Homework 4, Econ 606
Jonathan Heathcote
Due in class, Tuesday March 28th
Consider the following economy
Each period a continuum of mass
(1
−
δ
)
agents are born at age
0
Agents survive from age
a
to
a
+1
with constant probability
δ.
The total population is
(1
−
δ
)(1 +
δ
+
δ
2
+
...
)=1
Assume the environment is stationary, so we need not worry about time
subscripts
Agents maximize expected utility, which is given by
E
∞
P
a
=0
(
βδ
)
a
u
(
c
a
)
where
u
(
c
)=
c
1
−
γ
1
−
γ
Agents are subject to idiosyncratic wage shocks that are
iid
across agents.
Agents supply one unit of time per period. The initial wage at age zero is
lognormally distributed:
ln(
w
0
α
0
˜
N
³
−
v
0
2
,v
0
´
Wages subsequently evolve according to
α
a
+1
=
α
a
+
ω
a
+1
a
≥
0
ω
a
+1
˜
N
³
µ
−
v
ω
2
ω
´
where the actual (level) wage is
w
a
=exp(
α
a
)
.
The market structure is as follows. Agents are endowed with zero wealth
at birth. Then they can trade bonds at a constant price
q.
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 '05
 would
 Economics, Thermodynamics, Utility, idiosyncratic wage shocks, crosssectional consumption inequality

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