Answers to Problems in Textbook
1.
a.
Consumption equals 1,400
+
0.6(10,000

1,750)
=
1,400
+
4,950
=
6,350.
b. Saving equals disposable income minus consumption, which equals 8,250

6,350
=
1,900.
c. The level of planned investment equals 1,800. To compute the level of actual investment,
I
,
remember that income and expenditures (
E
) are always equal, and since net exports equal zero in
this problem,
E
=
C
+
I
+
G
, so that
I
=
Y

C

G
or
I
=
10,000

6,350

1950
=
1,700. Since
unintended inventory investment,
I
u
=
I

I
P
,
I
u
=
1,700

1,800
=

100.
d. Leakages equal saving plus taxes
=
1,900
+
1,750
=
3,650. Injections equal investment plus
government
=
1,700
+
1,950
=
3,650. So both leakages and injections equal 3,650.
e. Since planned expenditure exceeds income, the economy is not in equilibrium. In this economy,
the equilibrium level of income equals
A
p
/
s
, where
s
is the marginal propensity to save.
Autonomous planned spending,
A
p
, equals
C
a

cT
+
I
p
+
G
=
1,400

0.6(1,700)
+
1,800
+
1,950
=
4,100. The marginal propensity to save equals 1

c
=
1

0.6
=
0.4. Therefore, the
equilibrium level of income equals 4,100/0.4
=
10,250.
f.
At the equilibrium level of income, there is a government deficit of 200 billion since taxes equal
1,750 and government spending on goods and services equals 1,950.
2.
a.
The marginal propensity to save,
s
, equals 1

c
=
1

.6
=
.4.
b. Autonomous planned spending,
A
p
, equals
C
a

cT
a
+
I
p
+
G
+
NX
=
1,500

10
r

.6(1,800)
+
2,400

50
r
+
2,000

200
=
4,620

60
r
. Therefore, at an interest rate equal to 5, autonomous planned
spending equals 4,620

60(5)
=
4,320.
c. Since the marginal propensity to save equals .4 and the equilibrium level of income equals
A
p
/
s
,
the equilibrium level of income equals 4,320/.4
=
10,800, given the interest rate equals 5.
d. Since autonomous consumption changes by four percent of any change in household wealth and
the decline in the housing market in 2006–07 and drop in the stock market in the summer of 2007
reduces household wealth by 750 billion dollars, the decrease in autonomous consumption that
results from the decline in household wealth equals .04(750)
=
30 billion.
e. Since the decrease in autonomous consumption that results from the decline in household wealth
equals 30 billion, autonomous planned spending decreases by that amount as well. Therefore, the
new amount of autonomous planned spending equals 4,320

30
=
4,290. Therefore, the new
equilibrium level of income equals 4,290/.4
=
10,725, given the interest rate equals 5.
f. The multiplier,
k
, equals
∆
Y
/
∆
A
p
=
(10,725

10,800)/(4,290

4,320)
=
(

75)/(

30)
=
2.5.
g. Since the multiplier equals 2.5 and income must increase by 75 billion to restore income to its
initial equilibrium level of 10,800, fiscal or monetary policymakers must take actions that
increase autonomous planned spending by 30 billion in order to restore equilibrium income
to 10,800.
i.
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 Spring '11
 Staff
 Macroeconomics, Interest Rates, Consumption function, autonomous planned spending

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