Economics 210A
Graduate Economic Theory
Fall 2009


Ted Bergstrom

Economics Department, UCSB

Welcome to the Economics 210A Website. If you are taking this course,  please check this site regularly. I will use this site for posting announcements about assignments. 

Announcements: 

Scheduled Special Events:

Nov 4: Midterm Exam
Nov 6:  No section meeting
Nov 11:  Veterans' Day--No Class
Nov 25:  Day before Thanksgiving--No Class
Dec 9, 12-3pm:  Final Exam

Office Hours:  Tuesday 2-3 pm or by appointment.


Two old midterms: 
Midterm 2007
Midterm 2008
We have not yet covered expected utility theory and questions on expected utility theory will not appear on this year's midterm.

Please bring a bluebook to the exam.



Class Resources
The main textbook for this course is   Advanced Microeconomic Theory,  by Geoffrey Jehle and Philip Reny.    I have also ordered the massive Microeconomic Theory, by Andreu Mas Collel, Michael Whinston and Jerry Green, at the bookstore.  You will be using this text in other courses this term and I will assign occasional readings from it.  A third textbook, that we will use occasionally is the svelte Lectures in Microeconomic Theory by Ariel Rubinstein.  You could buy the Rubinstein book for $67 ($2 per page) from Amazon.com.   It would be worth the Amazon price if that were the only way you could get it, but Professor Rubinstein has put it online for free

More Free Resources.   I have put a pdf copy of Workouts in Microeconomic Theory by Bergstrom and Varian online for this class.   This is  a workbook that accompanies Varian's undergraduate intermediate microeconomics text  Intermediate Economics.  I will regularly assign problems from Workouts   If you want a paper copy, you can probably pick up an old edition  cheaply and old editions are just about as good as the new one.  Same goes for Varian's text (currently in its 7th edition).  Some of you might find the Varian text a good place to brush up on intermediate micro. 

Do you need to brush up on elementary logic and set theory?   I suggest reading two chapters from Kenneth May's ``Elements of
Modern Mathematics.''  Here  they are:  Elementary Logic,  Elementary Theory of Sets.   It has many nice problems and applications (with answers supplied) and is written with wit and charm.

Do you want a solid, clear exposition of the mysteries of concave and quasi-concave functions?  Let me suggest this chapter  from  Simon and Blume's ``Mathematics for Economists'' .  And while you are at it, why not have a look at their chapter on homogeneous and homothetic functions. In my opinion, most economists would benefit from having the Simon-Blume  book as a reference.

Want a quick brush-up on logic, sets, concavity, matrices, multivariate calculus, and related mathematical toos for economics?
Take a look at this tutorial by Martin Osborne.

Link to Matt Lang's answers to problem sets.

Tutorials on matrix algebra, eigenthings, and quadratic forms.   If you need more practice with the most elementary things in
matrix algebra, like multiplying matrices times other matrices, matrices, times vectors, transposing matrices, etc,
you might want to look at the Wikipedia discussion of matrix algebra.  For a nice discussion of Quadratic Forms and their relation to matrix algebra, I recommend Blume and Simon's Chapter 16, which you can find here.   Also you might want to look at this collection of notes on quadratic forms and eigenstuff, which your classmate, Sheetal Gavankar, put together.


A graphical demonstration of the directional derivative. You are standing  on a mountain, at point x, with your skis pointing in direction y.   What is the "slope" of your skis?
Check out the discussion at this site or the demo at this one.

Optional Readings:


The purpose of these readings are to show you some alternative views of utility theory and to help to motivate our study of preferences, utility and choice.  I recommend that during the term you take a  look at these works, though you may want to do some skipping.

Francis Ysidro Edgeworth's, Mathematical Psychics, written in 1881,  is one of the great books in the history of economics--and what a great title.  Through the wonders of Google Books, this book is available for free on the web..  You will note that it was scanned from the Stanford Library. ( In the first several pages, some annoying twit with a tin ear for good prose tried to copy-edit Edgeworth's text in the  library copy.  Fortunately this imbecile ran out of steam well before  the end of the book.)

