Question

1. How quickly will a country, growing at 2% a year, double its income? What about a country growing at 4% per year? How would that compare with a country growing at alternating rates of 0% and 8% per year? (in other words, which country grew faster, a steady 4% per year, or the “unstable” growth country, after, for example, 10 years) (b) Suppose a country's per capita income is currently growing at 4% per year. Then it adds an additional percentage point to its population growth rate for the next twenty years, but overall income continues to grow at the same rate. How much poorer/richer would the country be at the end of twenty years (per capita)?

Answer 1

Answer:

As per the given data

a)  As per rule of 40, Doubling Period = $\frac{40}{Annual growth rate}$

when annual growth rate =2 , Doubling period=$\frac{40}{2}$

=20 years

When annual growth rate=4%, Doubling period= $\frac{40}{4}$

= 10 years

b) per capita income is currently growing at 4% per year

per capita income=$\frac{overall\ income}{population}$

therefore

Increase in % growth in per capital income=% Growth in overall income - % growth in population

Increase in % growth in per capital income = 1%

New% growth in per capital income =4%+1%

=5%

If per capital income be M , then after 20 years

per capital income =  $M*(1.04)^{20}$

=

Therefore , per capital income will be higher by 2.1911 after 20 years (the country will be richer)