ECMC02H Intermediate Microeconomics - Topics in Price Theory

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1 1 ECMC02H Intermediate Microeconomics - Topics in Price Theory Answers to the Term Test June 23, 2010 Version A of the test Your name (Print clearly and underline your last name) Your student number 1. _ O 6. M 11. _L 2. A 7. C 12. O 3. A 8. I 13. L 4. V 9. Q 14. P 5. F 10. L 15. X This exam consists of TWO PARTS, both of which are to be answered in this exam booklet. For the first part, there are 15 multiple choice questions, each worth 5 marks, which are to be answered on this front sheet of the exam. Each question should be answered by indicating with a BLOCK CAPITAL LETTER the alternative which is correct (if you feel that a question is ambiguous or that no one answer is entirely correct, pick the answer which you believe to be the "best" answer). You will receive 5 marks for each correct answer, 0 for each wrong or blank response (thus you will not be penalized for wrong guesses). For the second part, there are two short answer and graphical problems. You should answer both of these questions; they are worth a total of 25 marks. These problems are provided at the end of the multiple choice questions, and you are to answer them in the space provided. If you make mistakes and need to redo the question, or if you need extra space for your answers, you can use the back of the pages, but clearly indicate that you are doing this below the question. The exam is out of 100. Your exam consists of 11 pages. NOW. FILL IN YOUR NAME

2 2 PART I - 15 Multiple Choice Questions - 75 marks 1. A profit-maximizing monopolist charges a price of $10 to all its customers. The elasticity of demand is -4. What is the marginal cost of production for this monopolist? A) $0 B) $1 C) $1.50 D) $2 E) $2.50 F) $3 G) $3.50 H) $4 I) $4.50 J) $5 K) $5.50 L) $6 M) $6.50 N) $7 O) $7.50 P) $8 Q) $8.50 R) $9 S) $9.50 T) $10 U) $10.50 V) $11 W) $11.50 X) $12 Y) $12.50 Z) none of the above 2-5. 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 400 firms in this industry. Questions 2 through 5 concern this firm and this industry. 2. In the short run there are 400 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 3. Continuing the situation described in question 2 (the short run, with 400 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

3 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) $16,000 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) $78,000 R) $80,000 S) $96,000 T) $112,000 U) $118,000 V) $128,000 W) $132,000 X) $142,000 Y) $158,000 Z) none of the above 5. Now imagine that demand rises to P = Q. What would be the the number of firms in the industry in a new long-run equilibrium (rounding to the nearest integer, if necessary)? A) 0 B) 620 C) 800 D) 933 E) 1046 F) 1100 G) 1235 H) 1280 I) 1300 J) none of the above 6. The World Cup is trying out a new scoring system for penalty kicks. The points for scoring on a penalty kick depend on which direction it is kicked and which direction the goalie jumps. A soccer player has been awarded a penalty shot on the opposing team s goal. Only the goalie is allowed to try to stop this penalty kick. The kicker has two possible strategies kick to the goalie s left or kick to the goalie s right. The goalie has two possible strategies in defence jump left or jump right. The payoffs are shown below: Goalie (#2) Jump Left Jump Right Kicker (#1) Kick Left (-1, 1) (2, -2) Kick Right (3, -3) (-4, 4) If the kicker and the goalie follow mixed strategies, what are the equilibrium probabilities that the kicker will kick right and that the goalie will jump right. A) 0, 1 B) 1/5, 1/5 C) 3/10, 3/10 D) 3/5, 3/5 E) 5/8, 5/8 F) 1/5, 2/5 G) ½, 7/10 H) 3/5, 2/5 I) 2/5, 3/5 J) 3/10, 3/5 K) 7/10, 3/5 L) 4/5, 3/10 M) 3/10, 2/5 N) 9/10, 1/5 O) 2/5, 3/10 P) 1, 0 Q) none of the above

4 You are given the following 5 strategic games involving two firms. Firm I can adopt either of strategy A or strategy B. Firm II can adopt either of strategy Y or strategy Z. Payoffs to the firms appear in the matrix. Questions 7 through 11 concern these five games. Firm II Strategy Y Strategy Z Game #1: Firm I Strategy A (3, 3) (6, 6) Strategy B (6, 6) (3, 3) Firm II Strategy Y Strategy Z Game #2: Firm I Strategy A (1, 6) (4, 5) Strategy B (2, 7) (3, 8) Firm II Strategy Y Strategy Z Game #3: Firm I Strategy A (1, 2) (5, 6) Strategy B (3, 4) (7, 8) Firm II Strategy Y Strategy Z Game #4: Firm I Strategy A (1, 8) (6, 4) Strategy B (5, 7) (2, 3) Firm II Strategy Y Strategy Z Game #5: Firm I Strategy A (1, 5) (4, 6) Strategy B (2, 8) (3, 7)