Much of the analysis, particularly the early part on exchange, is completely modern and remains extremely influential.  The discussion of utility, though lucid and clear, seems alien to current ways of thinking.  I suggest that you dip into the section on utilitarian calculus, starting on page 56, where we see that Edgeworth views utility as a tool for comparing the happiness of one person with that of another.   The passages on the utility of the "lower classes" and of women will remind us of how much attitudes have changed since Victorian England. The Appendix on Hedonimetry, pp 98-102, is  thought-provoking and worthwhile for every economist to read.  Who can resist passages like the following:

  "To precise the ideas, let there be granted to the science of
pleasure what is granted to the science of energy ; ' to imagine
an ideally perfect instrument, a psychophysical machine, continually
registering the height of pleasure experienced by an
individual, exactly according to the verdict of consciousness, or
rather diverging therefrom according to a law of errors. From
moment to moment the hedonimeter varies ; the delicate
index now flickering with the flutter of the passions, now
steadied by intellectual activity, low sunk whole hours in the
neighbourhood of zero, or momentarily springing up towards
infinity. The continually indicated height is registered by
photographic or other frictionless apparatus upon a uniformly
moving vertical plane. Then the quantity of happiness between
two epochs is represented by the area contained between the
zero-line, perpendiculars thereto at the points corresponding to
the epochs, and the curve traced by the index ..."

Here is an interesting take on an evolutionary explanation of preferences.

 Evolution and Human Nature  by Arthur Robson  Journal of Economic Perspectives,
Spring 2002, pp 89-106

Can utility be interpreted as a measure of happiness?   Here are two interesting papers relevant to this question.

Explaining Happiness  by Richard EasterlinProceedings of the National Academy of Sciences,
Sept 2003,  pp11176-11183

Hedonic Adaptation  by Shane Frederick and George Loewenstein in Scientific Perspectives on Enjoyment, Suffering, and Well-Being, edited by D. Kahneman, E. Diener, and N. Schwartz, 1999, Russell Sage Foundation, New York

Exposition of a New Theory on the Measurement of Risk  by Daniel Bernoulli,  published in Latin in 1738 in the Papers of the Imperial Academy at Saint Petersburg, Volume 5.  I have posted an English translation that was published in Econometrica, January 1954.   This  paper, written a generation before Adam Smith's Wealth of Nations,  is a beautiful illustration of how simple mathematical modeling and clear thinking can take one a long way  toward understanding economic affairs.

An Econometric Analysis of Residential Electric Appliance Holdings and Consumption, by
Daniel McFadden and Jeffrey Dubin.  This is a nice example of the use of indirect utility functions in empirical work.



Problems will be assigned each week. You will be required to work them and turn them in. Homework should be neat and legible. Unless you have unusually clear handwriting, I recommend typing your homework.*  Late homework will not be accepted.  I have no objections to your working together, but I will ask you to acknowledge any help that you have had on particular problems.

*How do you handle mathematical typing with all its notations and super and subscripts?  Now is a good time to start using LaTeX or Scientific Word. LaTeX is the standard language for scientific typesetting and I think a better long-run solution than Scientific Word.   Free installations are available for  Windows, Mac and Linux.  It takes a bit of learning, but this investment in human capital will repay itself many times over.
There are several tutorials available on the Web. Chris Albert likes this one:
http://haptonstahl.org/latex/index.php
Once you get going, you will probably want to buy a good LaTeX manual like Kopka and Daly's A Guide to Latex
http://www.amazon.com/exec/obidos/ASIN/0201398257/   I have found however that Google works very well as a reference. If I forget how to do something I type something like "matrix in LaTeX" into Google and am directed to a nice discussion of how to produce matrices (or whatever) in LaTeX.
Week 1
Reading Assignment:

(Logic Preparation Check: Read the brief chapter on logic in Martin Osborne's tutorial
. See that you can do the Exercises that go with it.  This is not to hand in.  If this material is new to you or you are not confident with it, spend some time with Kenneth May's chapter on logic.)

