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A Unified Introduction to Mathematical Economics, Harper and Row, 1975. Childress R.L., Calculus for Business and Economics, 2nd ed. Prentice-Hall, 1978.

Econ. 4808/5808 Summer 1993

INTRODUCTION TO MATIIEMATICAL ECONOMICS MTWRF 10:50-12:20 Gugg 206

I NSTRUCTOR: Professor Frank S.T. Hsiao OFFICE HOURS: MTR 10:00-10:45 PREREQUISITES:

TEXTBOOK:

OFFICE: Economics Building 103 OFFICE PHONE: 492-7908

Math 1050-1, 1060-1, 1070-1, 1080-1, 1090-1, 1100-1; or Math 1070-3 and Math 1080-3; or Math 1300; or higher.

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 exercies in the book) are reserved at the Norlin Library E. Dowling: Theory and Problems of Mathematics for Economists, Schawn's Outline Series, McGraw-Hill, 1980 (reserved at the Norlin Library), 2nd ed. 1992. Problem Sets from Dowling (three 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 organization. Methods of Static Analysis, Comparative Static Analysis, Optimization 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. There are two lectures per week. The second lecture 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. PREREQUISITES: 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 used in Math 1050-1 to Math 1100 as specified at the beginning of this syllabus. A review text will be given on the second session of the class. 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. 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 one large comprehensive question. 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.

2 SEMESTER GRADES: The semester grade will consist of 3 parts - Exam scores (50% for mid-term exams, 35% for the final), Homework scores (10% ), and quizzes (5% ). Probable cutoff points are in the vicinity of 90% (A-), 80% (B-), 70% (C-), 60% (D-), and some curving may be used. Graduates and undergraduates will be graded separately. To Graduate Students (taking Econ. 5808). In addition to regular classwork, the final exam will include the second part of chapter 8, the entire contents of chapter 10 and chapter 12. Extra classes may be held for these parts if desired. (These parts will not apply to the undergraduate students).

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.

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 corner 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.

3 Week of

Chapter

Topic

1

7/13/93

Ch. 3

Economic Models and Equilibrium Analysis (3 . 1-3.3, 3.5)

2

7/15

Ch. 4

Matrix Algebra (4.1, 4.2 , 4.4-4.6)

3

7/16

Ch. 5

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

4

7/19

Ch. 5

Input-Output Models (5.7)

5

7/20

Ch. 7

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

6

7/22

Ch. 7

Golden Rules of Differentiation and their use (7. 3-7 .5)

7

7/23

Ch. 8

Total Differential and Elasticity of Demand (8.1-8.4)

8

7/26

Ch. 8

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

9

7/28

Ch. 9

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

10

7/29

Ch. 10

Growth Equations (10.4-10.7)

11

7/30

Ch. 11

Multi-variable Model (11.1 , 11.2)

12

8/2

Ch. 11

Price Discrimination, (11.4, 11.5)

13

8/4

Ch. 12

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

14

8/6

Ch. 12

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

15

8/10

Ch. 12

Homogeneous Functions, Cost Minimizations, and Elasticity of Substitution (12.6, 12.7)

··:~

:~

:'. (§Jt~pteJJ:.3;+.J;i}~·[email protected]:n;J~~

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.

4

References for Econ. 4808/5808 The following references are available in Norlin Library: 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. 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. 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 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 Allen, C.L., (1962) Elementary Mathematics of Price Theory, Wadsworth. Very elementary 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 . Dernburg, (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, /, II, Braisdel. (An introductory to intermediate text, good examples.) Thomas, G.B., (1953) Calculus and Analytic Geometry, Addison-Wesley. (A popular introductory text.)

r 5

Introduction to Mathematical Economics Homework for Econ 4808/5808 Summer 1993, Frank Hsiao Exercise 3.2 p40 p45 3.3 3.4 p51 3.5 p53

1, 3, 4, 5 la, 3ad, 5a 3 1, 3

4.2 4.3 4.4 4.5 4.6

p66 p74 p78 p81 p87

labcd, 2ab, 4ac lacth, 2ab, Sae la, 3 labcd, 2abcd 1, 2, 4, 6a

5.2 5.4 5.5 5.6 5.7

p98 plO p112 p115 p123

lace, 3, 4a 2a, 4a, 5 la, 3ad 1 1,2,3,4,5

7.1 7.2 7.3 7.4 7.5

p159 p169 p173 p177 p184

led, 2be, 3cd 1, 3af, 4, 5 1, 4, 5 lac, 2cd, 3cd, 4, Sab 1

8.1 8.2 8.3 8.4 8.6

p193 p195 p198 p203 p255

lab, 2, 3, 4 lb, 2b, 3, 5 lb, 2b lb, 2b 1-6

9.2 9.3 9.4

p239 p244 p253

lad, 2ab, 3, 4 lad, 4 la, 3, 4, 6

10.1 10.2 10.3 10.4 10.5 10.7

p273 p281 p287 p291 p297 p305

1, 3b 3ab, 4ac 3abde labgh, 3abh 2, 3, 4, 6, 7, 9, 10

11.2

p318

1, 2

11.6

p363

1, 2, 6

12.2 12.5 12.6 12.7

p378 p409 p471 p430

lac, 3a 1, 2, 5 lac, 6, 7ab 1-7, Sad, 9ab

INTRODUCTION TO MATIIEMATICAL ECONOMICS MTWRF 10:50-12:20 Gugg 206

I NSTRUCTOR: Professor Frank S.T. Hsiao OFFICE HOURS: MTR 10:00-10:45 PREREQUISITES:

TEXTBOOK:

OFFICE: Economics Building 103 OFFICE PHONE: 492-7908

Math 1050-1, 1060-1, 1070-1, 1080-1, 1090-1, 1100-1; or Math 1070-3 and Math 1080-3; or Math 1300; or higher.

