Economics 206
Spring 2007 (Prof. G. Loury)
Assignment 3: Applications of Stochastic Dominance
1. Let
α
≥
0
be a random variable representing a worker’s true ability.
Consider two
tests of worker ability,
i
=1
,
2
, with test scores
t
1
and
t
2
given by:
t
1
=
α
+
ε
and
t
2
=
α
+
ε
+
η,
where
ε
and
η
are realvalued, zero mean, statistically independent random variables
representing error in the testing process. Suppose that a worker with test score
t
is
paid a wage equal to his conditional mean ability, given that test score. Thus:
μ
i
(
t
)=
E
[
α

t
i
=
t
]
,i
=1
,
2
.
gives the wage of a worker whose score on test
i
is
t.
Show that the population dis
tribution of wages under test
i
=1
is “more unequal” (i.e., “riskier” in the sense of
secondorder stochastic dominance) than is the population distribution of wages under
test
i
=2
.
2. Consider an expected utility maximizing agent who does not know how much money
is in his bank account. Let
˜
y
≥
0
be this uncertain balance, with
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 Spring '07
 G.LOURY
 Economics, Microeconomics, Probability theory, CDF, secondorder stochastic dominance, ﬁrst period

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