Question

In the past ten years, a country's total output has increased from 2000 to 3000, the capital stock has risen from 4000 to 5200, and the labour force has increased from 400 to 580. Suppose the elasticities aK = 0.4 and aN = 0.6. Show your work when you answer the following: a. How much did capital contribute to economic growth over the decade? b. How much did labour contribute to economic growth over the decade? c. How much did productivity contribute to economic growth over the decade?

Answer 1

To calculate the contribution of each factor to economic growth, we can apply the following formula:

Contribution of a factor to economic growth = Factor's share in output x (Factor's elasticity with respect to output) x 10-year change in output

Using the given data:

a. Contribution of capital to economic growth:

Capital's share in output = Capital stock / (Capital stock + Total output) = 5200 / (5200 + 3000) = 0.667

Capital's elasticity with respect to output = aK = 0.4

10-year change in output = 3000 - 2000 = 1000

Contribution of capital to economic growth = Capital's share in output x (Capital's elasticity with respect to output) x 10-year change in output = 0.667 x 0.4 x 1000 = 266.8

b. Contribution of labour to economic growth:

Labour's share in output = Labour force / (Labour force + Total output) = 580 / (580 + 3000) = 0.160

Labour's elasticity with respect to output = aN = 0.6

10-year change in output = 3000 - 2000 = 1000

Contribution of labour to economic growth = Labour's share in output x (Labour's elasticity with respect to output) x 10-year change in output = 0.160 x 0.6 x 1000 = 96

c. Contribution of productivity to economic growth:

Contribution of capital to economic growth + Contribution of labour to economic growth = 266.8 + 96 = 362.8

The country's total output has increased by 1000 over the decade. So the contribution of productivity to economic growth is 362.8 / 1000 = 0.3628

d. The productivity growth rate over the decade is:

Productivity growth rate = 10-year change in output / 10-year change in total factor inputs = 1000 / (0.667 x 400 + 0.160 x 580)