02541 - Mathematics for Economists

Learning outcomes

At the end of this module, students are expected to manage some of the mathematical tools that are required for advanced economic studies. Those allow to study solutions and perform qualitative analysis (stability of equilibria, bifurcations) for system of differential and difference equations and systems of linear and non-linear ordinary differential equation.

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, directions
   4. second order differential equations
   5. linear approximations
   
   
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 the free choice of the student, the written test can be integrated with a (group) project agreed with the instructor.

Evaluation judgment scale of the present module

· <18: nisufficient 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.

The final grade of the quantitative methods exam will be an average of the two modules

Teaching tools

fiiles of lectures, teacher's notes

Office hours

See the website of Lorenzo Cerboni-Baiardi