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Answer Key, Principles of Macroeconomics, 8e – Chapter 4
CHAPTER FOUR
Answers to Test Your Understanding Questions
1. a) 10 million (employed of 9 + unemployed of 1)
b) 66.66% (labour force/working age population x 100 = 10/15 x 100)
c) 10% (unemployed/labour force x 100 = 1/10 x 100)
2. a) 24 million (participation rate x working age population = 75% x 32 million)
b) 4 million (Labour force – employed = 24 – 20)
c) 16.66% (unemployed/labour force x 100 = 4/24 x 100)
3. a) Yes, since the category "working age population" includes everyone over the age of
15, etc. whether or not they are in the labour force.
b) Types of people in the category of “not in the labour force” would be: homemakers,
retirees, those receiving welfare or disability incomes, those who are
independently wealthy and discouraged workers.
c) Yes, if the size of the labour force increases by more than the number of employed
increases.
4. a) cyclical; b) frictional; c) structural
5. The size of the labour force would drop by 100 000, as would the number of people
unemployed. The unemployment rate would also fall.
6. The potential GDP is $840. (Since there is 2% cyclical unemployment, using Okun's
Law gives us 2% x 2.5 = 5% multiplied by $800 billion = a GDP gap of $40 billion.
The actual GDP of $800 plus the GDP gap of $40 equals potential GDP of $840.)
7.
Nominal GDP ($billion)
Real GDP ($billion)
GDP deflator (2009 = 100)
Population (millions)
Real GDP per capita
2013
443
374
118.4_
26.1
$14 330
2014
474.2
389
121.9
26.4
14 735
2015
507
402.1
126.1
27
14 893
8. a) Nominal GDP increased by 7.2%. (+3/42 x 100)
b) Real GDP increased by 2.2% (7.2% − 5%)
9. Increase in real income was 3 percent.
Her nominal income increased by $2,800, or by 2800/40000 x 100, which equals 7
percent. Since the inflation rate was 4 percent, her real income has increased by 7
percent minus 4 percent, or by 3 percent.
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Answer Key, Principles of Macroeconomics, 8e – Chapter 4
10. a) 10 years. The number of years to double is 70 divided by the growth rate (of
prices), i.e. 70/7 = 10.
b) 10 percent. Rearranging the rule of 70 formula gives: growth rate (interest rate) =
70/ # of years to double, i.e. 70/7 = 10.
11. a) Real interest rate: 7% (Real equals nominal minus inflation: 11 – 4%)
b) Real income: $10 830. Your real income falls by 5% or $600 to $11 400 in the
first year. It falls a further 5% or $570 in the second year to give a real income of
$10 830.
Answers to Connect Study Problems
1. a) GDP deflators: Year 2013: 105.1 (420/400 x 100); Year 2014: 108.1 (456/422 x
100);
Year 2015 = 111.9 (500/447 x 100)
b) Real GDP per capita: Year 2013: $25 000; (400 billion/16million)
Year 2014: $25 483 (422 billion/16.56 million);
Year 2015: $26 079 (447 billion/17.14 million).
c) Growth rate of real GDP per capita: Year 2014: 1.9% (+483/25000 x 100);
Year 2015: 2.3% (+596/25483 x 100).
2. a) Participation rates: Year 2013: 70% ((8.4/12 x 100); Year 2014: 72% (9/12.5 x
100);
Year 2015: 71.9% (9.2/12.8 x 100).
b) Unemployment rates: Year 2013: 8.3% (0.7/8.4 x 100); Year 2014: 8.9%
(0.8/9 x 100); Year 2015 = 9.2% (0.85/9.2 x 100).
c) 2014: 0.7% (+0.8/108.2 x 100); 2015: 1.2% (1.3/109 x 100)
d) 2014: 5% (+1/20 x 100);
2015: 5% (+1.05/21 x 100)
e) 14 years (70/5).
3. a) Real income: Year 2013: $24 138 (28 000/116 x 100);
Year 2014: $24 463 (29 600/121 x 100);
Year 2015: $25 000 (32 000/128 x 100).
b)
2014: 1.3% (325/24 138 x 100);
4.
1.
2.
3.
Bergan
Altria
Casper
2015 2.2% (537/24 463 x 100).
Country
real GDP per capita
$24 444
14 592
10 648
(2200/1.2/75 x 1000)
(715/1.4/35 x 1000)
(2875/1.8/150 x 1000)
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Answer Key, Principles of Macroeconomics, 8e – Chapter 4
5. a) Nominal GDP increased by 12%. (+24/200 x 100)
b) Real GDP increased by 5% (12% − 7%)
6. a) Unemployment rate: 10% (1.5/ (11.5 + 2.0 + 1.5) x 100.)
b) Participation rate: 75% ((11.5 + 2.0 + 1.5)/20.0 x 100.)
7. a) See the following table:
Table 4.13 (Completed)
2013
Nominal GDP
$850
GDP Deflator
109
Real GDP
779.8
Population
30
Real GDP per capita $25 993
b) 5.5% = (115 – 109) x 100;
109
8. GDP gaps:
9.
