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    Oligopoly profit maximization

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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 cannot successfully collude and instead produce where the market price equals marginal cost, their total output will be

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    To simplify your question I use TCa for TCHere and TCb for TCThere.

    first we write the profit function for each firm. Remember that Profit = Revenue - Cost. Also note that Q = Qa + Qb (total quantity = sum of quantities by each ...