Two firms with differentiated products compete by choosing price. Their demand functions are

Q1 = 10 - P1 + P2andQ2 = 10 + P1 - P2

where P1 and P2 are the prices charged by each firm, respectively, and Q1 and Q2 are the resulting demands. Marginal costs are zero. There are no costs. (AC = MC = 0 and FC = 0 for both firms.)

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 it sell, and what will its profit be? (Hint: Each firm maximizes its profit by choosing its own price.)

(A) [8 points] What are the reaction curves for the two firms (RC1 and RC2)? (Hint: in terms of prices)

(B) [4 points] What are the Nash (Cournot) equilibrium prices forthe two firms (P1 and P2)?

(C) [4 points] What are the Nash (Cournot) equilibrium quantities for the two firms (Q1 and Q2)?