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.

The Slutsky Equation and Cobb-Douglas Demand Example

Elasticity Relations and Using Complementary Slackness

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

2.4 Uncertainty.

Dealing with Multiple Constraints

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

2.4 Uncertainty, Midterm Exam

**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

The Firm’s Problem

*Week 9:*

3.3 Cost. 3.4 Duality in Production.

*Week 10: Oct 29,31*

3.5 The Competitive Firm.

Excludes: 2.3 (Revealed Preference)

Workout Problems for Practice

*Week 11:*

4.1 Perfect Competition.

*Week 12:*

4.2 Imperfect Competition.

Oligopoly Lecutre Notes

More Oligopoly Lecutre Notes

Collusion and Surplus

*Week 13:*

4.3 Equilibrium and Welfare.

*Week 14:* Collusion and Surplus

*Old Exams*

Midterm 1- 2019

Midterm 2- 2019

Final Exam- 2019

*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