## Class Times

*New time.*
Effective Monday, September 9, the class will
meet Monday and Wednesday from 3:00pm to 4:15pm in GC-271A.

## 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 optimiation.

## 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

Regular office hours are 1:00-2:30 on Monday, Wednesday, and Friday.
I am also available immediately after class.
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>.

### TA Office Hours

The TA for the class is Jiangyun Wan, who has office hours from 4:30-5:00pm MW in the Economics Tutoring Center.

## 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
**Monday, September 30**. Click here for answers. - The second midterm was on
**Monday, November 4**.
Click here for answers.
- The final is at
**12 noon on Friday, Dec. 13**(finals week) in GC-272. Click here for answers.

### Sample Exams

Here are some previous midterm exams from this course. Note that some questions may not be relevant.

- Exam 1
- Exam 2
- Final

### Homework Assignments and Answers

- Problems 3 and 5 from Chapter 6 and problems 7, 12, and 29 from Chapter 7 were due on Friday, Sept. 6. Click here for answers.
- Problems 8.4, 8.25, 9.16, 10.16, and 10.21 from the book were due on Monday, Sept. 16. Click here for answers.
- Problems 11.3, 11.12, 12.2, 12.6, 12.14, and 27.1 from the book were due on Wednesday, Sept. 25. Click here for answers.
- Problems 13.15, 14.6, 14.27, 14.28, 15.8, and 15.13 from the book are due on Monday, Oct. 21. Click here for answers.
- Problems 16.6, 17.2, 18.3, 18.10, and 18.17 from the book were due on Monday, Oct. 28. Click here for answers.
- Problems 23.5, 23.7, 23.12, and 23.15 from the book were due on Monday, Nov. 25. Click here for answers.

Answers will be posted sometime after the homework is collected.

## Course Outline

This schedule is based on 3 classes per week, and will be updated to two classes per week as the semester progresses.

Aug. 26 | 6: Intro to Linear Algebra (and use in Economics) |

Aug. 28, 30 | 7: Linear Systems |

Sept. 2 | Labor Day Holiday (no class) |

Sept. 4 | 8: Matrix Algebra |

Sept. 6 | 9: Determinants & some of 26: Determinants |

Sept. 9, 11 | 10: Euclidean Spaces |

Sept. 11, 16 | 11: Linear Independence, Bases |

Sept. 16, 18, 23 | 12: Limits and Open Sets |

Sept. 23 | 29: Limits and Compact Sets + Completeness (Chap. 29) |

Sept. 25 | 13: Functions of Several Variables + Weierstrass Thm (Chap. 30) |

Sept. 30 | Exam #1 — through Chapter 12 |

Sept. 25, Oct. 2 | 14: Calculus of Several Variables |

Oct. 2 | 29.3: Connected Sets |

Oct. 7 | 15: Implicit Functions and their Derivatives |

Oct. 9 | 16: Quadratic Forms and Definite Matrices |

Oct. 14 | 17: Unconstrained Optimization |

Oct. 14, 16 | 30: Calculus of Several Variables II |

Oct. 16 | 18: Constrained Optimization I: First-order Conditions |

Oct. 21, 23 | 19: Constrained Optimization II |

Oct. 23 | 20: Homogeneous and Homothetic Functions |

Oct. 28, 30 | 21: Concave and Quasiconcave Functions |

Nov. 4 | Exam #2 — Chapters 13-20 |

Nov. 6 | 22: Economic Applications |

Nov. 11 | Veteran's Day Holiday (no class) |

Nov. 13, 18, 20 | 23: Eigenvalues and Eigenvectors |

Nov. 25, 27 | 24: Ordinary Differential Equations: Scalar Equations |

Dec. 2, 4 | 25: Ordinary Differential Equations: Systems of Equations |

Dec. 13 | Final Exam at 12:00 noon in GC-271A |