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SYLLABUS

Course description

The course is designed to introduce students to techniques in mathematical modelling 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 modelling.

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.

Student Learning Outcomes

1. Students will demonstrate the use of first-order and second-order conditions in finding maxima and minima.
2. Students will demonstrate the use of matrices and determinants in solving systems of equations.
3. 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.
4. 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..

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Contents in brief

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

Applications: Demand and supply curves

8. Dynamic modelling

• Two-period optimization

Application: Optimal saving over the lifecycle

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The required textbook for the course is:
Chiang, A. and Wainwright, K. (2004). Fundamental Methods of Mathematical Economics. McGraw-Hill/Irwin.  
(The ISBN is 0070109109.  A used copy is fine.)

I shall provide a great deal of the course material on the web site 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 Department of Business, various sites for economic data and articles, even one devoted to economist jokes. Suggestions for improving the site are always welcome.

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Evaluation

Your grade for the course will be determined by your performance in tests, assignments, and quizzes. The assignments will include computer tasks involving the use of the Wolfram Alpha computation engine and Microsoft Excel.

Grades will be determined as shown in Tables 1 and 2.

Table 1. Tests, Assignments and Quizzes

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.

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Email communication etiquette

• Start emails with an appropriate salutation (Dear Dr. Paul, for example). End them with your name.
• Provide a subject in the subject line. Include “EC309” in the subject, so that I know right away it is from a student in the class.
• Use standard English, with proper spelling and grammar. If you write “i cant send u my sa til later ttyl”, I will not know what it means and will consequently ignore it altogether.
• Make sure your @etown.edu inbox is not full. If it is, my emails to you will not reach you, and you will be left in the dark. Do not be left in the dark!

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You are expected to abide by the College's Standards of Academic Integrity. Any breach of academic integrity will be dealt with in accordance with the policy stated in the College Catalog.

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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 would like to request accommodations in order to access course material, activities, or requirements, please contact the Director of Disability Services, Lynne Davies, by phone (361-1227) or e-mail daviesl@etown.edu. If your documentation meets the college’s documentation guidelines, you will be given a letter from Disability Services for each of your professors.  Students experiencing certain documented temporary conditions, such as post-concussive symptoms, may also qualify for temporary academic accommodations and adjustments. As early as possible in the semester, set up an appointment to meet with me, the instructor, to discuss the academic adjustments specified in your accommodations letter as they pertain to my class.

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