2)Suppose there are only two firms in the market, firm A and firm B. They produc

Question

2)Suppose there are only two firms in the market, firm A and firm B. They produce identical products. Firm A and firm B have the same constant marginal cost, MCa=MCb=10. The market demand function is given by Q=600-30P.. The goal of this problem is to evaluate the possibility of cooperation between two firms.

a)Assume that those two firms set up an agreement to cooperate and each firm produces half of the monopoly output. If they both keep the agreement, what is the market price? What is the output level for each firm?

b)Is the outcome in part a stable? If Firm B knows that Firm A will keep the agreement, will firm B keep the agreement? If yes, explain why. If no, what is firm B’s optimal choice of output level?

Explanation / Answer

a)

Profit would be maximized in a monopoly when MR = MC:

TR = PQ = 20Q - Q2/30

MR = d(TR)/dQ = 20 - Q/15

20 - Q/15 = 10

Q = 150

Output level of each firm = 75 and P = 15

b)

Outcome in part a is not stable, a firm can increase its profit by increasing production at the expense of other firms.

Therefore, firm B will not keep the agreement and would produce at a level so as to maximize own profit:

Qa = 75 (given)

Qb = 600 - 30P - 75 = 525 - 30P

P = 525/30 - Qb/30

TRb = 17.5Qb - Qb2/30

Profit would be maximized where MRb = MC = 10:

17.5 - Qb/15 = 10

Qb = 112.5

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