Chapter 6
16) The ________ elastic a firm's demand curve, the greater its ________. A) less; monopoly power B) less; output C) more; monopoly power D) more; costs
Answer: A Please refer to lecture slide #16 on page 8th of your power point slides.
36) Silverscreen Movie Rentals has market power in the previously viewed video sales market. The demand curve for Silverscreen movies is QD = 10 - 0.4P. Silverscreen's marginal cost curve is MC(Q) = 0.53 + 0.026Q. a) Determine Silverscreen's profit maximizing price. b) Calculate Silverscreen's elasticity of demand at this price. c) What is Silverscreen's mark-up over marginal cost as a percentage of price?
Answer: a) Inverse demand: P = 25 − 10Q/4. REV = (25 − 10Q/4)Q = 25Q − 5Q2 /2. MR = 25 − 5Q. Profit maximization MR = MC ⇒ 25 − 5Q = 0.53 + 0.026Q, so Q = 4.87 and P = 12.83; b) Notice that the slope of the demand function QD = 10-0.4P is -0.4. Elasticity is ED=(P/Q)(∆Q/∆P)=(12.83/4.87)(-0.4)=-1.05 c) It is (P − MC)/P = (12.83 − (0.53 + 0.026 * 4.87))/12.83 = 0.95
21) Suppose that the competitive market for rice in Japan was suddenly monopolized. The effect of such a change would be: A) to decrease the price of rice to the Japanese people. B) to decrease the consumer surplus of Japanese rice consumers. C) to decrease the producer surplus of Japanese rice producers. D) a welfare gain for the Japanese people. E) increase the consumption of rice by the Japanese people.
B
31) Which of the following statements about natural monopolies is true? A) Natural monopolies are only found in the markets for natural resources (like crude oil and coal). B) For natural monopolies, marginal cost is always below average cost. C) For natural monopolies, average cost is always increasing. D) Natural monopolies cannot be regulated.
B
4) Assume that a profit maximizing monopolist is producing a quantity such that marginal revenue exceeds marginal cost. We can conclude that the A) firm is maximizing profit. B) firm's output is smaller than the profit maximizing quantity. C) firm's output is larger than the profit maximizing quantity. D) firm's output does not maximize profit, but we cannot conclude whether the output is too large or too small.
B
7) Which of the following is NOT true for monopoly? A) The profit maximizing output is the one at which marginal revenue and marginal cost are equal. B) Average revenue equals price. C) The profit maximizing output is the one at which the difference between total revenue and total cost is largest. D) The monopolist's demand curve is the same as the market demand curve. E) At the profit maximizing output, price equals marginal cost.
E
15) When the demand curve is a horizontal line, marginal revenue is: A) less than price B) more than price C) equal to price D) first increasing, then decreasing E) first decreasing, then increasing
Answer: C When the demand is a horizontal line, it means perfectly elastic. That is, the firm is a price taker, and there is a given fixed price P. Then both marginal revenue and average revenue are equal to this price, P = AR = MR. Extra: If the demand is downward sloping, then average revenue continues to be equal to the price. This is so because if the firm sells Q units at a price P, then on average it receives price P per unit sold. In this case, the marginal revenue is less than the price, because if the firm sells Q units at a price P, then in order to sell one marginal (extra) unit it would have to charge a new, lower price. That is, P = AR > MR.
14) Firm Alpha is a monopolist with cost function C = Q2 . In addition to this cost, firm Alpha also needs to pay a $10 tax per unit sold. The demand for Alpha's output is QD = 260 - 2P. Alpha chooses quantity Q* that maximizes profit. Compute the profit of this monopolist. A) Profit = 2,400 B) Profit = 2,200 C) Profit = 2,600 D) Profit = 2,800 E) None of the above
Answer: A The demand is Q = 260−2P, hence 2P = 260−Q and the inverse demand function becomes P = 130 − 0.5Q REV = PQ REV = (130− 0.5Q) Q REV = 130Q − 0.5Q2 MR = 130− Q Note that the firm has to pay $10 in taxes for each unit produced, that is, the firm's cost with tax is Ctax = 10Q+Q2 , and the marginal cost with taxes is MCtax = 10+2Q. Optimal choice is MR = MC 130 − Q = 10+2Q 120 = 3Q QMonopolist = 40 The resulting price is P = 130 − 0.5Q = 130 − 0.5 * 40 = 110. The profit becomes Profit = REV − Ctax Profit = PQ − (10Q + Q2 ) Profit = 110 * 40 − (10 * 40 + 402 ) Profit = 4400 − 2000 Profit = 2400
20) Assume that a firm's marginal cost is $10 and the elasticity of demand is -2. We can conclude that the firm's profit maximizing price is approximately A) $20. B) $5. C) $10. D) The answer cannot be determined without additional information.
