Course Contents

• Multidimensional calculus, basics of optimization
• Linear Algebra
• Convex analysis and Kuhn-Tucker theorem
• Theory of probability and statistics
• Differential Equations
• Dynamic Optimization in Continuous Time
• Dynamic Optimization in Discrete Time

Assessment Elements

• Home assignment
• Exam
  «In order to get a passing grade for the course, the student must sit (all parts) of the final examination».

Interim Assessment

• 2024/2025 3rd module
  0.7 * Exam + 0.3 * Home assignment

Bibliography

Recommended Core Bibliography

• Dynamic optimization : the calculus of variations and optimal control in economics and management, Kamien, M. I., 2012
• Introduction to modern economic growth, Acemoglu, D., 2009
• Mathematics for economists, Simon, C. P., 1994

Recommended Additional Bibliography

• Stochastic calculus for finance. Vol.1: The binomial asset pricing model, Shreve, S. E., 2004

Authors

• Bukin Kirill Aleksandrovich