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 exercies in the book) are reserved at the Norlin Library E. Dowling: Theory and Problems of Mathematics for Economists, Schawn's Outline Series, McGraw-Hill, 1980 (reserved at the Norlin Library), 2nd ed. 1992. Problem Sets from Dowling (three 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 organization. Methods of Static Analysis, Comparative Static Analysis, Optimization 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. There are two lectures per week. The second lecture 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. PREREQUISITES: 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 used in Math 1050-1 to Math 1100 as specified at the beginning of this syllabus. A review text will be given on the second session of the class. 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. 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 one large comprehensive question. 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.

2 SEMESTER GRADES: The semester grade will consist of 3 parts - Exam scores (50% for mid-term exams, 35% for the final), Homework scores (10% ), and quizzes (5% ). Probable cutoff points are in the vicinity of 90% (A-), 80% (B-), 70% (C-), 60% (D-), and some curving may be used. Graduates and undergraduates will be graded separately. To Graduate Students (taking Econ. 5808). In addition to regular classwork, the final exam will include the second part of chapter 8, the entire contents of chapter 10 and chapter 12. Extra classes may be held for these parts if desired. (These parts will not apply to the undergraduate students).

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.

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 corner 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.

3 Week of

Chapter

Topic

1

7/13/93

Ch. 3

Economic Models and Equilibrium Analysis (3 . 1-3.3, 3.5)

2

7/15

Ch. 4

Matrix Algebra (4.1, 4.2 , 4.4-4.6)

3

7/16

Ch. 5

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

4

7/19

Ch. 5

Input-Output Models (5.7)

5

7/20

Ch. 7

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

6

7/22

Ch. 7

Golden Rules of Differentiation and their use (7. 3-7 .5)

7

7/23

Ch. 8

Total Differential and Elasticity of Demand (8.1-8.4)

8

7/26

Ch. 8

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

9

7/28

Ch. 9

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

10

7/29

Ch. 10

Growth Equations (10.4-10.7)

11

7/30

Ch. 11

Multi-variable Model (11.1 , 11.2)

12

8/2

Ch. 11

Price Discrimination, (11.4, 11.5)

13

8/4

Ch. 12

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

14

8/6

Ch. 12

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

15

8/10

Ch. 12

Homogeneous Functions, Cost Minimizations, and Elasticity of Substitution (12.6, 12.7)

··:~

:~

:'. (§Jt~pteJJ:.3;+.J;i}~·[email protected]:n;J~~

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.

4

References for Econ. 4808/5808 The following references are available in Norlin Library: 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. 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. 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 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 Allen, C.L., (1962) Elementary Mathematics of Price Theory, Wadsworth. Very elementary 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 . Dernburg, (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, /, II, Braisdel. (An introductory to intermediate text, good examples.) Thomas, G.B., (1953) Calculus and Analytic Geometry, Addison-Wesley. (A popular introductory text.)

r 5

Introduction to Mathematical Economics Homework for Econ 4808/5808 Summer 1993, Frank Hsiao Exercise 3.2 p40 p45 3.3 3.4 p51 3.5 p53

1, 3, 4, 5 la, 3ad, 5a 3 1, 3

4.2 4.3 4.4 4.5 4.6

p66 p74 p78 p81 p87

labcd, 2ab, 4ac lacth, 2ab, Sae la, 3 labcd, 2abcd 1, 2, 4, 6a

5.2 5.4 5.5 5.6 5.7

p98 plO p112 p115 p123

lace, 3, 4a 2a, 4a, 5 la, 3ad 1 1,2,3,4,5

7.1 7.2 7.3 7.4 7.5

p159 p169 p173 p177 p184

led, 2be, 3cd 1, 3af, 4, 5 1, 4, 5 lac, 2cd, 3cd, 4, Sab 1

8.1 8.2 8.3 8.4 8.6

p193 p195 p198 p203 p255

lab, 2, 3, 4 lb, 2b, 3, 5 lb, 2b lb, 2b 1-6

9.2 9.3 9.4

p239 p244 p253

lad, 2ab, 3, 4 lad, 4 la, 3, 4, 6

10.1 10.2 10.3 10.4 10.5 10.7

p273 p281 p287 p291 p297 p305

1, 3b 3ab, 4ac 3abde labgh, 3abh 2, 3, 4, 6, 7, 9, 10

11.2

p318

1, 2

11.6

p363

1, 2, 6

12.2 12.5 12.6 12.7

p378 p409 p471 p430

lac, 3a 1, 2, 5 lac, 6, 7ab 1-7, Sad, 9ab