The cost function for a product in a firm is given by 5q^2, where q is the amount of production. The firm can sell the p...

Question

The cost function for a product in a firm is given by 5q^2, where q is the amount of production. The firm can sell the product at a market price of 50 per unit. The number of units to be produced by the firm such that the profit is maximized is:

A. 5  B. 10  C. 15  D. 25

Accepted Answer

The firm should produce 5 units to maximize profit (pi_max = Rs.125). Profit equals revenue minus cost. Revenue grows linearly with quantity (price x units) while cost grows quadratically. The resulting profit function is a downward-opening parabola. Its maximum occurs where the marginal revenue equals the marginal cost, found by setting the first derivative to zero.