Final Exam Version A

Transcription

1 BA 210 Dr. Jon Burke Final Exam Version A This is a 150-minute exam (2hr. 30 min.). There are 9 questions (about 16 minutes per question). The exam begins exactly as scheduled. To avoid the temptation to cheat, you cannot take this exam if you arrive more than 10 minutes late, and you cannot (without permission) leave the room and re-enter during the exam. Exam Grading Each individual question on the following exam is graded on this 4-point scale: 4 points if all is correct --- or there is only a small error. 3 points for missing or doing wrong part of a problem, but the rest is correct. 2 points for a reasonable and substantive attempt. 1 point if there is at least something of value in the attempt. After all individual questions are graded, I sum the individual scores, and then compute that total as a percentage of the total of all points possible. I then apply a standard grading scale to determine your letter grade: % A; 80-89% B; 70-79% C; 60-70% D; 0-59% F Finally, curving points may be added to letter grades for the entire class (at my discretion), and the resulting curved letter grade will be recorded on a standard 4-point numerical scale: A = 4; A- = 3.7; B+ = 3.3; B = 3.0; B- = 2.7; C+ = 2.3; C = 2.0; C- = 1.7; D+ = 1.3; D = 1.0; F = 0 Tip: Pace yourself. When there is only ½ hour left, spend at least 5 minutes outlining an answer to each remaining question. 1

2 Question 1: Consider the following linear production possibilities of dresses and cans food each month from the U.S., Honduras (home to well known sweat shops), and the Congo (the poorest country in the world). Dresses Food U.S. 100 dresses 200 cans Honduras 10 dresses 10 cans Congo 4 dresses 2 cans If each country needs 3 dresses each month and if the competitive-market price of a can of food is $2, then what will be the competitive-market price of a dress? Answer to Question 1: 2

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4 Question 2: Consider the following demand curves for labor by Abby, Betty, Carla, Doug, Ernest, Frank: Potential buyers of labor Willingness to pay Abby $16 Betty $14 Carla $12 Doug $10 Ernest $8 Frank $6 And consider supply curves for labor by Gail, Heidi, Ingrid, Jim, Kyle, and Leo: Potential sellers of labor Cost to sell Gail $1 Heidi $3 Ingrid $4 Jim $6 Kyle $8 Leo $11 a. Compute the competitive equilibrium wage and employment. Compute consumer surplus and producer surplus (that is worker surplus). Now consider a minimum wage of $13 designed to help workers. b. Show the lost producer surplus from the inefficient allocation of employment. Specifically, suppose Kyle successfully competes to sell labor instead of Heidi. c. Show the lost total surplus as minimum wages reduce employment. d. Show the wasted resources from potential workers competing for employment. Specifically, suppose potential workers compete for jobs by waiting in line. Answer to Question 2: 4

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6 Question 3: Consider the market below for pizza in Chicago, where Giordano s, Gino s East, and Pizzeria Duo are just a few of the competitors. Chicago officials decide to impose an excise tax of $4 per pizza. Price of pizza Quantity of pizza demanded Quantity of pizza supplied $ $9 1 7 $8 2 6 $7 3 5 $6 4 4 $5 5 3 $4 6 2 $3 7 1 $2 8 0 $1 9 0 a. What is the quantity of pizza bought and sold after the imposition of the tax? What is the price paid by consumers? What is the price received by producers? b. Calculate the consumer surplus and the producer surplus after the imposition of the tax. By how much has the imposition of the tax reduced consumer surplus? By how much has it reduced producer surplus? c. How much tax revenue does Collegetown earn from this tax? d. Calculate the deadweight loss from this tax. Answer to Question 3: 6

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8 Question 4: Two companies, one based in Albuquerque and the other in Boston, are using the same Chicago-based lawyer. Each firm needs the lawyer s services in May, June, July, August, and September. As a result of coordinating schedules, the lawyer could each month make a triangle route (Chicago- Albuquerque -Boston) rather than making two separate trips. The airfares each month are: Triangle $1200, Chicago-Albuquerque roundtrip $800, Chicago-Boston roundtrip $600 Before the May trip, Albuquerque (the Albuquerque company) confronts Boston (the Boston company) over its share of the triangle airfare. Albuquerque presents its offer. Boston either accepts it for each of the five trips, or rejects it and returns after the May trip with a counteroffer. After the May trip, Albuquerque either accepts that counteroffer for each of the remaining four trips, or rejects it and returns after the June trip with a counteroffer. And so on, with alternating counter-offers before each of the remaining trips. What cost should Albuquerque agree to pay for each trip? Should Boston accept that initial offer? Answer to Question 4: 8

