28895 - Mathematical Economics

Learning outcomes

At the end of the course the student has acquired knowledge and skills essential to the study of dynamic economic systems. In particular, he/she is able to: - calculate explicitly the solution to systems of linear differential and difference equations; - study systems of nonlinear differential and difference equations using the phase diagram and through linearization around the steady state; - solve deterministic dynamic optimization problems in discrete time (dynamic programming) and continuous time (optimal control).

Course contents

1. Qualitative study of first-order ordinary differential and difference equations. Steady states and stability. The capital accumulation equation.

2. Linear systems of first-order ordinary difference and differential equations with constant coefficients

3. Qualitative study of first-order non-linear system of difference and differential equations.

4. Optimal intertemporal choice in continuous time (Hamiltonian based)

5. Optimal intertemporal choice in discrete time (Bellman-equation based)

Readings/Bibliography

Readings from the following sources will be assignes weekly. The level of knowledge to acquire is anyway determined by the contents of the lectures, not the readings:

Simon C. and L. Blume, Mathematics for Economists, any edition

Leonard D., N. van Long (1992), Optimal Control Theory and Static Optimization in Economics, CUP

Chiang A. (1992), Elements of Dynamic Optimization, McGraw-Hill

Pavoni N. (2008) Notes on dynamic macro

Stokey N, R. Lucas (1989), Recursive Methods in Economic Dynamics, HUP

Cugno F. and L. Montrucchio (1998). Scelte intertemporali. Teoria e modelli, Carocci

Teaching methods

Theory classes at the university premises, exercise sessions

Strong and reliable command of undergraduate mathematics at the level of the September crash course is an indispensable prerequisite for the Math Econ module. Students with good undergraduate training in maths (at the level of a demanding econ bachelor, or superior) are stronly suggested to attend the September crash course. Unfortunately, the September crash course will not be sufficient to fill in the gaps of mathematically more fragile students (with background in business, social sciences, etc ). It is therefore recommended that such students dedicate a part of their Summer to the self-study of undergraduate maths.

Assessment methods

The course grade is based exclusively on a final written exam that will take place at the university premises (unless this is explicitly outlawed by the legislation in force at the exam date). The exam will have a duration of 90 to 120 minutes. During the exam students may consult a two-sided self-written (not photocopied, not printed) A4 sheet with whatever contents they find appropriate; this sheet should be handed in together with the answers to the exam questions.

Each student is entitled to renounce a passing (>=17.5) grade of Mathematical Economics one time only.

Passing numerical grades are intended to match the following qualitative description:

17.5-23: sufficient
24-27: good
28-29: very good
30 - 30 cum laude: excellent.

Teaching tools

A course page on Virtuale

Office hours

See the website of Iliyan Georgiev