which are the information that you need? The only comment it\'s a \"yes\"???????
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which are the information that you need? The only comment it's a "yes"???????????
Consider the airline oligopolistic industry with two firms (carriers), A and B. Let the inverse demand function given by the equation p = 10-Q, where Q = qAT qB. Firms face the same total cost equal to TC,-4qi, where i = {A, B} 1) Compute the market equilibrium, assuming that the two firms simultaneously choose their output levels. As decision variables, are quantities strategic substitutes or complements and why? 2) Assume now the following timing of the game: at time 1, firm A chooses its output; at time 2 firm B chooses its output. Compute the market equilibrium. Which of the two firms has the advantage? Explain your answer 3) Assume now that the two firms decide to merge. In this case, the merging process requires an administrative cost equal to 2, independently of the quantities the two firms produce before or after the merger i) Do firms A and B have incentive to merge in case 1) above? ii) Do they have incentive to merge in case 2) above? Which firm must bear the administrative cost for the merger to be accepted by both parties in this case? iii) Return to case 1) (in the absence of merger the two firms play simultaneously) and assume that the two firms contemplate a merger that will reduce the marginal cost of the merged entity to 1, due to synergies. Should a Competition Commission allow this merger to occur? Explain your answerExplanation / Answer
Inverse demand function
P= 10 –Q; Q = qA +qB
Cost function
TCi = 4qi; i ={ A, B}
Under Cournot simultaneous game
Profit function of firm 1
A = (10-qA –qB)qA – 4qA
FOC
dA/dqA = 10- 2qA –qB -4 =0
3- ½ qB = qA -------------------------------------(1)
Profit function of firm 2
A = (10-qA –qB)qB – 4qB
FOC
dB/dqB = 10- 2qB –qA -4 =0
3- ½ qA = qB -------------------------------------(2)
Substitute eq. (2) in eq. (1) and solve for qA
½ -1/4 qA = qA
2/3 = qA
qB =2/3
Profit to each firm
Q = 4/3, price P = 26/3.
A = (26/3 - 4)*2/3 = (14/3)*(2/3) = 28/9 =3.1
B = (26/3 - 4)*2/3 = (14/3)*(2/3) = 28/9 =3.1
The slope of reaction function for both the firms are negative therefore the output levels are strategic substitutes.
Profit function of firm 1
A = (10-qA –qB)qA – 4qA
Reaction function of firm B
dB/dqB = 10- 2qB –qA -4 =0
3- ½ qA = qB -------------------------------------(3)
Substitute eq (3) in the profit function of firm A
A = (10-qA –(3- ½ qA))qA – 4qA
Now differentiate A wrt qA.
dA/dqA = 3-qA =0
qA = 3
qB = 3/2. Firm A has advantage because he chooses the output level first and the profit for firm B is higher . Q =9/2. Price P = 11/2
Profit firm A = 3/2*3 = 9/2 =4.5
Profit firm B = 3/2* 3/2 = 9/4 = 2.25. Therefore firm A has advantage.
3)
i) With merger the firms charge monopoly price
m = (10-Q)Q -4Q -2
dm/dQ = 10 -2Q -4.
Q = 3. P = 7. Profit to each firm = m/2
Profit to each firm = 9-2 =7/2 =3.5
Since the profit from merger is greater than that under simultaneous game so, both A nd B have incentive for merger.
ii) The profit for firm B will be higher under merger but not for firm A so, firm B has incentive for merger and will pay the administrative cost.
* For solution to other parts please post as a separate question.
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