Answer: A The firm's marginal cost is MC = 10. Compute the inverse demand function Q = 260− 2P 2P = 260− Q P = 130− 0.5Q. and the marginal revenue REV = PQ REV = (130− 0.5Q)Q REV = 130Q − 0.5Q2 MR = 130− Q. Optimal choice is MR = MC 130 − Q = 10 QMonopolist = 120. The price is then PMonopolist = 130 − 0.5Q = 130 − 0.5 * 120 = 70. To compute the DWL we also need the quantity and price of perfect competition. In perfect competition P = MC, that is, PPC = 10. The total demand is then QPC = 260 − 2P = 260 − 2 * 10 = 240. Draw the demand and marginal cost functions. At Q=120, MC=10 The DWL is the area of the triangle, DWL = (70 − 10)(240 − 120)1/2 = 3, 600.
38) Firm Gamma is a monopolist with cost function C = 10Q. The demand for Gamma's output is QD = 260 - 2P. Gamma chooses quantity Q* that maximizes profit. The deadweight loss generated by this monopolist is A) DWL = 3,600 B) DWL = 3,525 C) DWL = 3,500 D) DWL = 3,625 E) None of the above
Answer: A The firm's marginal cost is MC = 10. Compute the inverse demand function Q = 260− 2P 2P = 260− Q P = 130− 0.5Q. and the marginal revenue REV = PQ REV = (130− 0.5Q)Q REV = 130Q − 0.5Q2 MR = 130− Q. Optimal choice is MR = MC 130 − Q = 10 QMonopolist = 120. The price is then PMonopolist = 130 − 0.5Q = 130 − 0.5 * 120 = 70. To compute the DWL we also need the quantity and price of perfect competition. In perfect competition P = MC, that is, PPC = 10. The total demand is then QPC = 260 − 2P = 260 − 2 * 10 = 240. Draw the demand and marginal cost functions. At Q=120, MC=10 The DWL is the area of the triangle, DWL = (70 − 10)(240 − 120)1/2 = 3, 600.
33) The marginal cost of a monopolist is constant and is $10. The demand function is given as follows: Demand function: Q = 100 - P The deadweight loss from monopoly power is ________. A) $1,000.00 B) $1,012.50 C) $1,025.00 D) $1,037.50 E) none of the above
Answer: B Step 1: MR=MC MC=10; P=100-Q; REV=100Q-Q2 ; MR=100-2Q MC=MR; 10=100-2Q; Q*=45; P*=100-45=55 Step 2: MC=10=P Step 3: MC=P; MC=100-Q; 10=100-Q; Q*=90 Step 4: DWL=((90-45)*(55-10))/2=1,012.50
19) The more elastic the demand facing a firm, A) the higher the value of the Lerner index. B) the lower the value of the Lerner index. C) the more monopoly power it has. D) the higher its profit.
Answer: B L=(P-MC)/P= - 1/ED. The more elastic the demand curve, the larger ED is and the smaller 1/ED is and hence the L is smaller.
