Question

Below is the profit function for a household. Find the profit maximizing amount of capital to hire. Assume technology is 100, labor is 100, the real wage is 10 and the rental price of capital is1 5)- (W

Answer 1

Plugging in given values,

$\pi$/P = 100 x (K^0.5 x 100^0.5) - (10 x 100) - (1 x K)

$\pi$/P = 100 x (10K^0.5) - 1,000 - K

$\pi$/P = 1,000K^0.5 - 1,000 - K

Profit is maximized when d($\pi$/P)/dK = 0

1,000 x 0.5 x (1/K^0.5) - 1 = 0

(500/K^0.5) = 1

K^0.5 = 500/1 = 500

Squaring both sides,

K = 250,000