Scenario: Tobac Co. is a monopolist in the cigarette market in Nicotiana Republic, where the U.S. dollar is used as the official currency. The firm faces the demand curve shown below. The firm has a constant marginal cost of $2.00 per pack. The fixed cost of the firm is $50 million. To answer the questions below, it is useful to know that the equation of the (inverse) demand curve is P = 8 - 0.04Q, where Q is the quantity demanded (in millions of packs) and P is the price per pack (in $). Also, you should draw in the marginal revenue curve.

-Refer to the scenario above.The firm's maximum profit is ________.

Question

Scenario: Tobac Co. is a monopolist in the cigarette market in Nicotiana Republic, where the U.S. dollar is used as the official currency. The firm faces the demand curve shown below. The firm has a constant marginal cost of $2.00 per pack. The fixed cost of the firm is $50 million. To answer the questions below, it is useful to know that the equation of the (inverse) demand curve is P = 8 - 0.04Q, where Q is the quantity demanded (in millions of packs) and P is the price per pack (in $). Also, you should draw in the marginal revenue curve.
 
-Refer to the scenario above.The firm's maximum profit is ________.

Quizplus · Accepted Answer

To find the profit-maximizing quantity, we need to find where MR = MC. The marginal revenue can be found as the derivative of the demand function: MR = 8 - 0.08Q.

Setting MR = MC:
8 - 0.08Q = 2
6 = 0.08Q
Q = 75 million packs

To find the price, we can use the demand function:
P = 8 - 0.04Q
P = $5 per pack

Total revenue is:
TR = P x Q
TR = $5 x 75 million
TR = $375 million

Total cost is the sum of fixed and variable costs:
TC = $50 million + $2 x 75 million
TC = $200 million

Profit is:
π = TR - TC
π = $375 million - $200 million
π = $175 million

Therefore, the firm's maximum profit is $175 million (option B).