In Bertrand competition with differentiated goods, the demand curve for bags of Wilson tennis balls is q_W = 80 - 4P_W + 2P_D, and the demand curve for bags of Dunlop tennis balls is q_D = 80 - 2P_D + P_W. Two firms both have zero marginal costs. How many bags of tennis balls does each firm produce?

Question

Quizplus · Accepted Answer

To solve for the equilibrium quantity of each firm, we need to set their respective marginal costs to zero and the resulting price equal to their respective demand functions. For Firm 1 (producing bags of Wilson tennis balls): MC1 = 0 Price: P_W = (80 - q_W + 2P_D)/4 Setting MC1 = P_W, we get: 0 = (80 - q_W + 2P_D)/4 q_W = 64 - (1/2)P_D For Firm 2 (producing bags of Dunlop tennis balls): MC2 = 0 Price: P_D = (80 - q_D + P_W)/2 Setting MC2 = P_D, we get: 0 = (80 - q_D + P_W)/2 q_D = 48 - (1/2)P_W Substituting the equilibrium quantity of Firm 2 into the demand function for Firm 1 and solving for the price, we get: P_W = (80 - q_W + 2(48 - (1/2)P_W))/4 P_W = 38 Substituting the equilibrium quantity of Firm 1 into the demand function for Firm 2 and solving for the price, we get: P_D = (80 - q_D + 38)/2 P_D = 32 Thus, the equilibrium quantities for each firm are: q_W = 64 - (1/2)(32) = 48 q_D = 48 - (1/2)(38) = 29 Therefore, the answer is B, q_W = 64; q_D = 48.

In Bertrand Competition with Differentiated Goods, the Demand Curve for Bags