B2198 - MATHEMATICAL METHODS FOR ECONOMISTS

Learning outcomes

At the end of the course the student has acquired knowledge and skills essential to the study of advanced 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; - investigating the stability of the solutions in the steady state; - detecting and studying bifurcations of equilibria.

Course contents

1. Introduction
   1. Stock and flux variables
   2. Equilibria, local stability, nonlinearity
   
   
2. Continuous dynamical systems
   1. Solutions of linear differential equations
   2. isoclines
   3. phase diagram, eigendirections
   4. second order differential equations
   5. linear approximation
   
   
3. Sytems of differential equations:
   1. phase diagrams, fixed points, stability
   2. matrix notation
   3. solutions of homogeneous systems
      
   4. nodes, foci, saddles
   5. limit cycles
   
   
4. Discrete dynamical systems:
   1. solutions of linear difference equations
   2. equilibria and stability
   3. linear difference equations of the second degree
   4. linear approximations
      
   
   
5. Systems of difference equations:
   1. eigenvalues and eigenvectors
   2. solution of homogeneous systems
   3. trajectories
   4. stability and phase diagrams
      
   
   
6. Applications to Economics

Readings/Bibliography

Economic Dynamics, Gandolfo Giancarlo, Springer-Verlag Berlin Heidelberg

Economic Dynamics Phase Diagrams and their Economic Application, Ronald Shone, Cambridge University Press

Teaching methods

lectures and exercises

Assessment methods

For the Mathematics module, the exam includes a written test on the topics covered during the course.

At free choice, the written test can be possibly integrated with a (group) project agreed with the instructor.

Evaluation judgment scale of the present module

· <18: insufficient preparation

· 18-23: sufficient preparation but relating to a limited number of the course contents;

· 24-27: adequate preparation but with some gaps with respect to the course contents;

· 28-30: very in-depth knowledge of all the course contents;

· 30L: excellent knowledge of the course contents.

Teaching tools

pdf fiiles of lectures, teacher's notes

Office hours

See the website of Lorenzo Cerboni-Baiardi