Syllabus of『Fundamental Methods of Mathematical Economics』(数理经济学基础)Course DetailsSemester: 2005-2006学年,第2学期Lecturer 张明恒PhD., Associate ProfessorOffice: (教学行政大楼) Teachers Official Buildings 512RoomOffice Time: P.M.6:30 – 8:30, TuesdayTelephone: +86 21 6590 2567E-Mail: mingheng@Coordinator:Date: 3/4,Wed;1/2,FridayRoom: 1405Rm, No.1 Teaching Buildings(1405,国定路一教) Website: /~mingheng/MathEcon.htmlStudent Background(i)the pre-session mathematics course(ii)the background mathematical material(iii)the fundamental of EconomicsGeneral AdviceThe key to success in a course like mathematical economics is to work carefully and consistently on the course material as the semester progresses. Falling behind with the course material is a recipe for disaster. Therefore students are strongly urged to attempt to complete the exercise sheets prior to attending the examples class and to read the appropriate chapters in the course text in conjunction with their lecture notes.The learning resources(i)the office hours of the lecturer when he will be available to see students;or make appointment by email or phone to meet the lecturer at anothertime(ii)the textbooks (incl. the materials on the classroom)(iii)the materials on the course web page(iv)the discussion with (the advice from) colleagues and friends on the course AimsThe aims of this course are to(i)Provide an introduction to mathematical methods for economics that willassist students in understanding mathematical research in their field;(ii)Enable students to apply these mathematical methods in their own research.ObjectivesAt the end of the course students should be able to(i) Demonstrate their understanding of the mathematical methods foreconomics;(ii)Understand and study Equilibrium Analysis, Comparative Statics Analysis, Optimization (multivariate), Dynamic Economic, Simultaneous Equations andLinear Programming etc.;(iii)Ready to advanced microeconomics, macroeconomics and econometrics.List of Readings1)Chuang,A.C., Fundamental Methods of Mathematical Economics,McGraw-Hill Publishing Company, 1984, 3rd Ed. (刘学译, 数理经济学的基本方法, 商务印书馆,2003年)(Text Book).2)Silbergerg, E., The Structure of Economics – A Mathematical Analysis,McGraw-Hill Education - Europe, 1990, 2nd ed, paperback.3)Klein,M.W., Mathematical methods for Economics, Addison-Wesley, 1998.4)Dowling,E.,T., Theory and Problems of Introduction to Mathematical Economics, 3nd5)Handbook of Mathematical Economics Vol.1-6,6)International Journal on Mathematical Economics such asi.Journal of Mathematical Economicsii.Journal of Economics Theoryiii.Journal of Economics and Businessiv.Journal of Mathematical Financev.Journal of Econometricsvi.Mathematical Social Sciencesvii.Economics Modellingviii.Economics Lettersix.Economics Theoryx.Game TheoryLecturesChapter 1 Nature of Mathematical Economics/数理经济学的实质Chapter 2 Economic Models/经济模型Chapter 3 Equilibrium Analysis in Economics/静态均衡分析，市场均衡模型，国民收入均衡模型Chapter 4 Linear Models and Matrix Algebra/线性模型与矩阵代数Chapter 5 Linear Models and Matrix Algebra/线性模型与矩阵代数，市场模型，国民收入模型，Leontief投入产出模型Chapter 6 Comparative Statics and the Derivative/比较静态分析，变化率/导数/曲率，极限定理，函数的连续性与可微性Chapter 7 Rules of Differentiation and Comparative Statics，微分法则，偏微分，Jacobi行列式Chapter 8 Comparative Statics of General Function Models，全微分/全导数，隐函数存在定理，一般函数模型的比较静态分析Chapter 9 Optimization (univariate)，最优值与级值，导数检验，Maclaurin/Taylor 级数Chapter 10 Exponential and Logarithmic Functions/指数函数与对数函数，自然指数与增长问题，最优时间安排Chapter 11 Optimization (multivariate)/多变量的最优化，最优化条件的微分形式，二次型，目标函数，Hessian矩阵检验，函数的凹/凸性与极值问题，多产品厂商问题，价格歧视，投入决策Chapter 12 Optimization with Equality Constraints/具有约束方程的最优化，Lagrange Multiplier, Bordered Hessian Matrix检验，二阶条件效用最大化与消费需求，齐次函数/生产函数，投入最小成本组合Chapter 13 Economic Dynamics and Integral Calculus/动态经济学与积分学，动态与积分，定积分/不定积分/广义积分，Domar增长模型Chapter 14 First Order Differential Equations/连续时间的一阶微分方程，市场价格的动态过程，恰当微分方程，非线性微分方程Solow增长模型Chapter 15 Higher Order Differential Equations/高阶微分方程，复数，三角函数，复数根，具有价格预期的市场模型、通货膨胀与失业模型Chapter 16 First Order Difference Equations/离散时间的一阶差分方程，均衡的动态性，蛛网模型，具有存货的市场模型，非线性差分方程Chapter 