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31 January, 13:45

The demand for cigarettes is given by P = 450450 - 0.20.2Q. Cigarettes are manufactured at a constant marginal cost of 5050 and sold in a competitive market. What is the quantity of cigarettes sold in equilibrium? Upper Q Subscript PrivateQPrivate = nothing

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  1. 31 January, 16:10
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    Q = 1,000

    Explanation:

    The firms will product until marginal revenue matches marginal cost

    being marginal cost $50

    then the revenue per additional unit of cigarettes sold should be $50

    Revenue = P x Q

    Revenue = (450 - 0.20Q) x Q = - 0.20Q^2 + 450Q

    Marginal revenue: slope of the revenue function:

    dRq/dQ = - 0.4Q + 450

    Now we equalize and solve for Q

    Marignal Revenue = Marginal Cost

    -0.4Q + 450 = 50

    (450 - 50) = 0.4Q

    400 / 0.4 = Q

    Q = 1,000
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