<p>Practice Problems Cournot Oligopoly Two Firms, identical product. Each firm acts in the next round assuming that the other firm will continue to act as they did in the previous round. Mkt Demand : Q = 500 - .5P MCa = 20 MCb = 50</p><p>What is each firm’s reaction function? P = 1000 – 2Q P = 1000 – 2qa – 2qb 2 TRa = 1000qa – 2qa – 2qaqb MRa = 1000-4qa –2qb 20 = 1000-4qa –2qb 4qa = 980 -2qb qa = 245 -.5qb Reaction for a</p><p>P = 1000 – 2Q P = 1000 – 2qa – 2qb 2 TRb = 1000qb – 2qb – 2qaqb MRb = 1000-4qb –2qa 50 = 1000-4qb –2qa 4qb = 950 -2qa qb = 237.5 -.5qa Reaction for b</p><p>What is the Nash Equilibrium? Explain why your answer qualifies as a Nash equilibrium Set the reaction functions equal to each other: qa = 245 -.5(237.5 -.5qa) qa = 245 –118.75 +.25qa .75 qa = 126.25 qa = 168.67 qb = 237.5 -.5(168.67) Reaction for b qb = 153.16 check your work: qa = 245 -.5(153.16)= 168 (Reaction for a). So a and b react to each other, but nothing changes. Each is maximizing profit given the choice of the other (Nash), and nothing changes (Equilibrium)</p><p>Q= 153+168 = 321 P = 1000 – 2(321) = 358</p><p>What is the Monopoly outcome? Set Market MR = Marginal cost P = 1000 – 2Q TR = 1000Q-2Q2 MR = 1000-4Q 1000-4Q = 20 (why?) 4Q = 980 Q = 245 P = 1000 – 2(245) = 510</p><p>What is the competitive outcome?</p><p>P= 20, Q = 960</p><p>Of the three, which is most likely to occur in this case?</p><p>Dominant Firm with competitive fringe</p><p>Mkt Demand: Q = 500 - .5P</p><p>MCd = 50 + 2Q MCf = 40 + 4Q</p><p>What is the market share of the dominant firm? What will happen to their share in the future if there is entry by more fringe firms?</p><p>Dominant firm sets price based on residual demand (market demand – fringe supply) Fringe takes that price as given. QT = 500 - .5P Rewrite fringe supply in terms of Q (Q is a function of price since price = marginal cost) P = 25 + 4Qf -4Q = 40 – P Qf = -10 + .25P</p><p>Qd = QT -Qf = 500 - .5P – (-10 + .25P) Qd = 510 - .75P (residual demand faced by the dominant firm) .75P = 510 -Qd P =680 –1.33Qd 2 TR =680 Qd –1.33Qd MR =680 –2.66Qd 680 –2.66Qd = 50 + 2Qd 630 = 4.66 Qd Qd = 135 P = 680 –1.33( 135) P= 500</p><p>Qf = -10 + .25(500) Qf = 115</p><p>Sd = 135/(135+115) = 54%</p>