5 5 7. Assuming that each player tries to gain the maximum individual benefit, then dominant strategies for firm I are found in which of the following games: A) only #1 B) only #2 C) only #3 D) only #4 E) only #5 F) only #1 and #2 G) only #1 and #3 H) only #1 and #4 I) only #1 and #5 J) only #2 and #3 K) only #2 and #4 L) only #2 and #5 M) only #3 and #4 N) only #3 and #5 O) only #4 and #5 P) only #1, #2, and #3 Q) only #1, #2, and #4 R) only #1, #2, and #5 S) only #1, #3, and #4 T) only #1, #3, and #5 U) only #1, #4, and #5 V) only #2, #3, and #4 W) only #2, #3, and #5 X) only #2, #4, and #5 Y) only #3, #4, and #5 Z) none of the above 8. If the games are simultaneous, instead of sequential, then multiple Nash equilibria are found in which of the following games: A) only #1 B) only #2 C) only #3 D) only #4 E) only #5 F) only #1 and #2 G) only #1 and #3 H) only #1 and #4 I) only #1 and #5 J) only #2 and #3 K) only #2 and #4 L) only #2 and #5 M) only #3 and #4 N) only #3 and #5 O) only #4 and #5 P) only #1, #2, and #3 Q) only #1, #2, and #4 R) only #1, #2, and #5 S) only #1, #3, and #4 T) only #1, #3, and #5 U) only #1, #4, and #5 V) only #2, #3, and #4 W) only #2, #3, and #5 X) only #2, #4, and #5 Y) only #3, #4, and #5 Z) none of the above 9. If Firm II is risk averse, and tries to maximize its minimum gain (in a simultaneous game), while Firm I continues to seek its individual maximum, then which games will have Strategy B - Strategy Y as a Nash Equilibrium?: A) only #1 B) only #2 C) only #3 D) only #4 E) only #5 F) only #1 and #2 G) only #1 and #3 H) only #1 and #4 I) only #1 and #5 J) only #2 and #3 K) only #2 and #4 L) only #2 and #5 M) only #3 and #4 N) only #3 and #5 O) only #4 and #5 P) only #1, #2, and #3 Q) only #1, #2, and #4 R) only #1, #2, and #5 S) only #1, #3, and #4 T) only #1, #3, and #5 U) only #1, #4, and #5 V) only #2, #3, and #4 W) only #2, #3, and #5 X) only #2, #4, and #5 Y) only #3, #4, and #5 Z) none of the above

6 6 10. Now, ignore risk-averse maximin strategies and assume each firm is trying to maximize its individual benefit. If each of the five games shown above were a sequential game, with Firm I moving first (instead of a simultaneous game with each firm seeking maximum benefit), in which of these games would the Nash equilibrium be different? In other words, in which games is the Nash equilibrium different for a sequential game, in comparison to a simultaneous game? (Note: If there is no equilibrium in one case but an equilibrium in the other, count that as different. If there is one equilibrium in one case, but two equilibria in the other case, count that as different). A) only #1 B) only #2 C) only #3 D) only #4 E) only #5 F) only #1 and #2 G) only #1 and #3 H) only #1 and #4 I) only #1 and #5 J) only #2 and #3 K) only #2 and #4 L) only #2 and #5 M) only #3 and #4 N) only #3 and #5 O) only #4 and #5 P) only #1, #2, and #3 Q) only #1, #2, and #4 R) only #1, #2, and #5 S) only #1, #3, and #4 T) only #1, #3, and #5 U) only #1, #4, and #5 V) only #2, #3, and #4 W) only #2, #3, and #5 X) only #2, #4, and #5 Y) only #3, #4, and #5 Z) none of the above 11. Now, change the firm that moves first. If each of the five games shown above were a sequential game, with Firm II moving first (instead of Firm I), in which of these games would the Nash equilibrium be different from the sequential games in which Firm 1 moved first? In other words, in which games is the Nash equilibrium different for a sequential game with Firm II moving first, in comparison to a sequential game with Firm I moving first? (Note: If there is no equilibrium in one case but an equilibrium in the other, count that as different. If there is one equilibrium in one case, but two equilibria in the other case, count that as different). A) only #1 B) only #2 C) only #3 D) only #4 E) only #5 F) only #1 and #2 G) only #1 and #3 H) only #1 and #4 I) only #1 and #5 J) only #2 and #3 K) only #2 and #4 L) only #2 and #5 M) only #3 and #4 N) only #3 and #5 O) only #4 and #5 P) only #1, #2, and #3 Q) only #1, #2, and #4 R) only #1, #2, and #5 S) only #1, #3, and #4 T) only #1, #3, and #5 U) only #1, #4, and #5 V) only #2, #3, and #4 W) only #2, #3, and #5 X) only #2, #4, and #5 Y) only #3, #4, and #5 Z) none of the above

