ECMC02H Intermediate Microeconomics - Topics in Price Theory

Transcription

1 1 ECMC02H Intermediate Microeconomics - Topics in Price Theory Term Test October 19, 2009 Professor Gordon Cleveland Time: 80 minutes ANSWERS TO THE TEST QUESTIONS ARE SHOWN BELOW EACH QUESTION. DIFFERENT VERSIONS OF THE TEST HAD THE SAME QUESTIONS BUT IN A DIFFERENT ORDER PART I - 15 Multiple Choice Questions - 75 marks 1-5. A firm in a perfectly competitive constant cost industry has total costs in the short run given by: TC = 2.5q 2 + 5q + 40 where q is output per day and TC is the total cost per day in dollars. The firm has fixed costs of $30 (already included in the TC equation above). The TC equation generates minimum average costs of $25 (per unit) at q = 4. You are also told that this size firm generates minimum long run average costs (that is, minimum LRAC occurs at q = 4, with min LRAC = $25). In the short run, there are 200 firms in this industry. Questions 1 through 5 concern this firm and this industry. 1. In the short run there are 200 firms in the industry, all with the same cost curves described above. Suppose that the demand curve facing the industry is given by the equation P = Q where P is the price per unit and Q is the number of units demanded per day. The equilibrium price in the short run is: A) $25 B) $30 C) $35 D) $40 E) $45 F) $50 G) $55 H) $60 I) $65 J) none of the above MC = dtc/dq = 5 + 5q. Since the PC firm sets MC = P, we have P = 5 + 5q, which is the equation of the firm s supply curve (above min AVC). 200q = Q, so q =.005Q. Substituting, we can find the industry supply curve for this group of 200 firms. P = 5 + 5(.005Q) = Q. Since demand is P = Q, we have Q = Q or Q 0 *= 1200 and P 0 * = $35. The correct answer is (C). 2. Continuing the situation described in question 1 (the short run, with 200 firms and demand given by P = Q), the profit earned by an individual firm per day in the short run is: A) $0 B) -$50 C) -$30 D) -$20 E) $20 F) $30 G) $50 H) $70 I) $90 J) none of the above Profit = 35 x 6 (2.5[6 x 6] ) = = $50. The correct answer is (G).

2 2 3. How much is sum of consumer surplus and producer surplus in this industry in the short run? A) $0 B) -$5000 C) -$3000 D) -$2000 E) $2000 F) $4,500 G) $13,500 H) $18,000 I) $21,000 J) $24,000 K) $30,000 L) $36,000 M) $44,000 N) $54,000 O) $60,000 P) $66,000 Q) $70,000 R) $72,000 S) $76,000 T) $80,000 U) $88,000 V) $96,000 W) $100,000 X) $102,000 Y) $108,000 Z) none of the above The sum of consumer surplus and producer surplus is the whole area between the demand and supply curves up to the equilibrium quantity. This is:([125 5] x 1200)/2 = $72,000. The correct answer is (R). 4. Imagine that, somehow or other, the amount of output traded in this industry is not at its equilibrium level, but is artificially held down to 600 units of output, so that 600 units are consumed and 600 units are produced in this industry. What now would be the sum of consumer surplus and producer surplus in this industry? A) $0 B) -$5000 C) -$3000 D) -$2000 E) $2000 F) $4,500 G) $13,500 H) $18,000 I) $21,000 J) $24,000 K) $30,000 L) $36,000 M) $44,000 N) $54,000 O) $60,000 P) $66,000 Q) $70,000 R) $72,000 S) $76,000 T) $80,000 U) $88,000 V) $96,000 W) $100,000 X) $102,000 Y) $108,000 Z) none of the above If output is 600, then the demand price is $80 and the supply price is $20. The sum of CS and PS is [(125 80) x 600]/2 + [60 x 600] + [(20-5) x 600]/2 = $54,000. The correct answer is (N). 5. Continuing the situation described in question 1 (demand given by P = Q, 200 firms in the short run), suppose now that we move into the long run (you are reminded that information on long run costs was given at the beginning of the problem). The number of firms in the industry, rounding to the nearest integer, is: A) 0 B) 20 C) 100 D) 133 E) 146 F) 200 G) 233 H) 283 I) 333 J) none of the above Since we have constant costs and the min LRAC occurs at $25, the long run supply curve will be horizontal at P = 25. Therefore, LR equilibrium will be where 25 = Q or Q = Since the minimum cost size of an individual firm is at q = 4, n = /4 = firms. The correct answer is (I).

