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AK Macroeconomics – Chapter 6
CHAPTER SIX
Answers to Self-Test Questions
1. a)
National
Income
0
200
400
600
800
b) C = 60 + 0.8Y;
Consumption
Saving
60
220
380
540
700
–60
–20
20
60
100
S = –60 + 0.2Y
2. a)
C =
100 + 0.9Y
I
= 200
AE = 300 + 0.9Y
b) Let
Y = AE
Y = 300 + 0.9Y
Therefore, 0.1Y = 300
Y = 3000
3.
C
I
AE
Let
Y
Y
Therefore, 0.4Y
Y
4.
5.
a)
b)
c)
d)
=
=
=
=
=
=
=
80 + 0.6Y
120
200 + 0.6Y
AE
200 + 0.6Y
200
500
MLR = 0.1,
MLR = 0.25,
MLR = 0.4,
MLR = 0.5,
multiplier = 1/0.1
= 10;
multiplier = 1/0.25 = 4;
multiplier = 1/0.4 = 2.5;
multiplier = 1/0.5 = 2.
a) AE = 200 + 0.6Y; (0.6 is the slope of the AE line. Check any two points on it:
AE increase $300 for every $500 increase in national income).
b) $500. (You can either calculate this algebraically once you have the expression for
the AE line; alternatively, draw in a 450 line, where it crosses the AE line is equilibrium).
© 2009 McGraw-Hill Ryerson Limited
38
AK Macroeconomics – Chapter 6
6. This would suggest that irrespective of Canada's level of GDP it would always import a certain
amount from abroad. These goods and services could be regarded as "necessities" and would
include items that would be very difficult or very expensive to produce in Canada, e.g. many
food commodities like coffee, tea, tropical fruits; some building materials such as teak,
mahogany and Italian marble; specialised hi-tech equipment like satellites, radar and large
commercial aircraft.
7. a)
b)
c)
d)
T
T
T
T
-
G=
G=
G=
G=
50
50
50
50
+
+
+
+
0.25 (400) – 200 = –50;
0.25 (600) – 200 = 0;
0.25 (900) – 200 = +75;
0.25 (1200) – 200 = +150;
XN
XN
XN
XN
=
=
=
=
120
120
120
120
–
–
–
–
30
30
30
30
–
–
–
–
0.1 (400) = +50
0.1 (600) = +30
0.1 (900) = 0
0.1 (1200) = – 30
8. a)
Y
0
100
200
300
T
20
40
60
80
AE
Y
0.4Y
Y
YD
–20
60
140
220
=
=
=
=
C
30
102
174
246
S
–50
–42
–34
–26
I
50
50
50
50
G
70
70
70
70
X
20
20
20
20
IM
10
22
34
46
XN
10
–2
–14
–26
AE
160
220
280
340
160 + 0.6Y
160 + 0.6Y
160
400
= MPC (1 – MTR) – MPM
= 0.9 (1 – 0.25) – 0.075 =
0.675 – 0.075 = 0.6
MLR
= (1 – MPE) = (1 – 0.6) = 0.4
Multiplier = 1/ MLR
= 1/0.4 = 2.5
9. MPE
10.
a) ii), iii), and v) would cause an increase in national income.
b) iii) and v) would increase the size of the multiplier.
11. It can other obtain the funds by borrowing (likely) or by printing more money (unlikely).
12.
a) exports, because they would now be more competitive in world markets;
b) investment, because lower prices imply a lower interest rate which would
stimulate investment;
c) consumption, because lower prices would increase the value of real balances.
© 2009 McGraw-Hill Ryerson Limited
39
AK Macroeconomics – Chapter 6
Answers to Study Guide Questions
1. False: it is the other way around.
2. True
3. False: it is the other way around.
4. True
5. False: ....change in the price level has on....
6. True
7. True
8. True
9. False: consumption will fall too.
10. True
11. b
12. c
13. b
14. a
15. b
36A.
16. d
17. a
18. b
19. d
20. a
21. b
22. b
23. a
24. a
25. b
26. d
27. c
28. c
29. b
30. a
31. c
32. c
33. c
34. c
35. b
Key Problem
a) See Following table and figure:
Table 6.11 (completed)
Y
$0
100
200
300
400
500
600
700
800
T
25
50
75
100
125
150
175
200
225
YD
25
50
125
200
275
350
425
500
575
C
0
60
120
180
240
300
360
420
480
© 2009 McGraw-Hill Ryerson Limited
S
25
10
5
20
35
50
65
80
95
I
60
60
60
60
60
60
60
60
60
40
G
150
150
150
150
150
150
150
150
150
X
50
50
50
50
50
50
50
50
50
IM
10
20
30
40
50
60
70
80
90
XN
40
30
20
10
0
10
20
30
40
AE
250
300
350
400
450
500
550
600
650
AK Macroeconomics – Chapter 6
Figure 6.12 (completed)
b) Income: $500
Equilibrium National Income can be seen in Table 6.11 (completed) where Y (national
income) is equal to AE, which in this case is $500. In Figure 6.12 (completed) this is at
e1 where the AE curve intersects the 45o line which is also at an income level of $500.
c) Reading the values from Table 6.11 (completed) for income level of $500 shows the
following:
Total Injections: I (60) + G (150) + X (50) ) = $260
Total Leakages: S (50) + T (150) + IM (60) = $260.
d) MPE: 0.5
(Aggregate expenditures (AE) changes by 50 for every change of $100 in income (Y),
which is 50/100 or 0.5)
e) Multiplier: 2
(The value of the MLR is (1  0.5) = 0.5, and therefore the value of the multiplier is 1/0.5
= 2.)
f) See Figure 6.12 (completed)
g) Income: $800;
net exports: + $110.
