Question

Problem 1

In 1960 Botswana’s PPP adjusted GDP per capita was $990 and Brazil’s was $2440. Brazil is growing at a rate of 1% per annum, while Botswana is growing rapidly and equaled Brazil’s income level by 2000. What was the growth rate of Botswana?

Problem 2

In 1960 the population of Bangladesh was 50 million and in 2000 it was 130 million.
a. What was the population growth rate between 1960 and 2000?

b. At this rate, in which year will Bangladesh’s population reach 300 million?

c. The current population of Bangladesh is 165 million. What is average annual growth rate between 2000 and 2017?

d. What is the average annual growth rate over the 57-year period from 1960 to 2017?

Answer 1

Problem 1

In 1960 Botswana’s GDP per capita = $990

In 1960 Brazil’s GDP per capita = $2440.

Growth rate of GDP per capita = 1% per annum in Brazil

Growth rate of GDP per capita = x% per annum in Botswana

By 2000, Botswana’s GDP per capita = Brazil’s GDP per capita

990(1 + x%)^40 = 2440(1 + 1%)^40

x% = (3632.828/990)^(1/40) - 1 = 3.3%

Hence the growth rate of Botswana is 3.3%

Problem 2

In 1960 the population of Bangladesh was 50 million and in 2000 it was 130 million.
a.Population growth rate between 1960 and 2000 = (130/50)^(1/40) - 1 = 2.42%

b. At this rate, in , Bangladesh’s population reach 300 million

130*(1+2.42%)^n = 300

1.0242^n = 300/130

n = 35 years

c. The current population of Bangladesh is 165 million. The average annual growth rate between 2000 and 2017 is given by

165 = 130(1 + x%)^17

x% = 1.412%

d.Average annual growth rate over the 57-year period from 1960 to 2017 is given by

165 = 50(1 + x%)^57

x% = 2.12%