Question

4. [40%] Suppose there is an industry comprising of only two airlines, AirAlpha and AirBeta, which are Cournot duopolists serving a particular route. The demand curve for tickets per day is Q = 200 – p where Q is the total number of passengers in both airlines and p is the price of tickets. The number of passengers in AirAlpha and AirBeta are q4 and q respectively, while the total costs of are cA(q) = 400 + 10q, and cg (q)= 400 + 30qB respectively. • Using the indirect demand relationship to find the price, write down the profit function of each airline. Find the reaction functions of each firm. Obtain the output levels that will be produced in a Cournot-Nash equilibrium, the price in such an equilibrium and the profits for each firm. If these two firms are in Bertrand competition, explain what the outcome would be, highlighting the difference between Cournot and Bertrand competition.

Answer 1

P=200-Q, MCA = 10 MCB = 30. Now TA= (P- MCA) QA = (200-10-9A-9B) QA = (190-QB) 9A-912 Now aña (190-QB) - 29A =0 a 29 A So & QABR = (1 90-9B)/2 ñ B= (P-MCB) a B = (200-30-9A-9B)9B = (170-9A) 93-9B2 BRR: :) 170-9 A = 29B soap (170-9A)/2 | Ans 6) In CN Eq m two BR funch cut, 80. 9A = 190 / 180 - WAL 2A = 190 -140 + q= 394 = 380,740 QA=70, 9B = 100/2 =50 Ang

&= QA+ 9B = 70+ 50 =120. P = 200-120= $80, TA = (80-10) 70 = (70)2 TB = (80-30) 50 =(50) 2 = $4900 7 = $2500 e Ang have different Mc, C.) Now But In Bestrand game, then two froms products are homogeneous. So PB o can't be less than 30 & PA can't be less tha 10. So at 8am (PA, PB) = (30,30) So each will share Mkt share equally P=30 Q = 200-30=170. So as compared to cournot, In Bertrand Level 1, & Price is lower. Ans. Game, totalole