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 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% – %ΔP = .29/.19 = 1.53 = ΔQ + 1. Therefore, %ΔQ 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 Whitman’s Sampler candy. In addition, the margins on Whitman’s 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. π* = 20,000(125) − 800,000 + 5000(125) − 100(125)2 π* = $762,500

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

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.

105 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. π = TR − TC π* = 185(10) − [(10)3 −10(10)2 + 60(10) + 1000] = $250 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. π = [12Q − (Q2/10,000)] − (12,000 + 1.5Q) dπ/dQ = 0 dπ/dQ = 10.5 − Q/5000 Q* = 52,500 lamps P* = 12 − (52,500/10,000) = $6.75 π* = −12,000 + 10.5(52,500) − (52,500)2/10,000 = $263,625

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

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.

f. 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. π = TR – TC π = 3Q – Q2/4,000 – 4,000 – .5Q π = 2.5Q – Q2/4,000 – 4,000 dπ/dQ = 2.5 – Q/2,000 = 0 Q* = 5,000 P* = (12,000 – 5,000)/4000 = $1.75 π* = 1.75(5000) – 4000 – .5(5000) = $2250 f. .5 = 3 – Q/2000

Q* =5000 g. Monopoly or monopolistic competition

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

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.

107 8. a. Price($/pound) Quantity Total Revenue Marginal Revenue 25 0 0 - 18 1,000 18,000 18.00 16 2,000 32,000 14.00 14 3,000 42,000 10.00 12 4,000 48,000 6.00 10 5,000 50,000 2.00 8 6,000 48,000 –2.00 6 7,000 42,000 –6.00 4 8,000 32,000 –10.00 2 9,000 18,000 –14.00

b. Output VC/pound TVC FC TC MC ATC 0 0 0 14,000 14,000 - - 1000 10.00 10,000 14,000 24,000 10.00 24.00 2000 8.50 17,000 14,000 31,000 7.00 15.50 3000 7.33 22,000 14,000 36,000 5.00 12.00 4000 6.25 25,000 14,000 39,000 3.00 9.75 5000 5.40 27,000 14,000 41,000 2.00 8.20 6000 5.00 30,000 14,000 44,000 3.00 7.33 7000 5.14 36,000 14,000 50,000 6.00 7.14 8000 5.88 47,000 14,000 61,000 11.00 7.63 9000 7.00 63,000 14,000 77,000 16.00 8.56 c. MR = MC = $2 (profit maximizing output level)

Q* = 5,000 pounds/period P* = $10 per pound d. π* = TR – TC = 50,000 – 41,000= $9,000 e. P* = $6

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: π+ = TR – TC = 42,000 – 50,000 = – $8,000 (loss)

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

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.

9. a. ED = %ΔQD/%ΔP –2.0 = 15/%ΔP %ΔP = –7.5% –.075 = (P2 – 15.00)/[(P2 + 15)/2] P2 = $13.92 ΔP = $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 ΔTR = +$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 ΔTC = $8,271 iii. Before: π, = $450,000 – $270,000 = $180,000 After: π2 = $485,321 – $278,271 = $207,050 Δπ = + 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 ΔTR = $527,715 – $450,000 = $77,715

ii. CM2 = 12(19,545) = $234,540 ΔCM = $234,540 – $225,000 = $9,540

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

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

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.

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 ΔR = $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 ΔCM = 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 TC = 25,000 + 10Q

TR = 250Q–.15Q2 MC = 10 MR = 250 – .3Q MR = MC 250 – .3Q = 10 Q* = 800 P* = 250 –.15(800) = $130 π* = 800(130) – 25000 – 10(800) ROI = $71,000/$500,000 = $71,000 =.142 or 14.2%

b. 100 = 250–.15Q

Q = 1000 π = 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) .15Q2–240Q + 75,000 = 0

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

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.

12. a. 250 = 3514 − .08Q Q = 40,800 π = 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 Pharmaceuticals—The 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.

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

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.

111