Over many years, small differences in growth rates can have large effects on the level of income. This question will help you understand this important point. Consider an initial value of real GDP equal to Yo. If real GDP grows at a rate of g percent annually, after N years real GDP will equal Yo(1+g). Now consider the following table. Let the initial level of GDP in all cases be 100. a. By using the formula provided above, compute the level of real GDP in column 1 for each year. For example, in Year 1, real GDP will equal 100x (1.01)¹ 101. For each year, compute the GDP. Complete the rest of the columns. (Round your responses to two decimal places.) b. In year 20, how much larger (in percentage terms) is real GDP in the 2.0-percent growth case compared with the 1.5-percent growth case? Real GDP in the 2.0-percent growth case is % larger. (Round your response to the nearest whole number) c. In year 50, how much larger is real GDP in the 2.0-percent growth case compared to the 1.5-percent growth case? Real GDP in the 2.0-percent growth case is % larger. (Round your response to the nearest whole number.) Real GDP with Alternative Growth Rates 1.0% 1.5% 2.0% $100 $100 $100 $101 101.50 $102 103.03. 104.57 $106.12 122.02 134.69 148.59 $164.46 Year- 0 1 3 20 50 $210.52 2.5% 100 102.50 107.69 163.86 269.16 $343.71
Over many years, small differences in growth rates can have large effects on the level of income. This question will help you understand this important point. Consider an initial value of real GDP equal to Yo. If real GDP grows at a rate of g percent annually, after N years real GDP will equal Yo(1+g). Now consider the following table. Let the initial level of GDP in all cases be 100. a. By using the formula provided above, compute the level of real GDP in column 1 for each year. For example, in Year 1, real GDP will equal 100x (1.01)¹ 101. For each year, compute the GDP. Complete the rest of the columns. (Round your responses to two decimal places.) b. In year 20, how much larger (in percentage terms) is real GDP in the 2.0-percent growth case compared with the 1.5-percent growth case? Real GDP in the 2.0-percent growth case is % larger. (Round your response to the nearest whole number) c. In year 50, how much larger is real GDP in the 2.0-percent growth case compared to the 1.5-percent growth case? Real GDP in the 2.0-percent growth case is % larger. (Round your response to the nearest whole number.) Real GDP with Alternative Growth Rates 1.0% 1.5% 2.0% $100 $100 $100 $101 101.50 $102 103.03. 104.57 $106.12 122.02 134.69 148.59 $164.46 Year- 0 1 3 20 50 $210.52 2.5% 100 102.50 107.69 163.86 269.16 $343.71
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Over many years, small differences in growth rates can have large effects on
the level of income. This question will help you understand this important
point. Consider an initial value of real GDP equal to Yo. If real GDP grows at a
rate of g percent annually, after N years real GDP will equal Yo(1+g). Now
consider the following table. Let the initial level of GDP in all cases be 100.
a. By using the formula provided above, compute the level of real GDP in
column 1 for each year. For example, in Year 1, real GDP will equal
100x (1.01)¹=101.
For each year, compute the GDP. Complete the rest of the columns. (Round
your responses to two decimal places.)
b. In year 20, how much larger (in percentage terms) is real GDP in the
2.0-percent growth case compared with the 1.5-percent growth case?
Real GDP in the 2.0-percent growth case is% larger. (Round your
response to the nearest whole number.)
c. In year 50, how much larger is real GDP in the 2.0-percent growth case
compared to the 1.5-percent growth case?
Real GDP in the 2.0-percent growth case is % larger. (Round your
response to the nearest whole number.)
Year
0
1
3
20
50
Real GDP with Alternative Growth Rates.
2.0%
$100
$102
1.0%
$100
$101
$103.03.
122.02
$164.46
1.5%
2.5%
$100
100
101.50
$102.50
104.57
106.12
107.69
134.69
$ 148.59
163.86
$210.52 $269.16 343.71
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