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 the nonzero coordinates of and the
nonzero coordinates of
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 restrictions on the allowed trades
Six Models
V(a): DC
V(b):
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 securities.
Held-to-maturity securities.
Securities avail
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,
December 7. Problems are due: never. (Hence, the usual "
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, then x = y ).
Proof. Completeness Let x, y R2 be given
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 and wealth.
If you set up the Lagrangian
L(x1 , x2 , ) =
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 the
exam. Use the points as a guide to allocating your 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 22. Is due Tuesday, November 30, 12:39 p.m.
:
,
* Probl
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), two consumers, and two rms. The rms have production
funct
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 strictly positive prices.
Definition 5.1. Given a utility
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 the
exam. Use the points as a guide to allocating your t
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 excess demand
for that good goes to innity. Although intuiti
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 cost.
115.Which of the following is NOT true about the
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 since been
a
revised by Juan Sebastin and us. We are gra
9
von Neumann and Morgenstern Expected Utility
Let X be a finite set of size n and X be the space of probabilities on X, which can be represented
as
X = cfw_ Rn :
n
X
i = 1 and i 0, i,
i=1
by enumerating X = cfw_x1 , x2 , . . . , xn and letting (xi ) = i
Section 3 : Utility and Walrasian demand
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
revised by Juan Sebasti
an, Omar Nayeem an
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 and .
Assume x, y A B , x C (A), and y C (B ). Applying
Section 1 : Preference and Choice
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
revised by Juan Sebasti
an, Omar Nayeem and us. W
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 1.2. Suppose R, Q are two binary relations on X . Prove
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 (A) if there is no alternative which would be chosen b
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 2007 semester and have since been
revised by Juan Sebast
Proposition 2.10. If
is a preference relation, then C (A) = whenever A is nite.
Proof. The proof is by induction on the size of |A|. Base step: |A| = 1. Then if x A, x
x by
completeness and the only element of A is x, so C (A) = cfw_x.
Inductive step. Sup
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 the classic study of demand, which we study next, studies
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 and
many Short-Run Players: The Complete
Information Benc
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. Let G(T )
denote the extensive form game where:
At each
11
Basics of Savage expected utility
This entire section is totally optional.
In both the von NeumannMorgenstern and AnscombeAumann models, we assumed the existence of
some objective randomizing device. Ideally, all uncertainty in the model would be subje
7
Producer behavior
Definition 7.1. A production set is a subset Y Rn .
Definition 7.2. Y satisfies:
no free lunch if Y Rn+ cfw_0n ;
possibility of inaction if 0n Y ;
free disposal if y Y implies y 0 Y for all y 0 y;
irreversibility if y Y and y 6= 0n
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
revised by Juan Sebasti
an, Omar Nayeem and us. We are