Review Problems: Money in OLG Models
Econ720. Fall 2009. Lutz Hendricks
1
Government Purchases
Consider a twoperiod OLG model with money. At each date
t
a cohort of size
N
t
= (1 +
n
)
t
is born. Each household lives for two periods and derives utility from consumption at both ages
according to
u
(
c
y
t
;c
o
t
+1
)
Households receive endowments of goods when young
(
e
t
)
that cannot be stored. The only as
set available is money which is injected into the economy through government purchases. The
government buys
G
t
=
g
t
N
t
goods in each period and throws them into the ocean.
(a) Write down the government budget constraint. is. Show that it can be written as
P
t
=P
t
+1
= (1 +
n
m
t
+1
g
t
+1
)
=
m
t
where
m
=
M=
(
PN
)
denotes real, per capita money balances.
function.
(d) The money market clearing condition is
m
t
=
s
(
P
t
=P
t
+1
)
where
s
is a saving function. For what follows assume that
g
is constant over time and that
s
(1 +
n
)
>
0
(Samuelson case). Also assume that the o/er curve is convex, but not backward
bending. Using
m
t
=
s
((1 +
n
m
t
+1
g
t
+1
)
=
m
t
)
;
(1)
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 '09
 LUTZHENDRICKS
 Equilibrium, Inflation, Utility, Economic equilibrium, OLG models

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