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Earlier we mentioned the special case of a monopoly where MC = 0. Let’s find the firm’s best choice when more goods can be produced at no extra cost. Since so much e-commerce is close to this model—where the fixed cost of inventing the product and satisfying government regulators is the only cost that matters—the MC = 0 case will be more important in the future than it was in the past. In each case, be sure to see whether profits are positive. If the optimal level of profit is negative, then the monopoly should never start up in the first place; that’s the only way it can avoid paying the fixed cost.

If a firm's demand curve is given by the equation P = 200 − Q and fixed cost = 1,000, then the profit maximizing level of production would be and profit would be $. (Please enter only whole numbers.)

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Correct! A linear demand curve for a monopolist has an associated marginal revenue curve with the same intercept but twice the slope. Therefore, with the demand curve given by the equation, P = 200 − Q, MR = 200 − 2Q. Since MC = 0, and profit is maximized where MR = MC, the profit maximizing level of production occurs at Q = 100. With Q = 100, the demand curve equation yields P = $100. Total Revenue is P × Q = $100 x 100, or $10,000. Since total cost equals fixed cost of $1,000, the monopoly earns positive profits of $9,000.
Sorry! Consider how to apply the profit maximizing rule in this scenario. To review how to determine the profit maximizing level of output, please see the section “How a Firm Uses Market Power to Maximize Profit.”
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      If a firm's demand curve is given by the equation P = 4,000 − Q and fixed cost is $900,000
, then the profit maximizing level of production would be and profit would be $. (Please enter only whole numbers.)

      Correct! A linear demand curve for a monopolist has an associated marginal revenue curve with the same intercept but twice the slope. Therefore, with the demand curve given by the equation P = 4,000 − Q, MR = 4,000 − 2Q. Since MC = 0, and profit is maximized where MR = MC, the profit maximizing level of production occurs at Q = 2,000. With Q = 2,000, the demand curve equation yields P = $2,000. Total Revenue is P × Q = $2,000 × 2,000, or $4,000,000. Since total cost equals fixed cost of $900,000, the monopoly earns positive profits of $3,100,000.
      Sorry! Consider how to apply the profit maximizing rule in this scenario. To review how to determine the profit maximizing level of output, please see the section “How a Firm Uses Market Power to Maximize Profit.”

      If a firm's demand curve is given by the equation P = 120 − 12Q and fixed cost = 1,000, then the profit maximizing level of production would be and profit would be -$. (Please enter only whole numbers.)

      Correct! A linear demand curve for a monopolist has an associated marginal revenue curve with the same intercept but twice the slope. Therefore, with the demand curve given by the equation, P = 120 − 12Q, MR = 120 − 24Q. Since MC = 0, and profit maximized where MR = MC, the profit maximizing level of production occurs at Q = 5. With Q = 5, the demand curve equation yields P = $60. Total Revenue is P × Q = $60 × 5 = $300. Since total cost equals fixed cost of $1,000, the monopoly earns profits of -$700 and would therefore never start up in the first place.
      Sorry! Consider how to apply the profit maximizing rule in this scenario. To review how to determine the profit maximizing level of output, please see the section “How a Firm Uses Market Power to Maximize Profit.”