Consider 2 fifirms competing in a market with inverse market demand function P(Q) = 70-

Problem 3 - Doupolists (40 points) Consider 2 firms competing in a market with inverse market demand function P(Q) = 70 - 4Q. Firm A has cost function CA(Q) = 20 and firm B has cost function Cs (Q) = 180. Firms A and B are competing through quantity competition so that total supply to the market is Q = QA +QB, were Qais firm A's quantity choice and Qa is firm B's quantity choice. 1. (10 points) Determine firm A's profit maximizing choice of output for a given firm B output choice, QA(QB). [4's best response to B]. 2. (10 points) Determine firm B's profit maximizing choice of output for a given firm A output choice, QB(QA). [B's best response to A|. 3. (10 points) What is the Nash equilibrium in the quantity competition game between the two firms? What is the total supply to the market. What is the equilibram market price? 4. (10 points) Suppose, instead, firm B's cost function is, CB(Q) = 18Q + 25 ifQ >0 if Q = 0, that is, firm B has avoidable fixed costs F = 25 in addition to its variable costs. All else remains the same. (a) Determine firm B's best response function QB(QA). (b) Determine the Nash equilibrium (equilibria) of the duopoloy quantity competition be- tween firms A and B. State equilibrium price and quantity supplied by each firm