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Problems
Numerical Problems:
Ch. 2: 1, 6abc, 8
Ch. 8: 3
Chapter 2 Problem 1
Chapter 2 Problem 1 (Answer)
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Professor grows coconuts and catches fish. He harvested 1000
coconuts and caught 500 fish. He values 1 fish as being worth 2
coconuts. We assume that this rate of trade defines the relative
prices of the two goods. Given this rate of trade, we can value
the harvest of the two goods at 1000 fish.
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That is 1000 coconuts have the same value as 500 fish, so we have
500 fish, and we have coconuts valued at 500 fish, for total value of
of 1000 fish.
I'd like to skip down in the question to a new piece of information.
We're told that the professor used 100 fish as fertilizer for the
coconut trees. I assume that these 100 fish are used as an
intermediate good, and therefore should not be counted in GDP.
So although the value of the total harvest of coconuts and fish
was 1000 fish, GDP will be 900 fish.
Chapter 2 Problem 1 (Answer,
continued)
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We're also told that the professor gave 200 coconuts to Gilligan
in exchange for help in the harvest and he gave him 100 fish in
exchange for collecting worms used in fishing.
The value of 200 coconuts is 100 fish. So the value of Gilligan's
income is 200 fish; that is, 100 fish plus 200 coconuts worth 100
fish.
We have already claimed that GDP has been determined, but
what about the value of the worms that Gilligan collected?
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In fact, these are intermediate goods and should not be included in
GDP.
We are also told that the professor stored 100 coconuts in his hut
for consumption at some future time. I regard this as inventory
investment. The 100 coconuts have a value of 50 fish.
Chapter 2 Problem 1 (Answer,
continued)
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Now let's see what questions we've already answered and what
questions need to be answered.
I've already determined that GDP on Gilligan's Island is equal to 900
fish.
All of that output is consumption except for the 100 coconuts that
were stored by the professor. These coconuts, valued at 50 fish,
represented inventory investment. So total consumption is equal to
900 less 50, or 850 fish and investment is equal to 50.
Gilligan's income was 200 fish. All remaining income went to the
professor, so his income is 700 fish.
Chapter 2 Problem 6a,b,c
Chapter 2 Problem 6a,b,c
Chapter 2 Problem 6a,b,c
(Answer)
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The problem gives us information about production of goods in
an economy in two different years. The table shows production
and prices in the base year and also in a later year.
The first question asks us to find nominal GDP in the current year
and in the base year and then to determine the percentage
increase between the two.
Nominal GDP in the base year is measures the value of base
year quantities at base year prices. The total, given in the table,
is $56,000. Nominal GDP in the current year is equal to the
current year quantities at current year prices, or $200,000.
The percentage rate of change going for 56,000 to 200,000 is
257%.
Chapter 2 Problem 6a,b,c
(Answer, continued)
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Next we are asked to find real GDP in the current year and in the
base year. And then we are asked to find the percentage rate of
change in real GDP.
Real GDP and nominal GDP are the same in the base year, so
real GDP in the base year is equal to $56,000. Real GDP in the
current year is found by valuing current year output at base year
prices. The correct figure from the table is $178,000.
The percentage rate of change going from $56,000 $178,000 is
218%.
Chapter 2 Problem 6a,b,c
(Answer, continued)
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Finally we are asked to find the GDP deflator for the current year
and for the base year and then the rate of change in the GDP
deflator.
In the base year the GDP deflator has a value of 100. In the
current year, the GDP deflator would be equal to nominal GDP
divided by real GDP with that quotient multiplied by 100.
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Nominal GDP was $200,000 real GDP was $178,000; the quotient is
1.124. Multiply that by 100 to get a GDP deflator of 112.4.
The percentage rate of change in the GDP deflator, which goes from
100 to 112.4, is 12.4%.
Chapter 2 Problem 8
Chapter 2 Problem 8 (Answer)
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Hy purchases a one year government bond for $500 and one
year later receives principal plus interest of $545. The
percentage rate of return, which is the nominal rate of interest, is
9%.
The CPI went from 200 to 214 over the same period. That's a
percentage rate of increase of 7%.
Hy had been anticipating that the CPI would rise from 200 to
210, which would have been a 5% rate of increase. So Hy was
expecting 5% inflation.
Hy's expected real rate of interest was 9% -5% or 4%.
Chapter 8, Analytical
Question 3
Chapter 8, Analytical Question
3 (Answer)
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This question tells us that output, total hours worked, and average labor
productivity, are all pro-cyclical.
The question is: Which variable, output or total hours worked, increases
by a larger percentage in expansions and falls by a larger percentage in
recessions?
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Output equals hours times productivity. This implies that, the percentage
change in output equals the percentage change in hours multiplied by the
percentage change in productivity.
Output  Hours  Productivity
%Output  %Hours  %Productivity
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Both hours and productivity rise in an expansion, so the percentage
change in output must be larger than the percentage change in hours.
Chapter 8, Analytical Question
3 (Answer, continued)
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Yes, this is related to Okun's Law.
We just saw that output varies more in percentage terms than
employment does. This is close to what Okun’s Law says.
First assume that a 1% point change in unemployment implies
roughly a 1% change in employment (true, since the labor force
is about the same size as the number employed).
The answer to the previous question tells us that if employment
rises by 1%, output must rise by more that that.
Okun's Law tells us that the output increase is about 2% points,
consistent with what is required.
The End