(a) They compete in quantities (Cournot -Nash equilibrium = C).(b) They compete in quantities with the first firm (the Leader) choosing the output first (Stackelberg competition = S).(c) They collude and choose quantities in order to maximize the joint profits (behave like two plants of a multiplant monopoly = M). PROBLEM Two firms (1 and 2) with total costs TC:(q) = 60q and TC:(q)=120q (hence the marginal costs areconstant at 60 and 120 respectively) are facing a market demand Q= 1200 - 2p.Analyzing each of the 4 scenarios below, fill in the table below;Market organizationQ= q1+q2 (total output)q1q2P (market price)C = CournotS = Stackelberg%DM = CollusionP = Perfect competition%3D

TC1 = 60q MC1 = 60 TC2 = 120q MC2 = 120 Q = 1200 - 2P q1 + q2 = 1200 - 2P P = 600 - 0.5q1 - 0.5q2 For the Cournot model, we equate MR with MC for each firm: TR1 = P*q1 TR1 = (600 - 0.5q1 - 0.5q2 ) * q1 TR1 = 600q1 - 0.5q1 2 - 0.5q2 q1 MR1 = dTR1 / dq1 MR1 = 600 - q1 - 0.5q2 Equating MR1 with MC1 600 - q1 - 0.5q2 = 60 q1 = 540 - 0.5q2 ----------------------1 Similarly for firm 2: TR2 = P*q2 TR2= (600 - 0.5q1 - 0.5q2 ) * q2 TR2 = 600q2 - 0.5q2 2 - 0.5q2 q1 MR2 = dTR1 / dq2 MR2 = 600 - q2 - 0.5q1 Equating MR2 with MC2 600 - q2 - 0.5q1 = 120 q2 = 480 - 0.5q1 ------------------------2Putting equation 1 in equation 2: q1 = 540 - 0.5(480 - 0.5q1 ) q1 = 540 - 240 + 0.25q1 0.75q1 = 300 q1 = 400 units q2 = 480 - 0.5*400 q2 = 280 units Q = q1 + q2 Q = 400 + 280 = Q = 680 units Q = 1200 - 2P 680 = 1200 - 2P P = $260Stackelberg Competition: Let firm 1 be the leader. Now, we know firm 2's reaction function from equation 2: q2 = 480 - 0.5q1 Putting this in the price equation: P = 600 - 0.5q1 - 0.5q2 P = 600 - 0.5q1 - 0.5(480 - 0.5q1 ) P = 600 - 240 - 0.5q1 + 0.25q1 P = 360 - 0.25q1 Now, TR1= P*q1 TR1= 360q1 - 0.25q1 2 MR1 = dTR1 / dq1 MR1 = 360 - 0.5q1 MR1 = MC1 360 - 0.5q1 = 60 0.5q1 = 300 q1 = 600 units Now, putting the value of q1 in Firm 2's reaction function: q2 = 480 - 0.5q1 q2 = 480 - 0.5*600 q2 = 480 - 300 q2 = 180 units Total Q = 600 + 180 = 780 units Q = 780 units P = 600 - 0.5q1 - 0.5q2 P = 600 - 0.5*780 P = 600 - 390 P = $210Colluding monopoly: Let middle MC = 90 We know, P = 600 - 0.5Q MR = 600 - Q Now, the profit-maximizing point is where MR=MC MR = MC 600 - Q= 90 Q = 510 units q1 + q2 = 510 Both selling equal quantities: Equating both profits: TR1 - TC1 = TR2 - TC2 600q1 - 0.5q1 2 - 0.5q2 q1 - 60 q1 = 600q2 - 0.5q2 2 - 0.5q2 q1 - 120q2 540 q1 - 0.5q1 2 = 480q2 - 0.5q2 2 q1 (540 - 0.5q1 ) = q2 (480 - 0.5q2 ) By calculation: q1 = 1.125q2 1.125q2 + q2 = 510 q2 = 240 units Putting this in the value: q1 = 1.125*240 q1 = 270 units P= 600 - 0.5*510 P = $345