Econ 4721: Money and Banking, Fall 2009
Homework 1 Answer Key
Problem 1
(a)
A feasible consumption allocation for this economy is two sequences,
{
c
1
,t
}
and
{
c
2
,t
}
for
t
= 1
,
2
, . . .
satisfying:
N
t
c
1
,t
+
N
t

1
c
2
,t
≤
N
t
y
1
+
N
t

1
y
2
Other acceptable conditions for feasibility, using the assumptions for this problem,
Nc
1
,t
+
Nc
2
,t
≤
Ny
1
c
1
,t
+
c
2
,t
≤
y
1
Nc
1
,t
+
Nc
2
,t
≤
N
*
30
c
1
,t
+
c
2
,t
≤
30
(b)
A Pareto efficient stationary allocation:
1. Is a stationary feasible allocation  two numbers (
c
1
, c
2
) satisfying
c
1
+
c
2
≤
y
1
2. Has the property that no individual can be made better off without harming another
individual.
Or, solves the problem of maximizing the utility of each member of future generations
subject to the feasibility constraint
max
c
1
,c
2
ln (
c
1
) +
β
ln (
c
2
)
subject to:
c
1
+
c
2
≤
y
1
1
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(c)
The Pareto efficient stationary allocation is found by solving the maximization problem,
max
c
1
,c
2
ln (
c
1
) +
β
ln (
c
2
)
subject to:
c
1
+
c
2
≤
y
1
The first order condition for this problem is:
1
c
1
β
c
2
= 1
So,
c
2
=
βc
1
c
2
=
y
1

c
1
βc
1
=
y
1

c
1
c
1
=
y
1
1 +
β
=
30
1
.
5
= 20
c
2
=
βy
1
1 +
β
=
0
.
5
*
30
1
.
5
=
30
3
= 10
(d)
A competitive equilibrium without money must involve no trade.
Consumers are not
willing to exchange because the young cannot trade with the old.
There is absence of
double coincidence of wants. The old consumers want what the young have (consumption
now) but the old don’t have what the young want (consumption tomorrow), because the
old will not be alive tomorrow.
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 Spring '10
 SatoshiTanaka
 Economics, Inflation, Monetary economics, Quantity Theory of Money

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