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    Price and Output Determination: Monopoly and Dominant Firms

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    Rafael Leyva
    This document contains solutions to exercises related to monopoly and dominant firms. It includes: 1) Analyses of break-even sales changes, profit margins for branded vs generic products, and factors that influence costs. 2) Discussions of how demand elasticity and ability to drill own wells impact price and output. 3) Calculations of profit-maximizing quantity and price for a firm with given total cost and marginal cost functions. 4) Solutions involving demand, cost, revenue, and profit functions for monopolistic firms.

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    Price and Output Determination: Monopoly and Dominant Firms

    Uploaded by

    Rafael Leyva
    100 views8 pages
    This document contains solutions to exercises related to monopoly and dominant firms. It includes: 1) Analyses of break-even sales changes, profit margins for branded vs generic products, and factors that influence costs. 2) Discussions of how demand elasticity and ability to drill own wells impact price and output. 3) Calculations of profit-maximizing quantity and price for a firm with given total cost and marginal cost functions. 4) Solutions involving demand, cost, revenue, and profit functions for monopolistic firms.

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    Chapter11_McGuigan

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    This document contains solutions to exercises related to monopoly and dominant firms. It includes: 1) Analyses of break-even sales changes, profit margins for branded vs generic products, and factors that influence costs. 2) Discussions of how demand elasticity and ability to drill own wells impact price and output. 3) Calculations of profit-maximizing quantity and price for a firm with given total cost and marginal cost functions. 4) Solutions involving demand, cost, revenue, and profit functions for monopolistic firms.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    100 views8 pages

    Price and Output Determination: Monopoly and Dominant Firms

    Uploaded by

    Rafael Leyva
    This document contains solutions to exercises related to monopoly and dominant firms. It includes: 1) Analyses of break-even sales changes, profit margins for branded vs generic products, and factors that influence costs. 2) Discussions of how demand elasticity and ability to drill own wells impact price and output. 3) Calculations of profit-maximizing quantity and price for a firm with given total cost and marginal cost functions. 4) Solutions involving demand, cost, revenue, and profit functions for monopolistic firms.

    Copyright:

    Attribution Non-Commercial (BY-NC)
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    of 8

    Chapter 11

    Price and Output Determination: Monopoly


    and Dominant Firms
    Solutions to Exercises
    1. a. Gross margins differ by subtracting direct fixed costs of manufacturing (e.g., machinery setup
    costs) as variable costs from wholesale revenue.
    b. Use the break-even sales change analysis CM%/CM% %P = .29/.19 = 1.53 = Q + 1.
    Therefore, %Q required to raise total contributions when price is cut by 10% is 53%.
    c. Three possibilities---capital costs, selling costs, overhead costs; probably higher promotion
    and advertising expense for a branded product like Whitmans Sampler candy. In addition, the
    margins on Whitmans candy must be higher because the inventory of candy turns much less
    frequently (perhaps 5 times per year) than the inventory of pantyhose (14 times per year).
    2. a. The most important factor that needs to be considered is the price elasticity of demand. Given
    opportunities to conserve in both the long run and short run, it is possible that achieving a 16%
    rate of return is not feasible.
    b. If individuals are prohibited from drilling their own wells, the demand function would become
    relatively more inelastic.
    3. a. MC = d(TC)/dQ = 5000 + 200Q
    b. P = MR = $20,000
    c. MC = MR
    5000 + 200Q = 20,000
    200Q = 25,000
    Q* = 125
    d. * = 20,000(125) 800,000 + 5000(125) 100(125)2
    * = $762,500

    104

    This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
    copied, or distributed without the prior consent of the publisher.

    Chapter 11/Price and Output Determination: Monopoly and Dominant Firms


    4. a.

    AVC = Q2 10Q + 60
    TVC = Q3 10Q2 + 60Q
    TC = Q3 10Q2 + 60Q + 1000
    MC = 3Q2 20Q + 60

    b.

    Q = 60 .4P + 6(3) + 2(3)


    Q = 84 .4P
    P = 210 2.5Q
    TR = PQ = 210Q 2.5Q2
    MR = 210 5Q

    c.

    MC = MR
    3Q2 20Q + 60 = 210 5Q
    3Q2 15Q 150 = 0
    (3Q 30)(Q + 5) = 0
    Q* = 10
    P* = 210 2.5(10) = $185

    d.

    = TR TC
    * = 185(10) [(10)3 10(10)2 + 60(10) + 1000] = $250

    105

    e. Price and output would be unchanged. Profit would be reduced by $200 to a total of $50.
    5. a.

    P = 12 (Q/10,000)
    TR = 12Q (Q2/10,000)

    b.

    MR = 12 Q/5000

    c.

