Economics 210A
Graduate Economic Theory
Fall 2016

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.    

Other useful textbooks:  There are now several good alternative textbooks that you may want to consider purchasing.  These serve not only as texts, but as references that will be
useful for years to come.

One good option is Essential Microeconomics  by John Riley.    Take a look at this link to see a nice set of study resources related to this book.  This book will be useful not only in this course,
but also is likely to be assigned  in the next two quarters of the graduate micro sequence.    It is available new from Amazon at about $90 and used from Amazon at about half that price.

 David Kreps' book Microeconomic Foundations I   is a somewhat more mathematically rigorous treatment of this material.  I have  put the first chapter online for you at this link.
 Amazon has  Kreps' book  new for about $40. 

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.
If you want to develop upper-body strength, you might consider carrying the massive  Microeconomic Theory, by Andreu Mas Collel, Michael Whinston and Jerry Green in your backpack.
This is probably the most widely-used graduate micro textbook and serves well as a reference work.

Another textbook that  is worth looking at is  the svelte Lectures in Economic Theory by Ariel Rubinstein.  You could buy a hard copy of the Rubinstein book for about $30 from   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.  

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 undergraduate text.  Some of you might find the Varian text a good place to improve your background in  intermediate micro. 

A 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. 

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).

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.

Do you need a brain to have transitive preferences?  This paper offers evidence that slime molds, though they have even less brains than university administrators, do act transitively. 
The paper suggests however, that they do not have well-formed preference orderings, but make their choices by means of comparisons to
possibly irrelevant alternatives.

Some Old Exams


Midterm 2012
Midterm 2012 with answers

Final 2012
Final 2012 with some answers

Midterm 2013
Midterm 2013 with answers

Final Exam 2013
Final Exam 2013 with answers

First Midterm, 2014

Second Midterm, 2014
Final Exam 2014
Final Exam 2014 with answers

First Midterm 2015

First Midterm with answers
Second Midterm 2015
Final Exam 2015
Final Exam 2015 with answers


Optional Readings:

The purpose of these readings is 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 copyedit 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.

About your Homework.

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. 

If you are old-fashioned enough to like printed manuals,  you would probably want to buy  LaTeX manual like Kopka and Daly's A Guide to Latex.
  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.

                                                           Weekly Assignments, Midterms, and Final
The first week's assignment is posted below.  For the next two weeks, "tentative assignments" are posted.  I  may adjust these assignments as their time comes closer.
  Before the beginning of each week, you will see an updated version of the assignment  that applies for this year.  More assignments will appear as the weeks pass.

I plan to schedule two midterms, one after 3 weeks of class and one after about 6 weeks.  There will also be a 3 hour final exam during finals week  at the university-scheduled time for classes that meet when ours does.

Office Hours:   Tuesdays 2-3:45 and by appointment.  

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.)

Download Kreps Chapter 1
Jehle and Reny:  pages 1-18
Jehle and Reny:  pages 495-514 

Lecture slides: Transitivity of strict preference 

(Optional reading:
Download Rubinstein:  Introduction and  Lecture  1  )

Who can solve the puzzle downloaded by clicking here    and tell us the answer on Wednesday? 

Homework Assignment (Due Wednesday)

Problems from Kreps Chapter 1
The following problems from Kreps have answers which you can find by  downloading the student guide to Kreps' Chapter 1.
Problems 1.1, 1.3, 1.6 and 1.7.    You won't need to hand these in, but you should work them.  Try to do as much
as you can before looking at the answers.

To hand in: Kreps Problems 1.2,  1.4,  1.8 and 1.9.  

Jehle and Reny
Problems 1.2, 1.4, 1.5 (a), (d), and (f),  1.6, and 1.9  
(Note that there are hints for some of the J and R problems in the back of the book. )

Week 2
Reading Assignment:

Rubinstein:  Lecture  4 
Jehle and Reny:  pp 19-41
Jehle and Reny:  (3d edition pp 515-523 and 529-533)
(optional:  MWG pp 9-22 and 40-57)

Lecture slides: Continuity
Lecture slides: Convexity

Homework Assignment: (Due Wednesday)

Jehle and Reny:    (page 546   Exercises  A.1.5, A.1.7 Parts  c and d, A.1.9, A.1.10, A.1.16)
Jehle and Reny:  Exercises 1.12, 1.15, 1.20, 1.21, 1.26, 1.27, 1.29
(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 A1.40, A1.42, A1.46, A1.47 A.1.48

Download these three  problems and work them.  
  Try to make some progress with Problems 2 and 3 before class Wednesday and be ready to answer
questions in class about it.  

