# Economics 590: Mathematical Economics, fall 2011

Instructor: Jeremy Sandford

Office hour: by appointment

Lecture: TH 12:30-1:45pm, 308 B&E

Exam dates: Tuesday, September 27th (in class), Thursday, October 27th
(in class), and Tuesday, December 13th from 10:30am-12:30pm (B&E 308)

Required course books: "A first course in optimization theory," by Rangarajan Sundaram, Mathematics for Economists, by Carl Simon and Lawrence Blume

Homework 1,
answers

Homework 2, answers

Homework 3, answers

Homework 4, answers, Scott Hall's excel file for fish
hatchery problem

Homework 5, answers

Take-home portion of final exam, due 12/13/11 by 12:30pm

# Schedule

**Thursday, August 25:** Optimization introduction,
Weierstrass theorem

**Tuesday, August 30:** Basic topology: sets and functions

reading: Sundaram, 1.1.1, 1.2.9, 1.2.10, 1.4.1

Simon and Blume, 13

**Thursday, September 2:** Basic topology: open and closed
sets

reading: Sundaram, 1.2.7, 1.2.8, 1.2.2

Simon and Blume, 12

**Tuesday, September 7:** Derivatives, gradients

reading: Sundaram, 1.4

Simon and Blume, 14

**Thursday, September 9:** Directional derivatives, constrained
optimization

reading: Sundaram, chapters 2-5

Simon and Blume, chapters 17, 18.1-18.2

**Tuesday, September 13:** examples of equality-constrained
optimization

reading: Sundaram, chapters 2-5

Simon and Blume, chapters 17, 18.1-18.2

**Thursday, September 15:** equality-constrained optimization
problem with many variables, multiple constraints, formal statement of Theorem
of Lagrange

reading: Sundaram, chapters 2-5

Simon and Blume, chapters 17, 18.1-18.2

**Tuesday, September 20:** Still more examples of
equality-constrained optimization problems

reading: Sundaram, chapters 2-5

Simon and Blume, chapters 17, 18.1-18.2, 19.1, 19.3

**Thursday, September 22:** equality- and
inequality-constrained optimization problems

reading: Sundaram, chapters 2-6

Simon and Blume, chapters 17-18, 19.1, 19.3

**Tuesday, September 27:** Midterm 1

**Thursday, September 29:** Inequality-constrained optimization
problems

reading: Sundaram, chapter 6

Simon and Blume, chapter 18-19

**Tuesday, October 4:** Concave and convex functions and
optimization

reading: Sundaram, chapter 7

Simon and Blume, chapters 21-22

**Thursday, October 6:** optimization under
concavity, quasiconcave and quasiconvex functions
and optimization

reading: Sundaram, chapter 8
Simon and Blume, chapters 21-22

**Tuesday, October 11:** introduction to dynamic optimization

reading: Sundaram, chapter 11

**Thursday, October 13:** More on finite-horizon dynamic
programming

reading: Sundaram, chapter 11

**Tuesday, October 18:** Infinite horizon dynamic programming:
Ramsey growth model, guess and verify

reading: Sundaram, chapter 12
Adda and Cooper, chapter 2

**Thursday, October 20:** Infinite horizon dynamic programming:
adjustment cost model, examples of writing down Bellman equations

reading: Sundaram, chapter 12

Adda and Cooper, chapter 2

**Tuesday, October 25:** Infinite horizon dynamic programming:
Euler equations, convergence to steady state in Ramsey growth model

reading: Sundaram, chapter 12d

Adda and Cooper, chapter 2

**Thursday, October 27:** Midterm 2 (with answers)

I've updated the answer to question 3

**Tuesday, November 1:** Numerical value function iteration

reading: Adda and Cooper, chapter 3

Excel spreadsheet
generated in class

**Thursday, November 3:** Euler equations, steady states,
convergence to steady states

**Tuesday, November 8:** Labor market search: introduction

reading: Adda and Cooper, section 10.6

optional: Sargent and Ljunqvist, chapter 6 (see me if you need a copy of
the book to photocopy)

**Thursday, November 10:** Labor market search: unemployment
and mean-preserving spreads

reading: Sargent and Ljunqvist, chapter 6

**Tuesday, November 15:** Labor market search: Neal model of
career choice

reading: Sargent and Ljunqvist, section 6.5

Neal, D., 1999, "The complexity of job mobility among
young men", *Journal of Labor Economics*, 17.2, pp. 237-261

matlab code
Sargent and Ljungvist refer to (may be useful as example)

**Thursday, November 17:** Labor market search: examples
expanding on basic model

reading: Sargent and Ljungvist, chapter 6

**Tuesday, November 22:** No class

**Thursday, November 24:** No class (Thanksgiving)

**Tuesday, November 28:** Sequences and infinite sums

reading: Sundaram, sections 1.2.1-1.2.2

Simon and Blume, chapter 12

**Thursday, December 1:** Expected utility

reading: a micro book of your choice

**Tuesday, December 6:** Taylor polynomials

reading: Simon and Blume, sections 30.2-30.3

**Tuesday, December 13:** **final exam**,
10:30-12:30

topics: dynamic programming with an emphasis on search. You should
study the problems at the end of Sargent and Ljungqvist, chapter 6 to prepare
(among other things).