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    Calculate: Optimal Output, Price and Profit Levels

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    Two local ready-mix cement manufacturers, Here and There, have combined demand given by Q = 105 - P. Their total costs are given by TCHere = 5QHere + 0.5Q2Here and TCThere = 5QThere + 0.5Q2Here.

    If they successfully collude:

    Their total output will be?
    Their maximum joint profits will be ?

    If they cannot successfully collude and instead produce where the market price equals marginal cost

    Their total output will be?
    Each firm's profits will be?

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    Solution Preview

    If they successfully collude:

    Their total output will be?

    On rearranging, we get:

    Total Revenue=TR=P*Q=(105-Q)*Q=105Q-Q^2
    Marginal Revenue=MR=dTR/dQ=105-2Q

    Both firms have the same cost structure, So, combined Total Cost function is given by
    Total Cost=TC=5Q+0.5Q^2
    Marginal Cost=MC=dTC/dQ=5+Q

    Combined profit will be maximized if MR=MC i.e.
    Q=(100/3) i.e. 33.33 units

    Their maximum joint profits will be ? ...

    Solution Summary

    This solution is comprised of a detailed, step by step response which outlines how to calculate the optimal output and profit in the given cases.