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    TC equation

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    1)
    A monopoly firm in a small island country produces and supplies to the country. It faces a market demand curve for its products. The demand equation is linear, so is the firm's total cost (TC) function. The following table exhibits the data for Quantity, Price, and TC.

    (1) (1) Estimate the demand equation.
    [Show the estimated equation.]
    (2) (2) Estimate the TC function.
    [Show the estimated TC equation.]
    (3) (3) What is the profit-maximizing quantity?
    [Profit-max quantity is determined at the level where MC = MR. Hence, Derive MC function from the estimated TC function. Derive MR from TR function which is PQ, where P = P(Q). In other words, P is the estimated demand equation expressed by Q. But, since the demand function is linear, the MR function is linear with a twice steeper slope than the demand equation and with the same intercept.]
    (4) (4) What is the profit-maximizing price?
    [Once the quantity is determined, find the corresponding price at the demand curve.]
    (5) (5) What is the monopoly profit? [Profit = TR - TC.]

    Q P TC
    1 100 11
    2 97 19
    3 98 31
    4 95 39
    5 96 51
    6 93 59
    7 94 71
    8 91 79
    9 92 91
    10 89 99
    11 90 111
    12 87 119
    13 88 131
    14 85 139
    15 86 151
    16 83 159
    17 84 171
    18 81 179
    19 82 191
    20 79 199
    21 80 211
    22 77 219
    23 78 231
    24 75 239
    25 76 251

    2)
    A manufacturing firm operating in a perfectly-competitive market has the following cost function:
    TC = a + b Q + c Q2 + d Q3
    The TC data with respect to Q are provided in the table below.

    (1) (1) Estimate the TC equation and show the estimated equation.
    [a = round up to a whole number (no decimal), b = round up and no decimal, c = round up to the first decimal (one decimal), and d = round up to the first decimal (one decimal)]
    (2) (2) What are the equations for AC and MC?
    (3) (3) The market price is $637.5. What is the firm's profit-maximizing level of output?
    (4) (4) Does the firm make profit or loss? Show either the profit or loss?
    (5) (5) The market price changes. At which price will the firm shut down the operation?

    TC Q
    1780 1
    2021 2
    2238 3
    2435 4
    2626 5
    2814 6
    3013 7
    3227 8
    3472 9
    3750 10
    4074 11
    4451 12
    4893 13
    5405 14
    6001 15
    6684 16
    7468 17
    8357 18
    9366 19
    10500 20
    11770 21
    13182 22
    14749 23
    16475 24
    18375 25

    © BrainMass Inc. brainmass.com October 9, 2019, 5:52 pm ad1c9bdddf
    https://brainmass.com/economics/supply-and-demand/equation-economics-management-70552

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    1)
    A monopoly firm in a small island country produces and supplies to the country. It faces a market demand curve for its products. The demand equation is linear, so is the firm's total cost (TC) function. The following table exhibits the data for Quantity, Price, and TC.

    (1) Estimate the demand equation.
    [Show the estimated equation.]

    So demand is P = - Q + 100.04

    (2) Estimate the TC function.
    [Show the estimated TC equation.]
    TC = 10Q + 0.04

    (3) What is the profit-maximizing quantity?
    [Profit-max quantity is determined at the level where MC = MR. Hence, Derive MC function from the estimated TC function. Derive MR from TR function which is PQ, where P = P(Q). In other words, P is the estimated demand equation expressed by Q. But, since the demand function is ...

    Solution Summary

    The expert estimates the TC equation and show the estimated equation.

    $2.19