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.

The introductory topics of the course will be covered in a series of propedeutic tutorial sessions that will take place in the month of October. The purpose is to achieve a more uniform workload during the months of October and November that will hopefully allow for a more productive learning experience.

Assessment methods

The final grade is min{E+B, 31}, where

- E is a written exam grade in [0,30].

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

The final exam will have the 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.

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

A grade of at least 15 in Mathematical Economics and an average of at least 17.5 with Econometrics 1 are necessary for the successful completion of the Quantitative methods integrated course. Each student is entitled to renounce a passing grade one time only.

Teaching tools

A course page in Moodle: https://virtuale.unibo.it/course/view.php?id=17391

Links to further information

https://virtuale.unibo.it/course/view.php?id=17391

Office hours

See the website of Iliyan Georgiev