Syllabus for Econ 902: Mathematical Economics Fall 2014, Mondays 9-12 Instructor: Chris Laincz Office: GHall 1018 Office Hours: M 2-5:00. e-mail: [email protected] Course Website: http://faculty.lebow.drexel.edu/Laincz/econ902 TA: Adelia Mehmetaj, [email protected] Office Hours: Thursdays 4-5 PM Introduction The purpose of the Mathematics for Economics course is to provide Ph.D. students in the LeBow College of Business with a survey of the critical math tools applied in the study of Microeconomics, Macroeconomics, Econometrics and related areas such as Finance, Accounting, and Decision Sciences. All of the material covered will be used throughout the first year and much of it applies across all major fields. Because there is an enormous amount of material, the course cannot possibly cover all of the topics students will need to learn. Even after removing some advanced topics, there still remains a large amount of material to cover in a ten-week course. We will be covering three main topics: 1) Applied Calculus; 2) Linear Algebra; and 3) Dynamic Optimization. While the focus of the course is obviously math, it is math used in business and economic analysis and research. In most cases we will go over applications to microeconomics, macroeconomics, and econometrics and make the connections between the tools we cover and their uses. Economic interpretation of the math is more important than the math itself. Learning Objectives: Upon completion of the course, students should: 1) possess solid proficiency in linear algebra and calculus; 2) have developed intuition for how to read mathematical equations as statements of logic in the context of a model; 3) have learned the basics of differential equations, Hamiltonians and dynamic programming; 4) have reached a basic level of mastery of both Latex and MATLAB; and 5) most importantly, be equipped with a sufficient math background to succeed in PhD level Microeconomics, Macroeconomics, and Econometrics courses. Assignments There will be regular assignments based on the lecture material. I strongly encourage students to work in groups. Each homework will generally consist of two parts: (1) Pure math practice of the tools; and (2) economic applications of the tools. Be sure to spend time working out the economic intuition in these problems. Write down your interpretation of the math and the assumptions inherent in the structure. In addition, there will be several programming assignments using MATLAB. Given the state of economic and business science research today, computational work is essential for all fields and you should consider these assignments as important as any other, especially if you have very little programming experience. For certain portions of the assignments you are required to type your answers using Latex which is available on the server for Ph.D. students. Microsoft Word or other word processing programs are unacceptable. There will be two computer lab sessions apart from class to go over using MATLAB and Latex. These are scheduled for 3-4 PM in TBD in GHall on Thursday, September 25th for Latex and Thursday, October 2nd for MATLAB. Adelia Mehmetaj, the TA for this course, will lead these sessions. Information, announcements, and assignments (including data) will be posted on the course website at: Course Website: http://faculty.lebow.drexel.edu/LainczC/econ902 Grading The grade for this course will be allocated as follows: 40% for homework assignments; 25% for the midterm; and 35% for the final. Note that the midterm will be given at a date/time outside of regular lecture. Exact date/time will be announced at least 1 week prior to the exam. Texts The two main texts for this class are Dadkah, Foundations of Mathematical & Computational Economics, and Chiang and Wainwright, Fundamental Methods of Mathematical Economics, 4th Edition. In addition, there are several recommended texts which are helpful. There is an out of print book by Silberberg The Structure of Economics which is excellent and I highly recommend that you try to obtain a copy but it is not required. All three texts cover much the same material but in very different manners. Chiang is more basic and provides more intuition for the math. Silberberg is more rigorous and presents the material in a manner similar to that found in economics