## 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

- Carl Simon and Lawrence Blume,
*Mathematics for Economists*, W. W. Norton, New York, 1994.

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.

- The first midterm was on
**Thursday, October 5**in**DM-193**. Here are the answers. - The second midterm was on
**Thursday, November 9**in**DM-193**. Here are the answers. - The final will be held at the officially scheduled time:
**Tuesday, Dec. 12 at 5pm in DM-193**.

### 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.

- Exam 1
- Exam 2
- Final

### Homework Assignments and Answers

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

- Problems 3 and 5 from Chapter 6, and problems 11, 15, and 25 from Chapter 7 were due on Tuesday, Sept. 19, thanks to Hurricane Irma. Here are the answers.
- Problems 3, 18 from Chapter 8, problems 8 and 16 from Chapter 9 and problem 14 from Chap. 26 were due on Tuesday, Sept. 26. Here are the answers.
- Problems 10, 37, and 41 from Chapter 10, problems 4 and 13 from Chapter 11 and problem 7 from Chap. 12 were due on Tuesday, Oct. 3. Here are the answers.
- In class, I assigned the wrong problems. They were Problems 12 and 21 from Chapter 13 and Problems 7, 12, and 26 from Chapter 14. Here are the answers. The online assignement was Problems 15 and 17 from Chapter 13, and problems 2, 8, and 22 from Chapter 14. Here are the answers.
- Problems 18, 22, and 36 from Chapter 15, problems 3 and 6 from Chapter 16 and problem 12 from chapter 29 were due on Thursday, Nov. 2. Here are the answers.
- Problems 3, and 7 from Chapter 17, problems 6 and 15 from Chapter 18, and problems 14 (parts 2, 3, 5 only) and 21 from Chapter 19 are due on Tuesday, Nov. 21.

## Tentative Course Outline

Subject to change, as has already happened due to Hurricane Irma.

Aug. 22 | 6: Intro to Linear Algebra (and use in Economics) |

Aug. 22, 24 | 7: Linear Systems |

Aug. 29 | 8: Matrix Algebra |

Aug. 31 | 9: Determinants & some of 26: Determinants |

Sept. 5 | 10: Euclidean Spaces I |

Sept. 7, 12, 14 | No class! Hurricane Irma |

Sept. 19 | 10: Euclidean Spaces I |

Sept. 21 | 11: Linear Independence, Bases (see also Chap. 27) |

Sept. 26 | 12: Limits and Open Sets |

Sept. 28, Oct. 3 | 29: Limits and Compact Sets + Completeness |

Oct. 5 | Exam #1 — through Chapter 12 + part of 26 and 27 |

Oct. 10 | 13: Functions of Several Variables |

Oct. 12 | 14: Calculus of Several Variables 30.1: Weierstrass Thm |

Oct. 17 | 29.3: Connected Sets 30.1 Intermediate Value Thm |

Oct. 19 | 15: Implicit Functions and their Derivatives |

Oct. 24 | 16: Quadratic Forms and Definite Matrices |

Oct. 26 | 17: Unconstrained Optimization |

Oct. 31 | 30.2-3: Mean Value Thm & Taylor's Thm 18: Constrained Optimization I: First-order Conditions |

Nov. 2 | 18: Constrained Optimization I: First-order Conditions |

Nov. 7 | 19: Constrained Optimization II: Multipliers and Second-order Conditions |

Nov. 9 | Exam #2 — Chapters 13-18, 29 & 30 |

Nov. 14 | 20: Homogeneous and Homothetic Functions |

Nov. 16 | 21: Concave and Quasiconcave Functions |

Nov. 21 | 23: Eigenvalues and Eigenvectors |

Nov. 23 | Thanksgiving Holiday (no class) |

Nov. 28 | 23: Eigenvalues and Eigenvectors |

Nov. 30 | 24: Ordinary Differential Equations: Scalar Equations |

Dec. 5 | 25: Ordinary Differential Equations: Systems of Equations |

Dec. 7 | Introduction to Control Theory |

Dec. 12 | Final Exam: Tuesday, Dec. 12 at 5pm in DM-193 |