**ECO600E: Advanced
Microeconomics I**

*Last Updated: June 16*

Term / Time:
Spring 1st ses. / Tuesday 10:35-12:05 and 13:20-14:50

Class room: H
(5th floor)

Office hours:
Wednesday 11:00-13:00 (Room C911)

Syllabus: A word file

**0. Announcement** *Updated frequently!*

(Released
date, gCommentsh)

2008/06/16, gYour
graded answer sheets of problem set 3 and final exams were returned to your mail
boxes. Comments are available in the grading section below.h *New!*

2008/05/23,
gAnswer sheets for problem set 2 have been returned in your mail-boxes.h

2008/05/21,
gThere are typos in problem set 3. This is due on **May 27**, not on May 28. Utility functions for Ann in question 3
contain obvious mistakes.h

2008/05/20, g__The
final exam__ is scheduled on May 29, 9:00 to 10:30 at room H.h *Important!*

2008/05/20,
gThe third problem set is due in class on **May
27**. Remarks on problem sets 2 and 3 will be given in the lecture, then.h

2008/05/13,
gThere is a typo in the problem set 2. In question 2 (b) and (c), MRS of gother
goods for gasolineh should be MRS of ggasoline for other goods,h i.e., dx/dy
along the indifference curve.h

2008/05/12,
gOfficial Power Point Slides for Nicholson (9th ed.) is available for free here.h
*Important!*

2008/05/07,
gThe second problem set is due in class on May 14. Please bring your answer
sheet in the make-up class on Wednesday morningh

2008/04/22,
gThere will be a make-up class on May 14 from 9 to 10:30.h *Important!*

2008/04/22,
gThere will be make-up classes on April 30, May 7 and May 21, from 9 to 10:30
and 13:20-14:50.h *Important!*

2008/04/22,
gThere will be NO CLASS on April 29, May 6, and May 20.h *Important!*

2008/04/21,
gThe second lecture tomorrow (April 22, 13:20-14:50) will be cancelled. We will
arrange the schedule of its make-up class in the morning class.h

2008/04/15,
gI just sent an e-mail to those who are attending my class. If you havenft
received the e-mail but continue to attend my class, please let me know as soon
as possible. I will put you in the mailing list.h

2008/04/15,
gThe first problem set is due in class on April 22. Please bring your answer
sheet in the morning class on Tuesday!h *Important!*

2008/04/15,
gThe practice questions we covered in class and a note on preference are
available in eLecture Schedule and Topicsf.h

2008/04/13,
gThe sections for eTopics in Lecturef and eProblem Setf were added below.h

2008/03/31,
gThe first class will be on April 8th. See you then!h

**1. Course Description**

This is an
advanced course in microeconomics, emphasizing the applications of mathematical
tools and models to the study of individual economic decisions and their
aggregate consequences. We begin with a parsimonious set of hypotheses about
human behavior and the ways in which individual choices interact, and then
examine the implications for markets. This entails treatments and applications
of consumer theory and theory of the firm, including a general equilibrium
analysis, under the ideal conditions implied by our hypotheses.

