Optimization for Economists

This course (see Syllabus) is intended for giving a systematic grounding in a significant part of the mathematical theory that is most important for and widely used in economics. It will cover a range of topics in the calculus of several variables, real analysis, and optimization theory. Unlike traditional courses in mathematics, this set of lectures will motivate the theory by means of applications in economic problems. There will be extensive readings, which will be used in class to introduce the mathematical concepts and tools and to illustrate how they are used in economics. The course is open to all students at the Collegio but it would not be appropriate for those without solid foundations in the single variable calculus, linear algebra, and basic set theory but also some economic sophistication.

Lecture Notes

1. Introductory Concepts I

2. Introductory Concepts II

3. Introductory Concepts III

4. Constrained Optimization I

5. Constrained Optimization II

6. Constrained Optimization III

7. The Envelope and Maximum Theorems

8. Supermodularity and Parametric Monotonicity

Homework (incl. Suggested Solutions)

1. Introductory Concepts

2. Midterm

3. Final

Extra Material

1. The Rank of a Matrix

2. Quadratic Form

3. Practice Problems I

4. Constrained Optimization - Graphical Analysis

5. Constrained Optimization

6. The Maximum Theorem (Sundaram)

7. Parametric Monotonicity (Sundaram)

8. Final2009