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Econ. 6808 Fall 1993

Instructor:

Textbook:

r INTRODUCTION TO QUANTITATIVE ECONOMICS MWF 9:00-9:50

ECON Room 2

Professor F rank S.T. Hsiao Office Hours: M 10-12:15 & WF 10-11:30

Office: Economics Building 107 Office Phone: 492-7908

The Structure of Economics, A Mathematical Analysis, 2nd ed. E. Silberberg, 1990

Prerequisites: Econ 4808, Introduction to Mathematical Economics, we assume that students have completed Chapters 3 to 12 of A.C. Chiang: Fundamental Methods of Mathematical Economics, 3rd ed., McGraw-Hill, 1984. Two copies of Instructor's Manual (which contains answers to all the exercises in the book) are reserved at the Norlin Library. Other general background materials can be found in E . Dowling: Theory and Problems of Mathematics for Economists, Schaum's Outline Series , McGraw-Hill, 1980 (reserved at the Norlin Library), 2nd ed. 1992.

Objectives: The purpose of this course is to provide a comprehensive exposition of basic mathematical instruments that are commonly used in all fields in economics - microeconomics, macroeconomics, econometrics, international trade and finance, public finance, money and banking, resource and environmental economics, urban and regional economics , labor and human resources, and industrial organization.

This course is required for the M.A. students. Topics include multivariable optimization problems with and without constraints, simple difference and differential equations, uncertainty, introduction to linear and non-linear programming, and calculus of variations.

Students are required to attend all lectures. They are expected to read the assigned reading materials or chapters prior to the lecture and complete their homework assignments on time.

Homework & Quiz: Exercises from chapters will be announced in the classes. Each homework assignment will be graded on a 10-point scale. Credit will be given only to the homework that is handed-in before or on the due date and time. Occasionally, an exercise or quiz will be given in the class. The quiz will be graded on the basis of 10 points.

Exams: The mid-term exam will mainly be based on the class notes, textbook examples, and homework questions . The final exam will be comprehensive. Some questions in the final will test your ability of applying what you have learned in the class. They may combine several homework questions or textbook examples, or their variation, in one large comprehensive question. Thus, in addition to reviewing the class notes, homework, and examples, you are encouraged to be imaginative and innovative.

Semester Grades: The semester grade will consist of 2 parts - Exam scores (35 % for mid-term exams, 55 % for the final), Homework scores (10% ). Probable cutoff points are in the vicinity of 90% (A-), 80% (B-), 70% (C-), 60% (D-), and some curving may be used .

NOTES:

1. Please attend the classes regularly, I expect every student to. participate in all classes . Please make every attempt to attend the last four weeks of classes, otherwise, a surprise may be in store for you in the final.

2. Test dates will not be changed. Please prepare for the tests long before the test dates. 3. If you are going to miss or have missed the exams, hand in an explanatory statement and

documentation (from the doctor or the court) to the instructor. No credits will be given to unexcused absences in examinations.

4. Please come (or call) to talk with the instructor about any problems related to this course.

Part I: . Math Review

· 1. Exponential and Logarithmic Functions (S, 2.9)

2. Integration and Differential Equations (S, 2.12, 2.13)

3. Functions of Several Variables (S, 3.1 - 3.6)

4. Homogeneous functions (S, 3. 7, Appendix)

Part II: Static Analysis

5. Unconstrained Optimization (S, 4.1 - 4.5)

6. Taylor Series , Concavity and Implicit function Theorem (S, Ch. 4, Appendix, Ch. 5)

7. Constrained Optimization (S, 6.1 - 6.5)

8. The Envelope Theorem and Duality (S , 7 .1 - 7. 4)

9. Consumer Demands (S, 10.1 - 10.5)

Part III: Dynamic Analysis

10. Intertemporal Choice (S , 12.1 - 12.3)/

11. Uncertainty and Probability (S, 13.1 - 13.4)

12. Optimal Control Theory (S, 18.1 - 18.4)

Part IV: Mathematical Programming

13. Inequality Constraints (S, 14.1 - 14.5)

14. Linear Technology and Programming (S , 15.1 - 15.5)

15. Simplex Algorithm (S , 15.6)

:izlii.:Csat). it:30 a.m . . - 2:30p.m. Final Exam - 100 points

Check your final exam schedule during the first week of the semester. If you are concerned about the possibility of taking three or more final exams on the same day, please make any desired schedule adjustment during the drop-add period.

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Basic References for Econ. 6808

The following references are available in the Norlin Library.

Hsiao, F ., Mathematical Programming and Economic Theory, Lecture Notes, Chapters 2-5.

Arrow, K. and M.D. Intriligator, ed., Handbook of Mathematical Economics, Vols. 1 and 2, North-Holland, 1982 (All or Al2)

Varian, H.R. Microeconomic Analysis, W. W. Norton, New York.

Dorfman, R., P. A. Samuelson, R.M. Solow, Linear Programming and Economic Analysis, New York: McGraw-Hill, 1958. (DOSSO)

Takayama, A. Mathematical Economics, 2nd ed., Cambridge Univ. Press, 1985.

