TRENT UNIVERSITY
DEPARTMENT OF ECONOMICS
ECON 4250H
Advanced Topics in Mathematical Economics
2010-2011 WI – Peterborough
Instructor:
Dr. M. Arvin
Room 351, Gzowski College
Telephone: 748-1011 Ext. 7299
marvin@trentu.ca
(Office hours: see page 7)
Dept. Administrator: Ms. Carolyn Johns
Room 346, Gzowski College
Telephone: 748-1011 Ext. 7331
cjohns@trentu.ca
(Office hours: Mon-Fri 1:00 - 4:30 pm)
Course Format: Lectures: Monday: 11 – 1; Seminars (fortnightly): Monday 2 – 3: Please see
schedule on last page.
Please check http://www.trentu.ca/admin/mytrent/Timetable/TimeTableGen0.htm to confirm
times and locations.
Please Note: This course does NOT use myLearningSystem (the system formerly known as
WebCT). There is, however, a course homepage under “courses” under the Department of Economics
website http://www.trentu.ca/economics/courses.php where some course material (e.g. copies of past
midterms/exams) will be posted.
I.
Description of the Course
This is a course in advanced topics in mathematical economics. The course provides an
introduction to differential equations, phase diagrams and dynamic (in)stability, non-linear
programming, dynamic optimization, and theory of risk and uncertainty. A large fraction of
the class time will be reserved for discussion of economic problems and applications. This
course is intended as a continuation of (and presupposes) Economics 225H and Economics
325H. Since this course stresses the use of mathematical tools to model economic behaviour,
it is hoped that by the end of the course students will be competent enough to construct and
solve their own economic models using appropriate mathematical techniques.
II.
Textbooks
Most of the readings will come from the following textbook:
Chiang, Alpha C. and Kevin Wainwright (2005), Fundamental Methods of Mathematical
Economics, Fourth Edition, New York: McGraw-Hill Irwin.
Earlier editions of this book are also usable.
In addition, students may wish to consult the following references. However, note that some
of these are too advanced for the purpose of this course. If you have difficulty in getting any
of these from the Library, you may borrow my copy.
Apostol, T.M. (1967), Calculus: Volume I, Second Edition, New York: John Wiley and
Sons, Inc.
Archibald, G.C. and R.G. Lipsey (1977), An Introduction to a Mathematical Treatment of
Economics, Third Edition, London: Weidenfeld and Nicolson.
Arrow, K.J. and M.D. Intriligator (1987), Handbook of Mathematical Economics: Volumes
I, II, and III, New York: North-Holland.
Baumol, W.J. (1977), Economic Theory and Operations Analysis, Fourth Edition, New
Jersey: Prentice-Hall, Inc.
Bazaraa, M.S. and C.M. Shetty (1979), Nonlinear Programming: Theory and Algorithms,
Toronto: John Wiley and Sons.
Binmore, K.G. (1986), Calculus, Cambridge: Cambridge University Press.
Brock, W.A. and A.G. Malliaris (1989), Differential Equations, Stability and Chaos in
Dynamic Economics, New York: North-Holland.
Chiang, A.C. (1992), Elements of Dynamic Optimization, New York: McGraw Hill, Inc.
(Reissued with changes by Waveland Press, Inc., Long Grove, IL in 2000.)
Chirgwin, B.H. and C. Plumpton (1972), A Course of Mathematics for Engineers and
Scientists, Volume 2, Second Edition, Toronto: Pergamon Press.
Davidson, R. (1977), "An Economic Interpretation of Optimal Control Theory", Chapter 1 of
Ph.D. dissertation, University of British Columbia.
Deaton, A. and J. Muellbauer (1980), Economics and Consumer Behavior, New York:
Cambridge University Press.
Diamond, P. and M. Rothschild (1978), Uncertainty in Economics, Economic Theory and
Mathematical Economics Series, New York: Academic Press, Inc.
Dixit, A.K. (1979), Optimization in Economic Theory, Oxford: Oxford University Press.
Dorfman, R. (1969), "An Economic Interpretation of Optimal Control Theory", American
Economic Review 59: 817-31.
Dowling, E. (1992), Introduction to Mathematical Economics, Second Edition, New York:
McGraw-Hill, Inc.
Eatwell, J., M. Milgate, and P. Newman (eds.) (1989), Game Theory, New York: W.W.