3 A monopoly producer of a particular well-known economics textbook is able to sell them to consumers in North America and also to consumers in South America. Because the markets are geographically separated, producers are able to separate these two types of consumers and sell them the same product at two different prices. You are given the following demand curves per year for these distinct markets: North America: P 1 = Q 1 South America: P 2 = Q 2 where P refers to prices charged to each group and Q refers to quantities demanded by each group. The variable cost of producing textbooks is constant at $16 per textbook. In addition there are sunk fixed costs of $100,000 per period. Questions 6 through 10 concern this case. 6. If the producer of this textbook can price discriminate by charging different prices to each group, the profit-maximizing price charged to North American consumers will be: A) $0 B) $38 C) $40 D) $42 E) $44 F) $46 G) $48 H) $50 I) $52 J) $54 K) $56 L) $58 M) $60 N) $62 O) $64 P) $66 Q) $68 R) $70 S) $72 T) $74 U) $76 V) $78 W) $80 X) $82 Y) $84 Z) none of the above MR 1 = Q = 16, so Q 1 * = 4200 and P 1 * = $58. The correct answer is (L). 7. If the producer of this textbook can price discriminate by charging different prices to each group, the profit-maximizing price charged to South American consumers will be: A) $0 B) $38 C) $40 D) $42 E) $44 F) $46 G) $48 H) $50 I) $52 J) $54 K) $56 L) $58 M) $60 N) $62 O) $64 P) $66 Q) $68 R) $70 S) $72 T) $74 U) $76 V) $78 W) $80 X) $82 Y) $84 Z) none of the above MR 2 = Q = 16, so Q 2 * = 800 and P 2 * = $48. The correct answer is (G).

4 4 8. Assume now that the monopoly producer of textbooks is unable to discriminate between these groups but must sell at a uniform price. What price will now be charged? A) $0 B) $38 C) $40 D) $42 E) $44 F) $46 G) $48 H) $50 I) $52 J) $54 K) $56 L) $58 M) $60 N) $62 O) $64 P) $66 Q) $68 R) $70 S) $72 T) $74 U) $76 V) $78 W) $80 X) $82 Y) $84 Z) none of the above Q 1 = 10, P and Q 2 = P, so the sum of these is Q = 12, P. Putting P on the left-hand side, we have P = Q as the equation of the (bottom part of the) sum of the demand curves. MR = Q = 16, so Q 3 * = 5,000 and P 3 * = $56. The correct answer is (K). 9. By how much has total profit risen when the monopolist moves from charging a single price to both markets to charging two different prices in North America and South America? A) $0 B) -$5000 C) -$3000 D) -$2000 E) $2000 F) $4,500 G) $13,500 H) $18,000 I) $21,000 J) $24,000 K) $30,000 L) $36,000 M) $44,000 N) $54,000 O) $60,000 P) $66,000 Q) $70,000 R) $72,000 S) $76,000 T) $80,000 U) $88,000 V) $96,000 W) $100,000 X) $102,000 Y) $108,000 Z) none of the above Profit for the single-price monopolist is (56 x 5000) (100,000 + [16 x 5000]) = $100,000. The profit for the monopolist who is able to price-discriminate between the two markets is: (58 x 4200) + (48 x 800) (100,000 + [16 x 5000]) = $102,000. The price-discriminating profit is higher by $2,000. The correct answer is (E). 10. For North America only, by how much has consumer surplus fallen (-) or risen (+) in moving from the price discrimination situation to the normal monopoly situation with no price discrimination? A) -$18,000 B) -$12,800 C) -$10,600 D) -$9,800 E) -$8,600 F) -$7,900 G) -$6,400 H) -$5,200 I) -$4,800 J) -$4,200 K) -$3,200 L) +$0 M) +$3,200 N) +$4,200 O) +$4,800 P) +$5,200 Q) +$6,400 R) +$7,900 S) +$8,600 T) +$9,800 U) +$10,600 V) +$12,800 W) +$18,000 X) +$19,600 Y) +$21,200 Z) none of the above The consumer surplus in North American under price discrimination is [(100 58) x 4,200]/2 = $88,200. The consumer surplus under a single-price monopoly is [(100 56) x 4,400]/2 = $96,800. The difference is + $8,600. The correct answer is (S).