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10 Question 5: Sam s Club and Costco both sell emergency food supplies in a weather-proof bucket that provides 275 delicious easy-to-prepare meals, including potato soup and corn chowder. The unit cost to both retailers is $50. The retailers compete on price: the low-price retailer gets all the market and they split the market if they have equal prices. Suppose they consider prices $60, $70, and $80, and suppose market demands at those prices are 80, 50, and 20. Determine optimal prices and profits in that Price Competition Game. Sam s Club and Costco consider modifying the price competition game described above with the following low-price guarantee: We guarantee lower prices than any other store, and we do everything in our power to ensure that you re not paying too much for your purchase. That s why we offer our Low Price Guarantee. If you find a lower advertised price, simply let us know and we ll gladly meet that price! Determine optimal prices and profits in that Price Competition Game modified by the Low Price Guarantee, and compare with the original Price Competition Game above. Answer to Question 5: 10

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12 Question 6: R.J. Reynolds Tobacco Corp. (Player A) and Philip Morris Corp. (Player B) must decide how much money to spend on advertising each year. They consider spending either $20,000 or zero each year. If one advertises and the other does not, the advertiser pays $20,000, then takes $60,000 profit from the other. If each advertises, each pays $20,000 but the advertisements cancel out and neither player takes profit from the other. Suppose the yearly interest rate is 20%. What strategies (A One,B One ) should each player choose if they expect this game to last only one time period? Are there mutual gains from cooperative strategies (A Coop,B Coop ) rather than (A One,B One )? If they expect this game to repeat indefinitely, would Player A cooperate each period and choose A Coop if Player B followed the Grim Strategy of punishing noncooperation? and would B cooperate each period and choose B Coop if A followed the Grim Strategy of punishing non-cooperation? Answer to Question 6: 12

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14 Question 7: To understand how to discourage antisocial behavior, consider Grandma s demand for cigarettes. $ price per pack Packs demanded Suppose each pack Grandma smokes hurts 3 other senior citizens $0.25; that is, you would have to compensate each of them $0.25 for them to voluntarily let Grandma smoke a pack of cigarettes. Suppose the unit cost of supplying cigarettes is $1.50 per pack, and cigarette producers are perfect competitors. Assuming there are no taxes or subsidies, compute total surplus. Assuming the government imposes the optimal tax, compute the number of packs of cigarettes that are consumed. Assuming the government imposes the optimal tax, compute total surplus. Compare total surplus before and after the tax, and comment about the effect of the tax. Answer to Question 7: 14

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16 Question 8: Consider the Work-Shirk Game for an employee and an employer. Suppose if the employee chooses to work, he loses $130 of happiness from the effort of working, but he yields $500 to his employer. Suppose the employer can monitor the employee at a cost of $50. Finally, if the employee chooses to not work and the employer chooses to monitor, then the employee is not paid, but in every other case ( work or not monitor ), then the employee is paid $210. Predict strategies or recommend strategies if this game is repeated daily. Answer to Question 8: 16

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18 Question 9: Suppose Employer Earl has use for two kinds of employees. Skilled and hard working Type A employees contribute $140,000 per year to profits. And Type B employees contribute $70,000 per year to profits. Suppose Type A workers have existing jobs paying $60,000 per year, and Type B have existing jobs paying $50,000 per year. Suppose Type A workers regard the cost of completing a hard college class as $2,000 a year of salary, and Type B workers as $10,000 a year of salary. Suppose there is no way for the employer to directly tell Type A workers from Type B workers, but the employer can confirm the number of completed classes. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter). Determine wage demands, the number of completed classes, and which types work for Employer Earl. Answer to Question 9: 18

