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Econ 387L: Macro II
Spring 2008, University of Texas
Instructor: Dean Corbae
Problem Set #4 Due 2/14/08
1. Consider the following
static
version of the Hansen (1985) indivisibility paper. There
is a unit measure of exante identical agents. There are only two possible number of hours
per worker
h
∈
{
0
,
h
}
,
h<
1
, which implies there are only two possible levels of leisure
an agent can derive utility from given the normalization that
1=
h
+
c.
Let preferences be
given by
u
(
C, c
)=(1
−
α
)ln
C
+
α
ln
c.
The production technology is given by
y
=
zh
θ
with
θ<
1
where
z
is the state of technology.
a. Suppose that a planner has access to a randomization device which she can program
such that
π
=
prob
(
h
t
=
h
)
.
Assume further she can set this device to be i.i.d. across
all households, can see the outcome of the realization of the device in each case, and can
enforce that outcome. Given the state of technology
z,
state the planner’s problem using
the notation that a realization of the lottery which entails the agent should work (should not
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 Spring '07
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