28895 - MATHEMATICAL ECONOMICS

Conoscenze e abilità da conseguire

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).

Contenuti

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)

Testi/Bibliografia

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

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

Adda J. and R. Cooper (2003) . Dynamic Economics: Quantitative Methods and Applications, MIT (manuscript version)

Carter M., Dynamic Optimization

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

Metodi didattici

Theory classes and solved exercises, home assignments, on-line discussions

Modalità di verifica e valutazione dell'apprendimento

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

- P is a problem sets grade in [0,30],

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

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

Two problem sets will be assigned during the lecture period and individual solutions will be due one week after each assignment.

Students who do not submit problem sets solutions will have to solve an extra exercise at the written exam, with no extension of the duration of the exam. The grade for the extra exercise will substitute P in the calculation of the final grade.

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.

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

Strumenti a supporto della didattica

A course page in Moodle.

Link ad altre eventuali informazioni

https://iol.unibo.it/course/view.php?id=22307

Orario di ricevimento

Consulta il sito web di Iliyan Georgiev