EC309 INTRODUCTION TO MATHEMATICAL ECONOMICS
Fall 2017
SYLLABUS
Instructor: Prof. Sanjay PaulOffice: 206 Hoover Center for Business
Tel: (717) 361-1543
Email:
Web: http://users.etown.edu/p/pauls/ec309
Office hours
· Mon 1:00-3:00pm
· Tue 10:00-10:50am
· Wed 1:00-3:00pm
· Thu 10:00-10:50am
· And by appointment / Class location and times:
Hoover 112
Tue, Thu 2:00-3:40pm
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. Pre-requisite: MA121
Intended Student Learning Outcomes
· 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 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 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
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:
· Chiang, A. and Wainwright, K. (2005). Fundamental Methods of Mathematical Economics. Fourth edition. McGraw-Hill/Irwin. ISBN: 978-0070109100.
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.
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
Test 1 / Tue, Sept. 19 / 20%Test 2 / Tue, Oct. 31 / 20%
Test 3 / Finals week /
Tue, Dec. 12, 11:00 am / 30%
Assignments / 20%
Quizzes / 10%
Table 2. Grade Distribution
93-100 % / 90-92 / 87-89 / 83-86 / 80-82 / 77-79 / 73-76 / 70-72 / 67-69 / 63-66 / 60-62 / 0-59A / A- / B+ / B / B- / C+ / C / C- / D+ / D / D- / F
Tests: The tests may include graphs, mathematical problems, and short-answer questions. They are cumulative and will be conducted in the classroom.
Quizzes: Quizzes will be brief, lasting 20 minutes or less. They will be given in the classroom and without advance notice. In order to accommodate unforeseen absences, I will drop two of the lowest scores.
Assignments: Assignments will be will be assigned frequently. Late submissions will be penalized.
Missed exams
An exam will be given again only under exceptional circumstances - e.g., very poor health. Missed items will generally result in a score of zero.
Attendance
You are advised to attend all classes regularly. If you absent yourself from class, you are likely to do poorly on the tests, assignments and quizzes. You are responsible for acquiring any missed notes.
Academic integrity
Students are expected to adhere to the Pledge of Integrity at Elizabethtown College. In this course, you are expected to complete the assignments and tests entirely on your own. You will not discuss the tests or assignments with others, nor will you seek or receive assistance from others in completing them. Any breach of academic integrity will be dealt with in accordance with the policy stated in the College Catalog.
Email communication etiquette
· Start emails with an appropriate salutation (Dear Dr. Paul, for example). End them with your name.
· Always provide a subject in the subject line. Include “EC102” 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.
· 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!
General policies
Deadlines are extremely important. Pay close attention to the due dates. Plan ahead. Don’t wait until the last minute to complete your task. Your Internet connection may go down; your computer may crash; the world may come to an end.
There are no opportunities for extra credit.
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 .
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.
Class cancellation
Classes may be occasionally cancelled for reasons pertaining to adverse weather conditions, health, travel and other emergencies. In such cases, I will make every effort to notify you as soon as possible and make suitable alternative arrangements.
Religious observances
The College is willing to accommodate individual religious beliefs and practices. It is your responsibility to meet with the class instructor in advance to request accommodation related to your religious observances that may conflict with this class, and to make appropriate plans to make up any missed work.
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