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    Calculating optimal output and market price

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    Propylene is used to make plastic. The propylene industry is perfectly competitive and each producer has a long run total cost function given by

    LTC= 1/3 Q^3 -6Q^(2 )+40Q

    Where Q denotes the output of the individual firm.

    The market demand for propylene is

    X =2200 -100P

    Where X and P denote the market output and price respectively.

    1. Calculate the optimal output produced by each firm at the long run competitive equilibrium (LRCE).

    2. Calculate the market price and market output at the LRCE.

    3. Calculate the number of firms at the LRCE.

    Suppose the demand curve shifts to

    X =A -100P

    Where A is a positive number.

    Calculate how large A would have to be so that in the new LRCE, the number of firms is twice what it was in the initial equilibrium.

    © BrainMass Inc. brainmass.com April 1, 2020, 7:06 pm ad1c9bdddf
    https://brainmass.com/economics/general-equilibrium/calculating-optimal-output-and-market-price-393257

    Solution Preview

    1. Calculate the optimal output produced by each firm at the long run competitive equilibrium (LRCE).

    At LRCE, long run marginal Cost is equal to long run average cost.

    Given, LTC= 1/3 Q^3 -6Q^(2 )+40Q

    Long run marginal cost (LRMC) is given by
    LRMC=d(LTC)/dQ=Q^2-12Q+40

    Long run average cost (LRAC) is given by
    LRAC=LTC/Q=1/3 ...

    Solution Summary

    Solution describes the steps to calculate optimal output and market price. It also calculates number of firms present in the market in the given scenario.

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