Onsider a Bertrand oligopoly consisting of four firms that produce an identical product at a marginal cost of $260. The inverse market demand for this product is P = 800 – 4Q. a. Determine the equilibrium level of output in the market. b. Determine the equilibrium market price. $ c. Determine the profits of each firm. $

Level of output is 135 units, equilibrium price is $260 and the profit for each firm is zero.

Explanation:

(a) To determine the equilibrium level of output:

P = MC

Recall that the marginal cost is $260.

P = 260.

P = 800 - 4Q

260 = 800 - 4Q

4Q = 800 - 260

4Q = 540

Q = 540 / 4

Q = 135units

Therefore, the equilibrium level of output is 135units.

b. To determine the equilibrium market price:

P = 800 - 4Q

Recall that Q = 135

P = 800 - 4Q

= 800 - 4(135)

= 800 - 540

= $260.

c. Determine the profits for each firm.

Since the firms have an equilibrium price of $260 and an output of 135, each of the four firms will get a quarter of the market output which is (135 / 4) = 33.75.

Profit for each firm = TR - TC

=(PQ) - (MC × Q) =(260 × 33.75) - (260 × 33.75)

=8775 - 8775

= 0.

Each of the firm makes zero profit.

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