Question

Suppose the inverse demand for a product produced by a single firm is given by: P=78−4(Q) and this firm has a marginal cost of production of: MC=6 1. If the firm cannot price-discriminate, what is the profit-maximizing price and level of output?

Answer 1

The profit-maximizing output for the firm is 18 units, with a profit-maximizing price of $6 per unit when marginal cost equals marginal revenue.

Step-by-step explanation:

The student asks to determine the profit-maximizing price and level of output for a firm with a given inverse demand function and constant marginal cost. To find the profit-maximizing output, we set the marginal cost (MC) equal to marginal revenue (MR), which, for a single-price firm, equates to the market price P. Since the MC is constant at 6, we equate it to the inverse demand function P = 78 - 4Q to find Q. Solving for Q gives us Q = (78 - 6) / 4 = 18. The profit-maximizing price is then P = 78 - 4(18) = 78 - 72 = 6.

Therefore, the profit-maximizing level of output is 18 units, and the profit-maximizing price is $6. The firm should produce 18 units and sell them at a price of $6 each to maximize profits, assuming it cannot price discriminate and must charge all customers the same price.