Question

The Glorious Republic of Gisslovia has a population of 20 million. The current real GDP is $300 billion.

a) What is the current value of real per-capita GDP?

b) What would happen to your answer in part-a if, over the next 5 years, real GDP grew at 3% while the population grew at 2%?

c) What would happen to your answer in part-a if, over the next 5 years, real GDP grew at 3% while the population grew at 4%.

d) What growth rate for real GDP would you need over a 5 year period to achieve the real per-capita GDP value in part-b using the population growth rate in part-c

Answer 1

Population = 20,000,000

Real GDP = 300,000,000,000

a) Real per capita GDP = 300,000,000,000 / 20,000,000 = 15,000

b) If real GDP grow by 3% while population grew by 2%

Real GDP in 5 years would be = [300,000,000,000 * (1 + 0.03)^⁵] = 347,782,222,290

Population in 5 years would be = [20,000,000 * (1 + 0.02)^⁵] = 22,081,616

Real GDP per capita would be = 347,782,222,290 / 22,081,616 = 15,749.85

c) If real GDP grow by 3% while population grew by 4%

Real GDP in 5 years would be = [300,000,000,000 * (1 + 0.03)^⁵] = 347,782,222,290

Population in 5 years would be = [20,000,000 * (1 + 0.04)^⁵] = 24,333,058

Real GDP per capita would be = 347,782,222,290 / 24,033,058 = 14,292.58

d) To achieve real per capita GDP of 15,749.85 with population growth of 4%

Population in 5 years would be = [20,000,000 * (1 + 0.04)^⁵] = 24,033,058

Real GDP must be = 24,333,058 *15,749.85 = 383,242,014,297.29

Growth rate be r

383,242,014,297.29 = 300,000,000,000 * (1 + r)^⁵

r = 5.02%