This is the course website for Vanderbilt Economics 8100. This is the first course of the PhD microeconomics core sequence. The course will cover the fundamentals of consumer theory, theory of the firm, and simple markets in partial equilibrium. This page will be continuously updated throughout the semester. Please check it on a regular basis. Consider subscribing to changes using a service such as Visual Ping or Wachete.

Main textbook: *Advanced Microeconomic Theory*,

Geoffrey Jehle and Philip Reny.

Secondary textbook: *Microeconomic Theory*,

Andreu Mas-Colell, Michael D. Whinston, Jerry R. Green.

There will be an assignment *roughly* each week. Problems will be added to the schedule about two weeks before the assignment is due. *You must type your homework*. This is the perfect time for you to learn to type in $\text{LaTeX}$. There are many online resources for learning $\text{LaTeX}$. One particularly easy way to get started with $\text{LaTeX}$ is through the very user-friendly editor called Lyx. There will be a learning curve at first. Embrace it. This is an investment.

There will be one midterms and a final exam. They are tentatively placed in the schedule below. Grading will be based 30% on midterm exam, 50% on the final exam, and 20% on homework.

My office hours: Tuesday 11:00-12:00pm on zoom and by appointment. TA: Ji hye Heo. Office Hours: Wed 9:30-10:30am

All office hours held on zoom. For links, see brightspace.

*Week 1* (Sept 1,3) Choice. 1.1 Primitive Notions. 1.2 Preferences and Utility. A1.4 Real Value Functions.

Additional Reading: Rubinstein Lecture Notes Chapter 1.

Problem Set 1: (Due Sept 8. Please type and turn-on on Brightspace.) Prove that Choice Coherence implies Independence of Irelevant Alternatives J&R: 1.2, 1.4, 1.5 (a), (d), and (f), 1.6, and 1.9.

Rubinstein: 1,2,3,4,5,6.

Try these for a deeper understanding of lexicographic preferences.

*Week 2* (Sept 8,10) 1.3 The Consumer Problem. A2.1 Calculus. A2.2 Optimization.

Can preferences with a “Bad” be Strictly Monotonic?

What kind of preferences generate a Cobb-Douglas utility function?

Problem Set 2 (Due Sept 17): J&R: A.1.5, A.1.7 Parts c and d, A.1.9, A1.42, A1.46, A1.47 A.1.48

J&R: 1.12, 1.15, 1.20, 1.21, 1.27,

For A1.42 prove that the function has convex better-than sets. I am not sure what “A” refers to.

*Week 3 (Sept 15, 17)*

1.4 Indirect Utility and Expenditure. A2.3 Constrained Optimization. A2.4 Value Functions.

Homogeneous Functions Notes

Convexity Notes

Theorem of the Maximum and Envelope

Problem Set 3: (Due Oct 8) J&R: A.1.32, A.1.36, A.1.49, A.2.12, A.2.13, A.2.14

J&R: 1.37, 1.46, 1.53, 1,56, 1.64, 1.63, 1.67

Sketch some indifference curves of:

$U(x_1,x_2) = min(x_1*x_2,x_1)$ and find the Marshalian Demand, Hicksian Demand, Expendature Function, and Indirect Utility Function.

*Week 4: (Sept 22,24)*

1.5 Properties of Consumer Demand.

*Week 5: (Sept 29, Oct 1)*

1.5 Properties of Consumer Demand.

Live Lecture Notes Week 5 Part 1

Live Lecture Notes Week 5 Part 2

*Week 6: (Oct 6, Oct 8)*

2.4 Uncertainty.

Live Lecture Notes Week 6

*Week 7: (Oct 13, Oct 15)*

2.4 Uncertainty, Midterm Exam

Live Lecture Notes Week 7

**Midterm Exam Oct 15** Midterm exam covering material through and including 1.5.

Solutions

Problem Set: (Due Oct. 29)

These Problems and J&R 2.19, 2.25, 2.26 2.27.

- Prove that a consumer with utility $u(w) = 1 - e^{-w}$ has a risk premium for any binary lottery that does not depend on the level of inital wealth.
- Prove that if $\succsim $ is complete, transitive, strictly monotonic, continuous on the set $X=R^n$ then for every $x X$ there exists a number $i$ such that $(i,i,i,…,i)x$. Argue that CD utility functions of the form ${\prod}_{i=1}^{n}{x}_{i}^{{\alpha}_{i}}$ such that ${i=1}n _i = 1$ contain cardinal information about the underlying ordinal preferences.

*Week 8:*

3.1 Primitive Notions. 3.2 Production.

Some Analysis of CES Production

Live Lecture Notes Week 8

*Week 9:*

3.3 Cost. 3.4 Duality in Production.

*Week 10: Oct 29,31*

3.5 The Competitive Firm.

Live Lecture Notes Week 9 Part 1

Live Lecture Notes Week 9 Part 2

*Week 10:*

4.1 Perfect Competition.

Live Lecture Notes Week 10 Part 1

Live Lecture Notes Week 10 Part 2

*Week 11:*

4.2 Imperfect Competition.

Live Lecture Notes Week 11

*Week 12:*

4.3 Cournot and Friends.

Live Lecture Notes Week 12 1

*Week 13:* 5.1-4 General Equilibrium

*Other Stuff*

Workout Problems for Practice

Monopoly and Cournot Problem

*Old Exams*

Midterm 1- 2019

Midterm 2- 2019

Final Exam- 2019

Prelim- 2020

*Helpful Tips* I wrote these with my classmate Zach Bethune when I was a student. They have come in handy for me many times. If you find an error, or have a suggestion about something to add, let me know.

Helpful Tips