Problem 1 - Cournot (15 points) Two firms, A and B are engaged in Cournot competition in a market with inverse demand function P(Q) = 240 - 4Q where Q is aggregate demand. Firm A has cost function CA (QA) = 48QA and Firm B has cost function CB (QB) = 36QB. Aggregate supply in the market is Q = QA + QB for any QA 2 0 and QB 2 0. 1. Write up firm A's profits as a function of its own output choice and conditional on firm B's output choice, IIA (QA|QB). Write up firm B's profits as a function of its own output choice and conditional on firm A's output choice, IIB (QB|QA). 2. Determine firm A's optimal choice of output conditional on B's output choice, QA (QB). Be careful to argue how you obtain this function. 3. Determine firm B's optimal choice of output conditional on A's output choice, QB (QA). Be careful to argue how you obtain this function. 4. Determine the Nash equilibrium (QA, QB). Carefully argue why this is an equilibrium. What is the equilibrium price in the market? 5. For a given production allocation (QA, QB), define total surplus TS(QA, QB) = WTP (QA + QB)- CA(QA) - CB(QB), where consumer willingness to pay for Q units of output is WTP(Q) = So P(Q') dQ' = 240Q - 2Q2. (a) What is total surplus in the Nash equilibrium? (b) What is the total surplus maximizing production allocation (Q*, QB )? [Hint: For this you need to carefully ask yourself: If a total amount of output Q is to be produced such that Q = QA + QB, what is the cost minimizing way of doing so? In particular, ask yourself if it is efficient to use both firm technologies.] (c) What is the deadweight loss of the Nash equilibrium?Problem 1 - Cournot (15 points) Two firms, A and B are engaged in Cournot competition in a market with inverse demand function P (Q) = 240 - 4Q where Q is aggregate demand. Firm A has cost function CA (QA) = 48QA and Firm B has cost function CB (QB) = 36QB. Aggregate supply in the market is Q = QA + QB for any QA 2 0 and Q B 2 0. 1. Write up firm A's profits as a function of its own output choice and conditional on firm B's output choice, IIA (QA|QB). Write up firm B's profits as a function of its own output choice and conditional on firm A's putput choice, IIB (QB|QA). 2. Determine firm A's optimal choice of output conditional on B's output choice, QA (QB). Be careful to argue how you obtain this function. 3. Determine firm B's optimal choice of output conditional on A's output choice, QB (QA). Be careful to argue how you obtain this function. 4. Determine the Nash equilibrium (QA, QB). Carefully argue why this is an equilibrium. What is the equilibrium price in the market? 5. For a given production allocation (QA, Q B), define total surplus TS(QA, QB) = WTP (QA + QB)- CA(QA) -CB(QB), where consumer willingness to pay for Q units of output is WTP(Q) = So P(Q')dQ' = 240Q - 2Q2. (a) What is total surplus in the Nash equilibrium? (b) What is the total surplus maximizing production allocation (Q**, Q; )? [Hint: For this you need to carefully ask yourself: If a total amount of output Q is to be produced such that Q = QA + QB, what is the cost minimizing way of doing so? In particular, ask yourself if it is efficient to use both firm technologies.] (c) What is the deadweight loss of the Nash equilibrium