Download Intermediate Macroeconomics, Sciences Po, 2014 Zsófia Bárány

Intermediate Macroeconomics, Sciences Po, 2014
Zsófia Bárány
Answer Key to Problem Set 1
1. Production and expenditure approaches to GDP: Consider three firms: firm
A, a mining enterprise; firm B, a steelmaker; firm C, a car maker. Calculate the GDP of this economy by the product and the expenditure approach,
based on the following assumptions:
All values are in euros. Firm A extracts 10 million euros’ worth of ore.
Firm B produces steel sheet worth 25 million, having bought and used
all the ore produced by firm A. Firm C has manufactured 75 million euros’ worth of vehicles and sold them all to households, having purchased
steel sheets for 20 million from firm B. In addition, Firm C imported engines from abroad for 20 millions euro, and purchased 10 million worth
of robots also from abroad.
Answer:
The following table summarizes the production and distribution processes. All values are in millions of euros. Value added is computed by
deducting the value of intermediate (actually used) consumption from
the value of output. Inventories are all unsold production and we treat
them as it they were bought by firms who produced them as ’inventory
investment’. Final consumption is the value of all household purchases.
Bear in mind that buying robots is like buying machines - it’s not part of
the final good, unlike engines - and so can be used again production and
therefore doesn’t enter intermediate consumption.
Of course, machines wear out in production but remember that we are
computing the gross domestic product, which means that depreciation
(consumption of fixed capital as it is referred to in the national accounts)
should not enter GDP. Only if we needed to compute the net domestic
product, we would (1) subtract depreciation from the value added in the
output approach, and (2) use net fixed capital investment in the expenditure approach instead.
1
Intermediate
consumption
Output
Firm
A
B
C
10 (iron ore) 20 (steel)
20 (engines)
10 (iron ore) 25 (steel)
75 (cars)
Value Added
10
Investment
Final Consumption
Inventories
Net Exports
Expenditure
15
GDP
35
10 (robots)
75
60
10
75
5
-30 (engines, robots) -30
60
5 (steel)
2. Nominal and real GDP: In year 1 and year 2, two products are produced in
a given economy, bicycles and computers. Suppose there are no intermediate goods. In year 1, 500 bicycles are produced and sold at £500 each,
and in year 2, 420 bicycles are sold at £600 each. In year 1, 300 computers are sold for £800 each, and in year 2, 355 computers are sold for £850
each.
(a) Calculate nominal GDP in each year.
Answer:
Nominal GDP year in year t is given by
X
nominalGDPt =
qti · pit
i
where qti and qti the quantity and price of good i = bicycles, computers
in year t. Therefore, given the numbers,
X
nominalGDP1 =
q1i · pi1 = 500 · £500 + 300 · £800 = £490, 000
i
nominalGDP2 =
X
q2i · pi2 = 420 · £600 + 355 · £850 = £553, 750
i
(b) Calculate real GDP in each year, and the percentage increase in real
GDP from year 1 to year 2 using alternatively the first and second
year as the base year. What is real GDP growth using the chainweighted method? Show that real chain-weighted GDP in year 2
using year 1 as the base year is equal to £491,470.
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Answer:
With year 1 as the base year, we need to value both years’ production at year 1 prices:
X
realGDP1base=1 =
q1i · pi1 = 500 · £500 + 300 · £800 = £490, 000 = nominalGDP1
i
realGDP2base=1 =
X
q2i · pi1 = 420 · £500 + 355 · £800 = £494, 000
i
The percentage change in real GDP using year 1 as a base year
equals £494, 000/£490, 000 − 1 ≈ 0.8%.
With year 2 as the base year, we need to value both years’ production at year 2 prices:
X
q1i · pi2 = 500 · £600 + 300 · £850 = £555, 000
realGDP1base=2 =
i
realGDP2base=2
=
X
q2i · pi2 = 420 · £600 + 355 · £850 = £553, 750 = nominalGDP2
i
The percentage change in real GDP using year 2 as a base year
equals £553, 750/£555, 000 − 1 ≈ −0.2%.
Note that the choice of the base year matters. It is possible that, as
the relative price of bicycles increased, the relative demand for bicycles decreased (substitution to cheaper products, i.e. computers),
which is why their production did not increase as much. Because of
this substitution effect in demand, the growth in the production of
goods that see relative price increases tends to be relatively lower.
Now, when taking prices from year 1 as fixed, these goods are multiplied with a low price and thus receive little weight, and calculated
real GDP growth is high. When taking prices from year 2, they are
multiplied with a high price and receive a lot of weight, and calculated real GDP growth is low.
The difference between the two growth rates can lead to very different policy decisions (the economy is growing by the measure of
base year 1 while it is contracting by the measure of base year 2).
In practice, often chain-weighted real GDP growth is considered.
The chain-weighted ratio GDP growth is a geometric average of
the two growth factors (computed using the two base years). The
√
formula is g = g1 · g2 , where gi is the growth index computed
with prices from year i, i.e. g1 = £494, 000/£490, 000 ≈ 1.008 and
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g2 = £553, 750/£555, 000 ≈ 0.998. The chain-weighted ratio of real
√
GDP in the two years therefore is equal to g = g1 · g2 ≈ 1.003. The
percentage change in chain-weighted real GDP from year 1 to year
2 is therefore approximately 0.3%. If we designate year 1 as the base
year, then realGDP1chain−wg = £490, 000 and realGDP2chain−wg =
realGDP1chain−wg · g ≈ £491, 470. Note that here, the choice of the
base year does not affect the growth rate by construction and is only
a choice of units.
(c) Calculate the implicit GDP price deflator and the implied percentage inflation rate using year 1 as the base year. Calculate the CPI
and the CPI inflation rate using the same base year. Can you explain why the CPI inflation is different from the one computed from
the GDP deflator? Is it a systematic feature that you would expect
to find in the data?.
Answer:
The implicit GDP deflator is defined as the ratio of nominal GDP to
real GDP.
nominalGDPt
DF Lbase
=
t
realGDPtbase
Using year 1 as the base year, we have
DF Lbase=1
= 1
(why?)
1
P i i
q ·p
£553, 750
DF Lbase=1
= Pi 2i i2 =
≈ 1.121
2
£494, 000
i q 2 · p1
implying a rate of inflation of approximately 12.1%.
To compute the CPI with base year 1 we need to fix the quantities from
year 1 and compute how the expenditure on this basket changes relative
to the expenditure of year 1.
CP I1 = 1
(def inition)
P i i
q ·p
£555, 000
CP I2 = Pi 1i i2 =
≈ 1.133
£490, 000
i q1 · p1
implying a rate of inflation of approximately 13.3%.
Again, the source of the differences is the substitution away from goods
that have become more expensive (called the ‘substitution bias’). By fixing the basket structure from year 1 the CPI attaches a larger weight to
the price of bicycles, not taking into account that consumers were partly
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able to avoid the price increase by substituting towards computers, and
hence overstating inflation.
Other conceptual differences between the CPI and the implicit GDP deflator include the structure of the goods covered in both indices (the GDP
deflator includes all components of GDP, the CPI only a hypothetical basket of consumer goods) and the origin of goods (the GDP deflator covers
all domestically produced goods and services while the CPI covers goods
and services consumed by domestic households, even if imported).
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