g# Econ 8100

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 $\text{L}\phantom{\rule{-0.36em}{0ex}}$. There are many online resources for learning $\text{L}\phantom{\rule{-0.36em}{0ex}}$. One particularly easy way to get started with $\text{L}\phantom{\rule{-0.36em}{0ex}}$ 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 two midterms and a final exam. They are tentatively placed in the schedule below. Grading will be based 40% on midterm exams, 40% on the final exam, and 20% on homework.

My office hours: Tuesday 2:00-3:00 or by appointment in Calhoun 404. Matthew Chambers (TA) office hours: TBA.

*Week 1: Aug 27,29*

1.1 Primitive Notions. 1.2 Preferences and Utility. A1.4 Real Value Functions.

Additional Reading: Rubinstein Lecture Notes Chapter 1.

Problem Set (Due Sept. 3):

J&R: 1.2, 1.4, 1.5 (a), (d), and (f), 1.6, and 1.9.

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

*Week 2: Sept 3,5*

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: (Due Sept. 10): J&R: A.1.5, A.1.7 Parts c and d, A.1.9, A.1.10, A.1.16, A1.40, A1.42, A1.46, A1.47 A.1.48

J&R: 1.12, 1.15, 1.20, 1.21, 1.26, 1.27, 1.29

*Week 3: Sept 10,12*

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: (Due Sept. 19)

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, 1.57, 1.64

*Week 4: Sept 17,19*

1.5 Properties of Consumer Demand.

Problem Set: (Due Oct. 1) J&R: 1.61, 1.63 (prove each), 1.67

Sketch some indifference curves of:

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

Sketch some indifference curves of:

$U(x_1,x_2) = x_2(log(x_1)-1)$. For what values of $x_1,x_2$ does this consumer have monotonic preferences? Prove that the function is quasiconcave in this region. Find the Marshalian Demand. Hint: You will need a special function.

**Midterm Exam 1- Sept 26**

*Week 5: Sept 24,26*

2.3 Revealed Preference.

*Week 6: Oct 1,3*

2.4 Uncertainty.

*Week 7: Oct 8,10*

2.4 Uncertainty.

Problem Set: (Due Oct. 21)

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: Oct 15,17*

3.1 Primitive Notions. 3.2 Production.

Some Analysis of CES Production

*Week 9: Oct 22 (24 is Fall Break)*

3.3 Cost. 3.4 Duality in Production.

*Week 10: Oct 29,31*

3.5 The Competitive Firm.

**Midterm Exam 2 - Nov 5** Covers: 2.4 (Uncertainty), 3.1-3.4 (Firm’s Problem Excluding Profit-Max).

Excludes: 2.3 (Revealed Preference)

Workout Problems for Practice

*Week 11: Nov 5,7*

4.1 Perfect Competition.

*Week 12: Nov 12,14*

4.2 Imperfect Competition.

Interactive Lecutre Notes

*Week 13: Nov 19,21*

4.3 Equilibrium and Welfare.

*Week 14: Dec 3,5 (Catch-up Week)*

**Final Exam**