Question

as a monopolist. Illustrate your answer with a diagram d) Calculate the consumer surplus, producer surplus, and deadwelt os the m ss as a perfectly price-discriminated monopolist. Illustrate your answer with a diagram Consider about a duopoly case: two firms compete by choosing prices differentiated goods. Their demand functions are Qi-20-P Pa and Qa-20 Pr-Pa where Pi and Pa are the prices charged by each firm, respectively, and Qu and Qa are the resulting demands. Fixed costs and marginal costs are both zero. (a) Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will itsell, and what vwill its proft be? (b) Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be?

Answer 1

A. P1= P2=$20

Q1=Q2=20

Profit1=Profit2=$400

B.

P1= $30 ,P2=$25

Q1=15, Q2=25

Profit1=$450, Profit2=$625

Q_1 = 20 - P_1 + P_2 Q_2 = 20 + P_1 - P_2 and MC_1 = MC_2 = 0 irm 1 TR_1 = P_1 q_1 = 20 P_1 - P^2_1 + P_1 P_2 MR_1 = partial differential T R_1/ partial differential P_1 = 20 2 P_1 + P_2 at equilibrium M R_1 = M C_1 20 - 2 P_1 + P_2 = 0 20 + P_2/ 2 = P_1 bar (1) FIRM (2) T R_2 = P_2 theta_2 = 20 P_2 + P_1 P_2 - P^2_2 M R_2 = 20 + P_1 - 2 P_2 M R_2 = M C_2 20 + P_1 - 2 P_2 = 0 20 + P_1/ 2 = P_2 bar (2) since (1) and (3) are symmetric P_1 = P_2 or on solving 10 + 1/ 2 (10 + P_1/ 2) = P_1 P^*_1 = 20, P^*_2 = 20 Q_1 = 20 - 20 + 20 = 20 Q_2 = 20 + 20 - 20

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