Economics 210A
Graduate Economic Theory
Fall 2011

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. The syllabus that you see is a bit like the weather report. It is
a pretty accurate forecast of what we will do in the near future.  The long term forecasts are less reliable and will be updated as the course proceeds.


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 i n 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 Economic Theory by Ariel Rubinstein.  You could buy a hard copy of the Rubinstein book for about $30 from Amazon.com.   It would be probably be worth the Amazon price if that were the only way you could get it, but Professor Rubinstein has put it online for free.   Another slim and beautiful economic theory book that you might consider buying is Itzhak Gilboa's
Rational Choice.  I have put the first two chapters of this book online. 

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 8th edition).  Some of you might find the Varian text a good place to improve your background in  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).

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 purchasing the Simon-Blume  book as a reference.

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

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, put together by Sheetal Gavankar.

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.

Final Exam 2011

Final Exam without answers

Final Exam With Answers

Some Old Exams
Midterm 2007
Midterm 2008
 Midterm 2009
Midterm 2010
Answers to the 2010 Midterm


Final Exam 2007
The 2008 Final Exam
Answers to the 2008 final
The 2009 Final Exam with some answers.
  Final Exam, 2010
Some old Prelim Questions

Answers to old Prelim Questions

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.

Soldiers of Fortune Ted  Bergstrom,  This is an application of  ``state dependent  expected utility theory''  to study the alternatives of a professional volunteer army and a draft lottery.   The discussion moves on to the more general issue of the competitive
analysis of occupational choice.


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 407-417 2d edition) --(pages 495-505, 3d edition)
Selection from Itzhak Gilboa's book, Rational Choice
( I promised you a bit of philosopy, and some introduction to "behavioral economics".
I hope that you will find this discussion amusing and thought-provoking.  )

Homework Assignment (Due Oct 5)

Previously we had said Monday, Oct 3, but let's make it Weds Oct 5.

Rubinstein Problem Set 1--Problems 1, 2, and 4. 
Jehle and Reny:  Exercises 1.2 (b),(c),(d) (Hint: How do you show that two sets A and B are equal?
Try a two step procedure. You show if x is in B then  x is in A.  Next  you show that if x is in B, then x is in A.) 
1.3, 1.4, 1.5 (b),(c), and (g), 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 2d edition) (page 546 2d edition) Exercises   A.1.5, A.1.7 Parts  b,c  A.1.8, A.1.9, A.1.10, A.1.16, A.1.17, A1.18
Week 2

Reading Assignment:

Rubinstein:  Lecture  4 
Jehle and Reny:  pp 19-39
Jehle and Reny: (2d edition)  pp 418-432 and pages 436-452 (3d edition 505-523 and 529-533)
MWG pp 9-22


Homework Assignment: (Due Oct 12)

Jehle and Reny:  Exercises 1.12, 1.14, 1.16, 1.24, 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 (2d edition p 455)  (3d edition pp 548)
Jehle and Reny: Exercises A1.40, A1.42, A1.46, A1.47
Bergstrom and Varian Workouts   Problems 3.3, 3.5, 3.7,  3.9 and   3.13 
B-V Workouts  Problems 4.1, 4.3, 4.5, 4.7 and 4.11   
(You should make sure that you can do all of the problems in these chapters of Workouts.)
 

Week 3

Reading Assignment:

Simon and Blume on Homogeneous and Homothetic functions, Chapter 20
 Charles Wilson's Lecture on Homogeneous and Homothetic functions
Simon  and Blume on Concave and Quasiconcave functions, Chapter 21 , pp 505-527


Jehle and Reny pages 460-469, pp 484-494, Exercises A.2.5, A.2.12, A.2.13,A.2.14

Homework:
Simon and Blume Problem 20.17
Simon and Blume Problem 21.2

Workouts     Problems  5.1-5.8
  Problems 6.1-6.8, 6.12-6.13

Week 4
Reading Assignment:
Promised Proofs on Properties of indirect utility functions
Proof that for differentiable concave functions, tangent line lies above the graph
Proofs of Properties of Expenditure functions
Jehle and Reny pp 40-60,  Exercises  1.46, 1.50, 1.53, 1.56,
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
Useful properties of quasi-concave and homogeneous functions

Read Jehle and Reny pages 116-130.  I think that you will find this material to be reassuringly familiar.

No homework is due this week, but see that you can do the problems in
Workouts Chapter 8. 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.
Practice  problems on gradients and directional derivatives (not to be handed in) 

Midterm Exam on Wednesday, October 26.
 
 



Week 6

Notes on the elasticity of substitution
Problem set to hand in:
Problems on CES Functions
Suggested reading:
Arrow Chenery Minhas Solow paper on CES production functions
Remarks by Arrow on history of ACMS paper

Notes on Separable Preferences

Homework:
Turn in  Problems on CES Functions
  and Exercises found in Notes on Separable Preferences

Answer sheet for Midterm  

Week 7 
 Read Bernoulli on Expected utility (required) and
Anscombe and Aumann  (optional)
Read Jehle and Reny  Chapter 2, section on Uncertainty
(First edition pages 92-112)
 (Second edition pages 97-118)
Notes on Expected Utility

Homework to hand in:
Jehle and Reny (Second edition)  Problems 2.19, 2.23, 2.24, 2.25  
(Third edition) Problems 2.21, 2.25, 2.26 2.27
Also Problems at this link.
and Workouts Problems Chapter 12--odd-numbered problems


Week 8
Reading Assignment
Jehle and Reny, Section 2.3, Revealed Preference

Homework to hand in:
 
Jehle-Reny 2.8 and 2.10 (same in both editions)
Workouts 7.1, 7.3, 7.5,7.6, 7.7



Week 9
Reading Assignment
Finish Jehle and Reny Chapter 3:
 
This week you don't need to turn in your homework, but I recommend that you be sure that you can  do the following problems
from Jehle and Reny:
 Problems  3.1, 3.2, 3.3, 3.9, 3.10. 3.11,   3.33, 3.34, 3.52, 3.53 (2d edition)

Problems 3.1,3.2,3.3, 3.11,3.12, 3.13, 3.35, 3.36, 3.54, 3.55 (3d edition)
 


Week 10


Pure Exchange Equilibrium
 
Not to be handed in, but see that you can do these:
(Read the introductions to each of these chapters)
Workouts Problems from Chapter 9
Workouts Problems from Chapter 31

Jehle pp 187-192 Second Edition,  pp  201-206, Third edition
Mas Collel, Whinston, Green,  pp 515-525
Lecture notes on Pure Exchange Equilibrium