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, gThe 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 When are optimization problems well-defined? Can we assume utility functions?

  1.2.2 Foundation of market mechanism Existence of market equilibrium 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 Budget line Indifference curve

 2.3 Constrained optimization: equality constraints

  2.3.1 Lagrangefs method Technique Interpretation of Lagrangian multiplier


Lecture 3 (4/15) Practice question 2 (pdf)

 2.4 Constrained optimization: inequality constraints

  2.4.1 Kuhn Tucker theory Motivation Technique Example

 2.5 Other mathematical tools

  2.5.1 Envelope theorem Unconstrained problem 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 Homogeneity Royfs identity


Lecture 5 (4/22) Royfs identity (and envelope theorem) Other properties

 3.5 Hicksian (compensated) demands

3.5.1 Expenditure minimization problem (EMP)

3.5.2 Expenditure function Homogeneity Concavity 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 Graphical approach Negative own substitution 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 Cobb-Douglas function CES (Constant Elasticity of Substitution) function

  4.2.2 Key properties (Diminishing) Marginal product Returns to scale Marginal rate of technical substitution (RTS)


Lecture 9 (5/7)


Review of Problem Set 1 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 Homogeneous of degree 1 Concave in (w,r) Shephardfs Lemma


Lecture 10 (5/13) Monotonicity Contingent input demand

4.3.4 Properties 2: changing Q Monotonicity 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 Homogeneous of degree 1 Monotonicity Convex in p Hotellingfs Lemma

  4.4.3 Duality Contingent vs. unconditional demands 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, 10th 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, 2nd edition, 1990



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