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    Demand, Supply, Cost, Average Cost and Marginal Cost

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    The market demand function of a firm is given by 8P + Q - 64 = 0, and the firm's average cost function takes the form AC = 8/Q + 6 - 0.4Q + 0.08Q2.
    i)Determine the price and quantity for maximum sales revenue and calculate the maximum revenue.
    ii)Determine the price and quantity for minimum marginal costs and calculate the minimum marginal cost.
    iii)Determine the price and quantity for maximum profit and calculate the maximum profit.

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    Solution Preview

    Demand function: P = (64 - Q)/8 = 8 - (Q/8)

    AC function: AC(Q) = 8/Q + 6 - 0.4Q + 0.08Q^2

    Cost function: C(Q) = AC(Q) * Q = 8 + 6Q - 0.4Q^2 + 0.08Q^3

    (a) The revenue function is R(Q) = Q * P = Q[8 - (Q/8)] ...

    Solution Summary

    The expert examines the demand, supply, cost, average cost and marginal costs of a function. Neat, Step-by-step solutions to all the parts of the question are provided.