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

Using the formula for calculating future GDP based on growth rate and time: 
Future GDP per person in Flip = $10,000 x (1 + 0.1)^t where t is the number of years 
Future GDP per person in Flap = $20,000 x (1 + 0.05)^t

We want to find when Future GDP per person in Flip > Future GDP per person in Flap

$10,000 x (1 + 0.1)^t > $20,000 x (1 + 0.05)^t

Simplifying the equation: 
(1.1)^t > 2 x (1.05)^t

Taking the natural log of both sides: 
t ln(1.1) > ln(2) + t ln(1.05)

t > ln(2) / (ln(1.1) - ln(1.05)) ≈ 14.2

Therefore, in approximately 15 years, real GDP per person in Flip will be greater than in Flap.

Real GDP Per Person in the Country of Flip Is