Question

Assume that a leader country has real GDP per capita of \(40,000, whereas a follower country has real GDP per capita of \)20,000. Next, suppose that the growth of real GDP per capita falls to zero percent in the leader country and rises to 7 percent in the follower country. If these rates continue for long periods of time, how many years will it take for the follower country to catch up to the living standard of the leader country?

Short answer

The follower country will require ten years to catch up with the living standards of the leader country.

Step-by-step solution

Step 1. Understanding the growth rate and its effect on real GDP per capita for both countries.

Since the growth rate of real GDP per capita for the leader country is zero, the volume of real GDP per capita for the country will not increase in the future at this growth rate. But the volume of real GDP per capita of the follower country will increase by 7 percent each year because of the 7 percent growth rate.

The real GDP per capita of the leader country is $40,000, whereas the real GDP per capita of the follower country is $20,000. The real GDP per capita data suggests that if the follower country doubles its real GDP per capita, it will reach the level of leader country.

Step 2. Calculation of required number of years.

The required number of years for the follower country can be calculated using the “rule of 70” formula.

$$\begin{gathered} ApproximatenumberofyearsrequiredtodoubletherealGDP=\frac{70}{Annualpercentagerateofgrowth} \\ =\frac{70}{7} \\ =10years \end{gathered}$$

The follower country will require 10 years to reach the leader country's real GDP per capita level.