Class Times

The class meets on Tuesday and Thursday from 5:00pm to 6:15pm in GC-289.

Course Description

The most commonly used mathematical methods in economics relate to optimization problems, and this course focuses on methods of optimization.

The first part of the course develops some basic mathematical tools of analysis which we will use to solve optimization problems. This covers roughly parts II and III of the text, and may include excerpts from part VI. The second part (part IV of the text) covers classical, calculus-based methods of optimization—Lagrange multipliers and the Kuhn-Tucker theorem. The methods of Lagrange and Kuhn-Tucker have been invaluable in solving many of the problems you will typically encounter in economics (consumer and producer choice, social welfare max, etc.). The remainder of the course covers more advanced topics from Parts VII and V of the text. These include the issue of whether an optimization problem actually has a solution, and a look at economic dynamics. If time, we will look at dynamic optimization.

Textbook

Simon and Blume's book is the main text. I plan to cover Parts II-IV and VII of Simon and Blume, with some excerpts from Part VI. Time permitting, we will then turn our attention to Part V and dynamic models.

Optimization Handout

You may find this handout on basic optimization helpful: Constrained Optimization Survival Guide.

Office Hours and Contact Info

If you have questions, you may ask immediately after class, or come to my office. Regular office hours are 12:45-1:45pm and 3:30-4:15pm on Tuesdays and Thursdays. I will be happy to make an appointment for another time if that is more convenient. My office is DM-311A, my phone number is 348-3287, and my email is <boydj@fiu.edu>.

Exams and Homework

Grades will be based on two in-class midterm exams (worth 25% each), a final exam (40%), and homework assignments (10%). In addition to being announced in class, homework assignments will be posted on the class web page.

Exams

There will be two midterm exams, each worth 25% of your grade, and a final, worth 40% of your grade.

Sample Exams

Here are some previous midterm exams from this course. Note that some questions may not be relevant as the material covered has changed.

Homework Assignments and Answers

Assignments will appear here. Answers will be posted sometime after the homework is collected.

  1. Problems 2 and 7 from Chapter 6 and problems 6, 14, and 23 from Chapter 7 are due on Thursday, Sept. 1.
    Question 6.2 should read “In Missouri, federal income taxes are deducted from income before calculating state taxes. Write out and solve the system of equations which describes the state and federal taxes and charitable contributions of the firm in Example 1 if it were based in Missouri.”
    Here are the answers.
  2. Problems 20, 24, and 34 from Chapter 8, problems 9 and 20 from Chapter 9 and problem 13 from Chapter 26 were due on Thursday, Sept. 8. Here are the answers.
  3. Problems 14, 21, and 40 from Chapter 10, and problems 2 and 9 from Chapter 11 were due on Thursday, Sept. 15. Here are the answers.
  4. Problems 9, 20, and 25 from Chapter 12, and problems 2 and 3 from Chapter 27 were due on Thursday, Sept. 22. Here are the answers.
  5. Problems 12 and 23 from Chapter 13; 7, 16, and 28 from Chapter 14; and 11 from Chapter 29 were due on Tuesday, Oct. 18. Here are the answers.
  6. Problems 7 and 8 from Chapter 15; 1 and 2 from Chapter 16; and 2 and 7 from Chapter 17 were due on Thursday, Oct. 27. Here are the answers.
  7. Problem 21 from Chapter 19, problems 12 and 18 from Chapter 20, and problems 1 and 18 from Chapter 21 were due on Thursday, Nov. 17. Here are the answers.
  8. Problems 5, 11, 16, 21, and 28 from Chapter 23 are due on Tuesday, Nov. 29. Here are the answers.

Tentative Course Outline

Subject to change...

Aug. 23 6: Intro to Linear Algebra (and use in Economics)
Aug. 23, 25 7: Linear Systems
Aug. 30 8: Matrix Algebra
Sept. 1 9: Determinants & some of 26: Determinants
Sept. 6, 8 10: Euclidean Spaces
Sept. 13 11: Linear Independence, Bases (see also Chap. 27)
Sept. 15 12: Limits and Open Sets
Sept. 20, 22 29: Limits and Compact Sets + Completeness
Sept. 27 Exam #1 — through Chapter 12 + part of 26 and 27
Sept. 29 13: Functions of Several Variables
Oct. 4 14: Calculus of Several Variables
30.1: Weierstrass Thm
Oct. 6 No class: Hurrican Matthew
Oct. 8 29.3: Connected Sets
30.1 Intermediate Value Thm
Oct. 13 15: Implicit Functions and their Derivatives
Oct. 18 16: Quadratic Forms and Definite Matrices
Oct. 20 17: Unconstrained Optimization
Oct. 25 30.2-3: Mean Value Thm & Taylor's Thm
18: Constrained Optimization I: First-order Conditions
Oct. 27 18: Constrained Optimization I: First-order Conditions
Nov. 1 Exam #2 — Chapters 13-18, 29 & 30
Nov. 3 19: Constrained Optimization II: Multipliers and Second-order Conditions
Nov. 8 20: Homogeneous and Homothetic Functions
Nov. 10 21: Concave and Quasiconcave Functions
Nov. 15 23: Eigenvalues and Eigenvectors
Nov. 17 23: Eigenvalues and Eigenvectors
Nov. 22 24: Ordinary Differential Equations: Scalar Equations
Nov. 24 Thanksgiving Holiday (no class)
Nov. 29 25: Ordinary Differential Equations: Scalar Equations
Dec. 1 25: Ordinary Differential Equations: Systems of Equations
Dec. 6 Final Exam at 5:00 PM in GC-289