Problem Set - chapter 17-18
Econ 6233
Spring 2005
1. Suppose person 1 has a utility function U 1 ln x1 ln y1 while person 2 has utility U 2 ln x2 ln y 2 .
Person 1 starts with an endowment of 8x and 2y. The total amount of x in the economy is 10 and the t
Final Exam
Econ 6233
Spring 2005
Solution:
1) a)
i) x for sure
ii) y with probability or 0 with probability 1 -
y x x / y
b)
Jack believes y with probability p.
EU = pU(y) = U(x)
x y
x
EU pU
(1 p )U
2
2
Compare and show
x y
x
pU
(1 p )U pU
Final Exam
Econ 6233
Spring, 2004
1. Suppose a plaintiff and a defendant are negotiating a settlement as a result of a car
accident. The damages have been established to be $10,000, but the question is
whether the defendant is truly liable for the acciden
Econ 6233
Exam 1
Spring 2004
1.
Recall that a monopolist always produces on the elastic portion of the demand curve.
a) Is the same thing true for an oligopolist in a homogeneous, Cournot market? (Look at the
first order conditions).
b) Now assume that th
Problem Set - externalities
Econ 6233
1. For the problem we worked in class, show that internalizing the externality produces
the optimal output for both firms.
2. Now suppose firm 1 from problem 2 above produces X using only K but is adversely
affected b
Exam 1 Solutions
1) a)
= P(Q)Q C(Q)
d/dQ = P(Q) + P(Q)Q C(Q) = 0
add I
= P(Q,I) + PQ(Q,I)Q C(Q) 0
:
dP
dP
d 2P
d 2P
dQ dI Q
dQ Q
dI C ' ' (Q)dQ 0
dQ
dI
dQdI
dQ 2
dP
d 2P
Q
dI
dQdI
dQ / dI
2
dP
d P
Q
C ' ' (Q)
dQ
dQ 2
b)
P(Q,I) (1 + 1/) = MC
1/ becomes
Problem Set #1
Monopoly, Game Theory
1. Consider a monopolist facing customers in two markets. The first market has a
demand curve of P=20-2Q and the second has a demand of P=40-2Q. The monopolist
has marginal cost equal to 0.
a. If the monopolist can sep
Expectations for the Martin Chair in Economics
1. Produce research in nationally and internationally recognized peer reviewed
journals, scholarly books and book chapters and participate in national and
international conferences.
2. Provide academic leader
Problem Set # 3
Solution
1) 11.9:
EU 1 / 2 4 12 1 / 2 4 0 3
When is utility equal to 3?
4 p 3 p 5
2) 11.10:
max ln(w+x)+(1-)(w-x)
d
1
1
(1 )
( 1) 0
dx
w x
w x
Solve for x:
x = w (2-1)
when = 1/2, x = 0
3) 11.11:
U(w) = - 1/w
1
1
1
p
w (1 p ) w w
Problem Set - externalities
Econ 6233
Spring 2002
1. For the problem we worked in class, show that internalizing the externality produces
the optimal output for both firms.
2. Now suppose firm 1 produces X using only K but is adversely affected by the
pro
Problem Set -risk, externalities
Econ 6233
Spring 2005
1.
2.
3.
4.
Varian 11.9
Varian 11.10
Varian 11.11
Consider 2 gambles:
A: With probability 2/3 you receive payout of 10
With probability 1/3 you receive 20
B: With probability 1/3 you receive 5
With pr