Norton and Company.
Eatwell, J., M. Milgate, and P. Newman (eds.) (1990), Utility and Probability, New York:
W.W. Norton and Company, Inc.
Flanders, H. and J.J. Price (1975), Algebra and Trigonometry, New York: Academic Press,
Inc.
Garfunkel, S.A. et al. (eds.) (1988), For All Practical Purposes: Introduction to
Contemporary Mathematics, New York: W.H. Freeman and Company.
George, D.A.R. (1988), Mathematical Modelling for Economists, London: MacMillan
Education Ltd.
Glaister, S. (1972), Mathematical Methods for Economists, London: Gray-Mills Publishing
Ltd.
Grimshaw, R. (1990), Non-Linear Ordinary Differential Equations, London: Basil
Blackwell.
Hands, D.W. (1991), Introductory Mathematical Economics, Toronto: D.C. Heath and
Company.
Harris, M. (1987), Dynamic Economic Analysis, New York: Oxford University Press.
Henderson, J.M. and R.E. Quant (1980), Microeconomic Theory:
Approach, Third Edition, New York: McGraw-Hill Inc.
A Mathematical
Hoel, P.G., S.C. Port, and C.J. Stone (1987), Introduction to Stochastic Processes, Prospect
Heights: Waveland Press, Inc.
Hoy, M.G., J. Livernois, C. McKenna, R. Rees, and T. Stengos (1996), Mathematics for
Economics, Don Mills: Addison-Wesley Publishers Limited.
Huang, C.J. and P.S. Crooke (1997), Mathematics and Mathematica for Economists, Malden,
Massachusetts: Blackwell Publishers, Inc.
Intriligator, M.D. (1971), Mathematical Optimization and Economic Theory, New Jersey:
Prentice-Hall, Inc.
Jones, A.J. (1980), Game Theory: Mathematical Models of Conflict.
Kamien, M.I. and N.L. Schwartz (1983a), "Conjectural Variations", Canadian Journal of
Economics 16: 191-211.
Kamien, M.I. and N.L. Schwartz (1983b), Dynamic Optimization: The Calculus of
Variations and Optimal Control in Economics and Management, New York: Elsevier
Science Publishing Co., Inc.
Kreps, D.M. (1990), A Course in Microeconomic Theory, Princeton: Princeton University
Press.
Lambert, P.J. (1985), Advanced Mathematics for Economists: Static and Dynamic
Optimization, Oxford: Basil Blackwell Ltd.
Leonard, D. and N. Van Long (1992), Optimal Control Theory and Static Optimization in
Economics, New York: Cambridge University Press.
Lue, A.S.T. (1974), Basic Pure Mathematics II, London: Van Nostrand Reinhold Co.
Malliaris, A.G. and W.A. Brock (1982), Stochastic Methods in Economics and Finance, New
York: North Holland.
Miller, R.E. (1979), Dynamic Optimization and Economic Applications, New York:
McGraw-Hill Inc.
Neal, F. and R. Shone (1976), Economic Model Building, London: The MacMillan Press Ltd.
Nerlove, M. and K.J. Arrow (1962), "Optimal Advertising Policy Under Dynamic
Conditions", Economica 29: 129-42.
Ostaszewski, A. (1990), Advanced Mathematical Methods, New York: Cambridge University
Press.
Piskunov, N. (1965), Differential and Integral Calculus, Moscow: Peace Publishers.
Ross, S.M. (1989), Introduction to Probability Models, Fourth Edition, San Diego:
Academic Press, Inc.
Rowcroft, J.E. (1994), Mathematical Economics: An Integrated Approach, Scarborough:
Prentice-Hall Canada, Inc.
Samuelson, P.A. (1983), Foundations of Economic Analysis, Enlarged Edition, Cambridge:
Harvard University Press.
Sethi, S.P. and G.L. Thompson (1981a), "A Tutorial on Optimal Control Theory", Infor 19:
279-91.
Sethi, S.P. and G.L. Thompson (1981b), Optimal Control Theory: Applications to
Management Science.
Sethi, S.P. (1978), "A Survey of Management Science Applications of the Deterministic
Maximum Principle." TIMS Studies in Management Sciences 9: 33-67.
Shone, R. (1997), Economic Dynamics: Phase Diagrams and Their Economic Applications,
Cambridge: Cambridge University Press.
