Economics Department
ECON 416: MATHEMATICAL ECONOMICS
FALL 2011
Professor:
Office:
Office hours:
Email:
Phone:
Class Location:
Meeting Times:
Teaching assistant:
Karim Seghir
2122
S&W from 4.00 to 5.00pm, or by appointment.
[email protected]
3376
C107 Jameel Building.
U&W, 5.00-6.15pm.
Omar Ekram,
E-mail: [email protected]
1. Catalogue Description: Quasiconcave programming. Arrow-Einthoven and Kuhn-Tucker
conditions. Second-order difference and differential equations. Steady-state equilibrium and the
saddle path. Dynamic optimization. Hamiltonian function and Transversality conditions.
Applications to economic theory.
2. Objectives: Current students need several important mathematical tools in order to understand
modern issues in graduate studies in economics. A good handling of these tools will facilitate the
comprehension of advanced economic models used in graduate courses as well as the study of
modern research papers in top economics journals. Thus, the objective of this course is to make
the transition into graduate economics somewhat smooth.
Besides the technical tools that students will study in this course, they will also learn to be logic,
precise and systematic when dealing with economic models as well as mathematical statements
and proofs.
3. Course Learning Outcomes:
•
•
•
•
Solve (static/dynamic, constrained/unconstrained) optimization problems, advanced
matrix algebra, as well as difference equations and differential equations.
Competently use the above concepts in problems and economic applications including
comparative analysis, consumers’ decisions (under certainty/uncertainty), producers’
behavior, static/dynamic economic models.
Learn some rules of mathematical logic (theorems, proofs, and contrapositive forms, to
name some) that will develop students’ analytical thinking skills.
Work in group and present group works. This method aims to develop students’
communications skills, to share ideas and also to get accustomed to working with other
people, a likely situation in their future jobs.
4. Textbook:
Main Assigned Textbook:
M. Hoy, J. Livernois, C. McKenna, R. Rees and T. Stengo: Mathematics For Economics, The
MIT Press. 2nd edition. 2001.
Economics Department
Prof. K. Seghir
Other Recommended Readings:
• S.P. Simon and L. Blume: Mathemaics For Economists, W. W. Norton. 1994
• A. Chiang: Fundamental Methods of Mathematical Economics, McGraw-Hill/Irwin. 3rd
edition.1984.
• You may also find Matin Osborne’s online Mathematical Tutorial useful, especially for Part 1
and Part 2 of the course (see Section 6). The tutorial is available at:
http://www.chass.utoronto.ca/~osborne/MathTutorial/
5. Grading Policy:
There will be 3 quizzes and a comprehensive Final. Each quiz is worth 20% of your overall grade and
the Final exam is worth 30% of your grade. Attendance-Assignment-Participation is worth 10% of
your grade. If the final class average is below 70, I will give a raise. Whether you qualify for the raise
depends on your overall performance, attendance, academic integrity, and classroom behavior. We
will decide on the exact procedure of raises at the end of the semester.
The grading policy and exam dates are given by the following table:
EXAM
QUIZ 1
QUIZ 2
FINAL EXAM
Assignment
Attendance-Participation
WEIGHT
25%
25%
30%
10%
10%
DATE
Sunday, October 16th
Sunday, November 20th
TBA
6. Some Important Course Policies:
•
•
•
•
•
•
This course is Blackboard supported. I will communicate all essential information through
Blackboard. It is your responsibility to maintain a valid Blackboard account and to keep yourself
up-to-date regarding the information we communicate through Blackboard. I recommend you to
log on to Blackboard at least once a day! On Blackboard you will find essential lecture material,
problem sets, practice questions, and useful communication tools such as email and a discussion
board.
Students are expected to be punctual in coming to class. A student who is often late may be not
allowed to attend the lecture.
Missing an exam is serious and will be handled on a case-by-case basis. If you miss an exam, you
must inform me in advance, or immediately afterwards, to avoid receiving a failing grade. Written
documentation is required but not necessarily sufficient. All medical documentation must be issued
or confirmed by the AUC infirmary
The material presented in class will complement, not substitute, for the material covered in the
assigned readings. Appendices, boxes, and exercises are part of the assigned readings. We also
encourage you to make use of the internet resources that come with your textbook. There you will
find, for example, additional quizzes.
