Department of Economics
Prof. Derek DeLia
Health Economics 220:316:01
Spring 2010
HOMEWORK #3
This assignment is for practice purposes only. It will not be graded or collected.
1.) Consider a consumer with expected utility function U(X) = ln(X). The consumer has
wealth equal to $100,000 and faces the following risk: lose $1,000 with probability 0.1,
lose $10,000 with probability 0.01, and lose nothing with probability 0.89.
a.
Is the consumer risk averse?
b.
What is the maximum this consumer would be willing to pay (WTP) for full
insurance against this risk?
c.
What is this consumer’s risk premium?
2.) Consider a consumer with utility function U(W) = a + bW
c
where W is wealth and a,b,
and c are constants with the following restrictions: b>0, c>0, and a can be any number.
Assume the consumer has a wealth endowment of $25,000 and faces the following risk:
lose 5,000 with probability 0.05 and lose nothing with probability 0.95.
a.
For what values of a, b, and c, would this consumer be considered risk averse?
b.
Suppose a=0, b=2, and c=0.8. What is this consumer’s risk premium for full
insurance against this risk?
c.
How would your answer to part b change if a ≠ 0?
d.
Use the answer to part b to draw an expected utility diagram showing the consumer’s
WTP, expected loss, and risk premium.
3.) Consider a consumer with utility function
3
.
0
10
)
(
W
W
U
=
. Assume the wealth
endowment is $400,000 and the consumer will lose $50,000 with probability 0.05 and
lose nothing with probability 0.95. The consumer can choose an amount of insurance
a
where
1
0
≤
≤
a
. (If
0
=
a
, the consumer buys no insurance; if
1
=
a
, the consumer fully
insures against the risk.)
a.
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 Spring '10
 DELIA
 Economics, Utility, insurance policy

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