EC309 INTRODUCTION TO MATHEMATICAL ECONOMICS
Spring 2013
SYLLABUS
Instructor: Prof. Sanjay Paul
Office: 206 Hoover Center for Business
Tel: (717) 361-1543
Fax: (717) 361-1487
Email: pauls@etown.edu
Website: http://users.etown.edu/p/pauls/ec309
Class location and times
Hoover 213
Tue, Thu 11:00-12:40pm
Office hours:
Mon 2:00-3:30pm
Tue 2:00-3:30pm
Wed 2:00-3:30pm
Thu 2:00-3:30pm
And by appointment
Course description
The course is designed to introduce students to techniques in mathematical modeling which are then applied to
solving various problems in economics and business. Beginning with a review of concepts in calculus and linear
algebra, we move on to optimization techniques. These techniques are then used in a number of applications in
microeconomics, macroeconomics, operations management and finance. Finally, if time permits, we will look at
elements of dynamic modeling.
The use of mathematical software is integral to obtaining numerical solutions for the problems that we will
encounter in the course. We will use Microsoft Excel and the Wolfram Alpha computation engine (on the Web)
to solve systems of equations, plot graphs, compute derivatives, and obtain solutions to optimization problems.
Intended Student Learning Outcomes
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Students will demonstrate the use of first-order and second-order conditions in finding maxima and
minima.
Students will demonstrate the use of matrices and determinants in solving systems of equations.
Students will explain how economic decision making utilizes marginal benefit-marginal cost analysis.
Students will demonstrate the capacity to use online mathematical software Wolfram Alpha to solve
systems of equations, conduct matrix operations, plot graphs, and obtain ordinary and partial
derivatives.
Students will demonstrate the capacity to use Microsoft Excel’s Solver add-in to obtain solutions to
optimization problems, carry out comparative statics, and show the results on graphs.
Contents in brief
The following table provides an outline of the material that we expect to cover in the course. The topics
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mentioned below are not exhaustive. Also, paucity of time may force us to curtail some material.
1. The derivative
The concept of limit
Slope of a curve
Continuity
Differentiability
Applications: Marginal cost, marginal revenue, elasticity
2. Rules of differentiation
Product and quotient rules
Chain rule
Partial differentiation
Total differential and total derivative
Implicit differentiation
Application: Cobb-Douglas functions
3. Linear algebra
Matrices and determinants
Systems of simultaneous equations
Cramer's rule
Application: National income determination
4. Unconstrained optimization
Maxima and minima
First and second-order conditions
Concavity and convexity
Objective function with one variable
Objective function with more than one variable
The Hessian matrix
Applications: Profit maximization, inventory control, cost minimization
5. Constrained optimization: Linear programming
Inequality constraints
Feasible region
Application: Product mix
6. Constrained optimization: Non-linear programming
Linear constraints
The Lagrange-multiplier method
Necessary and sufficient conditions
The bordered Hessian matrix
Applications: Utility maximization, optimal portfolio choice
7. Comparative statics
Exogenous and endogenous variables
The concept of equilibrium
Changes in equilibrium
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Applications: Demand and supply curves
8. Dynamic modeling
Two-period optimization
Application: Optimal saving over the lifecycle
Readings
The required textbook for the course is "Mathematics for Economists" by Simon and Blume, W W Norton, 1994
(ISBN 0393957330).
I shall provide a great deal of the course material at http://users.etown.edu/p/pauls/ec309/ . At this site, you will
find an (undoubtedly) exciting panoply of lecture outlines, exercise sets, and assignments. These are updated
frequently as the course progresses. The site provides several additional links -- to the home page for the
Business department, various sites for economic data and articles, even one devoted to economist jokes.
Suggestions for improving the site are always welcome.
Evaluation
Your grade for the course will be determined by your performance in tests, assignments, and reports. The
assignments will include computer tasks involving the use of the Wolfram Alpha computation engine and Excel.
The reports will require you to attend, and write a report on, at least 5 department and college events during
the semester. Two of these events are required--the Student Conference in Business and Economics and the
Economics Symposium. For the remaining three, you may choose from the M&M Mars Executive Lecture
series—a list of planned events is available at http://etown.edu/depts/business/mmmars-lecture/index.aspx.
(Reports of 500 words each will be due the first class during the week immediately after the event.)
Grades will be determined as shown in Tables 1 and 2.
Table 1. Tests, Assignments and Reports
Test 1
Tue, Feb. 19
20%
Test 2
Tue, Mar 26
20%
Test 3
Finals week /
Fri, May 10, 11:00am
20%
Assignments
30%
Reports
10%
Total
100%
Table 2. Grade Distribution
3
93100
%
9092
8789
8386
8082
7779
73- 7076 72
6769
6366
6062
0-59
A
A-
B+
B
B-
C+
C
D+
D
D-
F
C-
Make-up tests
A test will be given again only under exceptional circumstances - e.g., very poor health. In all other cases, a
missed test will result in a score of zero for the test.
Attendance
Attendance is not mandatory. You are, however, well advised to attend all classes regularly. If you absent
yourself from class, you are likely to do poorly on the tests and assignments.
Academic integrity
It is expected that students will abide by the Code of Academic Integrity at Elizabethtown College. Any breach
of academic integrity will be dealt with in accordance with the policy stated in the College Catalog.
Disabilities
Elizabethtown College welcomes otherwise qualified students with disabilities to participate in all of its courses,
programs, services, and activities. If you have a documented disability and require accommodations to access
course material, activities, or requirements, you must:
1. Contact the Director of Disability Services, Lynne Davies, in the Center for Student Success, BSC 228, by
phone (361-1227) or email daviesl@etown.edu.
2. Meet with me, the instructor, within two weeks of receiving a copy of the accommodation letter from
Disability Services to discuss your accommodation needs and their implementation.
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