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

Simon C. and L. Blume, Mathematics for Economists, Part V

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, exercise sessions, solved exercises, on-line discussions.

Assessment methods

The final grade is min{max{E, 0.75E +0.25P}+B, 31}, where

- E is a written exam grade in [0,31].

- P in [0,30] is the average of two problem sets grades

- B is a Moodle forum participation bonus in [0,2].

The final exam 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 A4 sheet with whatever contents they find appropriate; this sheet should be handed in together with the answers to the exam questions.

As long as the legal obligation to offer on-line alternatives to the regular exams persists, these alternatives will employ written assignments similar to the regular ones. The alternative on-line exams will be implemented using the most recent surveillance tools approved by UniBo prior to the exam date. 

The problem sets will be assigned during the course and participation is voluntary but strongly encouraged.

Several discussion forums will be opened in Moodle during the lecture period. Participation in forum discussions is optional.

Each student is entitled to renounce a passing (>=18) grade of Mathematical Economics one time only.

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

18-23: sufficient
24-27: good
28-30: very good
30 cum laude: excellent.

Teaching tools

A course page on Moodle

Office hours

See the website of Iliyan Georgiev