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Unformatted text preview: Problem Set 1
ECOS3012 Strategic Behavior, 2011 Note. Just a couple of problems to get the hang of “Expected Utility” calculation and
some of its implications. Solutions will be taken up during Lecture 2.
Problem 1. Consider an urn ﬁlled with 100 balls, colored blue, red and yellow in some
unknown proportions. One ball will be drawn from this urn and the amount of money
you win depends on the color of the ball that is drawn. How much you win depends on
the lottery/action that you will choose. Since the payoﬀ depends only on the color of the
ball that is drawn, there are 3 states of the world, Ω = {r, b, y }. The four possible actions
available to you are shown in the table below: f 1 for instance is the lottery that pay $100
if r color ball is drawn and $0 otherwise.
f1
f2
f3
f4 b
0
100
0
100 y
0
0
100
100 r
100
0
100
0 Suppose u(x) denotes the utility of receiving $x of money and that the agent believes
that the probability of the three outcomes is pb , p y and pr.
1. Write down the expected utility of each action.
2. It is possible that the agent has a preference f 1 ≻ f 2 but f 4 f 3? Problem 2. Suppose that there are two states of the world, accident and safe. A consumer
who consumes ends ca > 0 units in state a and cs > 0 in state s is assumed to derive a utility
β
V (ca , cs) = cαcs
a where α > 0 and β > 0. Does this consumer satisfy the expected utility hypothesis?
Hint : Recall that a consumer’s preferences are ordinal. Think of taking a monotonic transformation of the above function so that the expression looks like an “Expected Utility”
calculation. ...
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This note was uploaded on 08/20/2011 for the course ECON 101 taught by Professor Etw during the Spring '11 term at UniversitÃ di Bologna.
 Spring '11
 etw
 Utility

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