In a perfectly competitive market, a firm's marginal cost (MC) is given by MC = 10 + 2q, where q is the quantity produced. If the market price is 20, what is the profit-maximizing quantity for the firm?

• A. 10
• B. 20
• C. 0
• D. 5

Answer: (D)

Verified step by step guidance

1. Recall that in a perfectly competitive market, the profit-maximizing quantity is found where the firm's marginal cost (MC) equals the market price (P). This is because firms maximize profit by producing up to the point where the cost of producing one more unit equals the revenue gained from selling that unit.
2. Write down the given marginal cost function: \(MC = 10 + 2q\), where \(q\) is the quantity produced.
3. Set the marginal cost equal to the market price to find the profit-maximizing quantity: \$10 + 2q = 20$.
4. Solve the equation for \(q\) by isolating \(q\): subtract 10 from both sides to get \$2q = 20 - 10\(, then divide both sides by 2 to find \)q$.
5. Interpret the result as the quantity the firm should produce to maximize profit in this perfectly competitive market.