Scenario 10.8: Adriana is a monopolist producing green calculators. The average cost curve and average revenue curve for her product are given as follows: AC = Q + (10,000/Q) AR = 30 - (Q/2) 34) Refer to Scenario 10.8. The deadweight loss from monopoly is ________. A) 0 B) 5 C) 10 D) 25 E) none of the above
Answer: B TC=AC*Q=Q2+10,000; TR=AR*Q=30Q-Q2 /2 Step 1: MR=MC 30-Q=2Q; 3Q=30; Q*=10; P=AR; P=30-(Q/2); P*=30-(10/2)=25 Step 2:MC at Q=10; MC=2(10)=20; Step 3: MC=P; 2Q=30-(Q/2); 5Q/2=30; Q=12; Step 4: DWL=((12-10)*(25-20))/2=5
37) The graph below represents Market A, where a monopolist faces many competitive buyers. It shows the marginal cost, average revenue, and marginal revenue. The firm's fixed cost is 30. The monopolist uses its market power to maximize its own profit. The profit of this monopolist is: CHART A) Profit = 260 B) Profit = 390 C) Profit = 230 D) Profit = 310 E) Profit = zero
Answer: B The monopolist optimally chooses quantity Q = 40 such that MR=MC, and charges the price is P = 17. From the graph we know that MC = 13, but we do not know the AC, so we cannot use Profit = (P −AC)Q to compute profit. However, the question gives us the fixed cost FC = 30 and from the graph we can compute the producer surplus, which equals the area between the price and the MC (a trapezoid in this case). Therefore, PS = (17 − 0 + 17 − 13) * 40 * 1/2 = 420. Recall that PS equals variable profit, and that Profit = Variable Profit − FC = 420 − 30 = 390
17) What is the value of the Lerner index under perfect competition? A) 1 B) 0 C) infinity D) two times the price
Answer: B. Lerner index is L = (P − MC)/P. Under perfect competition, P = MC, therefore L = 0.
28) If the monopolist is not regulated, the price will be set at: A) P1 B) P2 C) P3 D) P4 E) none of the above
Answer: B. The monopolist chooses quantity Q2, where MR=MC. At this quantity, the monopolist receives the highest price consumers are willing to pay, P2.
12) Bancroft Pharmaceuticals has a patent on a new medication used to treat high blood pressure, so it is the monopoly seller of this new drug product. The marginal cost of producing one dose of the drug is $10, and the elasticity of demand for the product is -3. What is the profit maximizing monopoly price for this patented drug product? A) $10 B) $12.50 C) $15 D) $30
Answer: C MC=10; ED=-3; (P-MC)/P=-1/ED; P=MC/(1+(1/ED)); P=10/(1+(1/-3))=15
25) You work as a marketing analyst for a pharmaceutical firm, and you are trying to gather information about the marginal cost of production for a competing firm. You know that they have a patent on a popular medication that sells for $20 per dose, and you believe the elasticity of demand for this product is roughly -4. Assuming the competing firm acts as a profitmaximizing monopolist, what is the competing firm's approximate marginal cost of production? A) $10 per dose B) $12.50 per dose C) $15 per dose D) $20 per dose
Answer: C P = MC/(1 + 1/ED) →20=MC/(1+(1/-4)) →20=MC/0.75→MC=15
32) Firm Sigma is a natural monopolist. The government decides to limit Sigma's monopoly power with price regulation. In order to find the minimum feasible price, the government must find the point where: A) price equals marginal cost B) average revenue equals marginal cost C) average cost equals average revenue D) marginal cost is greater than average cost E) Natural monopolies cannot be regulated
Answer: C. A monopolist is a natural monopolist when at the quantity Q such that P = MC we have P < AC, so that the firm would have a negative profit at this quantity. Hence, the lowest feasible price that the Government can impose on the natural monopolist is the price such that the firm has a zero profit, P = AC. Recall that price equals average revenue.
26) Suppose Orange Inc. sells MP3 players and initially has monopoly power because there are only a few close substitutes available to consumers. As more types of MP3 players are introduced into the market, the demand facing Orange becomes ------------elastic and the Lerner index achieved by the firm in this market ---------------. A) less, declines B) less, increases C) more, declines D) more, increases
Answer: C. Because more competitors are entering the market, consumers have more options. Consequently, consumers are more sensitive to changes in price by Orange Inc., that is, the demand becomes more elastic. The more elastic demand implies that Orange Inc. has less market power, that is, a lower Lerner index.
30) The minimum feasible price is: A) P1 B) P2 C) P3 D) P4 E) none of the above
Answer: C. The minimum feasible price is where average cost equals average revenue: price P3. At this price, profit is zero: π = (P − AC)Q, so if P=AC then π = 0. Any price below P3 yields a negative profit, therefore it is not feasible.
24) Roaring Lion Studios can produce DVDs at a constant marginal cost of $5 per disk, and the studio has just releasing the DVD for its latest hit film, Ernest Goes to the Hamptons. The retail price of the DVD is $25, and the elasticity of demand for this film is -2. Has the studio selected the profit-maximizing retail price for this DVD? A) Yes B) No, the retail price is too low C) No, the retail price is too high D) We do not have enough information to answer this question
Answer: C. The price should be P = MC/(1 + 1/ED) = 5/(1 − 1/2) = 10.
