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McMaster University

Economics

ECON 2HH3

Marc- Andre Letendre

Winter

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CHAPTER 2
Measurement
TEXTBOOK QUESTION SOLUTIONS
Problems
1. Product accounting adds up value added by all producers. The wheat producer has no
intermediate inputs and produces 3 million tonnes at $30/tonne for $90 million. The
bread producer produces 100 million loaves at $3.50/loaf for $350 million. The bread
producer uses $75 million worth of wheat as an input. Therefore, the bread producer’s
value added is $275 million. Total GDP is therefore, $90 million + $275 million =
$365 million.
Expenditure accounting adds up the value of expenditures on final output.
Consumers buy 100 million loaves at $3.50/loaf for $350 million. The wheat
producer adds 0.5 million tonnes of wheat to inventory. Therefore, investment
spending is equal to 0.5 million tonnes of wheat valued at $30/tonne, which costs $15
million. Total GDP is, therefore, $350 million + $15 million = $365 million.
2. Coal producer, steel producer, and consumers.
a) i) Product approach: Coal producer produces 15 million tonnes of coal at
$5/tonnes, which adds $75 million to GDP. The steel producer produces $10
million tonnes of steel at $20/tonne, which is worth $200 million. The steel
producer pays $125 million for 25 million tonnes of coal at $5/tonne. The
steel producer’s value added is, therefore, $75 million. GDP is equal to $75
million + $75 million = $150 million.
ii) Expenditure approach: Consumers buy 8 million tonnes of steel at $20/tonne,
so consumption is $160 million. There is no investment and no government
spending. Exports are 2 million tonnes of steel at $20/tonne, which is worth
$40 million. Imports are 10 million tonnes of coal at $5/tonne, which is worth
$50 million. Net exports are, therefore, equal to $40 million − $50 million =
− $10 million. GDP is, therefore, equal to $160 million + (− $10 million) =
$150 million.
iii) Income approach: The coal producer pays $50 million in wages and the steel
producer pays $40 million in wages, so total wages in the economy equal $90
million. The coal producer receives $75 million in revenue for selling 15
million tonnes at $5/tonne. The coal producer pays $50 million in wages, so
the coal producer’s profits are $25 million. The steel producer receives $200
million in revenue for selling 10 million tonnes of steel at $20/tonnes. The
steel producer pays $40 million in wages and pays $125 million for the 25
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- 11 - Instructor’s Manual for Macroeconomics, Second Canadian Edition
million tonnes of coal that it needs to produce steel. The steel producer’s
profits are, therefore, equal to $200 − $40 million − $125 million = $35
million. Total profit income in the economy is therefore $25 million + $35
million = $60 million. GDP is therefore equal to wage income ($90 million)
plus profit income ($60 million). GDP is therefore $150 million.
b) There are no net factor payments from abroad in this example. Therefore, the
current account surplus is equal to net exports, which is equal to (− $10 million).
c) As originally formulated, GNP is equal to GDP, which is equal to $150 million.
Alternatively, if foreigners receive $25 million in coal industry profits as income,
then net factor payments from abroad are −$25 million, so GNP is equal to $125
million.
3. Wheat and Bread
a) Following the product approach, value added by firm A is total revenue from
wheat sales (note that the inventory accumulation is treated as if the firm sold the
wheat to itself), or $150,000. For firm B, value added is revenue from sales of
bread minus the value of wheat purchased from firm A, or $100,000-$60,000 =
$40,000. Therefore, total GDP = $150,000 + $40,000 = $190,000.
b) For the expenditure approach, consumption expenditure on bread, C = $100,000 +
$15,000 = $115,000 (note that imports of bread are included), investment in
inventories is I = $15,000, and net exports are NX = $75,000 - $15,000 = $60,000.
Government expenditures are G = 0. Therefore,
GDP = C + I + G + NX = $115, 000 + $15,000 + 0 + $60,000 = $190,000.
c) For the income approach, in this case GDP is the sum of profits and wage income.
Profits for firm A are $150,000 - $50,000 = $100,000 (revenue minus wage costs,
where inventory accumulation is included as a positive amount) and profits for
firm B are $100,000 - $20,000 - $60,000 = $20,000 (revenue minus wage costs
minus the cost of the intermediate input). Total wages are $50,000 + $20,000 =
$70,000. Therefore, GDP = profits + wages = $100,000 + $20,000 + $70,000 =
$190,000.
4. Price and quantity data are given as the following:
Year 1
Good Quantity Price
Computers 20 $1,000