The new equilibrium income occurs where the new AE2 curve intersects the 45o line,
which is at an income of $800. (Since the multiplier is 2, then an increase in exports of
$150 will increase equilibrium income by 2 x $150, or $300 to the new value of $800.)
Table 6.6 (Completed) shows that imports increase by $10 for every $100 increase in the
level of income (the marginal propensity to import is 0.1). Therefore, if income increases
by $300, imports will increase by $300 x 0.1 or $30 to $90. Net exports will equal exports
of $200 (an increase of 150 from 50) minus imports of $90.
37A.
a) Balance of trade: + $100 XN = 400 – (100 + 0.25Y) = 300 – 0.25 (800) = 300 - 200
b) Balance of trade: – $200 XN = 400 – (100 + 0.25Y) = 300 – 0.25 (2000) = 300 - 500
c) Income: $1200 where X = IM i.e. 400 = 100 + 0.25Y; therefore
0.25Y = 300 and Y = 1200
© 2009 McGraw-Hill Ryerson Limited
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AK Macroeconomics – Chapter 6
38A a)
Y
0
50
100
150
200
C
40
70
100
130
160
S
–40
–20
0
20
40
b) MPC = ΔC/ΔY = 30/50 = 0.6;
MPS = ΔS/ΔY = 20/50 = 0.4
c) C = 40 + 0.6Y;
S = –40 + 0.4Y
39A. a) See Table 6.13 (completed)
Table 6.13 (completed)
Y
0
200
400
600
800
1000
C
100
250
400
550
700
850
S
–100
–50
0
50
100
150
b) $1000 (where Y and AE are equal.)
c) 4.
MPE = 0.75 (∆AE/∆Y = 150/200);
Multiplier = 1/MLR = 1/0.25 = 4
40A.
AE
250
400
550
700
850
1000
MLR = 0.25
a)
2125
b)
multiplier = 3.125 MPE = 0.68; MLR = 1 – 0.68 = 0.32; multiplier = 1/MLR =
1/0.32 = 3.125
2375
Income will increase by 80 x multiplier (3.125) = 250.
c)
C =
I
=
AE =
Y = AE
0.32Y
Y
I
150
150
150
150
150
150
© 2009 McGraw-Hill Ryerson Limited
240 + 0.68Y
440
680 + 0.68Y
= 680 + 0.68Y
= 680
= 680/0.32 = 2125
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AK Macroeconomics – Chapter 6
41A. See Table 6.14 (completed)
Table 6.14 (completed)
Y
0
100
200
300
400
500
600
700
800
900
1000
C
100
150
200
250
300
350
400
450
500
550
600
b) 800
c) Injections
=
S
– 100
– 50
0
50
100
150
200
250
300
350
400
C
I
AE
Y = AE
0.50Y
Y
leakages
© 2009 McGraw-Hill Ryerson Limited
= 100 + 0.50Y
= 300
= 400 + 0.50Y
= 400 + 0.50Y
= 400
= 400/0.5 = 800
= 300
43
I
300
300
300
300
300
300
300
300
300
300
300
AE
400
450
500
550
600
650
700
750
800
850
900
AK Macroeconomics – Chapter 6
d) See Figure 6.13 (completed)
Figure 6.13 (completed)
42A
a) $16 000
(where AE and (Y=AE) lines intersect)
b) MPE (slope of AE function) = 0.5; MLR = 0.5; multiplier = 1/0.5 = 2
c) $8000. (Draw in a new AE line $4000 lower and check where it crosses the 450 line;
alternatively note that with a multiplier of 2, a decrease of $4000 in investment will
decrease income by $8000).
d) $20 000. (Draw in a new AE line $2000 higher and check where it crosses the 450 line;
alternatively note that with a multiplier of 2, an increase of $2000 in investment will
increase income by $4000).
43A.
a) See the following table:
Table 6.15 (completed)
Y
T
Yd
C
S
400
450
500
550
40
40
40
40
360
410
460
510
320
365
410
455
40
45
50
55
© 2009 McGraw-Hill Ryerson Limited
44
Planned
I
60
60
60
60
G
Xn
50
50
50
50
+10
5
20
35
AE Unplanned
I
440
40
470
20
500
0
530
+20
AK Macroeconomics – Chapter 6
b) $500.
c) $450. (MPE = 30/50 =0.6;
MLR = 0.4;
by 20, Y will decrease by 20 x 2.5 = 50.)
multiplier = 2.5. Therefore, if I decreases
44A Autonomous expenditures is the portion of total spending that is independent of the level of
income, i.e. it is the amount of spending when income is zero.
