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March 30, 2017

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You are the manager of a monopoly, and your demand and cost functions are given by P = 300 – 2.5Q and C(Q)=1000 + 2.5Q2.

a.At what price and quantity are firm’s profits maximized?

  • Managerial Econ - ,

    revenue = price * quantity
    profit = revenue - cost
    so, the profit is

    Q(300-2.5Q) - (1000 + 2.5Q^2)
    = 300Q - 2.5Q^2 - 1000 - 2.5Q^2
    = -5Q^2 + 300Q - 1000
    = -5(Q^2 - 60Q + 200)
    max profit at Q=30, P(30)=225

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