Welcome to the Economics 210A Website. If you are
taking this course, please check this site regularly. I
announcements about assignments. The syllabus that you see is a
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.
|The main textbook for this course is Advanced
Theory, by Geoffrey Jehle and
Reny. I have also ordered the massive Microeconomic
Theory, by Andreu Mas Collel, Michael Whinston and
bookstore. You will be using this text i
n other courses this term
and I will assign occasional readings from it. A third
that we will use occasionally is the svelte Lectures
Economic Theory by Ariel
buy a hard copy of the Rubinstein book for about $30 from Amazon.com.
probably be worth the Amazon price if that were the only way
get it, but
Professor Rubinstein has put it online
free. Another slim and beautiful economic
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 2011Final Exam With Answers
Some Old ExamsMidterm 2007
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
|Problems will be assigned
week. You will be required to work them and turn them in.
should be neat and legible. Unless you have unusually
handwriting, I recommend typing your homework.* Late
will not be accepted. I have
no objections to your working together, but I will ask you
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.
(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
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.)
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
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
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.
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.
elasticity of substitution
Problem set to hand in:
Problems on CES Functions
Arrow Chenery Minhas Solow paper on CES production functions
Remarks by Arrow on history of ACMS paper
Notes on Separable Preferences
Turn in Problems on CES Functions
and Exercises found in Notes on Separable Preferences
Answer sheet for Midterm
| 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
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
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)
|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