**2. Lecture Schedule and Topics ***Under construction.*

__Lecture 1 (4/8)__

**1. Introduction**

1.1 Why are
mathematical models needed?

1.1.1 Physical vs. Economic phenomena

1.1.2 Institutional knowledge vs.
Economic theory

1.1.3 Economic law = each person acts for
her own interest

1.1.4 Advantages of economic theory

1.2 What are
advanced mathematical tools for?

1.2.1 Foundation of optimization

1.2.1.1 When are optimization
problems well-defined?

1.2.1.2 Can we assume utility
functions?

1.2.2 Foundation of market mechanism

1.2.2.1 Existence of market
equilibrium

1.2.2.2 Stability of market
equilibrium

1.3 Why do we need game theory?

1.3.1 Importance of strategic
interdependence

__Lecture 2 (4/8)__

**2. Optimization**

2.1 Single variable optimization

2.1.1 First order necessary condition

2.1.2 Second order sufficient condition

2.1.3 Point of inflection

2.1.4 Practice question 1 (pdf)

2.2 Multiple variable optimization

2.2.1 Implicit function theorem

2.2.2 Examples of implicit function
theorem

2.2.2.1 Budget line

2.2.2.2 Indifference curve

2.3 Constrained optimization: equality
constraints

2.3.1 Lagrangefs method

2.3.1.1 Technique

2.3.1.2 Interpretation of
Lagrangian multiplier

__Lecture 3 (4/15)__

2.3.1.3 Practice question 2 (pdf)

2.4 Constrained optimization: inequality
constraints

2.4.1 Kuhn Tucker theory

2.4.1.1 Motivation

2.4.1.2
Technique

2.4.1.3 Example

2.5 Other mathematical tools

2.5.1 Envelope theorem

2.5.1.2 Unconstrained problem

2.5.1.3 Constrained problem

2.5.2 Homogeneous functions

2.5.3 Concavity and convexity

2.5.4 Elasticity

__Lecture 4 (4/15)__

**3. Consumer theory**

3.1 Preference (a note in pdf is available)

3.1.1 Rational preference

3.1.2 Continuity

3.1.3 Utility representation theorem

3.1.4 Counter example

3.2 Utility functions

3.2.1 Definition

3.2.2 Monotone transformation

3.2.3 Marginal rate of substitution
(MRS)

3.4
Marshallian (ordinal) demands

3.4.1 Utility maximization problem (UMP)

3.4.2 Elasticity and some concepts

3.4.3 Indirect utility function

3.4.3.1
Homogeneity

3.4.3.2

__Lecture 5 (4/22)__

3.4.3.3

3.4.3.4 Other
properties

3.5 Hicksian (compensated) demands

3.5.1
Expenditure minimization problem (EMP)

3.5.2
Expenditure function

3.5.2.1 Homogeneity

3.5.2.2 Concavity

3.5.2.3
Shephardfs lemma

3.6. Duality

3.6.1 Relationship between UMP and EMP

3.6.2 Practice question 3 (pdf)

__Lecture 6 (4/30)__

**Handout**: Deaton and Muellbauer
(1980), *Economics and Consumer Behavior*,
Chapter 2 (Preferences and demand), pp. 37-47.