5 The province of Prince Edward Island specializes in the growing of potatoes. The government of Prince Edward Island is anxious to keep the potato farmers happy, and does not want the price of potatoes to fall too low. The current demand for potatoes is given by P = Q, with P representing the price in dollars per bushel of potatoes and Q representing the annual quantity in bushels of potatoes. The supply of potatoes is given by P = Q. The questions below refer to this potato-growing industry. This information can be used in answering questions If there is no government intervention in this perfectly competitive potato industry, what will be the total amount of consumer and producer surpluses? A) $0 B) $6000 C) $8000 D) $10,000 E) $20,000 F) $30,000 G) $40,000 H) $50,000 I) $60,000 J) $70,000 K) $80,000 L) $90,000 M) $100,000 N) $120,000 O) $140,000 P) $160,000 Q) $180,000 R) $200,000 S) $220,000 T) $240,000 U) $260,000 V) $280,000 W) $300,000 X) $320,000 Y) $340,000 Z) none of the above The equilibrium will be where Q = Q or where Q 0 * = 8,000 and P 0 * = $60. The sum of CS and PS will be [(100 20) x 8000]/2 = $320,000. The correct answer is (X). 12. Now, imagine that the government of Prince Edward Island decides to support the price of potatoes by establishing a price floor of $70 per bushel. Imagine that the potato farmers ignore the reduced demand for potatoes at this higher price, and decide to plant potatoes imagining they can sell as much as they want to at this new price. What will be the deadweight loss due to this system of price supports? A) $0 B) $6000 C) $8000 D) $10,000 E) $20,000 F) $30,000 G) $40,000 H) $50,000 I) $60,000 J) $70,000 K) $80,000 L) $90,000 M) $100,000 N) $120,000 O) $140,000 P) $160,000 Q) $180,000 R) $200,000 S) $220,000 T) $240,000 U) $260,000 V) $280,000 W) $300,000 X) $320,000 Y) $340,000 Z) none of the above At P = $70, the quantity demanded is 6,000 and the quantity supplied would be 10,000. The deadweight loss = (70 x [10,000 6,000]) ([70 60] x 4000)/2 = $260,000. The correct answer is (U).

6 6 13. Now, instead of this legislated price floor, the PEI government decides to enforce a quota that will keep the price up at $70. What is the amount of the deadweight loss as a result of this quota? A) $0 B) $6000 C) $8000 D) $10,000 E) $20,000 F) $30,000 G) $40,000 H) $50,000 I) $60,000 J) $70,000 K) $80,000 L) $90,000 M) $100,000 N) $120,000 O) $140,000 P) $160,000 Q) $180,000 R) $200,000 S) $220,000 T) $240,000 U) $260,000 V) $280,000 W) $300,000 X) $320,000 Y) $340,000 Z) none of the above With a quota, the supply is restricted to 6,000 units. The demand price is $70 at 6,000 units and the supply price is $50. The deadweight loss would be [(70 50) x ( )]/2 = $20,000. The correct answer is (E). 14. Now, instead of the price floor or the quota (discussed in questions 12 and 13), the government of Prince Edward Island decides to pay farmers not to produce potatoes until it reduces the quantity of output sufficient to keep the price at $70. How much will the government have to pay farmers in order to achieve its objectives? A) $0 B) $6000 C) $8000 D) $10,000 E) $20,000 F) $30,000 G) $40,000 H) $50,000 I) $60,000 J) $70,000 K) $80,000 L) $90,000 M) $100,000 N) $120,000 O) $140,000 P) $160,000 Q) $180,000 R) $200,000 S) $220,000 T) $240,000 U) $260,000 V) $280,000 W) $300,000 X) $320,000 Y) $340,000 Z) none of the above In order to encourage the farmers to reduce their output, the government would have to pay them the amount of producer surplus they would give up by reducing production. That would be [(70 50) x (10,000 6,000)]/2 = $40,000. The correct answer is (G). 15. Imagine a (different) situation in which a monopolist is serving two distinct markets. It is able to produce output from a single factory with a constant marginal cost. Imagine that you know that the elasticity of demand in the first market is 15. In the second market, the elasticity of demand is 3. The price in the first market is $60. Assuming the monopolist engages in third-degree price discrimination, what is the price in the second market? A) $0 B) $38 C) $40 D) $42 E) $44 F) $46 G) $48 H) $50 I) $52 J) $54 K) $56 L) $58 M) $60 N) $62 O) $64 P) $66 Q) $68 R) $70 S) $72 T) $74 U) $76 V) $78 W) $80 X) $82 Y) $84 Z) none of the above MR = P(1 + [1/E D ]) = 60(1 [1/15]) = $56. The producer will profit maximize by making MR equal in the second market, so 56 = P(1 [1/3]) = (2/3)P. Therefore, P in the second market = $84.

