The following equation represents the daily market demand for crude oil. Q = 10,

Question

The following equation represents the daily market demand for crude oil.
Q = 10, 000,000 - 500,000 P
Suppose there are four oil producers in the crude oil market, A, B , C and D. The marginal cost of A is $10. The marginal cost of B is $12. The marginal cost of C is 13. The marginal cost of D is $15. Note that in all three cases MC =AVC.
(Hint: Do not be concerned about fixed costs in this problem; assume TFC = zero for all producers.)
a. If collusion is not allowed, what kind of market arrangement do you think is likely to result from competitive interactions among these four firms?
b. Now suppose collusion is allowed. Is it possible for these firms to form an effective cartel?
c. Calculate the profits of these firms in either case (a and b).

Explanation / Answer

We will expect to see a modified Bertand model.

The producer A will maximize his profit if he sells crude oil at just less than $12. At this price he will capture the whole market and make a profit of $2 per barrel.

Yes, if collusion is allowed the firms can form a cartel. We can see that the we can pareto optimla condition (where everyone is better off) if the firms agree to increase the price. In this cartel producers will get to produce different amount of quantities.

In case (a) profit for firm A is 4,000,000*2 = $8,000,000.

In case (b) profit will be maximized at P=$15.

At P = 15. Q will be 250,000. The distribution of profit will be such that A gets more than $8,000,000. Hence A will get to produce more than 1,600,000 units. B will get to produce more than 277,778. This will leave 622222 units of crude to be shared among A,B and C.

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