3.6.3 Further properties of expenditure
function

3.6.3.1 Graphical approach

3.6.3.2
Negative own substitution

3.6.3.3 Symmetric cross
substitution

3.6.4 Slutsky
equation

3.6.5 Income and substitution effects

3.6.6 Further properties

3.7 Welfare evaluation

3.7.1 Compensating variation

3.7.2 Equivalent variation

__Lecture 7 (4/30)__

3.7.3
Consumer surplus

3.7.4
Graphical analysis

3.7.5 Slutsky
compensation

3.7.6
Quasi-linear utility

3.8 Aggregating demand

3.8.1 Gorman form

3.8.2 The proof of sufficiency

__Lecture 8 (5/7)__

**4. Firm theory**

4.1 What is a firm?

4.1.1 Market vs. organization

4.1.2 Complex of gprincipal-agenth
relationships

4.1.3 Orthodox view: production
technology

4.1.4 Sunk and fixed costs

4.1.5 Time span of analysis

4.2 Production function

4.2.1 Examples

4.2.1.1 Cobb-Douglas function

4.2.1.2 CES (Constant Elasticity
of Substitution) function

4.2.2 Key properties

4.2.2.1 (Diminishing) Marginal
product

4.2.2.2 Returns to scale

4.2.2.3 Marginal rate of technical
substitution (RTS)

__Lecture 9 (5/7)__

Review of Problem Set 1

4.2.2.4 Elasticity of substitution

4.3 Cost function

4.3.1 Cost minimization problem

4.3.2 Expansion path

4.3.3 Properties 1: changing w and r

4.3.3.1 Homogeneous of degree 1

4.3.3.2 Concave in (w,r)

4.3.3.3 Shephardfs Lemma

__Lecture 10 (5/13)__

4.3.3.4 Monotonicity

4.3.3.5 Contingent input demand

4.3.4
Properties 2: changing Q

4.3.4.1 Monotonicity

4.3.4.2 Total, average and marginal costs

4.3.5 Practice question 4 (pdf)

4.4 Profit maximization

4.4.1 Two step approach

4.4.2
Short-run and long-run supply curve

__Lecture 11 (5/13)__

**Handout**:
Varian (1992), *Microeconomic Analysis*,
Chapter 3 (Profit Function), pp. 40-47.

4.4.3 One step approach

4.4.4 Profit function

4.4.4.1 Homogeneous of degree 1

4.4.4.2 Monotonicity

4.4.4.3 Convex in p

4.4.4.4 Hotellingfs Lemma

4.4.3 Duality

4.4.3.1 Contingent vs.
unconditional demands

4.4.3.2 Substitution and output
effects

__Lecture 12 (5/14)__

**5. Partial equilibrium
analysis**

5.1 Perfect competition

5.1.1 Definition

5.1.2 Interpretation

5.1.3 Why gequilibriumh?

5.2 Long-run market supply

5.2.1 Free entry and exit

5.2.2 Flat supply curve

5.3 Practice question 5 (pdf)

5.4 Surplus analysis

5.5 Taxation and dead weight loss

__Lecture 13 (5/21)__

**6. General equilibrium
analysis**

6.1 Overview of GE

6.1.1 Existence of equilibrium

6.1.2 Efficiency of equilibrium

6.1.3 Implementation of efficient
allocations

6.2 Pareto efficiency

6.2.1 Strong Pareto efficiency

6.2.2 Weak Pareto efficiency

6.2.3 Equivalence between two concepts

6.3 Edgeworth box

6.3.1 Efficient allocations

6.3.2 Individually rational allocations

6.3.3 Contract curve

6.3.4 Budget line in the box

__Lecture 14 (5/21)__

6.4 Excess
demand

6.4.1 Homogeneous of degree 0

6.4.2 Walrasf law

6.5 Existence of GE

6.5.1 Practice question 6 (pdf)

6.5.2 Graphical illustration

6.5.3 Fixed point theorem

6.6 First welfare theorem

6.7 Second welfare theorem

__Lecture 15 (5/27)__

Review
of Problem Set 2 and Problem
Set 3

6.8 Fair
allocation

6.9
Production in GE

For
Lecture 16 to 30, see the website
for Advanced Microeconomics II.

**3. Problem Set**

There
will be three problem sets:

First (due on 4/22, pdf,
solutions)

Second (due on 5/14, pdf,
solutions)

Third (due on 5/28, pdf,
solutions)

**4. Grading**

Course grade
will be determined by combining grades on problem sets (**30%**) and a final exam (**70%**).

Problem sets
will be distributed in class and will be due a week later. Because solutions
are published, late problem sets cannot be accepted. You are encouraged to form
study group, but must write up solutions independently.

Final exam (pdf, comments,
comments on grading)

**5. Textbooks**

The textbook
for the course is:

Walter
Nicholson, *Microeconomic Theory: basic
principles and extensions*, 10^{th} edition 2007 *earlier versions
would be fine!*

The following
is a standard (and very rigorous) textbook for Economics Ph.D. students.

Andreu
Mas-Colell, Michael Whinston, and Jerry Green, *Microeconomic Theory*, 1995

A useful graduate
level textbook which provides full of intuitive explanation is:

Hal
Varian, *Microeconomic Analysis*, 1992

A classic
textbook for theory and applications on consumer demand is:

Angus
Deaton and John Muellbauer, *Economics and
Consumer Behavior*, 1980

A
well-written book for optimization techniques is:

Avinash
Dixit, *Optimization in Economic Theory*,
2^{nd} edition, 1990

*Go back to the front page.*