Question

At the beginning of 2018, the aggregate output in Atlantis was $15 billion and the population was 3 million. During 2018, aggregate output rose by 3.5%, the population rose by 2.5%, and the aggregate price level remained constant. For all calculations, calculate to 2 decimal places.

a) What was the aggregate output per capita in Atlantis at the beginning of 2018?

b) What was aggregate output in Atlantis at the end of 2018?

c) What was the population in Atlantis at the end of 2018?

d) What was aggregate output per capita in Atlantis at the end of 2018?

e) What was the annual growth rate of per capita output in Atlantis during 2018?

Answer 1

(a)

Aggregate output at the beginning of 2018 = $15 billion

Population at the beginning of 2018 = 3 million

Calculate the aggregate output per capita at the beginning of 2018 -

Aggregate output per capita = Aggregate output at the beginning of 2018/Population at the beginning of 2018

Aggregate output per capita = $15 billion/3 million = $5,000

The aggregate output per capita in Atlantis at the beginning of 2018 was $5,000.

(b)

Aggregate output at the beginning = $15 billion

Growth rate of output = 3.5% or 0.035

Calculate the aggregate output at the end -

Aggregate output at the end = $15 billion + ($15 billion * 0.035) = $15 billion + $0.525 billion = $15.525 billion

The aggregate output in Atlantis at the end of 2018 was $15.525 billion.

(c)

Population at the beginning = 3 million

Growth rate of population = 2.5% or 0.025

Calculate the population at the end -

Population at the end = 3 million + (3 million * 0.025) = 3 million + 0.075 million = 3.075 million

The population in Atlantis at the end of 2018 was 3.075 million.

(d)

Aggregate output at the end = $15.525 billion

Population at the end = 3.075 million

Calculate the aggregate output per capita at the end -

Aggregate output per capita = Aggregate output at the beginning of 2018/Population at the beginning of 2018

Aggregate output per capita = $15.525 billion/3.075 million = $5,048.78

The aggregate output per capita in Atlantis at the end of 2018 was $5,048.78

(e)

Aggregate outut per capita at the beginning = $5,000

Aggregate output per capita at the end = $5,048.78

Calculate the annual growth rate of per capita output -

Annual growth rate = [($5,048.78 - $5,000)/$5,000] * 100 = 0.97%

The annual growth rate of per capita output in Atlantis during 2018 was 0.97%