Question

3. Country B’s current GDP is $500,000. It is growing at the rate of 8% per year. It has a current population of 5,000 which is growing at 1.5% a year.

(a) Using the rule of 70, how long will it be before Country B’s GDP doubles (round off to the nearest value)? What will it’s per-capita GDP be in that year?

(b) Using the rule of 70, how long will it be before Country B’s population doubles (round off to the nearest value)? What will it’s per-capita GDP be in that year?

(c) Approximately when will Country B’s per-capita income equal Country A’s?

country A:

GDP Doubling period = 70 / 2 = 35 years

Population after 35 years = 2,500 x (1.03)35 = 2,500 x 2.8139 = 7,034.66

GDP per capita after 35 years = GDP / Population = ($1,000,000 x 2) / 7,034.66 = $284.31

Answer 1

Country B GDP = $500,000

Rate of growth of GDP = 8%

Population of country B = 5,000

Rate of growth of population = 1.5%

a) It will take 70 / annual % growth rate of GDP = 70 / 8 = 8.75 = 9 years

Current population = 5,000

Population after 9 years would be = 5,000 * 1.015⁹ = 5,716.94

Thus per capita GDP after 9 years would be = 1,000,000 / 5,716.94 = 174.91

b) It will take 70 / annual % growth rate of population = 70 / 1.5 = 46.67 = 47 years

In 47 years, GDP would be 500,000 * 1.08⁴⁷ = 18,616,006.08

Per capita GDP that time would be = 18,616,006.08 / 10,000 = 1,861.6

c) From the data given, country A:

Country B GDP = 1,000,000

Rate of growth of GDP = 2%

Population of country B = 2,500

Rate of growth of population = 3%

Assume it takes X years to equal both country per capita income:

(500,000 * 1.08^x / 5000 * 1.015^x) = (1,000,000 * 1.02^x / 2,500 * 1.03^x)

Solving this would give, X = 29