Economics 386-A1

Applications of Mathematics to Economics I

Course Outline Instructor: S Landon Fall 2003 Office: Tory 7-23 e-mail: Stuart.Landon@ualberta.ca (If you send me an e-mail, please include the course number in the subject area.) Office Hours: Monday and Wednesday, 1:00 – 2:00 pm. Other times can be arranged by

seeing me before or after class.

Note: Due to my teaching commitments, I will not be available from 8:00 – 10:00 am and 11:00 am – 1:00 pm on Mondays, Wednesdays and Fridays.

Course Web Page: http://www.arts.ualberta.ca/~econweb/landon/E38603.html This web page can also be accessed through the “Courses” section of my personal

web page which, in turn, can be reached through the “Faculty” section of the Economics Department web page.

On the course web page you will be able to find copies of current (after they are

written) and past exams and assignments as well as answers when they are available. Class notes will not be posted.

Text: The textbook for the course is:

Alpha C. Chiang, Fundamental Methods of Mathematical Economics, Third Edition, McGraw-Hill, 1984.

This book, which I have asked the Bookstore to order, has been used for a number of years in this course. It is outrageously expensive, but there may be used copies around and I have put it on Reserve in Rutherford Library. Chiang is a good book to use as a reference in the more mathematical economics courses. The textbook introduces most of the mathematical tools that will be employed in the course. However, the examples given in class, as well as the assignment and exam questions, will often stray far from the material in the textbook. I will also not cover in class all the topics in the assigned readings.

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In addition to Chiang, I have also asked the Bookstore to order the Schaum's Outline: Edward T. Dowling, Introduction to Mathematical Economics, Third Edition,

McGraw-Hill, 2001. This book gives a very terse introduction to much of the material covered in the course and, in the past, some students have found it to be useful. (It is also relatively cheap.) However, most of the examples in this book are math-based and, as a result, many do not relate directly to the type of economic analysis you are likely to see in higher-level economics courses. This is a problem with Chiang as well, but to a lesser extent. Note: Chiang is the principal text for the course while Dowling should be

considered a supplementary text which you might want to read if you are having trouble in the course or would like a very terse exposition of the basic material. Depending on your background, you may want to purchase one of these books, both of them, or neither.

Another book that is relatively good, but which has some problems with approach and notation is: K. Sydsaeter and P. J. Hammond, Mathematics for Economic Analysis,

Prentice-Hall, 1995. This book is a cheaper alternative to Chiang, but I have not ordered it (because I think Chiang is a better book for this course) and I have not included references to it in the readings below. This book can be ordered through bookshops, but if you use it, you will have to determine on your own which readings correspond to the readings in Chiang given below.

Prerequisites: Economics 281 and 282 as well as Math 113 and 120 (or equivalent). I will assume that you are familiar with the basic theory introduced in Economics 281 and 282 and will use this theory extensively in class examples. (If you do not have 281 and 282, you are unlikely to understand these examples and this will make mastering the material very difficult.) I will also assume you are familiar with the material that you should have been exposed to in the math prerequisite courses. However, I will quickly review much of this material when it is needed. The course prerequisites will be enforced for undergraduate students. If you do not have the prerequisites, your registration can be cancelled.

Economics 299 is not a prerequisite for this course. As a result, there may be

some overlap between this course and Economics 299.

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Course Purpose: To describe and provide examples of a variety of mathematical tools that are employed to analyze economic models and in econometric analysis. This is not an economic theory course. The economic theory used in this course should involve concepts with which students are already familiar, at least to some extent. This is also not a mathematics course in that it will not concentrate on proofs or the development of mathematical concepts. Rather, it uses basic mathematical concepts as tools to assist in the analysis of economic models.

Evaluation: Students will be evaluated on the basis of their performance on two term exams (to

be held in class) and a final exam. The questions on these exams will relate closely to the material and examples discussed in class. I will feel free to include questions and examples from the textbook on the exams (although these will generally relate closely to the material covered in class). The second term exam and the final exam will be cumulative, although more weight will generally be given to the material covered from the time of the previous exam. The questions on the exams will generally involve solving problems that you may never have seen before. Most, but not all, of the problems on the exams will relate to economic analysis. They will not simply be mathematical exercises.