Rubinstein:  Introduction and  Lecture  1  (Don't skip the introduction.)
Mas-Collel, Whinston, Green (MWG) pp 5-9
Jehle and Reny:  pages 1-18
Jehle and Reny pages 407-422

Homework Assignment (Due Oct 5)

Rubinstein Problem Set 1--Problems 1-3. 
Jehle and Reny:  Exercises 1.3, 1.4, 1.5(a),(c), and (e), 1.6, 1.7,  1.8, 1.9
(Note that there are hints for some of the J and R problems in the back of the book)
Jehle and Reny:  (page 453) Exercises A.1.5, A.1.7, A.1.8, A.1.16, A.1.17,A1.18
Week 2

Reading Assignment:

Rubinstein:  Lectures 2, 3, 4 (In Lecture 2, read the discussion and  the results.
Don't worry with these proofs unless you have a strong math background.)
Jehle and Reny:  pp 19-39
Jehle and Reny:  pp 423-431
Mas-Collel, Whinston, Green (MWG) pp 10-16

 
Homework Assignment: (Due Oct 12)

Jehle and Reny:  Exercises 1.12, 1.16, 1.24, 1.25, 1.26, 1.27
(Hint  for J and R. 1.27:  Draw the indifference curves for this utility function.  What do the indifference curves look like if  a=1?  What if a>1?  What if a<1?)
Jehle and Reny:  Exercises  A.1.24, A.1.26 (pp 454-455)
Bergstrom and Varian Workouts   Problems 3.2-3.9,  3.12, 3.13
B-V Workouts  Problems 4.1-4.8 and 4.11-4.12
 

Week 3

Reading Assignment:

Jehle and Reny pages 40-48  Exercises 1.43, 1.46
Jehle and Reny: pages 436-452 Exercises A1.40, A1.42, A1.46, A1.47, A1.48,
A1.49
Jehle and Reny pages 460-469, pp 484-494, Exercises A.2.5, A.2.12, A.2.13,A.2.14
Homework:
Workouts  Problems 4.1-4.8 and 4.11-4.12,  Problems  5.1-5.7
  Problems 6.1-6.8, 6.12-6.13

Week 4
Reading Assignment:
Proof that for differentiable concave functions, tangent line lies above the graph
Blume and Simon Chapter 21, Sections 21.1-21.3
Jehle and Reny pp 49-60
Jehle and  Reny pp 470-484 Exercises A. 2.9, A.2.19, A.2.20, A.2.24
Work the problems found at this link.


Week 5
Read this article on Transportation and Apple Quality
Charles Wilson's Lecture on Homogeneous and Homothetic functions
Simon and Blume Exercise 21.18
Jehle and Reny Exercises 1.53, 1.56, 1.60
Workouts Problems 8.1-8.6, 8.10, 8.11
Notice that unless otherwise stated,  these workout problems use the Slutsky rather than the Hicks decomposition of income and substitution effects.  The Hicks substitution effect is the change if you get enough "compensating" income to keep  you on the original indifference curve.  The Slutsky substitution effect is the effect if you get enough "compensating" income so you can just afford your old commodity bundle.
Read Jehle and Reny pp 484-509
Jehle and Reny  Exercise A2.25, A2.26

Week 6

 Midterm November 4
No new homework assignment will be made this week

Week 7 
 Read Bernoulli on Expected utility (required) and
Anscombe and Aumann  (optional)
Read Jehle and Reny pp 92-112 
Homework:  Jehle and Reny  Problems 2.19, 2.23, 2.24, 2.25
Also do the problems at this link.
Workouts Problems Chapter 12, 1-13
Practice  problems on gradients and directional derivatives (not to be handed in)


Week 8
Reading Assignment
Jehle and Reny pp 120-123, also read
Notes on Separable Preferences

Homework:
 Do problems found in Notes on Separable Preferences
Do Workouts Problems Chapter 10,  all except problems 6 and 11

Suggested reading:
Arrow Chenery Minhas Solow paper on CES production functions
Remarks by Arrow on history of ACMS paper


Week 9
Reading Assignment
Jehle and Reny Chapter 3:
Notes on elasticity of substitution
Homework:
Jehle and Reny Problems 3.1, 3.2, 3.3, 3.4, 3.6, 3.7, 3.9, 3.14, 3.24, 3.26, 3.33, 3.34, 3.42