2014
$958
115
833
30.5
$27 311
2015
1038.4
118
880
31
$28 390
c) 3.9% = (28 390 – 27 312) x 100
27 311
2013: $45 (3% (cyclical unemployment) x 2.5 x $600);
2014: $15 (1% (cyclical unemployment) x 2.5 x $600);
2015: $15.75 (1% (cyclical unemployment) x 2.5 x 630).
a) Yes, the size of the labour force will increase by 60 000 due to the fact that
half of those workers (120 000) not previously seeking work are now applying for
the new jobs.
b) Unemployment rate: 12.1%. Unemployed: 610 000; labour force: 5 060 000
c) Unemployment rate: 11.3%. Unemployed: 570 000; labour force: 5 060 000
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Answer Key, Principles of Macroeconomics, 8e – Chapter 4
10. See the following table:
Table 4.15 (Completed)
Year
Nominal income
Price index
Real income
1
$36 000
100.0
36 000
2
37 080
101.5
36 532
3
38 192
103.0
37 080
4
39 338
104.6
37 608
5
40 528
106.1
38 198
Alternatively, if you calculate on the basis that his real income increases by 1.5% (3%
increase in nominal income minus the 1.5% inflation rate), her real income after 4 years
(i.e., in year 5) is $38 209.
(Be careful with the price index; you can’t simply add on 1.5 each year. The index
increases by 1.5% from what it was the year before. So year 3, for instance, is 101.5 x
1.015 = 103.0225 (rounded to 103.0). Year 4 it is 103.0225 x 1.015 = 104.567 and so
on.)
11. We can figure the answer using Okun’s law :
GDP gap = potential - actual GDP = 450 – 400 = 50
And GDP gap = 2.5 x cyclical unemployment (%) x actual GDP
50 = 2.5 x cyclical unemployment x 400
Rearranging terms gives us: cyclical unemployment =
50
2.5 x 400
= 0.05 (or 5%)
Actual unemployment = natural unemployment + cyclical unemployment = 6% + 5% =
11%
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Answer Key, Principles of Macroeconomics, 8e – Chapter 4
12 a)
See the following table:
Table 4.16 (Completed)
Item
Rice
2013
2014
2014
Quantity Price Nominal Quantity Price Nominal Quantity 2013 RealGDP
GDP
GDP
Price
400
$5
$2000
430
$5.20 $2236
430
$5
$2150
Pajamas 220
Beer
125
$15
3300
250
$16
4000
250
15
3750
20
2500
130
24
3120
130
20
2600
Totals
$7800
$9356
$8500
b) GDP deflator: 110 (9356/8500 x 100)
c) See the following table:
Table 4.17 (Completed)
Item
Quantity
Prices 2013
Basket cost
Prices 2014
Basket cost
Rice
Beer
Pajamas
10
10
2
$5
20
15
$50
200
30
$280
$5.20
24
16
$52
240
32
$324
d) CPI in 2014: 324/280 x 100 = 115.7
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Answer Key, Principles of Macroeconomics, 8e – Chapter 4
Answer to Comprehensive Problem
a)
1
Table 4.18 (completed)
2
3
4
5
6
7
2013
Item
8
9
10
11
12
2014
13
14
2015
Qty
Prices
Year
2013
Nominal
GDP
Qty
Prices
Year
2014
Nominal
GDP
Prices
Year
2013
Real
GDP
Qty
Prices
Year
2015
Nominal
GDP
Prices
Year
2030
Real
GDP
Pizzas
30
12
360
35
13
455
12
420
40
14
560
12
480
Movie
tickets
20
10
200
22
11
242
10
220
24
12
288
10
240
Farm
tractors
3
100
300
4
95
380
100
400
4
110
440
100
400
Parking
meters
4
50
200
4
60
240
50
200
5
70
350
50
250
Totals
1060
1317
1240
1638
Column 7 in the table is completed by multiplying columns 5 and 6 together.
Columns 8 and 13 are simply a repeat of column 3.
Column 9 is completed by multiplying columns 5 and 8 together.
Column 12 is determined by multiplying columns 10 and 11 together.
Column 14 is determined by multiplying columns 10 and 13 together.
b)
From columns 4, 7 and 12:
2013: $ __1060_______ ; 2014: $ ____1317_____ ; . 2015: $ _____1638____
c)
From columns 4, 9 and 14:
2013: $ __1060_______ ; 2014: $ ____1240_____ ; . 2015: $ _____1370____
d)
Nominal GDP/real GDP x 100 for each year:
2013: ______100___ ;
e)
Inflation rate =
2014
f)
=
(price index this year – price index last year)
price index last year
6.2% (6.2/100 x 100); 2015
x 100
= 12.6% (13.4/106.2 x100).
5 pizzas + 5 movie tickets would cost each year:
2013: $
g)
2014: _____106.2_______ ; . 2015: _____119.6____
110 ; 2014: $ 120 ; 2015: $ 130
Price Index = (value of bundle in current year/ value of bundle in base year) x 100
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1370
Answer Key, Principles of Macroeconomics, 8e – Chapter 4
Price indexes:
h)
Inflation rate =
2013 = 100 (110/110 x100);
2014 = 109.1; (120/110 x 100)
2015 = 118.2. (130/110 x 100)
(price index this year – price index last year)
price index last year
2014 = 9.1% (9.1/100 x 100);
2015 = 8.3% (9.1/109.1 x 100)
7
x 100