Question

Assume the following production function: Y=8K^0.3N^0.7

a) Keeping capital constant, show graphically a technological improvement. b) If the capital stock is K = 30, and the prevailing wage rate is w* = $25, find the full

employment.

b) If the capital stock is K = 30, and the prevailing wage rate is w* = $25, find the full

employment.

Answer 1

a) The production function is given by:

Y=8K^0.3N^0.7

Keeping capital (K) constant, if the given technology improves, then the Real GDP curve will shift to the upward. It helps to increase the level of output. Better technology make the workers more productive.

The graphical representation is in the following:

b) The production function is given by:

Y=8K^0.3N^0.7

The capital stock is K = 30, and the prevailing wage rate is w* = $25

then, the marginal productivity of labour (MPN) = δY/δN= 5.6 (K/N)^0.3= w*

Suppose the full employment level is = N^d

then,

N^0.3= (5.6 x K^0.3/w)

or, N^d= (5.6 x K^0.3/w)^10/3

or, N^d= (5.6 x 30^0.3/25)^10/3

or, N^d= 0.2

So, the full employment level = 0.2