23) DVDs can be produced at a constant marginal cost of $5 per disk, and Roaring Lion Studios is releasing the DVDs for its last two major films. The DVD for Rambeau 17 is priced at $20 per disk, and the DVD for Schreck 10 is priced at $30 per disk. What are the price elasticities of demand for these two movies? A) Both equal -1.2. B) -0.75 and -5/6, respectively C) -1.33 and -1.2, respectively D) -1.33 and -2, respectively
Answer: C. We know that P = MC/(1+1/ED) . Therefore, 20 = 5/(1+1/E1) , that is, 20 + 20/E1= 5 →20/E1 = -15 → E1 = -20/15 = -1.33. Similarly, 30 = 5/(1+1/E2) implies E2 = -1.2.
11) The marginal cost of a monopolist is constant and is $10. The demand function is given as follows: Q = 100 - P. The profit maximizing price is A) $70. B) $65. C) $60. D) $55. E) $50
Answer: D Profit for a monopolist is maximized when MR=MC P=100-Q, REV=P*Q=100Q-Q2 ; MR=100-2Q MC=10 MC=MR; 10=100-2Q→Q*=45; P*=100-45=55
2) Which of the following is true at the output level where P=MC? A) The monopolist is always maximizing profit at the point where P=MC. B) The monopolist is maximizing profit if demand is elastic at the point where P=MC. C) The monopolist is not maximizing profit and should increase output. D) The monopolist is not maximizing profit and should decrease output. E) The monopolist is earning a positive profit.
Answer: D. At P = MC, the monopolist is producing the perfect competition output level. That does not maximize profits. It is better to decrease output and receive a higher price.
29) Suppose that the government decides to limit monopoly power with price regulation. If the government sets the price at the competitive level, it will set the price at: A) P1 B) P2 C) P3 D) P4 E) none of the above
Answer: D. The competitive price is where marginal cost equals demand: price P4 (recall that the demand curve is the same as the average revenue curve). Notice, however, that at a price P4, if the monopolist produces the competitive quantity Q4, it incurs in a negative profit, since price is below average total cost (ATC). This competitive price is clearly not feasible, that is why we have a natural monopoly in this example.
5) To find the profit maximizing level of output, a firm finds the output level where A) price equals marginal cost. B) marginal revenue equals average total cost. C) price equals marginal revenue. D) all of the above E) none of the above
Answer: E. The correct answer should be MR = MC. The condition P = MC only holds for perfectly competitive markets, not in general.
13) A firm's demand curve is given by P = 500 - 2Q. The firm's current price is $300 and the firm sells 100 units of output per week. Assuming that the firm's marginal cost is zero, is the firm maximizing profit?
Answer: If MC = 0, the firm is not maximizing profit since MR should be equal to MC. REV=500Q-2Q2 . MR = 500 - 4Q = 0 4Q = 500 Q = 125 The firm should expand output from 100 units to 125 units per week.
18) Firm Alpha is a Monopolist. The graph below shows Alpha's marginal cost, average cost, average revenue, and marginal revenue. The monopolist uses its market power to maximize its own profit. The Lerner Index of Monopoly Power is approximately A) L = 90 B) L = 0.500 C) L = 0.727 D) L = 0.818 E) L = 0.667
Answer: L = 0.727. The monopolist optimally chooses quantity Q = 10 such that MR=MC. When Q = 10, the price is P = 11, and the marginal cost is MC = 3. Hence L = (P-MC)/P = (11- 3)/11=0.727. Note that in this question the information about the AC is not relevant.
9) Barbara is a producer in a monopoly industry. Her demand curve and total cost curve are given as follows: Q = 160 - 4P, TC = 4Q. How much output will Barbara produce? Find the price and profit.
Answer: Rewrite demand Q = 160 − 4P to find the inverse demand P = 40 − 0.25Q. Consequently, REV = P Q = (40 − 0.25Q)Q = 40Q − 0.25Q2 . Marginal revenue becomes MR = 40 − 0.5Q. The optimal choice is M R = M C 40 − 0.5Q = 4 36 = 0.5Q Q*= 72 P *= 40 − 0.25*72=22 Q = 72, P = 22, π = 1, 296.
