Nonlinear Dynamical Systems in Economics
June 7, 2004 — June 11, 2004
- Marji Lines (Universita' di Udine, Udine, Italy)
Many problems in theoretical economics are mathematically formalized as nonlinear dynamical systems of difference and differential equations. Important examples of this class of problems to be covered in the school are overlapping generations models, disequilibrium models of business cycles of Keynesian inspiration, evolutionary models of market dynamics, models from oligopoly theory with nonlinear reaction functions, economic systems of many dimensions.
The study of such nonlinear dynamical systems is heavily based on numerical and graphical methods which support, complement and, at times, substitute “pure” mathematical investigation. The application of these methods has been greatly enhanced in recent years by the universal availability of powerful yet inexpensive computers. The school is organized on the assumption that, in order to maximize their fruitfulness for economics, the new computational methods of nonlinear dynamics must become part of the standard tool-box of economic theorists. This will permit economists to pursue a greater degree of independence from mathematicians and physical scientists, thus being able to adapt the methods to their models rather than vice versa. If will allow economists to distinguish between what is mere mathematical exercise what is significant to economics.
Each lecturer will deliver a set of lectures in which the economic models are presented and analyzed making use of theoretical tools and methodologies to be used in a computer lab session in which students will be guided through a set of associated exercises.
The course is addressed to PhD students and possibly master’s program students, as well as to those postdoctoral and other researchers in economics and related social sciences interested in broadening their knowledge and practical abilities in the application of the techniques of the analysis of nonlinear dynamical systems theory. A good mathematical background is needed from the students as well as their willingness to actively participate in the computer lab sessions. Relevant lecture material and computer exercises (and when possible software or instructions on how to obtain it) will be made available through the CISM website.