1
Economics 5202
Fall 2009
Exercise 6
Due date:
To be collected at the beginning of class on Tuesday, October 27.
Note:
The usual policy on cheating and plagiarism applies for this exercise.
1.
Suppose the utility function of a representative young agent is:
1,
2,
1
ln(
)
ln(
),
0
t
t
U
c
c
β
β
+
=
+
>
.
Each agent receives
y
endowment when young and nothing when old.
There is a fixed stock of money,
M, which is evenly distributed among the initial old.
a.
Write down the representative agent’s budget constraint when young and when old, and derive the
lifetime budget constraint.
b.
Show that the demand for real money balance is
1
t
t
t
y
v m
q
β
β
≡
=
+
.
c.
Derive the expressions for
*
1,
t
c
and
*
2,
2
t
c
+
, where “*” denotes equilibrium.
d.
Give an interpretation of the parameter
β
, and describe the effects on
*
1,
t
c
and
*
2,
2
t
c
+
when
β
increases.
2.
Consider an economy with a constant population of N = 100. Individuals are endowed with y = 20
units of the consumption good when young and nothing when old.
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 '09
 DR.BONNIEBAFFOE
 Economics, Microeconomics, Utility, Fiat Money

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