Silberberg, E. (1990), The Structure of Economics: A Mathematical Analysis, Second
Edition, New York: McGraw-Hill, Inc.
Simon, C.P. and L. Blume (1994), Mathematics for Economists, New York: W.W. Norton
and Company.
Sydsaeter, K. (1974), "Letter to the Editor on some Frequently Occurring Errors in the
Economic Literature Concerning Problems of Maxima and Minima", Journal of Economic
Theory 9: 464-66.
Sydsaeter, K. (1981), Topics in Mathematical Analysis for Economists, New York: Academic
Press, Inc.
Sydsaeter, K. and P.J. Hammond (1995), Mathematics for Economic Analysis, New Jersey:
Prentice-Hall, Inc.
Takayama, A. (1985), Mathematical Economics, Second Edition, New York: Cambridge
University Press.
Tapiero, C.S. (1978), "Time, Dynamics and the Process of Management Modeling", TIMS
Studies in Management Sciences, 9: 7-31.
Timbrell, M. (1985), Mathematics for Economists: An Introduction, New York: Basil
Blackwell, Inc.
Toumanoff, P. and F. Nourzad (1994), A Mathematical Approach to Economic Analysis,
Minneapolis/St.Paul: West Publishing Company.
Trustrum, K. (1978), Linear Programming, London: Routledge and Kegan Paul Ltd.
Varian, H.R. (1978), Microeconomic Analysis, New York: W.W. Norton and Company.
Weintraub, E.R. (1985), Mathematics for Economists: An Integrated Approach, New York:
Cambridge University Press.
III.
Evaluation
This will be as follows:
Assignments (3)
Mid-Term Test
Final Exam
30%
20%
50%
There are three assignments. Each one is worth 10%. You are to hand in all the assignments
at the end of class on the due date. Late assignments will get a reduction of 20 percentage
points for each day or part thereof for which the assignment is late. In any case, no
assignments will be accepted after answers are given in class.
Please note that if you choose not to hand-in an assignment during class, you may bring it only
to my office or to the Dept. Administrator’s office. Other than the Dept. Administrator, Ms.
Carolyn Johns, no one else at the University or outside the University is authorized to accept an
assignment on my behalf (or to put their signature on an assignment to certify that it was
complete by a certain date/time).
Please note that I do not accept assignments sent as e-mail attachments or through fax.
Assignments are to be handed-in during class, brought to my office, or the Dept.
Administrator’s office. Late assignments will have to bear the exact date and time when the
assignment was handed-in, so the appropriate penalty can be assessed.
It is important to work hard on your assignments. The best way to learn mathematical
economics is by working out problems. Past years have shown a strong positive correlation
between doing assignments and final grades. You may work in groups to study to complete the
assignments but you must write and hand in your own paper.
The mark will be in accordance with the University numerical and letter grading scale as set out
in the Trent University Calendar.
Academic Integrity: Academic dishonesty, which includes plagiarism and cheating, is an
extremely serious academic offence and carries penalties varying from a zero grade on an
assignment to expulsion from the University. Definitions, penalties, and procedures for
dealing with plagiarism and cheating are set out in Trent University’s Academic Integrity
Policy, which is printed in the University Calendar. You have a responsibility to educate
yourself – unfamiliarity with the policy is not an excuse. You are strongly encouraged to visit
Trent’s Academic Integrity website to learn more: www.trentu.ca/academicintegrity.
In marking your assignments, if I find two or more (nearly) identical assignments, you
will be asked to come to my office to explain. I may subsequently charge you with
plagiarism. Please do not plagiarise.
Access to Instruction: It is Trent University’s intent to create an inclusive learning
environment. If a student has a disability and/or health consideration and feels that he/she
may need accommodations to succeed in this course, the student should contact the Disability
Services Office (BL Suite 109, 748-1281, disabilityservices@trentu.ca) as soon as possible.
Complete text can be found under Access to Instruction in the Academic Calendar.
Please see the Trent University academic calendar for University Diary dates, Academic
Information and Regulations, and University and departmental degree requirements.
Last date to withdraw from Winter term half courses without academic penalty in 2010-11 is
Friday March 11, 2011.
IV.
Office Hours
My office hours are as follows:
Tuesday
1:00 p.m. – 2:00 p.m.
