Class Times

The class meets on Tuesday and Thursday from 5:00pm to 6:15pm in DM-193.

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 below.

Homework Assignments and Answers

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

  1. Problems 1 and 6 from Chapter 6 and problems 7, 12, and 29 from Chapter 7 were due on Thursday, September 6. Here are the answers.
  2. Problems 5 and 25 from Chapter 8, problems 8 and 17 from Chapter 9 and problem 22 from Chapter 26 were due on Thursday, September 13. Here are the answers.
  3. Problems 27 and 31 from Chapter 10, problems 3 and 14 from Chapter 11 and problem 6 from Chapter 12 were due on Thursday, September 20. Here are the answers.
  4. Problems 11 and 21 from Chapter 13 and problems 5, 6, and 17 from Chapter 14 were due on Tuesday, October 9. Here are the answers.
  5. Problems 1, 12, and 20 from Chapter 15 and problems 1 and 6 from Chapter 16 were due on Tuesday, October 16. Here are the answers.
  6. Problems 2 and 3 from Chapter 16 and problems 2, 4, and 6 from Chapter 17 were due on Thursday, October 25. Here are the answers.
  7. Problems 3 and 17 from Chapter 18, problem 18 from Chapter 19, and problems 1 and 17 from Chapter 20 were due on Tuesday, November 13. Here are the answers.
  8. Problems 2, 5, and 16 from Chapter 23 and problems 5 and 17 from Chapter 24 were due on Tuesday, November 27. Here are the answers.

Exams

There will be two in-class 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 over the years.

Tentative Course Outline

Subject to change, as happened last year due to Hurricane Irma.

Aug. 21 6: Intro to Linear Algebra (and use in Economics)
Aug. 21, 23 7: Linear Systems
Aug. 28 8: Matrix Algebra
Aug. 30 9: Determinants & some of 26: Determinants
Sept. 4 10: Euclidean Spaces I
Sept. 6 10: Euclidean Spaces I
Sept. 11 11: Linear Independence, Bases (see also Chap. 27)
Sept. 13 12: Limits and Open Sets
Sept. 18, 20 29: Limits and Compact Sets + Completeness
Sept. 25 Exam #1 — through Chapter 12 + part of 26 and 27
Sept. 27 13: Functions of Several Variables
Oct. 2 14: Calculus of Several Variables
30.1: Weierstrass Theorem
Oct. 4 29.3: Connected Sets
Intermediate Value Theorem
Oct. 9 15: Implicit Functions and their Derivatives
Oct. 11 16: Quadratic Forms and Definite Matrices
Oct. 16 17: Unconstrained Optimization
Oct. 18 30.1-3: Mean Value & Taylor's Theorems
18: Constrained Optimization I: First-order Conditions
Oct. 23 18: Constrained Optimization I: First-order Conditions
Oct. 25 19: Constrained Optimization II: Multipliers and Second-order Conditions
Oct. 30 Exam #2 — Chapters 13-18, 29 & 30
Nov. 1 20: Homogeneous and Homothetic Functions
Nov. 6 21: Concave and Quasiconcave Functions
Nov. 8, 13 23: Eigenvalues and Eigenvectors
Nov. 15 23: Eigenvalues and Eigenvectors, Complex Solutions
Nov. 20 24: Ordinary Differential Equations: Scalar Equations
Nov. 22 Thanksgiving Holiday (no class)
Nov. 27 25: Ordinary Differential Equations: Systems of Equations
Nov. 29 Introduction to Control Theory
Dec. 4 Final Exam: 5-7 pm in DM-193