C h a p t e r
2 3
1.
Japan’s real GDP was561 trillion yen in 2007 and569 trillion
yen in 2008. Japan’s population was 127.7 million in 2007 and
127.8 million in 2008. Calculate
a. The economic growth rate.
The economic growth rate is the growth rate of real GDP. Between
2007 and 2008 this growth rate equals [(569 trillion yen
561
trillion yen)/561 trillion yen]
100, which is 1.4 percent.
b. The growth rate of real GDP per person.
Japan’s population grew at [(127.8 million
127.7 million)/127.7
million]
10
0, which is 0.1 percent. Japan’s economic growth rate
is 1.4 percent, so the growth rate of real GDP per person is 1.4
percent
0.1 percent, or 1.3 percent.
c. The approximate number of years it takes for real GDP per
person in Japan to double if the 2008 economic growth rate
and population growth rate are maintained.
Japan’s real GDP per person is growing at 1.3 percent a year. The
rule of 70 tells us that Japan’s real GDP per person will double
in 70/1.3 = 54 years.
2. For three years, there was no technological change in Longland
but capital per hour of labor increased from $10 to $20 to $30
and real GDP per hour of labor increased from $3.80 to $5.70
to $7.13. Then, in the fourth year, capital per hour of labor
remained constant but real GDP per hour of labor increased to
$10.
a. Does Longland experience diminishing returns? Explain why or
why not.
Longlandexperiencesdiminishingreturns.Diminishingreturnsare
present if the marginal product of capital diminishes as capital
increases, holding technology constant. When capital per hour of
labor increases by $10 from $10 to $20, real GDP per hour of labor
increases by $1.90 (from $3.80 to $5.70). But when capital per
hour increases by another $10 from $20 to $30, real GDP per hour
of labor increases by only $1.43 (from $5.70 to $7.13).
b. Does Longland conform to the one third rule? If so, explain
why. If not, explain why not and explain what rule, if any,
it does conform to.
The economy doe not conform to the one third rule; instead it
conformstoaonehalfrule.Inthiseconomy,an
x
percentincrease
in capital per hour of labor leads to a 0.25
x
percent increase
in real GDP per hour of labor. To determine the rule in Longland,
calculatethepercentagechangeincapitalperhourlaborandreal
GDPperhouroflaborateachofthelevelsprovidedinthequestion,
andthendividethepercentagechangeinrealGDPperhouroflabor
bythepercentagechangeincapitalperhouroflabor.Forexample,
when capital per hour of labor increases by 100 percent from $10
to $20, real GDP per hour of labor increases by 50 percent from
$3.80 to $5.70. Or when capital per hour of labor increases 50
percent from $20 to $30, real GDP per hour of labor increases by
25 percent from $5.70 to $7.13.
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c. Explain how you would do the growth accounting for Longland
and calculate the effect of technological change on growth
in the fourth year described above.
Growth accounting would be done in qualitatively the same way as
intheU.S.economywiththedifferencethatanypercentage change
in the capital per hour of labor increases real GDP per hour of
labor by 50 percent rather than 33 percent. In the fourth year,
because capital per hour of labor remained constant,
all
the
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 Spring '11
 Gispy

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