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3 Risk, Uncertainty
So far we assumed that people’s choices are not uncertain  once they decide how to spend their
income, they get what they want. However, very often this is not true and people makes choices
that involve incomplete information (unknown quality of used car, future value of investment,
...
)
These events have not certain outcome but
expected outcome (expected value.)
Example:
Suppose that a consumer currently has $10 of wealth and is contemplating a gamble
that gives him a 50 percent probability of winning $5 and a 50 percent probability of losing $5.
His wealth will therefore be random: he has a 50 percent probability of ending up with $5 and a
50 percent probability of ending up with $15. The
expected value
of his wealth is:
1
2
*
$5 +
1
2
*
$15 = $10
Generally,
R
E
=
X
π
i
R
i
,
where
R
i
are possible outcomes and
π
i
are their probabilities.
Fair gamble (game)
A friend of yours oﬀers you to play the following game: ”Bet 100CZK and we will ﬂip the coin. If
we get a Head you will get additional 50CZK if we get a Tail you will lose 100CZK that you bet.”
Will you accept this kind of game? The
expected proﬁt
of this game is
0
.
5
·
50 + 0
.
5
·
(

100) =

25
The expected proﬁt is negative and therefore you should refuse this game.
Instead, you oﬀer your friend a following game: ”Bet 110CZK and we will ﬂip the coin. If we get
a Tail you will get additional 90CZK if we get a Head you will lose 110CZK that you bet.” Will
your friend accept? His expected proﬁt is
0
.
5
·
90 + 0
.
5
·
(

110) =

10
The expected proﬁt is negative and therefore your friend should refuse this game.
The only possible game that you both will agree to play is as follows: ”Bet 100CZK and we will
ﬂip the coin. If we get a Head you will get additional 100CZK if we get a Tail you will lose 100CZK
that you bet.” In this game your expected proﬁt as well as the expected proﬁt of your friend is
0CZK and we refer to it as a
fair game
.
10
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 Spring '11
 mark
 Microeconomics

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