EC 336 MATHEMATICAL ECONOMICS SYLLABUS

Transcription

1 EC 336 MATHEMATICAL ECONOMICS SYLLABUS Colby College Department of Economics Fall 2008 Professor: Guillermo Vuletin ( Office: Diamond 359 Phone: 5235 Lecture time and location: Tuesdays and Thursdays 9:30-10:45 am, DIAM 341. Office hours: Tuesdays and Thursdays 3:00-4:30 pm. TA: Ling Zhu ( TA office hours: Wednesdays 7:00-8:30pm (DIAM 354) Course web page: Description A course in advanced economic theory designed to provide students the fundamental mathematical tools necessary to prepare for graduate work in economics or business administration. Topics include the development of portions of consumer, producer and macro (fiscal and monetary) theory. The material includes comparative static analysis, single and multiple agent unconstraint and constraint optimization problems and dynamic analysis. Course objectives By the end of the course, students are expected to i) learn how to read and understand most current journal articles in economics without stumbling over the mathematics, ii) develop an initial understanding of how to frame economic modeling ideas in mathematical format, iii) prepare students to use a wide range of mathematical techniques used in senior undergraduate and graduate level courses and, iv) develop a set of problem-solving and analytical skills to solve problems in other fields of study and everyday decisions. Prerequisites Economics 224 and either Mathematics 122 or 162. Text Fundamental Methods of Mathematical Economics (4th Edition) by Alpha C. Chiang and Kevin Wainwright.

2 Course policies Course web site: You should frequently access the course web site to find updated course information. There, you will find problem sets and their solutions and postings of important announcements. Software: You will learn to use two software packages (Mathematica 6 and Scientific WorkPlace 5.5) that will prove to be very handy. Both packages are currently installed in DIAM 322. We will spend a class in DIAM 322 (day TBA) learning the basics of those programs. Office hours: Tuesdays and Thursdays 3:00-4:30 pm, Diamond 359. If you need to meet with me and cannot make one of those times, please schedule an appointment by . If you feel that you are not making as good progress in the course as you should, please talk to me as soon as possible. It is my job to help you understand the material and this is the reason why office hours are held, so make use of them. Do not wait until the week before the final exam! Class and exam attendance: I do not take attendance. However, I expect students to attend all classes and actively participate in class discussions. Please note ahead the scheduled dates of exams. Unexcused absences from exams will result in a zero grade. Acceptable reasons for missing an exam include critical emergencies, athletic trips or illness. If some athletic event overlaps with a course exam please contact me as soon as you know about such event (at least one week in advance) so I can help you to resolve the problem. Grading policy: The grades for this course will be based on class participation, problem sets, a final exam, and a paper. The final exam will Thursday, December 4 (during class time). That is to say, there will be no final during finals week. The paper will be due Sunday, December 14 at 11:00am. Late problem sets or paper will not be accepted. There will not be extra credit assigned for this course. Your final grade will be determined as follows: Problem sets 45% Final 25% Paper 20% Class participation 10% Paper: The paper consists on modeling some real-life phenomenon using the techniques and tools learned in the course. Topics must be chosen by the first week of November, and a short (one page) paper proposal must be turned in at the beginning of Thursday, November 6 class. The final paper must have a maximum of 7 single-spaced pages of text (including a list of references) and must be typed using Scientific WorkPlace 5.5. Academic honesty: Colby s policy on academic honesty can be found in fm. I encourage you to work with other classmates; however, all problem sets (and exams!) must be your own. Electronic device policy: Please turn off all electronic devices during class. If there is a legitimate reason for you to be within reach during class times, please see me prior to using the cell phone.

3 Tentative course outline Topic Textbook chapters I. INTRODUCTION TO MATHEMATICAL ECONOMICS 1, II. EQUILIBRIUM (OR STATIC) ANALYSIS II.1. Equilibrium analysis in Economics 3 Definition of equilibrium. Solution of equilibrium. Single vs. multiple equilibrium. Application: labor supply. Partial vs. general equilibrium. Application: single vs. multiple commodity markets. II.2 Linear Models and Matrix Algebra Matrix algebra with special emphasis on Cramer s rule. i) multiple commodity markets. ii) wage gaps and international trade. 4, 5 Problem set 1 (II.1 and II.2): i) National-Income model (macro). ii) Heckscher-Ohlin model (trade). III. COMPARATIVE STATIC ANALISYS Review of comparative static analysis using IS-LM model. Alternative approaches. 6, 7, 8 Problem set 2 (III): i) Mundell-Fleming model (IS-LM with small open economy) (macro). ii) Rybczynski model(trade). IV. UNCONSTRAINT OPTIMIZATION PROBLEMS IV.1 Optimization of functions of one variable Main concepts First-derivative test or first order conditions (necessary conditions) Second-derivative or second order conditions (sufficient conditions) Profit maximization (one product) under: - perfect competition. - monopoly. - Cournot competition (duopoly).

4 IV.2 Optimization of functions of more than one variable The differential version of optimization conditions. Extreme values of function of two variables and comparative static aspect of optimization. Application: Profit maximization (two products) under perfect competition. Extreme values of function of n variables , i) Monopolist selling in segmented markets. ii) Ordinary least squares (OLS) estimators. Problem set 3 (IV.1 and IV.2): i) Inputs -labor and capital- selection under perfect competition. The role of elasticity of substitution (micro). ii) Technical vs. policy journal articles selection (micro). iii) Profit maximization (two products) under monopoly (complementary vs. substitutable goods). V. CONSTRAINT OPTIMIZATION PROBLEMS Lagrange-multiplier method. First-derivative test or first order conditions. Second-derivative or second order conditions , 12.5, 12.7 i) Utility maximization and consumer demand (two goods, one period) (micro). ii) Utility maximization and consumer demand (one goods, two periods) (macro). ii.a) perfect access to international capital markets. ii.b) financial autarky. ii.c) welfare implications. ii.a) vs. ii.b). iii) Presidential preferences for inflation versus unemployment. Peter A. Zaleski, Presidential preferences for inflation versus unemployment, Journal of Macroeconomics. Volume 14, Issue 3, Summer 1992, Pages ( 4ND1M0B-B/2/2953b08d790a6a4acfd4bb75c4ddcd02) Problem set 4 (VI): i) Technical vs. policy journal articles selection revisited (micro). ii) Utility maximization and consumer demand. The role of non time-separable preferences. iii) Utility maximization, consumer demand, and labor decisions. VI. INTRODUCTION TO MATHEMATICA 6 AND SCIENTIFIC WORKPLACE 5.5 (This class will take place in DIAM 322)

5 VII. FURTHER TOPICS IN OPTIMIZATION VII.1 Uncertainty and consumption under capital markets imperfections (incomplete vs. complete asset markets) i) Utility maximization and consumption under uncertainty of output path and incomplete markets. Certainty equivalence and precautionary savings. Problem set 5 (VII.1): i) Utility maximization and consumption under uncertainty of output path and complete markets. The role of state contingent assets. VII.2 Multiple agents optimization. i) Optimal taxation. Exogenous government spending. Benevolent government. Problem set 6 (VII.2): i) Optimal taxation. Endogenous government spending. Benevolent and nonbenevolent government. VIII. DYNAMIC ANALYSIS TBA 14, 15, 17, 19, 20