Duopolists A and B face the following demand curves: Q_A = 120 - 2P_A + P_B and Q_B = 120 - 2P_B + P_A.If both firms have zero marginal cost and they form a cartel,what is the profit-maximizing price and quantity? A) P = 30, Q = 180. B) P = 40, Q = 160. C) P = 60, Q = 120. D) P = 80, Q = 80. E) P = 75, Q = 90.

Question

Quizplus · Accepted Answer

To find the profit-maximizing price and quantity, we need to first find the combined demand curve faced by the cartel. Adding the two demand curves together, we get:

Q = 240 - 2P

Setting marginal cost equal to zero, we get:

MC = 0

Therefore, the profit-maximizing quantity is where marginal revenue equals zero.

MR = 240 - 4Q

240 - 4Q = 0

Q = 60

Substituting this quantity into the combined demand curve, we can find the profit-maximizing price:

P = (240 - Q)/2 = 90/2 = 45

However, in a cartel, firms will typically agree to restrict output in order to drive up price and maximize profits. If the two firms in this duopoly agree to split the market evenly, each firm will produce half of the total quantity of 60, or 30 units. Therefore, the profit-maximizing price for each firm is:

P = (120 - 30)/2 = 45

So the final answer is (C) P = 60, Q = 120.

Duopolists a and B Face the Following Demand Curves: QA

Duopolists a and B Face the Following Demand Curves: Q_A