## ** Winter 2008/2009: Mathematical Economics **

### **Lectures: Thu 1.00 - 3.00 p.m. in G03-214 and Fri 9.00 - 11.00 a.m. in G22A-111 **

### **Tutorials (M.Sc. Jochen Güntner): Wed 11 a.m. - 1.00 p.m.
in G22A-122 **

### ** Contents **

#### The lecture consists of two major parts:

Nonlinear Programming and Microeconomics and

Differential Equations, Optimal Control Theory and Macroeconomics.

Chapters:

1. Multivariable Calculus

(Preliminaries, Convex sets, Convex and concave functions, Quasi-convex and quasi-concave functions)

2. Nonlinear Programming

(Extreme points, Equality constraints, Inequality constraints, Non-negativity constraints,
Constraint qualifications)

3. Sensitivity Analysis

(Comparative statics, Envelope theorem, Elements of microeconomic theory, Elasticity of factor substitution)

4. Some Applications to Microeconomic Theory

(Inferior inputs, Marginal and average costs, Marginal cost pricing,
Factor prices, Supply of labour, Peak-load problem)

5. Differential Equations and Elements of Nonlinear Systems

(First- and second-order differential equations, Higher-order equations, Systems of equations)

6. Some Applications to Macroeconomic Theory

(Macroequilibrium, Money and growth)

7. Optimal Control Theory and Applications

(Elements of control theory, Infinite horizon control problem and applications, Some extensions of
optimal control themes)

### ** Literature (Textbooks): **

####
1) Takayama, A.: Analytical Methods in Economics, Harvester-Wheatsheaf, 1994.

2) Sydsaeter, K.; Hammond, P.; Seierstad, A.; Strom, A.:
Further Mathematics for Economic Analysis, Financial Times/Prentice Hall, 2005.

3) Takayama, A.: Mathematical Economics, Cambridge University Press, 2nd edition, 1985.

Mathematical Prerequisites:

4) Werner, F.; Sotskov, Y.N.:
Mathematics of Economics and Business, Routledge, Abingdon, New York, 2006.

### ** Some presented slides from the lecture: **

####

pdf-File (53 pages)

### ** Exercises for the tutorials: **

####

Series 1: pdf-File

Series 2: pdf-File

Series 3: pdf-File

Series 4: pdf-File

Series 5: pdf-File

Series 6: pdf-File

Series 7: pdf-File

Series 8: pdf-File

### ** Examination: **

#### There is a two-hour written examination in February. As working tools are allowed:

TWO individually prepared doubled-sided sheets of paper (with arbitrary material);

a pocket calculator;

- for mathematical prerequisites:

a printed collection of formulas;

textbook: Werner and Sotskov, Mathematics of Economics and Business,
Routledge, 2006;

### Past Examinations:

**Examination February 2007 (pdf)**

**Retake Examination July 2007 (pdf)**

**Examination February 2009 (pdf)**

####
Quotation: I came to the position that mathematical analysis is not one of many ways
of doing economic theory: It is the only way. Economic theory is mathematical analysis.
Everything else is just pictures and talk.

(R.E. Lucas Jr., 2001)