Question 3. Two energy firms, Az and Bx, compete in an oligopolistic market, where the market demand is Q (P) = 450 - P and P is the price of one unit of energy. The firms have identical fixed marginal costs MCAZ (QAZ) = MCBx(QBx) = 150 (QAZ is the quantity produced by Az and Qx is the quantity produced by Bx). a. For a given QAZ, find the residual demand and the residual marginal revenue of Firm Bx. Answer: The residual demand is QBx (P) = 450 - QAZ - P. The residual inverse demand is P(QBx) = 450 - QAZ - QBX, hence Bx's residual MR is MRBx (QBx) = 450 - QAZ - 2Q Bx b. Similarly, for a given QBX, find the residual demand and the residual marginal revenue of Firm Az. Answer: Similarly, QAZ(P) = 450 - QBx - P, P(QAZ) = 450 - QBZ - QAZ and MRAZ (QAZ) = 450 - QBx - 2QAZ c. Calculate the best response functions of the two firms. Answer: Setting MRAZ (QAZ) = 450 - QBx - 2QAZ = 150 yields the best response for Firm Az: QAZ (QBx) = 150 - QBX. Similarly, the best response of Firm Bx is QBx (QAZ) = 150 - 1 Q Ax. d. Determine the outcomes of the Nash-Cournot equilibrium of this market. Answer: Solving the equations QAZ = 150 - 2QBx and QBx = 150 - 1QAZ yields the unique equilibrium QAZ = QBx = 100