Do No Harm: 3 4. Working backward: Calculating growth rates from changes in outp

Question

Do No Harm: 3 4. 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) (Billions of 2005 dollars) Real Output 1950 1990 313 5,846 2,084 7,982 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

Explanation / Answer

As per Rule of 70,

Number of years a variable will take to double = 70/Average annual growth rate of variable

Real output gets doubled in 20 years.

So,

20 = 70/Average annual rate of growth of real output

Average annual rate of growth of real output = 70/20 = 3.5%

Thus,

Over this 40-year period, the average annual rate of growth of real output was 3.5%.

Nominal output gets doubled in 10 years.

So,

10 = 70/Average annual rate of growth of nominal output

Average annual rate of growth of nominal output = 70/10 = 7%

Thus,

The annual growth rate for nominal output was 7%.

Inflation rate = Nominal growth rate - Real growth rate = 7% - 3.5% = 3.5%

So,

The resulting estimate of the average rate of inflation over this 40-year period is between 3.5% per year.

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