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6 August, 04:39

Seth owns a local business that provides email updates on surf conditions. He is the only supplier of these email updates in Santa Barbara and Goleta, which gives him a monopoly in both cities. The marginal cost of producing another update is zero (and we'll ignore fixed costs). The inverse demand for these updates in Santa Barbara is p = 74-q and the inverse demand in Goleta is p = 39 - 4q. Suppose Seth charges different uniform prices in SB and Goleta. If Seth sets each price such that he is maximizing his total profits, what are Seth's total profits?

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  1. 6 August, 05:51
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    Seth's total profits is $1,535.359

    Explanation:

    According to the given data we have the following:

    MC = 0 and we will ignore fixed costs

    Therefore TC = 0

    Demand function in Santa barbara is

    p = 74 - q

    MR = 74 - 2q

    Since Seth sets different uniform prices in two markets to maximizes his profit therefore,

    MR = MC

    74 - 2q = 0

    2q = 74

    q=37

    p = 74 - 37 = 37

    Profit = pq - TC

    = 37*37 - 0

    = $1,369

    Inverse demand finction Goleta is

    p = 39 - 4q

    MR = 39 - 8q

    MR = MC

    39 - 8q = 0

    8q = 39

    q = 4.875

    p = 39 - 4.875 = 34.125

    Profit = pq - TC

    = 34.125*4.875 - 0

    = $166.359

    Therefore, Seth's total profits = $1,369 + $166.359

    Seth's total profits = $1,535.359

    Seth's total profits is $1,535.359
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