Some References on the Importance of Mathematics in Economics

Arrow, K.J. and M.D. Intriligator, Historical Introduction, All, 1-14.

Fisher, I., "Mathematical Method in the Social Sciences" Econometrica, 1941.

Koopmans, T., Three Essays of the State of Economic Science, Chs. 2 and 3.

Samuelson, P. , "Economic Theory and Mathematics, An Appraisal," AER, 1952, 56.

____ , "Some Psychological Aspects of Mathematics and Economics," Rev. of Econ. Stat. 1954, pp. 380.

____ , "Comments on Professor Samuelson on Operationalism in Economic Theory."

____ , "Comment on Earnest Nagel's Assumptions in Economic Theory," AER/P 1962, pp. 231-232.

(Samuelson's papers are collected in part XVIII of The Collected Scientific Papers of Paul A. Samuelson, Vol. 2, ed., by J. E. Stiglitz, 1966).

Franklin, J. "Mathematical Methods of Economics," American Mathematical Monthly, 90(4), April 1983, pp. 229-244.

Other References:

Allen, R.G.D., Mathematical Analysis for Economists, St. Martins Press, 1938. Paperback edition available. This is a classic work with which every economist, whether or not he is interested in Mathematical Economics, must be acquainted. A must for graduate students .

Archibald, G.C. & R.G. Lipsey, An Introduction to Mathematical Economics--Methods and Applications, Harper and Row, 1976. ·

Birchenhall, C., Mathematics for Modern Economics, Barnes and Noble Books, 1984. Bressler, B., A Unified Introduction to Mathematical Economics, Harper and Row, 1975. Childress R.L., Calculus for Business and Economics , 2nd ed. Prentice-Hall, 1978. Dixit, A.K., Optimization in Economic Theory, Oxford Univ. Press, 2nd ed., 1989. Dowling, E.T., Introduction to Mathematical Economics, 2nd ed., Schaum's Outline Series in Economics,

McGraw-Hill, 1992. Glaister, S. , Mathematical Methods for Economists , Blackwell, 1984. Glass, J.C., An Introduction to Mathematical Methods in Economics, McGraw-Hill, 1980. Hands, D.W. Introductory Mathematical Economics, Mass: D.C. Heath and Company, 1991. Khoury, S. J., Mathematical Methods in Finance and Economics , North Holland, 1981.

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Lancaster, K., Mathematical Economics, 1968. Ostrosky, A.L. and J.V. Koch, Introduction to Mathematical Economics, Waveland Press, 1979. Smith, A., A Mathematical Introduction to Economics, Barnes and Noble Books, 1982. Schofield, N., Mathematical Methods in Economics, New York University Press, 1984. Tintner, G. and C.B. Millham, Mathematics and Statistics for Economists, Holt, Rinehart and Winston, Inc . ,

1970. A brief survey of the elementary quantitative methods used in Economics. Originally published in 1953 for beginning economists.

Weber, J. E., Mathematical Analysis - Business and Economics Weintraub, E.R., Mathematics for Economists: An Integrated Approach, Cambridge Univ. Press, 1982. Yamane, T. , Mathematics for Economists: An Elementary Survey, Prentice-Hall, 1962. Good exposition of

basic quantitative methods (differentiation, matrix, statistics). Fewer economic applications.

There are many other textbooks on mathematics for economists. Most of them are survey type with more emphasis in techniques than economic applications. The following texts emphasize applications.

Textbooks on Micro and Macroeconomics which use more Mathematics

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Allen, C.L., (1962) Elementary Mathematics of Price Theory, Wadsworth. Very elementary applications. In paperback.

Binger, B.R. and E . Hoffman, Microeconomics with Calculus, Harper-Collins, 1988. Blanchard, O.J . and S. Fischer, Lectures on Macroeconomics, M.I.T. Press, 1989. Dernburg, T.F. and J.D. Dernburg, (1969) Macroeconomic Analysis, An Introduction to Comparative

Statistics and Dynamics, Addison-Wesley. For the first year graduate student. Henderson, J. M. and R.E. Quandt, (1971) Microeconomic Theory, A Mathematical Approach, 2nd ed.,

McGraw-Hill. Upper level or graduate level text. Jehle, G.A. , Advanced Microeconomic Theory, Prentice Hall, 1991. Russell, R.R. and M. Wilkinson, Microeconomics, A Synthesis of Modern and Neoclassical Theory, John

Wiley & Sons, 1979. Walsh, V.C., (1970) Introduction to Contemporary Microeconomics, McGraw-Hill, 1970. Set theoretic

approach. Upper level.

Textbooks on Calculus Recommended Apostol, T.M., (1962, 67) Calculus. I. II, Braisdel. (An introductory to intermediate text, good examples.) Thomas, G.B., (1953) Calculus and Analytic Geometry, Addison-Wesley, 1st ed., (A popular introductory

text.) 5th ed., 1989.