DISCUSSION SECTION 5
Risk and Uncertainty

Expected Utility
:
)
(
...
)
(
)
(
2
2
1
1
N
N
x
U
p
x
U
p
x
U
p
EU
×
+
+
×
+
×
=
,
1
1
=
∑
N
i
p

A premium
is a payment to an insurance company in return to a commitment to pay a claim in a
possible future event.
A fair insurance
is an insurance policy for which the premium is equal to the expected value of
the claim.

An individual is riskaverse
if he strictly prefers a certain payment to an uncertain payment with
the same expected value.
Riskaverse individuals have diminishing marginal utility.

QUESTION 1
Maria has invested her savings to a lottery. Next week, there is a 25% chance that she will get
$400, otherwise she will get $1,600. Her utility is given by:
x
x
U
=
)
(
.
a. What is Maria’s expected income next week?
b. What is her expected utility?
c. What is Maria’s expected utility if she received the value of the expected income with
probability one? Is it smaller or bigger than the value in part b? Is Maria riskaverse, risk neutral
or risklover?
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 Spring '08
 Hansen
 Microeconomics, Supply And Demand, Utility, demand function

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