ECON~l Spring 1997

INTRODUCTION TO MATHEMATICAL ECONOMICS TR 12:30-1:45 Econ 117

INSTRUCTOR: Professor Frank S. T. Hsiao OFFICE HOURS: TR 10:50-12:00; F 1:50-3:00

OFFICE: Economics Building 107 OFFICE PHONE: 492-7908

PREREQUISITF.S: Math 1050-1, 1060-1, 1070-1, 1080-1, 1090-1, 1100-1; or Math 1070-3 and 1080-3; or Econ 1078-3 and 1088-3; or Math 1300-5; or higher.

TEXTBOOKS: A. C. Chiang: Fundamental Methods of Mathematical Economics, 4th ed., McGraw-Hill, 1995 (3rd ed., 1984). Two copies of Instructor's Manual (which contains answers to all the

exercies in the book) are reserved at the Norlin Library.

E. Dowling: Theory and Problems of Mathematics for Economists, Shaum's Outline Series, McGraw-Hill, 1980 (reserved at the Norlin Library), 2nd ed. 1992. Problem Sets from Dowling (two copies are reserved in the Norlin Library).

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 organiz.ation. Methods of Static Analysis, Comparative Static Analysis, Optimi7.ation will be introduced. Major emphasis is on illustrating how these tools can be used to analyze theoretical and practical economic problems which arise in the behaviors of households, firms, and markets. To assure homogeneity of the student background, the prerequisites of this course will be enforced.

The last lecture of the week may be devoted to problem solving exercises and quizzes. Students are required to attend all lectures. They are expected to read the assigned reading materials on chapters prior to the lecture and complete their homework assignments on time.

PREREQUISITF.S: We assume that the students have completed the following textbook: Mizrahi, Abe, and M. Sullivan, Mathematics for Business and Social Sciences, An Applied Approach, 4th ed., John Wiley and Sons. This book is generally used in Math 1050-1 to Math 1100 as specified at the beginning of this syllabus.

HOMEWORK and 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.

There are two copies of Instructor's Manual reserved in the Norlin Library. Students are responsible for checking their homework answers with the answers in the Instructor's Manual. Generally, we devote the first 5-10 minutes of each class to answer the homework questions.

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EXAMS: The two mid-term exams 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 large comprehensive questions. Thus, in addition to reviewing the class notes, homework, and examples, you are encouraged to be imaginative and innovative. Two copies of a previous final exam will be reserved in the Norlin Library. Please aquaint yourselves with them.

SEMESTER GRADES: The semester grade will consist of 3 parts - Exam seores (40% for mid-term exams, 40% for the final), Homework: seores (15%), and qnizres (5%). Probable cutoff points are in the vicinity of 90% (A-), 80% (B-), 70% (C-), (,()% (D-), and some curving may be used.

Please KEEP the returned quizx.es and homework assignments until the end of the semester. Check the grades of your mid-term exams and homework with the instructor during the last week of the semester. This will ensure that your semester work is properly credited.

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. Please prepare for the tests long before the test dates.

3. If you are going to miss or have missed the final exam, hand in an explanatory statement and documentation 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.

5. If you come to ask questions, please be well prepared for the questions you want to ask. Don't come to the office looking for questions all over the book or your notes, wasting valuable time.

The following Examination Rules will be strictly enforced.

1. Spread the chairs - you should not be too close to each other.

2. Put books in front under the blackboard, out of reach.

3. Use only the sheets of paper distributed to you in class. Do not use your own paper for tests and calculations.

4. Hand in all of the test papers and materials you have used in the test. Write "scrap" at the upper right comer of the paper if it does not contain your answers.

5. Make sure to number the questions clearly and write your name on each page of your test sheets.

6. No students are allowed to leave the classroom during the test. Please go to the washroom before the test starts.

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Date

1 1/14/97

2 1/14

3 1/21 .

4 2/4 .

5 2/11.

6 2/18 .

7 2/25 .

8 3/4

9 3/11

Chapter

Ch. 3

Ch. 4

Ch. 5

Ch.5

Ch. 7

Ch. 7

Ch. 8

Ch.8

Ch. 9

COURSE OUTLINE

Economic Models and Equilibrium Analysis (3 .1-3. 3, 3 .5)

Matrix Algebra (4.1, 4.2, 4.4-4.6)

Inverse Matrix and Cramer's Rule (5.2, 5.4-5.6)

Input-Output Models (5. 7)

Marginal Function and Average Function (6.1-6.3, 7.1-7.2)

Golden Rules of Differentiation and their use (7.3-7.5)

Total Differential and Elasticity of Demand (8.1-8.4)

lsoquants and Comparative Static Analysis of the IS-LM Model (8.6)

Optimization Without Constraints (9 .1-9. 4)

