The production function is given by f(x)=4x^1/2.If the price of the commodity produced is $80 per unit and the cost of the input is $40 per unit, how much profits will the firm make if it maximizes profits? A)$318 B)$1,284 C)$640 D)$625 E)$323

Question

Quizplus · Accepted Answer

To maximize profits, set marginal revenue equal to marginal cost. The marginal product is the derivative of f(x), which is 2x^(-1/2). Setting 80 * 2x^(-1/2) = 40 gives x = 16. The output is f(16) = 16. Profit is (80*16) - (40*16) = 640.

The Production Function Is Given by F(x)=4x1/2

The Production Function Is Given by F(x)=4x^1/2