    TC = 12,000 + 1.5Q

    d.

    MC = 1.5

    e.

    = [12Q (Q2/10,000)] (12,000 + 1.5Q)


    d/dQ = 0
    d/dQ = 10.5 Q/5000
    Q* = 52,500 lamps
    P* = 12 (52,500/10,000) = $6.75
    * = 12,000 + 10.5(52,500) (52,500)2/10,000 = $263,625

    This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
    copied, or distributed without the prior consent of the publisher.

    106
    f.

    Chapter 11/Price and Output Determination: Monopoly and Dominant Firms


    MR = MC
    12 Q/5000 = 1.5
    Q* = 52,500 lamps

    g. The negative sloping demand curve indicates that Lumins could be a non-discriminating
    monopolist. This view is reinforced by the existence of above "normal" profits.
    6. a. MC = dTC/dQ = 20
    b. MR = P(1 + 1/ed)
    20 = P[1+ (1/1.5)]
    P* = $60
    c. MR = 60(1 + 1/1.5) = $20
    d. MR = P(1 + 1/3) = 20 = MC
    P* = $30
    7. QD = 12,000 4,000P
    a.

    TC = 4000 + .5Q

    b.

    MC = d(TC)/dQ = .5

    c.

    P = 3 Q/4,000
    TR = 3Q Q2/4,000

    d.

    MR = 3 Q/2,000

    e.

    = TR TC
    = 3Q Q2/4,000 4,000 .5Q
    = 2.5Q Q2/4,000 4,000
    d/dQ = 2.5 Q/2,000 = 0
    Q* = 5,000
    P* = (12,000 5,000)/4000 = $1.75
    * = 1.75(5000) 4000 .5(5000) = $2250

    f.

    .5 = 3 Q/2000
    Q* =5000

    g.

    Monopoly or monopolistic competition

    This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
    copied, or distributed without the prior consent of the publisher.

    Chapter 11/Price and Output Determination: Monopoly and Dominant Firms


    8. a. Price($/pound) Quantity
    25
    0
    18
    1,000
    16
    2,000
    14
    3,000
    12
    4,000
    10
    5,000
    8
    6,000
    6
    7,000
    4
    8,000
    2
    9,000
    b.

    Output
    0
    1000
    2000
    3000
    4000
    5000
    6000
    7000
    8000
    9000

    VC/pound
    0
    10.00
    8.50
    7.33
    6.25
    5.40
    5.00
    5.14
    5.88
    7.00

    Total Revenue
    0
    18,000
    32,000
    42,000
    48,000
    50,000
    48,000
    42,000
    32,000
    18,000
    TVC
    0
    10,000
    17,000
    22,000
    25,000
    27,000
    30,000
    36,000
    47,000
    63,000

    FC
    14,000
    14,000
    14,000
    14,000
    14,000
    14,000
    14,000
    14,000
    14,000
    14,000

    c.

    MR = MC = $2 (profit maximizing output level)


    Q* = 5,000 pounds/period
    P* = $10 per pound

    d.

    * = TR TC = 50,000 41,000= $9,000

    e.

    P* = $6

    107

    Marginal Revenue
    18.00
    14.00
    10.00
    6.00
    2.00
    2.00
    6.00
    10.00
    14.00
    TC
    14,000
    24,000
    31,000
    36,000
    39,000
    41,000
    44,000
    50,000
    61,000
    77,000

    MC
    10.00
    7.00
    5.00
    3.00
    2.00
    3.00
    6.00
    11.00
    16.00

    ATC
    24.00
    15.50
    12.00
    9.75
    8.20
    7.33
    7.14
    7.63
    8.56

    Exotic Metals cannot charge more than $6.00 per pound, otherwise its customers will buy from
    the federal government. By charging slightly under $6.00 per pound, e.g., $5,999, it could sell
    approximately 7,000 pounds of zirilium per period. Under these conditions, Exotic Metal's profit
    (loss) would be:
    + = TR TC = 42,000 50,000 = $8,000 (loss)

    This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
    copied, or distributed without the prior consent of the publisher.

    108
    9. a.

    Chapter 11/Price and Output Determination: Monopoly and Dominant Firms


    ED = %QD/%P
    2.0 = 15/%P
    %P = 7.5%
    .075 = (P2 15.00)/[(P2 + 15)/2]
    P2 = $13.92
    P = $15 $13.92 = $1.08
    .15 = (Q2 30,000)/[(Q2 + 30,000)/2]
    Q2 = 34,865 gallons

    b. i. Before: TR, = 15(30,000) = $450,000


    After: TR2 = 13.92(34,865) = $485,321
    TR = +$35,321
    ii.

