7 Homework Solutions
ECON 010, Fall 2011
Question 1: Calculating GDP in a Simple Economy
a. What is the Gross Domestic Product (GDP)?
Answer:
Gross Domestic Product (GDP) is the market value of all nal goods and services produced within a country in a given period of time (year, quarter, month, etc.).
b. What is the dierence between nominal GDP and real GDP? Why do we need to distinguish
between the two?
Answer:
Nominal GDP is calculated by summing the current values of nal goods and services
(using current prices). Real GDP is calculated by designating a particular year as the
base year and then using the prices of goods and services in the base year to calculate
the value of goods and services in all other years.
Suppose that the GDP increased from one year to the next. This increase could be
attributed to two dierent things: an increase in the production in the economy and
an increase in the prices (which would increase the value of production). We like to
distinguish between nominal and real GDP in the hope of isolating both of these eects.
The problem with this approach, however is choosing which year to set as a base year.
Part d) of this question illustrates this.
c. Is GDP a stock value or a ow value? Give examples of each.
Answer:
GDP is a ow value since the GDP for a particular year measures the market value of
the all of the nal goods and services produced in that particular year. Other examples
of ow variables are: prots earned by rms in a year, tax revenue collected in a quarter,
etc. Some examples of stock variables are: value of the capital stock, population, etc.
For Business students: Balance Sheet of a rm is meant to show all of the stock variables
of a rm: assets, liabilities, etc. and an Income Statement is meant to show the ow
variables of a rm: Sales in a quarter, wages paid in a quarter, etc.
d. Below are some data from the land of milk, honey, and haircuts.
1
Year
2008
2009
2010
Price
of Milk
$1
$1
$2
Quantity
of Milk
100 quarts
200
200
Price
of Honey
$2
$2
$4
Quantity
of Honey
50 quarts
100
100
Price of
Haircuts
$ 10
$ 10
$ 20
Quantity
Haircuts
30
60
60
1. Calculate the nominal GDP in each year.
Answer:
2008 : GDP2008
=
100($1) + 50($2) + 30($10) = $500
2009 : GDP2009
=
200($1) + 100($2) + 60($10) = $1000
2010 : GDP2010
=
200($2) + 100($4) + 60($20) = $2000
2. Calculate the real GDP in each year using 2008 as a base year.
Answer:
2008 : GDP2008
=
100($1) + 50($2) + 30($10) = $500
2009 : GDP2009
=
200($1) + 100($2) + 60($10) = $1000
2008 : GDP2008
=
200($1) + 100($2) + 60($10) = $1000
3. Why did the nominal GDP increase from 2008 to 2009? Why did the nominal GDP increase
from 2009 to 2010?
Answer:
Nominal GDP increased from 2008 to 2009 because production doubled. Nominal
GDP increased from 2009 to 2010 because prices doubled.
Question 2: CPI and Ination
a. What is Ination? How do we measure ination?
Answer:
The ination rate is the percentage change in the price level from one year to the next.
However, since there are many dierent prices in the economy, we need a method to
aggregate them. One way the can aggregate prices is the CPI (described below). Another
way is the GDP Deator (Nominal GDP/Real GDP), which is a broader measurement
than the CPI.
b. What is the Consumer Price Index (CPI)?
Answer:
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The Consumer Price Index (CPI) is an average of the prices of a basket of goods and
services purchased by the typical urban family of four. One year is chosen to be the base
year and the CPI is set equal to 100 for that year. In any other year besides the base
year, the CPI is equal to the ratio of the dollar amount necessary to buy the market
basket of goods in that year divided by the dollar amount necessary buy to the market
basket of goods in the base year, multiplied by 100.
c. A typical family on Sandy Island consumes only juice and cloth. Last year, which was the base
year, the family spent $40 on juice and $25 on cloth. In the base year, juice was $4 a bottle and cloth
was $5 a length. This year, juice is $4.50 a bottle and cloth is $6 a length. Calculate:
1. The CPI basket.
Answer:
The CPI basket is 10 bottles of juice and 5 units of cloth.
2. The CPI in the current year.
Answer:
CP IP revious Y ear
=
CP ICurrent Y ear
=
$4(10) + $5(5)
100 = 100
$4(10) + $5(5)
$4.5(10) + $6(5)
100 = 115.38
$4(10) + $5(5)
3. The ination rate in the current year.
Answer:
i=
CP I1 CP I0
CP I0
115.38 100
100 = 15.38%
100
100 =
Question 3: Decomposing Economic Growth
a. Japans real GDP was 561trillion yen in 2007 and 569 trillion yen in 2008. Japans population was
127.7 million in 2007 and 127.8 million in 2008. Calculate
1. The economic growth rate.
Answer:
Growth Rate =
569 561
100 = 1.43%
561
2. The growth rate of real GDP per person.
Answer:
Growth Rate =
569/127.8 561/127.7
4.452 4.393
100 =
100 = 1.34%
561/127.7
4.393
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Therefore, we can see that some of the growth in GDP came from the rise in population.
b. 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.
1. Does Longland experience diminishing returns? Explain why or why not.
Answer:
Longland experiences diminishing returns. Diminishing returns are 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).
2. 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.
Answer:
The economy does not conform to the one third rule; instead it conforms to a one
half rule. In this economy, an x percent increase in capital per hour of labor leads to a
0.25x percent increase in real GDP per hour of labor. To determine the rule in Longland,
calculate the percentage change in capital per hour labor and real GDP per hour of labor
at each of the levels provided in the question, and then divide the percentage change in
real GDP per hour of labor by the percentage change in capital per hour of labor. For
example, 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.
3. Explain how you would do the growth accounting for Longland and calculate the eect of
technological change on growth in the fourth year described above.
Answer:
Growth accounting would be done in qualitatively the same way as in the U.S. economy with the dierence that any percentage 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 increase in real
GDP per hour of labor is the result of technological growth. So the 40 percent increase
in real GDP per hour of labor is the result of technological change.
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