Question

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

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

（can you please anwering with the detailed calculation steps? Thanks!)

Answer 1

Y = 8K^0.3N^0.7

When K = 30,

Y = 8 x (30)^0.3N^0.7 = 8 x 2.7742 x N^0.7 = 22.19N^0.7

In full-employment equilibrium, MPN = w*

MPN = dY / dN = 22.19 x 0.7 / N^0.3 = 15.53 / N^0.3 = 25

N^0.3 = 0.6214

Raising each side to the power of (1/0.3),

N = 0.20

Substituting in production function,

Y = 22.19N^0.7 = 22.19 x (0.20)^0.7 = 22.19 x 0.32 = 7.19 (Full employment output)