7 7 PART II - Graphical and Short Answer Questions - 25 marks Price 100 Short-run Supply 70 Demand ,000 16(a) Assume that the graph above refers to a perfectly competitive industry that produces hula hoops. In this industry there is no international trade. Now imagine that international trade is possible in fact, hula hoops are perfectly elastically supplied from international producers at a price of $30. What is the extra amount of economic welfare or economic well-being due to opening up international trade and who receives it? The demand curve is P = Q and the supply curve is P = Q. This generates an equilibrium price of $70 and equilibrium quantity of 3000 units. At a price of $30, we can calculate that 7,000 hula hoops will be demanded and 1,000 hula hoops will be domestically supplied. The extra well-being = ([70 30] x [ ])/2 = $120,000 (b) How many hula hoops will be imported? From the calculations above, 7,000 1,000 = 6,000 hula hoops will be imported. (c) If a tariff of $10 per hula hoop is placed on imports, what will be the amount of deadweight loss due to the tariff? A tariff of $10 will drive the equilibrium price up to $40. At $40, the quantity demanded will be 6,000 units and the quantity supplied domestically will be 1,500 units. There will be three areas of loss of consumer surplus compared to the situation without a tariff. There are two areas of deadweight loss: (10 x 500)/2 = $2,500 and (10 x 1000)/2 = $5,000 Quantity

8 8 for a total deadweight loss of $7,500. There is also the tariff revenue, which, on 4,500 units of imports = 4500 x 10 = $45,000. The tariff revenue is not part of deadweight loss (and you don t need to calculate it for this question ). (d) Imagine now that the curve labelled short run supply is actually a long-run supply curve in this industry (and international trade still happens and there is a tariff of $10). How much is the producer surplus? Who gets this producer surplus? Invent an example to give an illustration of who might get this producer surplus. The producer surplus is ([40 10] x 1500)/2 = $22,500. The producer surplus in the long run is received by the owners of scarce productive inputs whose input prices rise as the industry expands (as Q rises). The scarce input could be labour. If there was some kind of scarce specialized labour required in the production of hula hoops, its price might rise as the industry expands. Or, it could be some material used in the production of hula hoops (a rare mineral or metal) whose price would rise as output in this industry expands. For this to happen, the hula hoop industry would have to be a major consumer of this mineral or metal.

9 9 $ per device 17. There are two types of consumers in the market for hand-held digital devices. Type A consumers are wary and uncertain, Type B consumers are enthusiastic. The demand per week by each Type A consumer is given on the graph below (labelled Type A Demand ). The demand per week by each Type B consumer is given on the graph below (labelled Type B Demand ). You can assume that the cost of producing digital devices is zero. The monopoly producer of digital devices is trying to figure out how to price digital devices so that each type of consumer will pay a different price, so that the monopolist can price discriminate. Since the consumers are not distinguished by any obvious characteristic, the monopolist will have to design different price-quantity packages that encourage consumers to self-select into the two types. For the purposes of this question, you can assume that there is one Type A consumer and one Type B consumer in the market. The questions on the next page refer to this diagram Type B Demand Type A Demand Number of digital devices

10 10 17 (a) Assume that 20 digital devices is the optimum quantity to sell to the Type A consumer to allow self-selection by consumers and to maximize profit for the producer. Show on the diagram (i.e., shade in the area or colour it in and indicate with arrows etc.) the area that corresponds to the price charged to the Type A consumer. What is the dollar value of the price charged to the Type A consumer? The self-selecting price to charge to the Type A consumer will be ([ ] x20)/2 + (400 x 20) = $12,000. The area is coloured in red on the graph above. (b) Using a different colour or a different pattern of cross-hatching, indicate on the diagram the area that corresponds to the amount of consumer surplus that the Type B consumer will receive. What is the dollar value of this amount of consumer surplus? The consumer surplus received by the Type B consumer is shown in blue with a pattern of small squares on the diagram above. The amount of consumer surplus will be 400 x 20 = $8,000. (c) What price will the Type B consumer have to pay? The type B consumer will have to pay a price that exactly leaves the amount of consumer surplus calculated in part (b). That price is $12,000 (i.e., the Type A price) + ([800 x 40]/2) which is another $16,000. The total price for the Type B package will be $28,000.