Question

The production function is f(x₁, x₂) = x₁^1/2 x₂^1/2 . If the price of factor 1 is $12 and the price of factor 2 is $24, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?
(a) x₁ = x₂

(b) x₁ = 0.50x₂

(c) x₁ = 2x₂

(d) x₁ = 24x₂

(e) We can't tell without knowing the price of output.

 

Answer 1

(c) x₁ = 2x₂

At max: MP(x1)/P(x1) = MP(x2)/P(x2)

=> (0.5x1^-0.5x2^0.5)/12 = (0.5x1^0.5x2^-0.5)/24

=> x2/12 = x1/24

=> x2 = x1/2

=> 2x2 = x1 (or x1 = 2x2)