In: Economics
The production function is f(x1, x2) = x11/2 x21/2 . 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.
(c) x1 = 2x2
At max: MP(x1)/P(x1) = MP(x2)/P(x2)
=> (0.5x1-0.5x20.5)/12 = (0.5x10.5x2-0.5)/24
=> x2/12 = x1/24
=> x2 = x1/2
=> 2x2 = x1 (or x1 = 2x2)