Thursday
10:00 a.m. – 12:00 noon
If something is unclear during a lecture, do not hesitate to ask questions. Also feel free to
come and see me if you have any further questions or problems. You never need an
appointment to see me during an office hour.
V.
Reading List
Those readings marked with an asterisk are minimal required readings. Others are
alternate/additional references to which you may like to refer. Readings may be added or
deleted as the term progresses. Note that students should use the reading list as a guide to the
location of the material covered in the lectures. Students will be held responsible for the
topics specifically discussed in lectures, not for all the material listed below.
1.
Review of some Basic Material; Eigenvalues and Eigenvectors
* As in the EC 325H Syllabus
* Chiang and Wainwright, 2005, Chapter11
2.
Non-Linear Programming
* Chiang and Wainwright, 2005, Chapter 13
Lambert, 1985, Chapter 5
* Intriligator, 1971, Chapter 4
Hands, 1991, Chapter 9
Silberberg, 190, Chapter 14
Weintraub, 1985, Chapter 12
George, 1988, Chapter 3
Arrow and Intriligator, 1987, Volume I, Chapter 2
Kreps, 1990, especially pp. 775-85.
3.
Differential Equations
* Chiang and Wainwright, 2005, Chapters 15 and 16
Intriligator, 1971, Appendix A-7
Takayama, 1985, Chapter 3, Section B
Lue, 1974, Chapter 5
Binmore, 1983, Chapters 11 and 13
* Chirgwin and Plumpton, 1972, Chapters I and II
George, 1988, Chapter 6
4.
Phase Diagrams and Dynamic Stability/Instability
* Chiang and Wainwright, 2005, Chapter 19
* Chiang, 2000, Chapter 5.4
Lambert, 1985, Chapter 5.5
Leonard and Van Long, 1992, Chapter 2, Sections 4,5
Intriligator, 1971, Chapter 5
George, 1988, Chapter 6
* Weintraub, 1985, Chapter 8
Shone, 1997
5.
Dynamic Optimization
* Chiang and Wainwright, 2005, Chapter 20
* Chiang, 2000, Chapter 7
* Sethi and Thompson, 1981a
* Silberberg, 1990, Chapter 18
Lambert, 1985, Chapter 7
Intriligator, 1971, Chapters 11 and 14
Kamien and Schwartz, 1983b, Part II
Dixit, 1979, Chapter 9
Arrow and Intriligator, 1987, Volume I, Chapter 4
Leonard and Van long, 1992, Chapters 3 and 4
George, 1988, Chapter 7
6.
VI.
Theory of Risk and Uncertainty
* Deaton and Muellbauer, 1980, Chapter 14
Silberberg, 1990, Chapter 13
Baumol, 1977, Chapter 17
* Varian, 1978, Chapter 3.15
Hands, 1991, Chapter 4.3
Schedule of Assignments and the Mid-Term Test
Assignment #
Date Given
Date Due
1
January 17
February 7
2
February 7
March 7
3
March 7
March 28
Please note that you are given at least three weeks for preparation of each assignment.
The Mid-Term test is scheduled for Monday, February 28, 2011. The Mid-term is
held during class time and will be 1½ hours long. The date for the final exam is set by the
Registrar's Office and published in the University Examination Timetable. The exam will be
3 hours long.
The date for the final examination will be set by the Registrar's Office and published in the
University Examination Timetable. You must plan to be available during the test/exam
period. No permission will be given to a student to write a test or exam after or in
advance of a regularly scheduled test/exam except because of a documented illness or
documented emergency.
Please also note that paper and electronic dictionaries, blackberries, mobile telephones, and
other aids and electronic devices are not allowed during the midterm and exam. Approved
scientific calculators are allowed and must be shown to the instructor during the test/exam.
Please visit the Department of Economics website for the list of approved calculators.
Sharing of calculators during the midterm and exam is strictly forbidden.
Finally, please use pen (not pencil) to write your assignments and the midterm. (If
you plan to use pencil to complete your assignment, please hand-in a legible photocopy of
your work.)
.
VII.
Schedule of Seminars
We shall meet six times (fortnightly). Seminars will take the form of a lecture or they will be
devoted to discussion of corrected assignments or questions that may arise. The dates for the
seminars are: January 17, January 31, February 14, February 28, March 14, and March
28.