    Before: FC1 =$90,000


    VC/unit = $180,000/30,000 = $6.00
    VC1 = 6(30,000) = 180,000
    TC1 = 90,000 + 180,000 = $270,000
    After: FC2 = $90,000
    VC/unit = $6.00 .60 = $5.40
    VC2 = $5.40 34,865 = $188,271
    TC2 = 90,000 + 188,271 = $278,271
    TC = $8,271

    iii.

    Before:
    , = $450,000 $270,000 = $180,000
    After:
    2 = $485,321 $278,271 = $207,050
    = + 27,050

    10. a. i. ED = [(Q2 Q1)/(Q2 + Q1)] [(P2 + P1)/(P2 P1)]


    2.5 = [(Q2 15,000)/(Q2 + 15,000)] [ (27 + 30)/(27 30)]
    Q2 =19,545 units
    TR2 = 27(19,545) = $527,715
    TR = $527,715 $450,000 = $77,715
    ii.

    CM2 = 12(19,545) = $234,540


    CM = $234,540 $225,000 = $9,540

    Since the change in the contribution margin is positive, the price change would appear to be
    worthwhile.

    This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
    copied, or distributed without the prior consent of the publisher.

    Chapter 11/Price and Output Determination: Monopoly and Dominant Firms

    109

    b. i. Ex = .5 = [(QB2 5000)/(QB2 + 5000)] [(27 + 30)/(27 30)]


    QB2 = 4,744 units
    Ex = .2 = [(QC2 10000/(0^ + 10,000)] [(27 + 30)/(27 30)]
    QC2 = 9,792 units
    Total Revenue
    A: 27(19,545) = $527,715
    B: 35(4,744) = $166,040
    C: 45(9.792) = $440,640 Total Revenue=$ 1,134,395
    R = $1,134,395 $1,075,000 = +$59,395
    ii. Contribution margin:
    A: 19,545(12) = $234,540
    B: 4,744(17)=
    $80,648
    C: 9,792(25)= $244,800
    Total
    $559,988
    CM = 559,988 565,000 = $5,012
    Since the change in the contribution margin is negative, the price change should not be
    undertaken.
    11. a. P = 250.15Q
    TR = 250Q.15Q2
    MR = 250 .3Q
    MR = MC
    250 .3Q = 10
    Q* = 800
    P* = 250 .15(800)
    = $130

    TC = 25,000 + 10Q
    MC = 10

    * = 800(130) 25000 10(800)


    = $71,000

    ROI = $71,000/$500,000
    =.142 or 14.2%

    b. 100 = 250.15Q
    Q = 1000
    = 100(1000) 25,000 10(1000) = $65,000
    ROI = $65,000/$500,000 = .13 or 13%
    c. P = ATC + Average profit/unit
    250 .15Q = (25,000/Q) + 10 + (.10(500,000)/Q)
    .15Q2240Q + 75,000 = 0

    This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
    copied, or distributed without the prior consent of the publisher.

    110

    Chapter 11/Price and Output Determination: Monopoly and Dominant Firms

    12. a. 250 = 3514 .08Q


    Q = 40,800
    = 250(40,800) 2,300,000 130(40,800)
    = $2,596,000
    ROI = $2,596,000/$20,000,000 = 12.98%
    b. .11(20,000,000) = $2,200,000
    2,200,000 = (3514 .08Q)Q 2,300,000 130Q
    .08Q2 3384Q + 4,500,000 = 0
    Using the quadratic formula:
    Q = 1375 or 40,925
    P = 3514 .08(40,925) = $240
    c. This problem illustrates the importance of having good estimates of the firm's cost and demand
    functions when rates are set.

    Solution to Case Exercise: Differential Pricing of PharmaceuticalsThe


    HIV/AIDS Crisis
    1. No, even state and federal governments have threatened to buy unauthorized generic imitation
    products abroad in order to reduce Medicare costs. Only trade barriers involving border inspections
    and tariff policies bar American citizens from buying pharmaceuticals abroad..
    2. Pharmaceutical margins are even higher than 70% cereal margins because of massive R&D costs
    to develop investigational new drugs, only one in fifteen of which will make it to market as a
    patented, profitable pharmaceutical.
    3. Perhaps the cooperation of developed country governments in preventing parallel importing of
    overseas-purchased patented and generic products could be obtained by offering to donate HIV drugs
    in exchange for future R&D tax credits. The following decision tree can be used to explain why this
    exchange of hostages may be necessary for the big pharmaceutical companies to distinguish
    themselves from gougers not fully committed to the partnership required to solve the public health
    crisis.

    This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
    copied, or distributed without the prior consent of the publisher.

    Chapter 11/Price and Output Determination: Monopoly and Dominant Firms

    111

    This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
    copied, or distributed without the prior consent of the publisher.

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