6. Working backward: Calculating growth rates from changes in output Aa Aa If yo
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6. Working backward: Calculating growth rates from changes in output Aa Aa If you start with a growth rate, you can use the rule of 70 to estimate the change in a variable. This question shows you that sometimes you can also do the reverse and use the rule of 70 to work back from changes in a variable to calculate the underlying rate of growth. This table shows the two measures of output in the years 1950 and 1990. Nominal output is measured in current dollars. Real output is measured in constant 2005 dollars. Nominal Output (Billions of dollars) 313 5,846 Real Output (Billions of 2005 dollars) 2,084 7,982 1950 1990 In round numbers, real output doubled two times in the 40 years between 1950 and 1990, so it doubled every 20 years. This means that real output grew at a rate z that solves the equation 20 = 70 / z. Over this 40-year period, the average annual rate of growth of real output was Between 1950 and 1990, nominal output increased by a factor of nearly 19, doubling more than four times To simplify the calculation, assume that nominal output doubled exactly four times in 40 years, or doubled every 10 years. This would imply the annual growth rate for nominal output was First you used the rule of 70 to estimate the rate of growth of real output. Then you used it to estimate the rate of growth of nominal output. Now you can use these two estimates to construct an estimate of the inflation rate The difference between the growth rate of nominal output and the growth rate of real output is the inflation rate. The resulting estimate of the average rate of inflation over this 40-year period is between per year. ONA 3 :6 © 2004-2016 /pl k, rights reserved. © 2013 Cengage Leaning e-ape as noted rights reserved Grade it Now Save & ContinueExplanation / Answer
Answer
rule of 70
is used to measure the number of years to double a value
required years to double=70/growth rate
growth rate=z=70/required years
Growth of real output
z=70/20=3.5%..............(using the given equation)
the growth of nominal output
the equation is
10=70/z...................(where assuming 10 years is required to double the amount)
z=70/10=7%
Approximate inflation rate between 1950 to 1990
e=growth of nominal output-growth of real output
=7-3.5
=3.5%
the inflation is between 3% to 4%.
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