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    Monoply Profit

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    Pavati Fluid Controls, Inc, (PDC) is a major supplier of reverse osmosis and ultra-filtration equipment, which helps industrial and commercial customers achieve improved production processes and a cleaner work environment. The company has recently introduced a new line of ceramic filters that enjoy patent protection. Are relevant cost and revenue relations for this product are as follows:

    TR = $300Q - $0.001Q2
    MR = ΔTR/ΔQ = $300-$0.002Q
    TC = $9,000,000 + $20Q + $0.0004Q2
    MC = ΔTC/ΔQ = $20 + $0.0008Q

    Where TR is total revenue, Q is output , MR is marginal revenue, TC is total cost, including a risk-adjusted normal rate of return on investment, and MC is marginal cost.

    A. As a monopoly, calculate PFC's optimal price/output combination.
    B. Calculate monopoly profits and the optimal profit margin at this profit-maximizing activity level.

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    Solution Preview

    Answer A:
    Optimal price/output combination is where MR = MC. So
    300 - .002Q = 20 + .0008Q
    => 280 = .0028Q
    => Q = 100,000
    Because TR = PXQ
    P = ...

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