5 Question This question is supposed to familiarize you with the calculation of growth over multiple periods. In the lectures you learned that the growth rate of a variable from one period to the next is given by Yt - Yt-1 9y= Yt-1 where g, denotes the growth rate, y, the value of the variable y in period t, and yt-1 the value of the same variable in period t- 1. Very often we are dealing with growth over many periods, say 50 years, in which case the above formula is not helpful. In that case we use the following formula: Yt = Yo (1+9y), where yo is the value of the variable at the beginning of the period, y, is the value of the variable after t periods, and g, is the (constant) growth rate. Depending on what information is given, you can solve the formula for either yt, Yo, gy, or for t. Now turn to the actual problem: The poorest countries in the world currently have an annual per capita income of about $600. We can reasonably assume that it is nearly impossible to live on an income below half this level (below $300). Per capita income in the United States in 2000 was about $33,000. With this information in mind, consider the following questions. a) For how long is it possible that per capita income in the United States has been growing at an average rate of 2% per year? b) Some economists have argued that growth rates are mismeasured. For example, it may be difficult to compare per capita income today with per capita income a century ago when so many of the goods we can buy today were not available at any price then. Suppose the true growth rate in the last century was 3% per year rather than 2%. What would the level of per capita income in 1800 have been in this case? Is this answer plausible?
5 Question This question is supposed to familiarize you with the calculation of growth over multiple periods. In the lectures you learned that the growth rate of a variable from one period to the next is given by Yt - Yt-1 9y= Yt-1 where g, denotes the growth rate, y, the value of the variable y in period t, and yt-1 the value of the same variable in period t- 1. Very often we are dealing with growth over many periods, say 50 years, in which case the above formula is not helpful. In that case we use the following formula: Yt = Yo (1+9y), where yo is the value of the variable at the beginning of the period, y, is the value of the variable after t periods, and g, is the (constant) growth rate. Depending on what information is given, you can solve the formula for either yt, Yo, gy, or for t. Now turn to the actual problem: The poorest countries in the world currently have an annual per capita income of about $600. We can reasonably assume that it is nearly impossible to live on an income below half this level (below $300). Per capita income in the United States in 2000 was about $33,000. With this information in mind, consider the following questions. a) For how long is it possible that per capita income in the United States has been growing at an average rate of 2% per year? b) Some economists have argued that growth rates are mismeasured. For example, it may be difficult to compare per capita income today with per capita income a century ago when so many of the goods we can buy today were not available at any price then. Suppose the true growth rate in the last century was 3% per year rather than 2%. What would the level of per capita income in 1800 have been in this case? Is this answer plausible?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:5 Question
This question is supposed to familiarize you with the calculation of growth over
multiple periods. In the lectures you learned that the growth rate of a variable from
one period to the next is given by
Yt - Yt-1
9y=
Yt-1
where g, denotes the growth rate, y, the value of the variable y in period t, and yt-1
the value of the same variable in period t- 1. Very often we are dealing with growth
over many periods, say 50 years, in which case the above formula is not helpful. In
that case we use the following formula:
Yt = Yo (1+9y),
where yo is the value of the variable at the beginning of the period, y, is the value of
the variable after t periods, and g, is the (constant) growth rate. Depending on what
information is given, you can solve the formula for either yt, Yo, gy, or for t.
Now turn to the actual problem:
The poorest countries in the world currently have an annual per capita income
of about $600. We can reasonably assume that it is nearly impossible to live on an
income below half this level (below $300). Per capita income in the United States
in 2000 was about $33,000. With this information in mind, consider the following
questions.
a) For how long is it possible that per capita income in the United States has been
growing at an average rate of 2% per year?
b) Some economists have argued that growth rates are mismeasured. For example,
it may be difficult to compare per capita income today with per capita income
a century ago when so many of the goods we can buy today were not available
at any price then. Suppose the true growth rate in the last century was 3% per
year rather than 2%. What would the level of per capita income in 1800 have
been in this case? Is this answer plausible?
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