Question

1) Labor Input = 100 million worker hours / year

   Capital Input =   $ 20 billion

   Exponent α = 0.65

   Total Factor Productivity, A = 7.5

1. What are the $ shares of the total output contributed by Labour and Capital?
2. Suppose the Labor input is increased by 20% with capital input remaining constant, how it will change the output shares of Labor and Capital in $?

Answer 1

Labor Input = 100 million worker hours / year

   Capital Input =   $ 20 billion

   Exponent α = 0.65

   Total Factor Productivity, A = 7.5

a) Cobb Douglas production function is of the form

y=k^α

Y=AK^αL^1-α

=7.5*20^0.65*100^0.35

=$263.47 billion

$ share of capital in output = 0.65*$263.47 = $171.26 billion

$ share of Labour in output = 0.35*$263.47 = $92.21 billion

b) Labour = 120 million worker hours per million

Y=AK^αL^1-α

=7.5*20^0.65*120^0.35

=$280.83 million

$ share of capital in output = 0.65*$280.83 = $182.54 billion (increases)

$ share of Labour in output = 0.35*$280.83 = $98.29 billion (increases)