Distribution of Marks: Term Exam 1 20% Term Exam 2 25% Final Exam 55% Practice Assignments: I will hand out three sets of practice questions. These questions will not be marked, but I

will post answers to them on the course web page. The purpose of these practice assignments is to expose you to the concepts and types of questions that will form the basis for the exams. In fact, many of the questions have appeared on previous exams as I use previous exam questions as the basis for these assignments. (Note: This means that most of the questions from last year's exams will be included on one of these assignments and answers provided.) You can learn a lot by working through these questions before looking at the answers. At least some of the questions on the exams may be very similar to some of the questions on these assignments (although they are unlikely to be identical).

Note: Since the answers to the assignements are relatively complicated, I will write them

out by hand. As a result, to be posted on the course web page they must be scanned and this means that they will be very large files. If this becomes a problem, I will also put the answers on Reserve in Rutherford Library.

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Old Exams: You can find both term exams and the final exam from last year on the course web page. Answers to the two term exams are also provided.

Important Dates: September 24 Distribution of Practice Assignment 1 (Approximate) October 8 Term Exam 1 (in class) October 29 Distribution of Practice Assignment 2 (Approximate) November 12 Term Exam 2 (in class) November 26 Distribution of Practice Assignment 3 (Approximate) December 10 Final Exam Important Notes:

1. The dates given above for the term exams will not be changed. Please do not ask to write the exams on days other than those scheduled above. If you know that you cannot write the exams on the days scheduled, you should not register in this course.

2. All the exams will involve solving problems using the mathematical tools introduced

in class. The examples given in class and the questions on the assignments are good indicators of the types of questions that will be on the exams.

3. There will be no choice of questions on the exams. 4. The exams are all of the closed book type. No notes can be used during the exams. 5. I do not allow students to borrow my notes. If you miss a class, it is your

responsibility to obtain the class notes from another student. 6. This course is taken by students with widely differing backgrounds in mathematics

and economics. The class generally includes majors and honours students in Economics as well as graduate (qualifying-year, MA and PhD) students in Economics, Business and Rural Economy. It is intended as a course for students who plan to do a graduate degree in Economics and is aimed particularly at Economics honours and qualifying-year students. Despite the large number of graduate students generally enrolled in the course, all students are treated identically.

7. Attendance is not a course requirement and I do not take attendance. If you do not

wish to attend, you should not feel obliged to do so.

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8. The weight of the term exams, if they are missed for legitimate medical reasons, will be added to the weight of the final exam (implying a 75, 80 or 100% final depending on the exam(s) missed).

Readings

Readings may be added or deleted as the term progresses. 1. Introduction, Functions and the Solution to Simple Models Chiang, Chapters 1, 2 and 3. Dowling, Chapters 1 and 2. 2. Linear Algebra Chiang, Chapters 4 and 5 (excluding Section 5.7). Dowling, Chapters 10, and 11 (excluding Sections 11.7-11.8). 3. Differentiation Chiang, Chapter 6 (excluding pages 136-53) and Chapter 7. Dowling, Chapter 3. 4. Comparative Statics Chiang, Chapter 8. Dowling, Sections 6.1 to 6.4, 12.1, and 13.1 to 13.3. 5. Optimization with One Choice Variable

Chiang, Chapter 9 (excluding “Maclaurin Series of a Polynomial Function,” pages 254-6, and pages 261-7) and pages 312-14. Dowling, Chapter 4.

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6. Exponential and Logarithmic Functions

Chiang, Chapter 10 (excluding “Base Conversion,” pages 290-1, and “The Case of Base b,” pages 295-7). Dowling, Chapters 7 and 9.

7. Optimization with More than One Choice Variable Chiang, Chapter 11 (excluding pages 314-331).

Dowling, Chapter 5 (excluding Sections 5.5 and 5.6) and Sections 6.5, 12.2, 12.4 and 13.4.

8. Constrained Optimization Chiang, Chapter 12 (excluding "n-Variable and Multiconstraint Cases", pages 377-

78; the "Multiconstraint Case", pages 385-386; Sections 12.4 and 12.6; and pages 423-30).

Dowling, Sections 5.5, 5.6, 6.6, 6.9, 6.10, 12.5 and 13.5 to 13.6. Note: If time permits, I will cover the material in pages 314-31 of Chapter 11, and Sections 12.4

and 12.6 of Chapter 12 in Chiang. I will announce in class if this material is to be covered.

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