Australian The National University School of Economics
ECON2127 Mathematics for Economists B ECON8014 Mathematical Techniques in Economics II
Semester 2, 2008 The foundations of economic theory are based on mathematical models. Thus, a thorough understanding of the economic content of such models is not possible without a clear understanding of the mathematical concepts that underpin the modeling. The objective of this course is to prepare students for advanced courses in economic theory, such as the ones required of students enrolled in Honours, Masters and PhD programs, by discussing fundamental tools and concepts of mathematics on which these courses are based. The common thread in our approach will be the analysis of dynamical systems and of dynamic optimization methods. On a more fundamental level, we will attempt to understand the corresponding techniques by analysing how and why they can be derived from certain basic assumptions using standard mathematical ideas and results. Lecturer Ronald Stauber office: Room 2026, HW Arndt Building 25a email: [e-mail] office hours: Tuesday, 4:30-6:30pm, and by appointment Shane Evans office: Room 1009, HW Arndt Building 25a email: [e-mail] office hours: tba Monday, 5-6pm, Arndt Lecture Theatre 1 Tuesday, 1-3pm, Arndt Lecture Theatre 1 Tutorial signup will be via the ETA system to sign up, follow the instructions given at http://teaching.fec.anu.edu.au/eta.asp. Tutorials will be scheduled on Monday. The first tutorial will take place during the second week of class. One additional tutorial session will be scheduled on Friday during the last week of the semester. Website https://webct.anu.edu.au/login/
Tutor
Lectures Tutorials
All relevant course material will be posted on the WebCT site for ECON2127. Please follow the Lecture Log link on that site for a list of topics covered, associated readings, lecture slides and tutorial problems. The lecture log will be updated throughout the semester, and will also include information about exam times and locations. The lecture slides used in class will be posted on the Lecture Log before the respective lectures. Please print out a copy of these slides and bring them to class. Note that the slides are incomplete and do not contain graphs and various explanations, so you should not expect to be able to follow the lectures without attending class. The tutorial problems corresponding to each week's lectures will be discussed in the tutorials during the following week. Even though you are not required to submit answers to the tutorial problems, you will only benefit from the tutorials if you seriously attempt solving the problems 1
before they are discussed in the tutorials. I strongly recommend you that form study groups, and meet each week to work together on the tutorial problems. References There is no single textbook that covers all the material we need at an appropriate level. We will therefore use various chapters from a number of different books as references. Most of these chapters will be available in electronic format from the university library electronic reserve. You are however expected to own a copy of the book by Blanchard, Devaney and Hall.
Sheldon Axler, Linear Algebra Done Right, 2nd edition, Springer, 1997 (AXL) Kenneth A. Ross, Elementary Analysis: The Theory of Calculus, Springer, 1980 (ROS) P. Blanchard, R.L. Devaney, and G.R. Hall, Differential Equations, 3rd edition, Thomson Brooks/Cole, 2006 (BDH) Carl P. Simon and Lawrence Blume, Mathematics for Economists, W.W. Norton, 1994 (SBL) Charles M. Grinstead and J. Laurie Snell, Introduction to Probability, Second Revised Edition, American Mathematical Society, 1997 (GSN) James R. Norris, Markov Chains, Cambridge University Press, 1997 (NOR) P.R. Kumar, Dynamic Programming, ch. 63 in The Control Handbook, W.S. Levine, ed. (KUM) Dimitri P. Bertsekas, Dynamic Programming and Optimal Control, vol. 2, 3rd edition, Athena Scientific, 2007 (BER) Daniel Leonard and Ngo Van Long, Optimal Control Theory and Static Optimization in Economics, Cambridge University Press, 1992 (LVL)
Course outline 1. Preliminaries: Polynomials and sequences ( AXL ch.4; ROS ch.2) 2. Difference equations (BDH ch.8) 3. Euclidean spaces (SBL chs.10-12) 4. Markov chains (GSN ch.11; NOR ch.1) 5. Dynamic programming (KUM; BER ch.1) Midterm exam (week 8) 6. Review of integrat...