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PROBLEM SET 1 - SOLUTIONS
Due: April 11, 2001 (Wednesday)
ECN - 105
Spring 2001
Instructions: Please complete you assignment in the space allotted. You must you show
your work (albeit concisely). Reporting the answer alone will earn you no credit. This
will allow the problem sets to be much more quickly and accurately graded.
Chapter 2, Problem 6 (pp 38-39)
a. Nominal GDP2000 = $ 10,000,000
Nominal GDP2010 = $ 15,200,000
Real GDP2010 = $ 10,000,000
Implicit Price Deflator2010 = 1.52 or 152
Consumer Price Index2010 = 1.60 or 160
b. How much have prices risen between 2000 and 2010?
Laspeyres Index: prices have risen 60%
Paasche Index: prices have risen 52%
c. Advantages of CPI: A more focused measure of the consumer’s cost of living.
Advantages of GDP deflator: Gives a more comprehensive view of the economy
since it includes all goods and services.
Conclusion: This answer can vary as it is not definitive. The student should
mention the advantages and disadvantages of either measure.
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Chapter 3, Problem 6, (pp 71-72)
a. Sprivate = $ 750
Spublic = $ 0
S = $ 750
b. r = 5%
c. Sprivate = $ 750
Spublic = $ - 250
S = $ 500
d. r = 10%
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Working with Percentage Changes
Economists often examine percentage changes in variables. The percentage change in
real GDP from one year to the next, for example, represents economic growth during that
year. The percentage change in the CPI or in the GDP deflator measure the rate of
inflation for that year. The percentage change of the product of two variables is
approximately equal to the sum of the percentage changes in each variable (the
approximation is only valid for rather small percentage changes).
Recall, nominal GDP = P  Y where P is equal to the GDP deflator and Y is real GDP.
Consequently, the percentage change in nominal GDP is approximately equal to the
percentage change in P plus the percentage change in Y. Consider Table 2.
Table 2
(1)
Period
1
2
(2)
Nominal GDP (PY)
100
105.06
(3)
(4)
% in PY P
-1.00
5%
1.02
(5)
% in P
-2%
(6)
Y
100
103
(7)
% in Y
-3%
a. Calculate the percentage changes in Y and P between periods 1 and 2 in Table 2
and complete columns (5) and (7).
b. Using your answers in (5) and (7), calculate % change () in PY = _2_% + 3_% =
__5_%. Place this number in column (3).
c. Compute nominal GDP in period 2 exactly by calculating PY in period 2 =
1.02103 = 105.06. Therefore, the actual % in nominal GDP is equal to 100
(105.06 -100)/100=_5.06_%.
d. If % in PY = % in P + % in Y, one can subtract % in Y from both sides to
obtain: % in PY - % in Y = % in P. Recall that the GDP deflator = (Nominal
GDP)/(Real GDP), or P = PY/Y. The % in a quotient is approximately equal to
the % change in the numerator minus the % change in the denominator. Suppose
you did not know the level of P in Table 2, but you knew the % in PY and Y in
columns (3) and (7). You could then calculate % in P = % in PY - % in Y =
__2_%
e. As another example, consider labor productivity Y/L, which represents output per
worker. Its percentage change from one year to the next is approximately equal to
% change in Y plus/minus % change in L. Consequently, if Y grew by 5% in a
year and L grew by 2%, the labor productivity would grow by approximately
3 or 7 %
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