1
Econ. 511b
Spring 1998
G. Hall and C. Sims
Final Exam
The exam contains five questions.
Answer all five questions.
Points for each question are
indicated beside the question.
If you spend one minute per point you will use two hours and 35
minutes.
You will have 3 hours to finish the exam.
1.
(45 points) Consider an economy in which identical agents maximize
E
C
L
t
t
t
t
±
²
±
²
±
²
³
´
µ
¶
³
´
µ
log
2
0
·
¸
(1)
subject to
C
B
P
R
B
P
A L
t
t
t
t
t
t
t
t
t
¶
¶
·
¶
²
²
³
´
1
1
,
(2)
B
t
¸
0 ,
(3)
choosing time paths for
B
,
C
and
L
, taking
A
,
P
and
R
as given.
As usual, agents know all
variables dated
t
and earlier when making choices dated
t
, but do not know the values of variables
dated later than
t
when making choices at
t
.
The government budget constraint is
B
P
R
B
P
G
t
t
t
t
t
t
t
¶
³
¶
²
²
³
1
1
,
(4)
where
G
is real government purchases.
Government policy sets
R
R
t
³
³
²
±
1
(5)
³
³
t
t
C
³
(6)
G
C
G
t
t
³
.
(7)
Note that the relationships in (6) and (7) characterize the behavior of the economywide average
of taxes and spending.
Individuals as usual treat taxes as lumpsum, i.e. as invariant to their
individual consumption choices.
We assume that the economy starts up with a positive
B
.
a) Find the firstorder conditions for a solution to the consumer’s optimization problem.
b) Show that the economy has a competitive equilibrium in which
PC
t
t
remains constant.
c) Show that this equilibrium is unique.
[It is likely to be helpful to divide the government
budget constraint (4) by
C
t
and to take
E
t
²
1
of it, using the FOC with respect to
B
.]
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d) Find the the equilibrium paths of
P
,
C
and
L
as functions of constants and the disturbance
A
t
.
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 Spring '11
 Tikk
 Economics, Trigraph

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