Problems that you should work, but don't need to turn in:
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   


Week 3 (tentative schedule)

We will have our first midterm on Friday at the TA section meeting.  It will
deal with material assigned  in Weeks 1-3.  I won't ask you to turn in homework problems
this week, but do recommend that you work the assigned problems.

Answers for first midterm

Lecture Slides:  Calculus and Concavity
Quasi-concavity and hyperplanes

Reading Assignment:
 Jehle and Reny pp 42-50
Simon and Blume on Homogeneous and Homothetic functions, Chapter 20
 Charles Wilson's Lecture on Homogeneous and Homothetic functfile:///Volumes/tedb-1/public_html/Courses/GraduateTheoryUCSB/RooftopTheorem.pdfions
Simon  and Blume on Concave and Quasiconcave functions, Chapter 21 , pp 505-527

Proof that for differentiable concave functions, tangent line lies above the graph

Jehle and Reny pages 533-545, pp 551-595

Is Campbell Hall really a convex set?

Recommended problems:
An easy one?
If  this problem made you want to cry,  maybe economics isn't for you.


Jehle and Reny Appendix Exercises  A.1.32,  A.1.36,  A.1.49,  A.2.12,  A.2.13, A.2.14
Simon and Blume Problem 20.17
Simon and Blume Problem 21.2

Workouts     Problems  5.1,5.3, 5.7
  Problems 6.1, 6.3, 6.5,  6.13

Week 4

Reading Assignment:
Jehle and Reny pages 595-611

Jehle and Reny pp 50-60,
  Proofs of Properties of indirect utility functions

Proofs of Properties of Expenditure functions

Notes on Envelope Theory

Lecture Slides
Indirect Utility and Continuity
Expenditure Functions
Homework to do but not turn in:

Jehle and Reny  Exercises A. 2.9, A.2.19, A.2.20, A.2.24
Problem 1.50
Notes on Jehle Problem 1.50: indirect utility
Practice  problems on gradients and directional derivatives (not to be handed in) 
Homework to turn in
Jehle and Reny Exercises   1.53, 1.57,
1.64 (for 1.64, you should prove your answers)
Three problems found at this link.

Optional Readings from Kreps Microeconomic Foundations
 Continuity of Demand Functions
Functions and Correspondences and Berge's theorem

Week 5

Announcement:  There will be no class on Wednesday, the day before Thanksgiving holiday.


Useful properties of quasi-concave and homogeneous functions
Notes on Gorman Polar Form  (10/29/15  In response to a student's question, I have added a remark about monotonic transforms of Gorman polar form utility to these notes.)
Notes on Translated Homothetic Utility and Stone-Geary Utility
Jehle and Reny pp 60-63
Read Jehle and Reny pages 125-135.  I think that you will find this material to be reassuringly familiar.

Notes on the elasticity of substitution
Problems to hand in:
Jehle and Reny, 1.55 and 1.56
Problems on CES Functions
Problems with Funny Budgets

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


Week 6

Notes on When is a CES function concave?
 Notes on Separable Preferences

Homework (not to be handed in): 
  Exercises found in Notes on Separable Preferences

Second Midterm  this Friday in  your TA section meeting.   
Answers for Second Midterm

Will this question be on the midterm?

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

Be sure that you can do the problems in  Workouts Problems Chapter 12, but you don't need to hand them in.

Jehle and Reny
  Problems 2.21, 2.25, 2.26 2.27
Also Problems at this link.

Week 8  
Further discussion of Expected Utility Theory
Classroom exercise-- Finding von Neumann Morgenstern utilities by survey
Results of Classroom Exercise
Update: Kent Strauss used MatLab to graph the estimated utility of income functions from classroom surveys taken in 2015 and 2016.
I have attached his graphs to the file at this link.
As part of your homework,  find some interesting things to say, based on the results of this classroom exercise.

Optional Readings:  (If you want to follow up on the empirics of estimated values of risk to life)
Kip Viscusi on Value of Statistical Life
 Viscusi and Aldy on Value of a Statistical Life

Required  Reading  Soldiers of Fortune
Homework to hand in: Work the problems at this link.
Jehle and Reny Problems 2.32, 2.33, 2.34

Week 9 

Reading Assignment
Jehle and Reny, Section 2.3, Revealed Preference
Revealed Preference,  from Microeconomic Analysis by Hal Varian
Lecture notes on revealed preference
Lecture notes on Pure Exchange Equilibrium
Jehle and Reny Chapter 3, pp 135-145

Week 10

 Pure Exchange Equilibrium
Lecture notes on 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 and Reny  pp  201-206

2016 Final Exam with Answers