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    Determining supply curves

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    Stanford Plastics, Inc. and Cal-Tech Associates, Inc. supply a generic phone jack that connects telephone cords to phone outlets. Proprietary cost and output information for each company reveal the following relations between marginal cost and output:

    MCS=dTCS/dQ=$1+$0.00002QS (Stanford)

    MCC=dTCC/dQ=$1.50+$0.000005QC (Cal-Tech)

    The wholesale market for modular phone jacks is vigorously price-competitive, and neither firm is able to charge a premium for its products. Thus, P = MR in this market.

    A. Determine the supply curve for each firm. Express price as a function of quantity and quantity as a function of price. (Hint: Set P = MR = MC to find each firm's supply curve.)
    B. Calculate the quantity supplied by each firm at prices of $1, $1.50, and $2. What is the minimum price necessary for each individual firm to supply output?
    C. Determine the industry supply curve when P < $1.50.
    D. Determine the industry supply curve when P > $1.50. To check your answer, calculate quantity at an industry price of $2 and compare your answer with part B.

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    Solution Preview

    A. Determine the supply curve for each firm. Express price as a function of quantity and quantity as a function of price. (Hint: Set P = MR = MC to find each firm's supply curve.)

    For Standard Associates, Marginal cost function is given by
    MCS=1+0.00002Qs

    Every firm sets its output level such that MR=MC to maximize its profits. In the price competitive industry P=MR.
    So, Put P=MC

    P=1+0.00002Qs
    0.00002Qs=-1+P
    Qs=-50000+50000P

    For Cal-Tech, Marginal cost function is given by

    MCC=1.50 ...

    Solution Summary

    Solution describes the steps to determine supply curve for the given firms. It also determines the industry supply curves for the given price ranges.

    $2.19