Partial Answers: Final Practice Questions
May 5, 2006
Question 1
Solve for the price of stocks,
p
t
Let’s assume that the total income of the young is
y
t
,
so per capita income
of the young is
y
t
/
(1
−
δ
)
(we could assume
y
t
is per capita income for the young  the expressions
would end up slightly di
ff
erent, but with exactly the same
fl
avor)
Given the conjecture for individual consumption rules, aggregate consump
tion is given by
C
t
=
(1
−
δ
)
∞
P
a
=1
δ
a
−
1
c
a
t
=
(1
−
δ
)
∙
(1
−
βδ
)
y
t
1
−
δ
+
δ
(1
−
βδ
)(
s
2
t
(
p
t
+
d
t
)) +
δ
2
(1
−
βδ
)(
s
3
t
(
p
t
+
d
t
)) +
...
¸
=
(1
−
δ
)(1
−
βδ
)
∙
y
t
1
−
δ
+
δ
(
s
2
t
(
p
t
+
d
t
)) +
δ
2
(
s
3
t
(
p
t
+
d
t
)) +
...
¸
=
(1
−
βδ
)
y
t
+ (1
−
δ
)(1
−
βδ
)(
p
t
+
d
t
)
£
δ
(
s
2
t
) +
δ
2
(
s
3
t
) +
...
¤
=
(1
−
βδ
)(
y
t
+
p
t
+
d
t
)
where in the last step we use the fact that the old, in total, hold all the shares,
so
(1
−
δ
)
£
δ
(
s
2
t
) +
δ
2
(
s
3
t
) +
...
¤
= 1
From market clearing
C
t
=
y
t
+
d
t
Combining the two expressions for
C
t
gives the equilibrium price
p
t
=
βδ
(
y
t
+
d
t
)
1
−
βδ
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 '05
 would
 Trigraph, per capita, Per capita income, Economic equilibrium

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