Question

Year	Nominal GDP	Economic Growth	Workers	GDP Deflator	Capital	Population	CPI	M1	Inflation (with GDP Deflator)
2019	$22,000,000	2.10%	100	110	20,000,000	200	300	$4,000,000	1.10%
2069	$384,000,000	2.80%	150	320	60,000,000	300	1200	$40,000,000	2.90%

As you might expect from the increase in nominal GDP compared to the increased in the GDP deflator, real GDP grew over these projected 50 years. Also, population growth was modest given the span of 50 years. Will all of this in mind, by how much did real GDP per person grew on average over these 50 years? Don't forget that this will be an annual growth rate.

Please show your work and explain you reasoning.

Answer 1

ANSWER:

Real gdp in 2019 = (Nominal gdp in 2019 / GDP deflator) * 100

Real gdp in 2019 = (22,000,000 / 200) * 100

Real gdp in 2019 = 110,000 * 100

Real gdp in 2019 = 11,000,000

Real gdp per person in 2019 = Real gdp in 2019 / population = 11,000,000 / 200 = 55,000

Real gdp in 2069 = (Nominal gdp in 2069 / GDP deflator) * 100

Real gdp in 2069 = (384,000,000 / 300) * 100

Real gdp in 2069 = 1,280,000 * 100

Real gdp in 2069 = 128,000,000

Real gdp per person in 2069 = Real gdp in 2069 / population = 128,000,000 / 300 = 426,666.67

Annual growth rate = (Real gdp per person in 2069 / Real gdp per person in 2019) ^ 1 / n - 1

Annual growth rate = (426,666.67 / 55,000) ^ 1 / 50 - 1

Annual growth rate = (8.5333) ^ 1 / 50 - 1

Annual growth rate = 1.04381 - 1

Annual growth rate = 0.04381 or 4.381%

so the annual growth rate of real gdp per person from 2019 to 2069 is 4.381%