Real GDP per person in the country of Flip is $10,000, and the growth rate is 10 percent a year.Real GDP per person in the country of Flap is $20,000 and the growth rate is 5 percent a year.When will real GDP per person be greater in Flip than in Flap?

Question

Quizplus · Accepted Answer

After x years, the real GDP per person in Flip will be $10,000(1+0.1)^x = $10,000(1.1)^x.
After x years, the real GDP per person in Flap will be $20,000(1+0.05)^x = $20,000(1.05)^x.
We want to find the value of x such that $10,000(1.1)^x > $20,000(1.05)^x.
Divide both sides by $10,000(1.05)^x:
(1.1/1.05)^x > 2
(1.047619)^x > 2
Take the logarithm of both sides:
x*log(1.047619) > log(2)
x > log(2)/log(1.047619)
x > 14.9
Therefore, real GDP per person in Flip will be greater than in Flap after 15 years.

Real GDP Per Person in the Country of Flip Is