- Docente: Lorenzo Cerboni-Baiardi
- Credits: 6
- SSD: SECS-S/06
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Economics and Economic Policy (cod. 8420)
-
from Nov 08, 2022 to Dec 16, 2022
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
- Introduction
- Stock and flux variables
- Equilibria, local stability, nonlinearity
- Continuous dynamical systems
- Solutions of linear differential equations
- isoclines
- phase diagram, directions
- second order differential equations
- linear approximations
- Sytems of differential equations:
- phase diagrams, fixed points, stability
- matrix notation
- solutions of homogeneous systems
- nodes, foci, saddles
- limit cycles
- Discrete dynamical systems:
- solutions of linear difference equations
- equilibria and stability
- linear difference equations of the second degree
- linear approximations
- Systems of difference equations:
- eigenvalues and eigenvectors
- solution of homogeneous systems
- trajectories
- stability and phase diagrams
- 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