Bread 10,000 $1.00
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- 12 - Chapter 2: Measurement
Year 2
Good Quantity Price
Computers 25 $1,500
Bread 12,000 $1.10
a) Year 1 nominal GDP = 20 × $1,000 + 10,000 × $1.00 = $30,000.
Year 2 nominal GDP = 25 × $1,500 + 12,000 × $1.10 = $50,700.
b) With year 1 as the base year, we need to value both years’ production at year 1
prices. In the base year, year 1, real GDP equals nominal GDP equals $30,000.
In year 2, we need to value year 2’s output at year 1 prices. Year 2 real GDP
= 25 × $1,000 + 12,000 × $1.00 = $37,000. The percentage change in real GDP
equals [($37,000 − $30,000)/$30,000] × 100 = 23.3%.
We next calculate chain-weighted real GDP. At year 1 prices, the ratio of year 2
real GDP to year 1 real GDP equals g1 = ($37,000/$30,000) = 1.2333. We must
next compute real GDP using year 2 prices. Year 2 GDP valued at year 2 prices
equals year 2 nominal GDP = $50,700. Year 1 GDP valued at year 2 prices equals
(20 × $1,500 10,000× $1.10) $41,000). The ratio of year 2 GDP at year 2
prices to year 1 GDP at year 2 prices equalg 2 = ($50,700/$41,000) = 1.2367.
The chain-weighted ratio of real GDP in the two years therefore is equal
togc= gg 12 =1.23496 .The percentage change chain-weighted real GDP from year
1 to year 2 is therefore approximately 23.5%.
If we (arbitrarily) designate year 1 as the base year, then year 1 chain-weighted
GDP equals nominal GDP equals $30,000.Year 2 chain-weighted real GDP is
equal to (1.23496 × $30,000) = $37,049, approximately.
Alternatively, we could use the average price method.To perform a calculation
using this method, we first compute average prices. The average price for
computers equals ($1,000 + $1,500)/2 = $1,250. The average price for bread
equals ($1.00 + $1.10)/2 = $1.05. Year 1 output valued at average prices equals
20 × $1,250 + 10,000 × $1.05 = $35,500. Year 2 output valued at average prices
equals 25 × $1,250 + 12,000 × $1.05 = $43,850. The percentage change in chain-
weighted GDP is therefore equal to[($43,850 − $35,500)/$35,500] × 100 =
23.5%.
c) To calculate the implicit GDP deflator, we divide nominal GDP by real GDP, and
then multiply by 100 to express GDP deflator as an index number. With year 1 as
the base year, base year nominal GDP equals base year real GDP, so the base year
implicit GDP deflator is 100. For year 2, the implicit GDP deflator is
($50,700/$37,000) × 100 = 137.0. The percentage change in the deflator is equal
to 37.0%.
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- 13 - Instructor’s Manual for Macroeconomics, Second Canadian Edition
With chain weighting, the base year is now the midpoint between the two years.
The year 1 GDP deflator equals ($30,000/$30,000) × 100 = 100. The chain-
weighted deflator for year 2 equals ($50,700/$37,049) × 100 = 136.9. The
percentage change in the chain-weighted deflator equals [(136.9 − 100)/100] ×
100 = 36.9%.
d) Let us consider the possibility that year 2 computers are twice as productive as
year 1 computers. As one possibility, let us define a “computer” as a year 1
computer. In this case, the 25 computers produced in year 2 are the equivalent of
50 year 1 computers. Each year 1 computer now sells for $750 in year 2. We now
revise the original data as:
Year 1
Good Quantity Price
Year 1 Computers 20 $1,000
Bread 10,000 $1.00
Year 2
Good Quantity Price
Year 1 Computers 50 $750
Bread 12,000 $1.10
First, note that the change in the definition of a “computer” does not affect the
calculations of nominal GDP. We next compute real GDP with year 1 as the base
year. Year 2 real GDP, in year 1 prices is now50×$1+,000 =12,000 $1.00 $62,000 .
The percentage change in real GDP is equal to[($62,000 − $30,000)/$30,000] ×
100 = 106.7%.
We next revise the calculation of chain-weighted real GDP. From above,
g1equals ($62,000/$30,000) = 2.07. The value of year 1 GDP at year 2 prices
equals $26,000. Therefore, g equals ($50,700/$26,000) = 1.95. The chain-
2
weighted ratio of real GDP in the two years therefore is equal
to gc= gg 1 2 = 2.0075 . The percentage change chain-weighted real GDP from
year 1 to year 2 is therefore 100.8%.
If we (arbitrarily) designate year 1 as the base year, then year 1 chain-weighted
GDP equals nominal GDP equals $30,000. Year 2 chain-weighted real GDP is
equal to (2.0075 × $30,000) = $60,225. The chain-weighted deflator for year 1 is
automatically 100. The chain-weighted deflator for year 2 equals
($50,700/$60,225) × 100 = 84.2. The percentage rate of change of the chain-
weighted deflator equals−15.8%.
Copyright © 2007 Pearson Education Canada
- 14 - Chapter 2: Measurement
When there is no quality change, the difference between using year 1 as the base
year and using chain wei

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