.. . ..................... ··········.····· ...... ····· ·.·.·.·.·.····.·.· ·.·.· ·.· ·.·.·.·.·.·.· ···.··· , .... , .. .... ... ·. ··.· •'• .. .. . ,• ••,·.·· ·.·· · .. ·· · ·.·. . .. .. . . .. . . ... .... ,•,•,•,•,•,•·.·,·,· ···

m 11::1::::::;:::!!;!1!iffi:li1:J:::::::::.:;1lJ!1!!!!lillit~l::!lt1i I:1~:1:1,i~!!::• 11~11i1\;::;:::iiiI:!;:ii::::::::!::fI:ii:::i::::::ii:/t!t::·;,:::::I:j:;i:::i:::;:;:::::::!,::i:::!!1':::1J1;i:::l:!:J:~;i;;:~ii!:~i11il

10 3/18

11 4/1

12 4/15

13 4/22

14 4/22

15 4/29

Ch. 10

Ch. 11

Ch. 11

Ch. 12

Ch. 12

Ch. 12

Growth Equations ( 10.4-10. 7)

Multi-variable Model (11.1, 11.2)

Price Discrimination, ( 11. 4, 11. 5)

Constrained Optimization (12.1,-12.3) Utility Maximization and Consumer Demand (12.5)

Game Theoretic Approach of Oligopoly: Nash Equilibrium, Reaction Function, Cooperative Equilibrium, Stackelbert Equilibrium (materials reserved in Norlin).

Homogeneous Functions, Cost Minimizations, and Elasticity of Substitution (12.6, 12. 7)

Check your rmal exam schedule during the first week of the semester. H you are concerned about the ~ibility 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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References for ECON 3808

The following references are available in Norlin Libracy:

Allen, R.G.D., Mathematical Analysis for Economists, St. Martins Press, 1938. Paperback edition available. This is a classic work with which evecy 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 Modem 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. 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. Khoucy, S. J., Mathematical Methods in Finance and Economics, North Holland, 1981. Ostaszewski, A., Mathematics in Economics, Models and Methods, Oxford: Blackwell, 1993. 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 elementacy quantitative methods used in Economics. Originally published in 1953 for beginning economists.

Weber, J.E. , Mathematical Analysis - Business and Economics Yamane, T. , Mathematics for Economists: An Elementary Survey, Prentice-Hall, 1,962. 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 Allen, C .L., (1962) Elementary Mathematics of Price Theory, Wadsworth. Vecy elementacy

applications. In paperback. Walsh, V.C., (1970) Introduction to Contemporary Microeconomics, McGraw-Hill, 1970. Set theoretic

approach. Upper level. Henderson, J.M. and R.E. Quandt, (1971} Microeconomic Theory, A Mathematical Approach, 2nd ed.,

McGraw-Hill. Upper level or graduate level text. Demburg, T.F. and J.D. Demburg, (1969} Macroeconomic Analysis, An Introduction to Comparative

Statistics and Dynamics, Addison-Wesley. For the first year graduate student.

Textbooks on Calculus Recommended Apostol, T.M., (1962, 67) Calculus, I, II, Braisdel. (An introductocy to intermediate text, good

examples.) Thomas, G.B., (1953) Calculus and Analytic Geometry, Addison-Wesley. (A popular introductocy text.)

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Introduction to Mathematical Economics Homework ~igmnents for ECON 3808

Spring 1997, Frank Hsiao

Exercise

3.2 p40 l, 3, 4, 5 3.3 p45 la, 3ad, Sa 3.4 p51 3 3.5 p53 l, 3

4.2 p66 labcd, 2ab, 4ac 4.3 p74 lacfb., 2ab, Sae 4.4 p78 la, 3 4.5 p81 labcd, 2abcd 4.6 p87 1, 2, 4, 6a

5.2 p98 lace, 3 5.4 pl()() 2a, 5 5.5 p112 la, 3ad 5.6 p115 lb 5.7 p123 1, 2, 3, 4, 5

7.1 p159 led, 2be, 3cd 7.2 pl69 1, 3af, 4, 5 7.3 p173 1, 4, 5 7.4 p177 lac, 2cd, 3cd, 4, Sab 7.5 p184 l

8.1 p193 lab, 2, 3, 4 8.2 p195 lb, 2b, 3, 5 8.3 p198 lb, 2b 8.4 p203 lb, 2b 8.6 p255 1-6

9.2 p239 lad, 2ab, 3, 4 9.3 p244 lad, 4 9.4 p253 la, 3, 4, 5, 6

10.1 p273 1, 3b 10.2 p281 3ab, 4ac 10.3 p287 3abde 10.4 p291 10.5 p297 labgh, 3abh 10.7 p305 2, 3, 4, 6, 7, 9, 10

11.2 p318 1, 2 11.6 p363 1, 2, 6

12.2 p378 lac 12.5 p40'} 1, 2 12.6 p417 lac, 6, 7ab 12.7 p430 1 - 7, Sad, 9ab

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