Question

The production function is given by the equation Y = K1/2 N1/2 and the wage rate is W = 0.5 and K = 4.
(i) Find the marginal benefit of adding an additional unit of labor to this economy.
(ii) Show using sketches the point of profit maximization.
(iii) What is the profit maximizing the number of workers hired?

Answer 1

(i) The marginal benefit (product) of adding an additional unit of labor to this economy is:

$MPN = Y'(N) = 0.5\frac{K^{0.5}}{N^{0.5}}.$

(ii) The point of profit maximization is:

$\frac{MPN}{W} = \frac{MPK}{K},$

(iii) The profit maximizing number of workers hired is:

$\frac{MPN}{W} = \frac{MPK}{K},$

$\frac{0.5K^{0.5}}{0.5N^{0.5}} = \frac{0.5N^{0.5}}{4K^{0.5}},$

$N = 8K.$