Question

Country A and country B start with the same GDP per capita of $50,000. Country A's GDP per capita grows at a constant rate of 2.8%, and country B's GDP per capita grows at a constant rate of 1.4%. Compute the difference in GDP per capita for these two countries after 100 years.
HINT: use the rule of 70 to see how long it will take each country to double its GDP per capita.

Answer 1

The rule of 70 is a technique used to forecast how many years would take to a variable to double its value. It consists on dividing number 70 by the growth rate of the variable of interest, which in this case is the GDP of countries A and B.

According to the rule of 70, let's compute how long will take for the GDP of each country to double:

• Country A: 70/2.8= 25 years
• Country B: 70/1.4=  50 years

As the growth rates are constant, it is possible to compute the exact value of the GDP of each country in 100 years time using the number of years for output duplication.

• Country A duplicates its growth every 25 years. Hence, it will happen 4 times in 100 years. In year 25, the output will be $100,000. In year 50, it will duplicate again and reach $200,000. The third duplicate will take place in year 75 and GDP will sum $400,000. Finally, in year 100 it will duplicate one last time and country A will end up the century with a GDP per capita of $800,000.
• Country B duplicates its growth every 50 years. Therefore, it will happen twice in 100 years.  In year 50, the output will be $100,000. In year 100, the last duplicate will take place, and country B will end up with a GDP per capita of $200,000.