Masaryk University in Brno Faculty of Science

                             Department of Mathematics and Statistics



                                          Course syllabus


Course name:

Mathematical methods in Economics (Spring 2016).



Schedule

Lectures: Wednesdays, 16:00 – 19:00. Office hours: Wednesdays, 15:00 – 16:00. Midterm and final
exams: TBA.



Instructor

Mgr. Sherzod Tashpulatov, M.A., Ph.D.                               Email: stashpul@cerge‐ei.cz


Course objective and structure

The purpose of the course is to familiarize students with the basic concepts of modern Economics.
The course shows the application of optimization and regulation on the economic examples of
consumer and producer theories, taxation, price regulation, growth theory, finance, auctions, and
network industries. Students are expected to have elementary knowledge of calculus and the basics
of Microeconomics.

The first block of the course starts with the consumer choice theory using graphical and formal
approaches. Next, using illustrative examples we will see how consumers and producers interact and
the endogenous price vector is determined. Then we start game theory applications. In particular we
cover the following types of games: static, dynamic, (in)complete, and (im)perfect information
games. We will also cover dominating strategies, pure strategies, mixed strategies, normal and
extensive form representations, Nash equilibrium, subgame perfection.

In the second block we cover Fisher’s intertemporal choice model under various settings. Then we
review consumption and money multiplier models, which are followed by growth accounting and Solow
residual. Before starting Solow growth model we study phase diagrams for continuous time. A
numerical example will be presented in Excel and MatLab.

In the third block we study shorter economic models and problems. They are trade, input-output,
ratings, and Markov transition matrix models. We will also consider constrained optimization
problem in electricity economics.

In the fourth block we study finance topics: valuing of cash flow, net present value, and internal
rate of return. We will review probability density and cumulative distribution functions with the
application to the value at risk (VaR) model. We will also cover option valuing. The last topic in
this block is devoted to risk analysis and measurement. We conclude this topic by the capital asset
pricing model (CAPM).

In the last block we will look into the mathematical apparatus for the auction theory and market
design. We will also review liberalization in network industries and in particular electricity
supply industry in Great Britain. Finally, we will look at the application of regression models in
the energy sector. In particular we will review estimation of the demand equation for natural gas,
hedging strategy, and stress test in EViews.


Grading

Midterm exam – 20%, final exam – 40%, two quizzes – 10%, two HW assignments – 10%, class
participation – 20%.


Principal textbooks:

1.     Varian H. Intermediate Microeconomic: A Modern Approach (any edition)

2.     Gibbons (1992). A Primer in Game Theory.

3.     Doepke, M., Lehnert, A. and Sellgren, A. (1999). Macroeconomics.


Additional textbooks:

1.     Robert J. Barro and Xavier Sala-i-Martin (2004). Economic Growth.

2.     Bhattacharyya, S.C. (2011). Energy Economics: Concepts, Issues, Markets and Governance.

3.     Tashpulatov S. (2014). Network industry liberalization: The case of the England and Wales
electricity market

        Journal articles will be provided in due course.