The demand function in a duopoly is: P = 100

Question

The demand function in a duopoly is: P = 100 - 2(Q1 + Q2). If the first firm decides to sell 10 units while the second firm sells 20 units, which of the following will be true?
A) The second firm will earn twice as much revenue as the first firm.
B) The second firm will sell at a lower price than the first firm.
C) An increase in one firm's output will not affect the other firm's revenue.
D) The first firm will earn a higher profit than the second firm.
E) The market price will be determined by the second firm's output which is larger than the first firm's output.

Quizplus · Accepted Answer

EThe market price is determined by the total quantity sold by both firms, which is $P = 100 - 2(Q1 + Q2) = 100 - 2(10 + 20) = 60$. Both firms sell at this price, so the revenue of the second firm, selling 20 units, will indeed be twice as much as the first firm, which sells 10 units, making choice A correct. Choice E is incorrect because the market price is determined by the combined output of both firms, not just the output of the firm with the larger quantity.