Suppose the airline industry consists of two firms, A and B. These two firms eng

Question

Suppose the airline industry consists of two firms, A and B. These two
firms engage in Cournot competition with each other over a certain route for which inverse demand is

P(Q) = 1000 Q with Q = qA + qB. The main component of each airline’s marginal cost
is fuel which is assumed to cost 400 per flight (regardless of the number of passengers).

(a) Solve for the Cournot equilibrium price.
Suppose the airlines figure out a way to collude with each other and still have the same fuel cost
of 400 per flight.
(b) Solve for the market price when the two firms collude
Suppose for whatever reason the world price of oil falls (as it has), and fuel costs for the airlines
fall with it so that their marginal cost is now 100 per flight.
(c) Solve for the new Cournot equilibrium price assuming the firms are not colluding.
(d) Solve for the new market price assuming the firms are colluding.

Explanation / Answer

a. P = 1000 - Q , Q = Qa + Qb , MC = 400

Now TRa = [1000 - Qa -Qb] Qa

MRa = 1000 - 2Qa - Qb

At equilibrium, MRa = MC

1000 - 2Qa - Qb = 400

2Qa + Qb = 600 ............... (1)

Similarly equating MRb = MC, we get

2Qb + Qa = 600 .......... (2)

Solving eq (1) and (2), we get

Qa = Qb = 200 .......... (3)

Inserting these values from (3) in price equation, we get

P = 1000 - (Qa + Qb) = 1000 - 400 = 600

b. When firms collide and form cartel, we have

P = 1000 - Q

TR = 1000Q - Q2

MR = 1000 - 2Q

Equating MR = MC, we get

1000 - 2Q = 400

Q = 300

P = 1000 - 300 = 700

c. Now as MC is reduced to 100, we can repeat the concept in part (a) and (b) to solve part (c) and (d) with MC = 100 instead of 400

MRa = 1000 - 2Qa - Qb and MC = 100, solving MRa = MC, we get

2Qa + Qb = 900 ........ (4)

With MRb = MC, we get

2Qb + Qa = 900 ......... (5)

solving (4) and (5) , we get

Qa = Qb = 300 ........... (6)

Inserting the values of Qa and Qb from (6) in price equation P = 1000 - (Qa + Qb), we get

P = 1000 - 600 = 400

d. Now if firms enters into the cartel, we have TR = 1000Q - Q2

thus MR = 1000 - 2Q and MC = 100

Equating it, we get

1000 - 2Q = 100

Q = 450

hence P = 1000 - 450 = 550

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