Question

Assume a competitive firm faces a market price of ​$90​, a cost curve​ of: C​ =1/3q³ + 9q + 1,250​, and a marginal cost​ of: MC = q² +9.

What is the​ firm's profit maximizing output​ level? ___units.

Answer 1

The profit-maximizing output level for the firm is 9 units.

Step-by-step explanation:

The profit-maximizing output level for the firm can be determined by setting marginal revenue equal to marginal cost. In a perfectly competitive market, where price is equal to marginal revenue, this equation can be simplified to: P = MR = MC. Using the provided information, the marginal cost equation is MC = q² + 9. To find the profit-maximizing output level, we need to find the quantity (q) where marginal cost is equal to the market price (P). Substituting the given market price of $90 into the marginal cost equation, we get:

90 = q² + 9

Subtract 9 from both sides:

81 = q²

Take the square root of both sides:

q = ±9

Since quantity cannot be negative in this context, the profit-maximizing output level is q = 9 units.