Homework 5 Solutions
Question 1
a) We can write the expected utility as
EU =
1
1
ln (w + h) + ln (w d)
2
2
the first-order condition for this problem is
1
h
1 (d)
dEU
=
+
=0
d
2 w + h 2 w d
which we can solve to get
=
w
2
1
1
d h
.
c) d1 is decreasing in
Homework 4 (Due April 19)
Question 1
John has an initial wealth of $10000, including the value of his car, which he
is considering insuring. He figures that if he has an accident, there are two
possible scenarios that could occur: he might damage only his
Homework 5 (Due April 28)
Question 1
Exercise 4.1 a), c), and d)
Question 2
Exercise 4.2 a) and b). (Adding the background risk is the same as assuming
that the initial wealth is random, with a distribution given by 21 , 8; 12 , 12 ,
instead of being alwa
Econ 417 Homework 3 Suggested solutions
March 23, 2016
Question 1
No. They cant be ranked. This is because FL (5) =
7
.
FL (20) = 34 > FM (20) = 12
2
4
< FM (5) =
7
12 ,
but
Question 2
Cumulative probability
Cumulative $1 $2 $4 $8 $10
A
15 40 70 80 100
B
Homework 2 (Due Feb 16th)
Question 1
For each of the following utility functions, determine what attitude to risk they
display (risk-averse, risk-loving, or risk-neutral) and calculate the Arrow-Pratt
measure of risk aversion (as a function of x).
1. x
2.
Homework 3 (Due March 22)
Question 1
Consider the following lotteries:
L $0, $5, $20, and $50 with equal probability
M
1
4
probability of $0,
bility of $50
1
3
probability of $5,
1
4
probability of $30, and
1
6
proba-
Does M first-order stochastically dom
Homework 1 (Due Feb 4th)
Question 1
Suppose that an agent has the following utility function for outcomes: u ($0) =
1, u ($10) = 4, u ($20) = 5. For each of the following lotteries, compute their
expected value and their expected utility.
1. 21 , $0; 21 ,
Homework 4 Suggested Solutions
Question 1
The situation is summarized as follows:
Scenario
Only his
Probability
20%*50%=10%
Loss
$1000
Final Wealth
$9000
Expected Wealth
His and the other
20%*50%=10%
$5000
$5000
$9400
No accident
80%
$0
$10000
a) Buying a