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13 October, 20:22

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. $

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  1. 13 October, 20:27
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    Answer: 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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