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Econ 451: Homework 3
(Due Mar. 4)
1. Consider a classical overlapping generations model. Population grows by
20%
each
generation. Each agent is endowed with
8
units of consumption good when young
and nothing when old. When young, each agent consumes half of her endowment and
invests the other half into money and capital.
If
k
units of consumption goods are invested into capital this period, then next
period, output will be
f
(
k
) = 3 log(1+
k
)
. The marginal rate of return on capital
is, therefore, given by
f
0
(
k
) =
3
1+
k
, which is decreasing in
k
.
The money supply is growing
60%
each period. Seigniorage revenue is used to
g
is
constant over time, so total government expenditure at period
t
is
G
t
=
N
t
g
; it
grows by the same rate as population growth,
20%
each period.
Agents treat &at money and capital investment as perfect substitutes; they are both
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This note was uploaded on 04/06/2010 for the course ECON 0 at Pennsylvania State University, University Park.
 '09
 DR.BONNIEBAFFOE
 Microeconomics

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