A drug company produces a new drug to treat baldness. The inverse demand curve for the drug is P = 205 - 20Q, where Q measures the number of pills in millions. The various costs of production are given by TC = 100 + 5Q, ATC = 5 + 100/Q, and MC = 5. If the government grants this firm a patent, it will earn profits of _____. If the government revokes the patent and the firm must sell its drug at marginal cost because of competition, it will earn profits or losses of _____.

Question

Quizplus · Accepted Answer

To find the profits with a patent, we first determine the monopolist's quantity by setting MR = MC. The inverse demand curve is P = 205 - 20Q, so the total revenue (TR) = P*Q = (205 - 20Q)Q. The marginal revenue (MR) is the derivative of TR with respect to Q, which is MR = 205 - 40Q. Setting MR = MC gives 205 - 40Q = 5, solving for Q gives Q = 5 million pills. The price from the demand curve at this quantity is P = 205 - 20*5 = $105. The total revenue at this quantity is TR = P*Q = $105 * 5 = $525 million. The total cost (TC) at this quantity is TC = 100 + 5*5 = $125 million. Thus, the profit with a patent is Profit = TR - TC = $525 million - $125 million = $400 million.Without the patent, the firm sells at MC = $5. The quantity at this price can be found from the demand curve: 5 = 205 - 20Q, which gives Q = 10 million pills. However, since the price equals the marginal cost, the firm makes zero economic profit in the long run due to perfect competition. The profit or loss without the patent is $0 - TC, where TC at Q = 10 is 100 + 5*10 = $150 million. However, since we're considering the profit relative to selling at marginal cost, the firm doesn't make a traditional "profit" or "loss" in the same sense as with a patent because it's selling at the cost of production. The initial calculation for losses without the patent was incorrect because it considered the total cost at a specific quantity without accounting for the fact that selling at marginal cost in a competitive market typically means firms earn zero economic profit, not a loss in the traditional sense. Therefore, the correct interpretation is that the firm would not earn traditional profits when selling at marginal cost due to competition, but the calculation of a specific loss amount was not directly asked for in the second part of the question. The correct answer is that the firm earns $400 million with a patent and would theoretically earn $0 in economic profit without the patent due to competition forcing prices to equal marginal costs.

A Drug Company Produces a New Drug to Treat Baldness