textbooks and papers. Silberberg also does a much better job of linking the math to the economic applications than Chiang. Dadkah is somewhere in between, but Dadkah also incorporates some basic Matlab (programming) into the text. Finally, there is a linear algebra text by Strang, Linear Algebra and Its Applications which is outstanding, but is optional – especially for those who are comfortable with linear algebra through eigenvalues. Unless you have a very strong background in matrix algebra, it is recommended that you have a copy of this book as it will be useful. In addition, for the final 2-3 weeks we will be working on dynamic optimization. There will be a series of handouts, but I highly recommend that everyone download the draft chapters of a book by Peter Thompson at: http://pthompsonecon.com Another helpful book is Varian’s Microeconomics. You do not need to buy this book, but it is recommended. It will be a particularly helpful supplement when you take the Microeconomics courses in the Winter and Spring quarters. The last two chapters in Varian are very useful references. IMPORTANT SCHEDULE NOTES: We will have class the week of Monday, October 13th even though this is a University holiday (Columbus Day). My strong preference is to have class on the Monday as scheduled unless anyone strongly objects by the end of week 1. If that is the case we will reschedule for another day/time that week. An announcement will be made close to that date. Finally, note that there is zero tolerance for academic dishonesty. That applies even more so at this level because research is worthless without integrity. Academic dishonesty by a Ph.D. will almost certainly result in immediate dismissal from the program. Please see this link for further information: http://drexel.edu/studentaffairs/community_standards/studentHandbook/ Lecture Schedule Note: *Indicates a handout will be available. Week 1 1. Introduction: Math and Economics. Proof Methodology, Readings: Handout; and Mas-Collel Handout, Chiang Ch. 1, Dadkhah Ch.1. 2. Reed* Derivatives and marginal interpretation, partial derivatives, gradients, hessians. Readings: Dadkhah Ch 2, 6, 7.1, Chiang Ch. 6, 7. Week 2 Calculus topics: Basic Optimization, Total Derivatives, Homogenous Functions, Euler’s Theorem, Implicit Functions. Readings: Dadkhah Ch. 7.2-7.4, 9.1: Chiang Ch. 8.1-8.5, 9.1-9.4 Week 3 1. Basic computation and programming, Taylor Expansion. Readings: Dadkhah: Ch. 3.3, 8, Chiang Ch. 9.5-9.6. 2. Concavity, convexity, quasi-concavity, quasi-convexity, Constrained Optimization. Readings: Dadkhah: Ch. 9.2, Ch. 10.1. Chiang Ch. 12.1-12.5. Week 4 Linear Algebra: Matrices, vector spaces, orthogonality, projections, determinants, inverses. Dadkhah: Ch. 4, 5.1, Chiang Ch. 4, 5. Week 5 More Linear Algebra: Quadratic Forms, eigenvalues, eigenvectors, markov chains. Readings: Dadkhah Chapter 5.1-5.4, 5.7 Chiang Ch. 5, 11.3 Midterm Exam Week of October 27th Week 6 1. Constrained optimization, interpretation of Lagrangian multiplier. Readings: Dadkhah: Ch. 10, Chiang: Ch. 10, 11. 2. Envelope Theorem, Duality, Quasi-concavity with constraints Readings: Dadkhah: Ch. 10, Silberberg: Ch. 7 and 8 (Handout), Chiang Ch. 12. Week 7 1. Integration – definite and indefinite, interpretation, infinite horizon, Leibniz rule. Dadkhah: Ch. 11, Chiang Ch. 13. 2. Differential Equations. FOLDES, forward integration, and phase diagrams. Readings: Barro & Sala-I-Martin* Handout: 463-510, Sargent and Wallace* Handout, Dadkhah: Ch. 13, Chiang Ch. 15. Week 8 Dynamic Optimization: Systems of Differential Equations, Hamiltonians, transversality conditions, current value and present value. Readings: Chiang* Handout (from a different book), Barro & Sala-I-Martin* Handout: 463-510, Dadkhah: Ch. 12.1-3, 13. Weeks 9-10 Readings: Dynamic Programming, Value Functions. Dadkhah: 10.2, 12.4, 14.1-14.2, Sargent*: Ch. 1., Stokey & Lucas*: Ch. 2, Chapters from Peter Thompson (see above). FINAL EXAM WEEK OF DECEMBER 8th The exact date of the final exam will be set according to the University schedule which is usually announced in November. The final exam will consist of two parts: 1) and inclass 2 hour exam; and 2) a 48 hour take home-exam immediately following the in-class exam. PLEASE PLAN ACCORDINGLY.
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