7 There are two producers of mineral water in Canada. The demand curve for mineral water is given by P = Q, where Q is total output of the two firms together and P is the market price. The total cost function of each producer is given by TC = 24q, where q is the output of the individual firm. This information will be useful in answering questions 12 through What is the Cournot equilibrium price, if both firms behave as Cournot duopolists? A) $0 B) $22 C) $24 D) $26 E) $28 F) $30 G) $32 H) $34 I) $36 J) $38 K) $40 L) $42 M) $44 N) $46 O) $48 P) $50 Q) $52 R) $54 S) $56 T) $58 U) $60 V) $62 W) $64 X) $66 Y) $68 Z) none of the above 13. If Firm #1 is a Stackelberg leader and the other is a follower, what price will be charged by the Stackelberg leader? A) $0 B) $22 C) $24 D) $26 E) $28 F) $30 G) $32 H) $34 I) $36 J) $38 K) $40 L) $42 M) $44 N) $46 O) $48 P) $50 Q) $52 R) $54 S) $56 T) $58 U) $60 V) $62 W) $64 X) $66 Y) $68 Z) none of the above 14. Deadweight loss is a measure of industry performance. The amount of deadweight loss falls in moving from the Cournot equilibrium to the Stackelberg equilibrium. By how much does the amount of deadweight loss fall? A) $0 B) $960 C) $1800 D) $2160 E) $2400 F) $3600 G) $4800 H) $5600 I) $6300 J) $7200 K) $8100 L) $9400 M) $9900 N) $10800 O) $11200 P) $12600 Q) $13600 R) $14400 S) $16200 T) $18600 U) $21600 V) $24800 W) $28800 X) $29640 Y) $33600 Z) none of the above 15. There are four individuals in the market for cable channels provided by a cable television company. Tom is willing to pay $7 for the Sports channel and $14 for the History channel and $6 for the Movie channel. Dick is willing to pay $18 for the Sports channel, $5 for the History channel and $2 for the Movie channel. Harry is willing to pay $12 for the Sports channel, $1 for the History channel and $13 for the Movie channel. Sue is willing to pay $1 for the Sports channel, $10 for the History channel and $20 for the Movie channel. The cable company has the option of pricing each channel separately or of bundling together channels in order to maximize its revenue from these four individuals. When the cable company adopts the revenuemaximizing strategy, how much revenue will it be able to earn? A) $0 B) $10 C) $12 D) $17 E) $18 F) $20 G) $25 H) $28 I) $30 J) $31 K) $32 L) $37 M) $40 N) $45 O) $48 P) $52 Q) $54 R) $57 S) $60 T) $61 U) $62 V) $70 W) $88 X) $100 Y) $109 Z) none of the above

8 8 Price Short Answer Questions (total marks = 25) 16. The graph below shows the situation in the market for wheat in Western Canada, with an equilibrium price of $40 and an equilibrium quantity of 60 tonnes of wheat traded each year. The demand curve is given by P = 100 Q and the supply curve is given by P = Q. Now, the government of Canada decides to help the western Canadian farmers by purchasing wheat on the open market in order to keep its price higher than equilibrium. Assume that this wheat cannot be stored. The target price that the Canadian government is aiming for (and achieves) is $80. (a) show on this graph the shifts that occur in demand and supply as a result of this policy to keep the price of wheat high. Label clearly any lines that you add to the graph and show the value of their intercepts with the vertical and horizontal axes, and show the new equilibrium position that results. $220 Note: the part shaded in dark blue is part of both shadings (i.e., part of extra PS and also DWL) 100 Additional Government Demand P 1 * =$80 40 New Demand Curve Q 1 * = Quantity

9 9 (b) On the diagram, shade in the area that shows the amount of producer surplus that this policy has added to the previous amount. Shade this area of new producer surplus using the pattern below: (c) On the diagram, shade in the area that shows the amount of deadweight loss due to this policy described above. Shade the area using the pattern below. (d) What is the total amount of consumer surplus after this policy is implemented? (you do not need to shade in the area of consumer surplus) Consumer Surplus = $200 (e) Now imagine that the government changes its mind. Now, it wants to keep the price at this same elevated level, but it will achieve this by paying farmers not to grow wheat. Assuming that this policy will work, how much would the government have to pay the farmers in total to encourage them to sufficiently reduce their production of wheat? The government will have to pay the farmers the amount of producer surplus they have lost by reducing their output. This is $3,600.

10 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 $4 per textbook. In addition there are sunk fixed costs of $800 per period. (a) In the space below, draw two quadrants of a single graph and show the demand curves and cost curves in these two markets and show the equilibrium amounts of quantity and the prices charged in the two markets. For clarity, below the graph write down what the equilibrium quantities and prices are in the two markets. Also write down the amount of profit earned. Price $20 P 1 * = $12, Q 1 * = 80. P 2 * = $7, Q 2 * = 120. Profit under price discrimination = $200 D 1 $12 $10 $7 D 2 MC Q Q 1 MR 2 MR 1

11 11 (b) If the monopolist was unable to price discriminate between these two markets, what price and quantity would be charged and how much profit would be made by this monopolist? P* = $8. Q* = 200. Profit = $0 (c) 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? Consumer Surplus under price discrimination = $320. Consumer Surplus under monopoly in the North American market = $720. Consumer Surplus rises in the move from price discrimination to monopoly by $400. (d) If this producer were able to engage in perfect price discrimination in these two markets, how much profit would this producer be able to make? Under perfect price discrimination, profit would be $1200.

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