Question

17) (12 points) Two sellers (seller A and seller B) operate in a market in which the demand is given by (= 200 - p. Each seller has the same constant MC or AC, which is $100. Suppose that the consumers don't differentiate between the two sellers, and each seller chooses to maximize its profit. For each seller, there are only two options to choose from: (= 40 or (= 50. Assuming that collusion (cartel) is illegal, which will each seller choose? (Hint: You will have to find out the Nash equilibrium in the payoff matrix you can create using the above information.) A) QA = 50, QB = 50 B) QA = 50, QB = 40 C) QA = 40, QB = 40 D) QA = 40, QB = 50 E) None of the above

Answer 1

Market demand Q = 200-p P- 200-9 A - 98 mc, = MC₂ = $100. To When QA = 50 and QB = 50 u. P = 200-50-50 = $100 TA = (P-MC) QA - (200 GA-AB7 700) g. (100-100) X 50 TA = 0 To = 0 (identical sellers) When QA = 50 QB = 40 - P= 200-90 = $110 TA = (10 -100)x50 - 10x50 - $500 AB = (110-100) x 40 = $ 400 when QA = 40 QB=40 = P = 200-80= $120 TA = (120-100) x 40 = 20x 40 - $ 800 TB = $800 When QA = 40; QB = 50 ; P = $110 TA = 10x40 - $400 TB = 10 x 50 = $ 500 produce 9A = qb=40 Since, profit is maxi num when they both Hence, option (c) is correct.