Question

1. In 1999, real GDP per capita in the US was $43,820 (2012 dollars). In 2018, real GDP per capita was $56,803.

(a) What was the annual growth rate of real GDP per capita from 1999 to 2018.

(b) Suppose when you graduate, you get a good job and your income is equal to GDP per capita. Also suppose your income grows at exactly the same rate as the growth rate in GDP per capita each year that you work. Additionally, suppose the real GDP per capita growth rate remains the same as it did from 1999-2018 throughout your working life. I expect you will work 45 years from now and retire in the year 2064. Given our scenario, how much will your income be when you retire in 2064?

Answer #1

In 1999, real GDP per capita in the US was $43,820 (2012 dollars). In 2018, real GDP per capita was $56,803.

(a) Annual growth rate of real GDP per capita during 19 years is given by 56,803 = 43,820(1+r)^19. This gives rate

of growth = (56,803/43,820)^(1/19) - 1 = 1.3752%

(b) Now income = GDP per capita. Growth rate of income = growth rate in GDP per capita each year = 1.3752%.

Real GDP per capita growth rate remains the same at 1.3752%. Working period = 45 years. The value of income

in 2064 = 56,803(1 + 3.752%)^45 = $297,998

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The following table depicts statistics on GDP per capita (ie,
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A
B
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Average annual growth rate of real GDP per capita (Year
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GDP per capita (Year 2088)
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$
$
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value)/ previous year
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(1)
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