Econ 4721: Money and Banking, Fall 2009
Homework 2
Wednesday, October 14, at the beginning of class.
Problem 1. Inﬂation
Consider an overlapping generations model in which consumers live for two periods. The
number of people born in each generation grows in each period, according to
N
t
=
nN
t

1
,
where
n
= 1
.
2. In each period, young consumers are endowed with
y
= 60 and old
consumers are endowed with 0 units of the single consumption good. Each member of
the generations born in period 1 and later have the following utility function:
u
(
c
1
,t
,c
2
,t
+1
) = log
c
1
,t
+
β
log
c
2
,t
+1
(1)
with
β
= 0
.
5.
Members of the initial old generation only live for one period and have utility
u
(
c
0
,
1
) =
log
c
0
,
1
.
The government expands the money supply by a factor of
z
each period,
M
t
=
zM
t

1
.
Assume that
z
= 1
.
5. The money created each period is used to ﬁnance a lumpsum
subsidy of
a
t
+1
goods to each old person.
(a) Solve for the (stationary) Pareto eﬃcient allocation. The answer should be two num
bers
(
c
PO
1
,c
PO
2
)
.
(b) Write the government’s budget constraint in period
t
+ 1.
(c) Deﬁne a competitive equilibrium with money for this economy.
(d) Solve for the rate of return of money (
v
t
+1
/v
t
) and the growth rate of the price level
(
p
t
+1
/p
t
) in a stationary equilibrium. The answer should be two numbers.
(e) Solve for the consumption allocation (
c
*
1
,c
*
2
) and a lumpsum subsidy
a
*
in a stationary
equilibrium. The answer should be three numbers.
1
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View Full Document(f) Verify that agents prefer the Pareto Optimal allocation to the competitive equilibrium
allocation with inﬂation.
(g) Illustrate the Pareto Optimal allocation
(
c
PO
1
,c
PO
2
)
and the competitive equilibrium
allocation (
c
*
1
,c
*
2
) on the (
c
1
,c
2
) plane. Your graph should also include the feasibility
line, the lifetime budget constraint, and their indiﬀerence curves.
Problem 2. Financing Government Expenses
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 Spring '08
 Staff
 Economics, Inflation, Foreign exchange market, United States dollar, stationary equilibrium

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