10) A monopolist faces the following demand curve and total cost curve for its product: Q = 200 - 2P, TC = 5Q. a) What is the profit maximizing level of output and price? How much profit does the monopolist earn? b) Suppose that a tax of $5 for each unit produced is imposed by state government. What is the profit maximizing level of output and price? How much profit does the monopolist earn? c) Suppose that in addition to the tax, a business license is required to stay in business. The license costs $1000. What is the profit maximizing level of output and price? How much profit does the monopolist earn?
Answer: a) Inverse demand: P = 100 − Q/2. REV = P (Q)Q = (100 − Q/2)Q = 100 − Q2 /2. M R = 100 − Q. Profit maximization: MR = MC ⇒ 100 − Q = 5 and Q = 95. Price: P = 100 − 95/2 = 52.50. Profit: π = REV − COST = P Q − 5Q = 52.50 * 95 − 5 * 95 = 4, 512.50 b) The firm now pays $5 in taxes for each unit sold, therefore TC=5Q+5Q and the new marginal cost is $10 (=5+5). Profit maximization: MR = MC ⇒ 100 − Q = 10 and Q = 90. Price: P = 100 − 90/2 = 55. Profit (remember to include the tax as a cost): π = REV − COST = P Q − (5 + T AX) Q = 55 * 90 − (5 + 5) * 90 = 4, 050. Notice that the firm pays in taxes 5 * 90 = $450. c) The license is a fixed cost, therefore it does not change the marginal cost nor marginal revenue. The optimal choice of the monopolist remains the same, Q = 90 and P = 55. Profit, however, decreases by the license fee amount: π = REV −COST = PQ − (5 + TAX )Q − License = 55 * 90 − (5 + 5) * 90 − 1, 000 = 3, 050.
35) Maui Macadamia Inc. has a monopoly in the macadamia nut industry. The demand curve and marginal cost curve for macadamia nuts are given as follows: P = 360 - 4Q, MC = 4Q. a) What level of output maximizes the sum of consumer surplus and producer surplus? b) What is the profit maximizing level of output? c) At the profit maximizing level of output, what is the deadweight loss?
Answer: a) It is the perfectly competitive output, where price equals marginal cost: 360 − 4Q = 4Q, so Q = 45 b) Revenue: REV = P (Q)Q = (360 − 4Q)Q = 360Q − 4Q2 . Marginal revenue MR = 360 − 8Q. Profit maximization: MR = MC ⇒ 360 − 8Q = 4Q, so Q = 30 c) (Draw the graph) Q=30; P=360-4(30)=240 At Q=30, MC= 4(30)=120 The DWL is the area of the triangle: DW L = (240−120)*15/2 = 900.
1) When the demand curve is downward sloping, marginal revenue is A) equal to price. B) equal to average revenue. C) less than price. D) more than price.
C
22) DVDs can be produced at a constant marginal cost of $10 per disk, and Roaring Lion Studios is releasing the DVDs for its last two major films. The DVD for Rambeau 17 is priced at $20 per disk, and the DVD for Schreck 10 is priced at $30 per disk. What are the Lerner indices for these two movies? A) Both equal one. B) 2 and 3, respectively C) 1/2 and 2/3, respectively D) 1 and 2, respectively
C
27) Which of the following is NOT associated with a high degree of monopoly power? A) A relatively inelastic demand curve for the firm B) A small number of firms in the market C) Significant price competition among firms in the market D) Significant barriers to entry
C
3) Compared to the equilibrium price and quantity sold in a competitive market, a monopolist will charge a ----------- price and sell a --------------quantity. A) higher; larger B) lower; larger C) higher; smaller D) lower; smaller E) none of these
C
8) A monopolist has set her level of output to maximize profit. The firm's marginal revenue is $20, and the price elasticity of demand is -2.0. The firm's profit maximizing price is approximately: A) $0 B) $20 C) $40 D) $10 E) This problem cannot be answered without knowing the marginal cost
C. The monopolist maximizes profit when MR = MC. The question states that MR = 20, therefore MC = 20. We also know that, in order to maximize profits, the monopolist implements a price P = MC/(1+(1/ED)) . Since ED = -2, P = 20 / (1-(1/2)) = 40.
6) For a monopolist, changes in demand will lead to changes in A) price with no change in output. B) output with no change in price. C) both price and quantity. D) any of the above can be true.
D