If you enter the classroom after class has started, please take your seat as quickly and quietly
as possible. We reserve the right to deny you access to the classroom if we feel it may disturb
the class. Three occasions of tardiness count as one absence.
You are urged to express your views, ask questions freely, and discuss the points you don’t
understand or don’t agree.
2
Economics Department
•
•
Prof. K. Seghir
Office hours are an excellent venue for asking questions and assessing your progress. If you fail
an exam, pass by and see your instructors as soon as possible so that they can advice you
appropriately.
I expect every student to maintain a high standard of academic integrity and to be familiar with
the policies and principles of student conduct. Please, visit the following AUC page for more
information on types of violations and recommended punishments:
http://www.aucegypt.edu/resources/acadintegrity/Disciplinaryprocedures/Typesofviolations.html
7. Problem Sets:
Problem sets must be turned in at the beginning of class on the due date. Late assignments will not be
accepted. If you are not able to attend class on the day that the problem set is due or will be more than
fifteen minutes late to that class, you must make arrangements to hand in the problem set early (send it to
class with another student, turn it in during office hours prior to the due date. Problem sets submitted in
any other way (e-mail, fax, etc.) will not be accepted.
8. List of Topics:
Introduction.
•
•
Why Economists Use Mathematics.
A Few Aspects of Logic (necessary/sufficient conditions, quantifiers, mathematical
proofs).
PART 1. Static Optimization.
•
•
•
•
•
•
•
•
•
•
•
Unconstrained optimization of two-variable functions. Chapter 12.
Economic Applications: Production function, profit function, cost function,
Multiproduct monopoly, Price-discriminating Monopoly, Cournot duopoly. Chapter
12.
Constrained optimization of two-variable functions. Chapter 13.
Convex sets: Definition and Properties. Chapter 2, Section 3, pp.40-41.
Concave and convex functions: Definitions, Properties and Examples. Chapter 11,
Section 4, pp. 502-504.
Hessian Matrix and Concavity. Chapter 11, Section 4, pp. 505-512.
Quasiconcave functions: Definition and Bordered Hessians. Chapter 11, Section 5,
pp. 513-518.
Quasiconcave programming with one equality constraint using Kuhn- Tucker
Theorem and Arrow-Einthoven Theorem. Chapter 15.
Economic Applications: Derivation of Marshalian and Hicksian Demand
functions, Profit function and Cost function. Chapter 15.
Linear Programming: Existence of solutions (Slater condition). Chapter 5, Section
2.pp. 689-694.
Economic Applications: profit maximization, multiproduct monopoly, pricediscriminating monopoly, Cournot duopoly, utility maximization and derivation of
Marshalian demand functions, constrained cost minimization.
PART 2. Difference Equations and Differential Equations.
•
Eigenvalues and Eigenvectors. Chapter 10, Section 2, pp. 421-432
3
Economics Department
•
•
•
•
•
•
Prof. K. Seghir
Linear, first-order and second-order difference equations. Economic applications: The
Cobweb model of price adjustment, A Walrasian price-adjustment model with entry
and exit, Cournot duopoly. Chapters 18 and 20.
Nonlinear, first-order difference equations and applications (An economic growth
model, Cycles and chaos). Chapter 19.
Linear, first-order/second-order, autonomous/nonautonomous differential equations.
Economic applications: A Walrasian price-adjustment model, an aggregate growth
model with technological change, a price adjustment model with inventories. Chapter
21.
Nonlinear, first-order differential equations, stability analysis, Bernoulli’s equation.
Chapter 22.
Simultaneous systems of differential and difference equations: Chapter 24.
Steady state, stability of equilibrium, types of equilibrium, saddle path (uniqueness),
discrete stochastic dynamic models. Chapter 24.
PART 3. Dynamic Optimization
•
•
•
•
Finite time horizon models, the Maximum Principle, the Hamiltonian function,
Necessary conditions, sufficient conditions, Transversality condition.
Optimization problems involving discounting, the current-valued Hamiltonian and
optimality conditions.
Infinite time horizon problems
Economic applications: investment problems, optimal consumption models, optimal
depletion of an exhaustible resource, the neoclassical growth model, dynamic
monopolistic price model.
9. Grading System:
MIN
93
90
85
80
75
70
65
60
55
50
0
MAX
100
92
89
84
79
74
69
64
59
54
49
GRADE
A
AB+
B
BC+
C
CD+
D
F
HAVE A PRODUCTIVE SEMESTER!
4