17 Higher Order Difference Equations/高阶差分方程，Samuelson数乘加速模型，通货膨胀与失业模型Chapter 18 Simultaneous Differential and Difference Equations/联立微分和差分方程动态投入产出模型Chapter 19 Linear Programming/线性规划，单纯形SimplexChapter 20 Linear programming - cont./线性规划（续），对偶定理，活动的微观和宏观水平Chapter 21 Non-Linear Programming/非线性规划，Kuhn-Tucker定理，约束规范，Arrow-Enthoven定理Chapter 22 Game Theory / 搏弈论Chapter 23 1st Seminarspetitive Equilibrium Hyperinflation under Rational Expectations, Also see epge.fgv.br/portal/arquivo/1792.pdf2.Multiple Equilibria with Externalities，Also see/depts/econ/dp/0409.pdfChapter 23 2nd Seminars1.Dynamic Analysis of a Solow-Romer model of endgenous Economical GrowthAlso see .au/policy/ftp/workpapr/ip-68.pdf2.Seignorage, Productive Government Spending and Growth in a Lucasian General Equilibrium Model Also see /economics/staff/hmk/paper/HMKAW96.PDFSupplemental Materials for a ChoiceChapter 51)Leontief, Wassily W. “Input-Output Economics.” Scientific American, October1951, pp.15-21.2)Iris Jensen ,The Leontief Open Production Model or Input-Output Analysis3)Internet Resources for the Leontief Model/mathews/n2003/leontiefmodel/LeontiefModelBib/Links/LeontiefMo delBib_lnk_1.htmlChapter 71)The Financial Returns to Education2)Why Does’t Capital Flow to Poor Counters?, See Robert E. Lucas,Jr., American EconomicView, V ol.80,No.2,pp.92 – 96, 1990(May)Chapter 81)Growth Accounting,Cobb-Douglas Production Function2)The Division of national IncomeChapter 111)Properties of a Valid Cost Function2)Government Revenue3)Isabel Correia and Pedro Teles,The Optimal Inflation Tax4)Jens Suedekum, Profit maximization and firm supply under perfect competition,University of Konstanz,Chapter 121)Dan Segal, A Multi-Product Cost Study of the U.S. Life Insurance Industry, RotmanSchool of Management,University of Toronto2)Martin Feldstein, “College Scholarship Rules and Private Savings”, American EconomicReview, Vol.85, No. 3,pp. 552 –566(June, 1995)Chapter 131)Economics Growth modelChapter 141)Charles I. Jones, A Note on the Closed-Form Solution of the Solow Model2)Fadhel Kaboub, Long-run Keynesian Growth Theory: Harrod and Domar vs.Solow Chapter 151)Tor Jacobson, Johan Lyhagen†, Rolf Larsson and MarianneNessén,Inflation, Exchange Rates and PPP in a Multivariate Panel Cointegration Model, Sveriges Riksbank Working Paper Series No. 145,December 20022)Pierre L. Siklos, INFLATION AND HYPERINFLATION, Department of EconomicsWilfrid Laurier UniversityChapter 161)Money and Prices Model2)Philip Cagan “The monetary Dynamics of Hyperinflation”, Studies in the Quanlity Theory ofMoney, ed., Milton Friedman (Univ. of Chicago Press, 1956)Chapter 171)Nicholas Rau,Introduction to Growth Theory, University College London2)Economic Problems of Developing AreasChapter 181)The Dynamic Variable Input-Output Model: An Advancement From The Leontief DynamicInput-Output Model,Annals of Regional Science, Vol. 34, No. 4, January 20012)Obst,N.M., “Stabilization Policy with an Inflation Adjustment Mechanism,” The Quarterly,Journal of Economics, 92 (May 1978), pp.355-359Chapter 191)Linear programming2)/otc/Guide/OptWeb/3)Global Optimization4)http://www.fi.uib.no/~antonych/glob.html5)Tom Cavalier's Optimization Links/faculty/t/m/tmc7/tmclinks.html6)Optimization Center at Northwestern Univ.7)/OTC/8)Yinyu ye at Stanfod9)/~yyye/Chapter 201)J. J. H. Forrest and J. A. Tomlin,Implementing the simplex method for the OptimizationSubroutine Library, IBM SYSTEMS JOURNAL, VOL 31,NO 1, 1992ATTENDANCESince exams will test your knowledge of materials covered in class, you are expected to attend class. You are responsible for material covered in class (including changes in assignment or rescheduling the test) even if you are unavoidably absent.GRADING POLICYYour final grade will be based on your performance on two exams and homework and it will be determined as follows:Mid exam 15%Final exam 60%Homework 15%Class participation 10%Total 100%Your total will be converted into final course grade and plus and minus grading will be used in this course.。
