Schedule for MatFuII fall 2000
This course introduces methods to analyze dynamic systems. The course can be thought of as a preparation for the macro sequence and most examples will come from macro. Dynamic considerations have, however, become very important in literally all areas of economics so the contents should be useful for everybody.
The first part of the course discusses how one can completely characterize the behavior over time of a dynamic systems, for example a macroeconomic model, using information about its law of motion. For this purpose, we will learn to solve difference and differential equations of different types, e.g., first and higher order linear equations and systems of linear equations. Phase diagrams and stability of non-linear differential equations will also be discussed.
During the second part of the course, will learn how to solve maximization problems in a dynamic context, i.e., in situations where today’s actions affects also the future so that a myopic behavior is sub-optimal. We will discuss dynamic programming in discrete time optimal control (and possibly calculus of variation) in continuous time.
Finally, we will introduce some numerical methods to solve problems that are to hard to solve analytically.
There is no single textbook that covers all the material discussed in the course. The first sections of the course as well as most of the material in the second section is covered in Hammond and Sydsæter. A more complete treatment of dynamic systems can be found in de la Fuente, which also covers section 3 of the course. Fuente also contain important economic examples. Both books should be useful for everyone, and we recommend them for purchase. However, it should be noted that we will not follow the books perfectly. Students should, however, read all material. Classnotes will be made available.
A more rigorous treatment of dynamic optimization can be found in Seierstad and Sydsæter (Optimal Control), Sargent (Dynamic Programming) and Ross. An alternative book for the part on Optimal Control is Kamien and Schwartz.