Economics 154a, Spring 2005
Intermediate Macroeconomics
Problem Set 4: Answer Key
1. Consider an economy that consists of a single consumer who lives for two time periods.
The consumers income in the current period is Y and the consumers income in the
future period is
Y
f
...
(a) Let
Y
= 2100,
Y
f
= 1050,
G
=
T
= 0
.
3
Y
,
G
f
=
T
f
= 0
.
3
Y
f
, and
r
= 0
.
1.
Find C and
C
f
. What is national saving in the current period, i.e., what is
S
=
Y

C

G
?
ANSWER: We can ﬁnd consumption and saving by solving:
C
+
C
f
1 +
r
=
Y

T
+
Y
f

T
f
1 +
r
(1 +
r
)
C
+
C
f
= (1 +
r
)(
Y

T
) + (
Y
f

T
f
)
(1)
which, after plugging in
C
=
C
F
and the values above, is:
(2
.
1)
C
= (1
.
1)(0
.
7)(
Y
) + (0
.
7)(
Y
f
)
(2
.
1)
C
=
.
77(2100) + 0
.
7(1050)
C
= 1120
.
Therefore:
S
=
Y

C

G
= 2100

1120

630 = 350
also, note that
Y
f

C
f

G
f
= 1050

1120

315 =

385
= (1
.
1)350 = (1 +
r
)
S
(2)
(b) Suppose that T increases by 50 (but government expenditures in the two time
periods remain unchanged). By how much must
T
f
decrease so that the govern
ments budget constraint is satisﬁed? How does the increase in T (and accompa
nying decrease in
T
f
) aﬀect C,
C
f
, and S?
1
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View Full DocumentANSWER: The rate at which money can be passed on from one period to the next
is 1+r. From the government’s intertemporal budget constraint in particular we
can see that Δ
T
+
Δ
T
f
1
.
1
= 0 which implies that Δ
T
f
=

1
.
1Δ
T
= 55. The agent’s
budget constraint doesn’t change at all, since the changes in taxes cancel out:
C
+
C
f
1 +
r
=
Y
+
Y
f
1 +
r

ˆ
T
+ Δ
T
+
T
f
+ Δ
T
f
1 +
r
!
=
Y
+
Y
f
1 +
r

ˆ
T
+
T
f
1 +
r
!
Therefore consumption does not change, and since government consumption
doesn’t change either, savings are also unchanged.
(c) Suppose instead that there is a temporary increase in government spending: G
increases by 50 but
G
f
remains unchanged. At the same time, T increases by
50, so that the governments budget constraint is still satisﬁed. How does the
increase in G (and accompanying increase in T) aﬀect C,
C
f
, and S?
ANSWER:Intuitively, with the change from
T
= 630 to
ˆ
T
= 680 the consumer
will be $50 poorer the ﬁrst period than he used to be, but he still wants to equalize
consumption in both periods, so he’ll spread the loss across periods. Since private
consumption does not fall as much as government spending increases, national
saving decreases in the ﬁrst period. Since consumption decreases in the second
period, then savings increases.
Analytically:
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 Spring '07
 BjoernBruegemann
 Macroeconomics, Inflation, Supply And Demand, government spending, real money demand

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