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Masaryk University in Brno
Faculty of Science
Department of Mathematics and Statistics
Course syllabus
Course name:
Mathematical methodsin Economics (Spring 2013).
Schedule
Lectures: Tuesday, 1300 – 1600.
Office hours: Tuesday, 1600 – 1700.
Midterm and final exams: TBA.
Instructor
Dmytro Vikhrov (CERGE‐EI).
Email: dmytro.vikhrov@cerge‐ei.cz
Web: home.cerge‐ei.cz/vikhrov
Course objective and structure
The purpose of the course is to familiarize students with the basic concepts of the modern Economics and
show their application on the examples of individual labor supply, taxation, social security systems and
auctions. Students are expected to have elementary knowledge of calculus and the basics of
Microeconomics.
The course starts with the revision of consumer theory, which is directly applicable to the model of labor
supply and the discrete version of the human capital accumulation model. We will later show the distortive
role of taxation and generalize the consumer problem to the infinite setup. This generalization will allow
consideration of the overlapping generations model and discussion of its predictions for funded and
unfunded social security systems.
After the midterm examination we will go over the basics of the producer theory. Next, using illustrative
examples we will see how two consumers, consumers and producers, consumers and the government
interact and the endogenous price vector is determined. On the last two lectures we will look into the
mathematical apparatus for the auction theory.
Grading
Midterm exam – 30%, final exam – 30%, two homeworks – 20%, class participation – 20%.
Principal textbooks:
1. Acemoglu, D. (2008). Introduction to Modern Economic Growth. Princeton University Press.
2. Borjas, G. (2009). Labor economics. McGraw‐Hill Education.
3. Doepke, M., Lehnert, A. and Sellgren, A. (1999). Macroeconomics. UCLA.
4. Jehle, G. and Reny, P. (2011). Advanced Microeconomic Theory, 3rd
ed.
5. Krishna, V. (2009). Auction Theory. Elsevier Science.
6. Varian, H. R. (2005) Intermediate microeoconomics, 7th
ed.
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Course outline
Lectures 1 ‐ 2.
Setup of the consumer’s maximization problem, properties of consumer demand, duality.
Varian: Chapters 4 – 6, Jehle: Chapters 1.3 – 2.3.
Lecture 3 ‐ 4
The model of labor supply, taxation of labor. Government budget constraint, the Laffer curve.
Doepke: Chapter 13, Borjas: Chapter 2.
Lecture 5
Generalizationto the infinite period model. The Bellman equation.
Acemoglu: Chapter 6.
Homework 1
Lecture 6
The model of human capital accumulation.
Borjas: Chapter 7, Acemoglu: Chapter 10.2.
Midterm examination
Lectures 7
Setup of the producer’s maximization problem, production costs, duality in production.
Jehle: Chapters 3.2 – 3.5
Lecture 8 ‐ 9
Illustrative examples of the general equilibrium: The endowment economies, equilibrium in production (Jehle,
Chapter 5), equilibrium in the labor market (Doepke, Chapter 6), model of trade (Acemoglu, Chapter 19).
Lecture 10 ‐ 11
Overlapping generations model. Social security systems.
Acemoglu: Chapter 9, Doepke: Chapter 12.
Homework 2
Lecture 12 ‐ 13
First and second price sealed‐bid auctions. Revenue equivalence theorem.
Krishna: Chapter 1.
Final examination