45A The marginal propensity to import refers to the change in total imports that results from a
change in income, expressed as a ratio, i.e. MPM = Δ imports/ Δ income.
46A.
MLR = 0.4; (Leakages increased by 40 + 16 + 24 = 80 when Y increased by 200. So,
MLR = 80/200); MPE = 0.6;
multiplier = 2.5
47A.
MPE = (1 – MTR)MPCD – MPM = (1 – 0.25) x 0.9 – 0.175 = 0.5
MLR = (1 – MPE) = 0.5;
multiplier = 1/MLR = 2
48A.
See the following table:
Table 6.16 (completed)
Y
800
49A.
T
160
YD
640
C
530
S
110
a) Equilibrium income: $800
I
80
G
180
X
90
IM
80
XN
10
AE
800
X
200
IM
302
XN
-102
AE
800
C = 42 + 0.65Y
I = 120
G = 220
XN = 18 – 0.15Y
AE = 400 + 0.5Y
Y = 800
b) See following table:
Y
800
T
220
YD
580
C
562
S
18
I
120
G
220
c) Equilibrium income: $700 (MPE = 0.5; MLR = 0.5; multiplier = 1/0.5 = 2.. If X
decreases by 50, then Y decreases 50 x 2 = 100)
© 2009 McGraw-Hill Ryerson Limited
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AK Macroeconomics – Chapter 6
50A.
a) $1200
C = 32 + 0.9(Y – 30 – 0.1Y)
C = 5 + 0.81Y
I = 110
G = 170
XN = 15 – 0.06Y
AE = 300 + 0.75Y
Y = 1200
b) Leakages/injections: $337 each. (I = 110, G = 170, IM = 114)
(S = 73, T = 150, IM = 114)
c) Multiplier: 4 (MPE = 0.75; MLR = 0.25; multiplier = 1/0.25)
51A



Expenditures equilibrium is the income at which the value of production and aggregate
expenditures are equal. It can be expressed in three equivalent ways:
Income (Y) = Aggregate expenditures (AE)
Unplanned investment is zero, i.e. there is no shortage or surplus
The value of total leakages = the value of total injections
52A The following will cause a change in autonomous consumption:
 changes in wealth
 changes in the price level
 changes in the age of consumer durables
 changes in consumer confidence (expectations)
53A.
a) Y2: $600
( A is an increase of 50; if the multiplier is 4, Y increases by 200.
Therefore, initial income, Y2 must be $200 less.)
b) multiplier: 1.67 (Multiplier = ΔY/AE = 100/60)
c) B: $400
(If multiplier is 2, MPE = 0.5. AE function is: AE = B + 0.5Y. Since
equilibrium is at 800, 800 = B + 0.5(800). Therefore B = 800 – 400)
54A.
a) Equilibrium income: $1440.
C = 80 + 0.6Y
I = 200
G = 300
XN = 140 – 0.1Y
AE = 720 + 0.5Y
Y = 1440
b) Equilibrium income: $1500 ( Since multiplier is 2, if X increases by 30, Y increases
by 60)
c) XN= + 20
(XN = 170 – 0.1(1500))
d) Decrease of $45 in government spending. (With a multiplier of 2, if Y is to decrease
by 90, then G must decrease by ½ x 90.)
© 2009 McGraw-Hill Ryerson Limited
46
AK Macroeconomics – Chapter 6
55A.
a) Taxes, savings and net exports (imports) depend on the level of income.
b) No, it’s not in equilibrium. Y = $500; AE = C (200) + I (100) + G (200) + XN (70) =
570; therefore the level of inventories will fall.
c) Output and GDP will rise next year.
56A a) See Table 6.20 (completed)
Table 6.20 (completed)
Y
T
YD
0
50
–50
100
60
40
200
70
130
300
80
220
400
90
310
b) T = 50 + 0.1Y;
c)
C
20
92
164
236
308
S
–70
–52
–34
–16
+2
I
60
60
60
60
60
G
70
70
70
70
70
X
100
100
100
100
100
C = 20 + 0.72Y; XN = 50 – 0.12Y;
IM
50
62
74
86
98
XN
+50
+38
+26
+14
+2
AE
200
260
320
380
440
AE = 200 + 0.6Y
500
AE
Let Y
Y
(Y – 0.6Y)
0.4Y
Y
= 200 + 0.6Y
= AE,
= 200 + 0.6Y
= 200
= 200
= 500
57A Expenditures equilibrium can occur at any output level in the economy, i.e. the economy may
be suffering a serious recessionary or inflationary gap yet the economy may still be at
equilibrium. Full employment equilibrium, in contrast, means that not only is the economy
in equilibrium, but the economy is also producing at full-employment.
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47