Economics 201b
Spring 2010
Solutions to Problem Set 7
John Zhu
1a. Suppose there is a portfolio z such that Rz 0 and Rz = 0. Then q z = Rz > 0. If,
however, we only have 0, then it is possible that th
Matthew Rabin
Department of Economics
University of CaliforniaBerkeley
Economics 201A
Fall 2010
Problem Set D
Handed Out: Tuesday, November 23. Optimal perception for when problems are due: tuesday,
D
35. Both fair values and subsequent growth of the investee are not as relevant for investments in which of the
following categories?
A.
B.
C.
D.
Securities reported under the equity method.
Trading se
Economics 201BSecond Half
Lecture 13, 4/27/10
Uncertainty, including GEI Model
GEI (General Equilibrium, Incomplete Markets) Model studies situations in which markets are incomplete: there are restri
Econ 201A
Fall 2010
Problem Set 2 Suggested Solutions
1. Prove that the lexicographic preference (dened in Example 3.10 in the course notes)
is complete, transitive, and antisymmetric (if x y and y x,
Econ 201A
Fall 2010
Problem Set 1 Suggested Solutions
1. Suppose
(a) x
is a preference relation. Prove the following:
y and y
z imply x
z;
Proof. By denition, x
y implies x
y ; and y
z implies y
z . T
201B Final Spring 2004
Answer all of the questions below. Be as complete, correct, and concise as possible. There
are 6 questions for a total of 180 points possible. You have 180 minutes to complete t
Matthew Rabin
Department of Economics
University of CaliforniaBerkeley
Economics 201A
Fall 2010
Problem Set C
Handed Out: Thursday, November 4.
Optimal Perception for when it is Due: Monday,
November
Economics 201b
Spring 2011
Chris Shannon
Problem Set 3 Due Thursday April 7
1. Consider a production economy with three goods (two outputs denoted good 1 and good 2,
and one input, denoted good 3), tw
201b Final Spring 2008
Answer all of the questions below. Be as complete, correct, and concise as possible. There
are 6 questions for a total of 180 points possible. You have 180 minutes to complete t
Econ 201A
Fall 2010
Problem Set 4 Suggested Solutions
1. MWG 3.G.15. Consider the utility function
u(x1 , x2 ) = 2 x1 + 4 x2
(a) Find the demand functions for goods 1 and 2 as they depend on prices an
5
Consumer behavior, part 1
5.1
Walrasian demand
Consider an economy with n goods or commodities. The consumer can use her fixed wage to
purchase weakly positive amounts of these goods at exogenous st
Economics 201b
Spring 2011
Problem Set 4 Solutions
1. A common misperception about the boundary condition on excess demand is to
think that it says that if the price of a good goes to zero, then exces
114.Under IFRS No. 9: which is not a category for accounting for investments?
A.
B.
C.
D.
Fair value through profit and loss.
Fair value through other comprehensive income.
Held-to-maturity.
Amortized
Section 2 : Choice, Preferences, and Utility
ECON 201A, Fall 2010
GSIs: Omar Nayeem and Aniko Oery
These notes were originally prepared by Juan Sebastin Lleras during the Fall 2007 semester and have s
8
The Mixture Space Theorem
Let be a convex subset of Rn , i.e. if , , then + (1 ) for all (0, 1).
Definition 8.1. A binary relation % on is independent if, for all , , and (0, 1),
% + (1 ) % + (1 ).
10
Anscombe and Aumann Expected Utility
Let be a finite set of m states of the world, with generic elements s, t . Let X be a finite
set of n consequences with a generic element x X. It will often be
Econ 201A (2011)
Microeconomic Theory I
Haluk Ergin
Game Theory - Basics II
General Extensive Form Games and
Sequential Equilibrium
An extensive form game
l
(5,-2)
t
1
c
a
r
2
m
y
z
x
b
y
2
y
(2,0)
x
Econ 201A (2011)
Microeconomic Theory I
Haluk Ergin
Repeated Games with Observable
Actions (Perfect Monitoring)
Repeated Games with Observable Actions
Let G = (N, A, u) be a finite normal form game. L
Econ 201A (2011)
Microeconomic Theory I
Haluk Ergin
Reputation Formation
Reputation & Equilibrium Selection
in Games with a Patient Player
Fudenberg & Levine (1989)
Repeated Games with one Long-Run an
Theorem 2.30 shows that we can check the rationality of C by verifying certain axioms.
We now will apply the theory of choice to a specic application, namely the direct study of
consumer choice. In th
1. C meets Sens and ;
2. C meets Houthakkers axiom;
3. C is rationalizable.
Proof. We will show (1) implies (2) implies (3) implies (1).
Step 1: Sens and imply Houthakkers Axiom. Suppose C meets Sens
1
Binary relations
Denition 1.1. R X Y is a binary relation from X to Y . We write xRy if (x, y ) R and
not xRy if (x, y ) R.
/
When X = Y and R X X , we write R is a binary relation on X .
Exercise 1
complete and transitive preferences over cfw_a, b, c as follows:
a
1
b
1
c
b
2
a
2
c.
c
3
a
3
b
Now suppose we let
C (A) = cfw_x A : |cfw_i : x C i (A)| |cfw_i : y C i (A)|, for all y A.
In words, x C
Section 7 : vNM expected utility, AA expected utility & Risk
ECON 201A, Fall 2011
GSIs: Aniko Oery and Mich`ele M
uller
These notes were originally prepared by Juan Sebasti
an Lleras during the Fall 2
Econ 201A (2011)
Microeconomic Theory I
Haluk Ergin
Game Theory - Basics I
Normal Form Games
Game Theory
How may a group of self-interested
individuals behave if each of them
is affected by the others
Section 2 : Choice, Preferences, and Utility
ECON 201A, Fall 2011
GSIs: Aniko Oery and Mich`ele M
uller
These notes were originally prepared by Juan Sebasti
an Lleras during the Fall 2007 semester and
Section 5 : Afriats Theorem
ECON 201A, Fall 2011
GSIs: Aniko Oery and Mich`ele M
uller
These notes were originally prepared by Juan Sebasti
an Lleras during the Fall 2007 semester and have since been
Fetr.l.3i I
s
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