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20 Answers to Final Exam Version A (remember to try each problem before looking at these answers) Answer to Question 1: Step 1. Find who should make food. That is, who has the comparative advantage. For each citizen of the U.S., each can of food takes up 1/200 of his month, during which time he could complete 1/ = ½ dress. For each citizen of Honduras, each can of food takes up 1/10 of his month, during which time he could complete 1/10 10 = 1 dress. For each citizen of the Congo, each can of food takes up 1/2 of his month, during which time he could complete 1/2 4 = 2 dresses. Conclusion: The U.S. has the lowest opportunity cost and the comparative advantage in making food, then Honduras. And the Congo has the lowest opportunity cost and the comparative advantage in making dresses, then Honduras. Since you need 9 dresses, the Congo should produce only dresses and Honduras should produce 5 dresses, which takes 5/10 of its month, which leaves 5/10 for food. Step 2. Find the price P D per dress. Given that the market price of food is $2, here is what that price P D must satisfy to get the solution above: For U.S. to choose food full time, potential income from dresses 100P D must be no more than potential income from food, so 100 P D < 400. Conclusion: P D < 4. For Honduras to choose dresses part time, potential income from dresses 10P D must equal potential income from food, so 10P D = 20. Conclusion: P D = 2. 20

21 For Congo to choose dresses full-time, potential income from dresses 4P D must be no less than potential income from food, so 4P D > 4. Conclusion: P D > 1. Putting it all together, the competitive-market price is P D = 2. (See how the non-specialist determines price, and that the specialists inequalities are satisfied at that price.) 21

22 Answer to Question 2: a. At price $8, Abby, Betty, Carla, Doug, and Ernest buy labor from Gail, Heidi, Ingrid, Jim, and Kyle. In particular, competitive equilibrium wage is $8 and employment is 5. Consumer surplus from Abby, Betty, Carla, Doug, and Ernest is the difference between their willingness to pay and $8, which is $8 = $16-$8, $6 = $14-$8, $4 = $12-$8, $2 = $10-$8, and $0 = $8-$8, making aggregate consumer surplus $20 = $8+$6+$4+$2+$0. Producer surplus from Gail, Heidi, Ingrid, Jim, and Kyle is the difference between $8 and their cost to sell, which is $7 = $8-$1, $5 = $8-$3, $4 = $8-$4, $2 = $8-$6, and $0 = $8-$8, making aggregate producer surplus $18 = $7+$5+$4+$2+$0. (There is a technical simplification we make to work with integers when we assume someone will buy or someone will sell even when they get surplus 0. Make the same simplification on your homework and exams.) Now consider a minimum wage of $13 designed to help workers. b. Show the lost producer surplus from the inefficient allocation of employment. Specifically, suppose Kyle successfully competes to sell labor instead of Heidi. Kyle s cost to sell is $8 and Heidi s is $3, so there is $5 lost producer surplus from Kyle selling rather than Heidi. c. Show the lost total surplus as minimum wages reduce employment. Carla and Doug and Ernest no longer employ labor and, if only the least cost workers get jobs, Ingrid and Jim and Kyle are no longer employed. Carla and Doug and Ernest value labor at $12 and $10 and $8 and Ingrid s and Jim s and Kyle s cost to sell are $4 and $6 and $8, so the minimum lost total surplus from reduced employment is $12 = ($12+$10+$8)-($4+$6+$8). d. Show the wasted resources from potential workers competing for employment. Specifically, suppose potential workers compete for jobs by waiting in line. Since only the first 2 potential workers will be employed, only Gail and Heidi will work since they have the most to gain from employment. They have to wait in line long enough so that the cost of the line makes unemployment unattractive to Ingrid and the rest of the potential sellers of labor. For Ingrid to find work 22

23 unattractive, her net wage must be below her cost of $4 to sell, so the line must reduce wages from the minimum of $13 down to just below $4. That is, $9 is wasted in line by Gail and Heidi as they compete for employment. 23

24 Answer to Question 3: a. The tax drives a wedge between the price paid by consumers and the price received by producers. Consumers now pay $8, and producers receive $4. So after the imposition of the tax, the quantity bought and sold will be 2 pizzas. b. Consumer surplus is now $1 (one consumer who buys a pizza at $8 has a willingness to pay of $9, so that the consumer surplus is $9 $8 = $1, and the other consumer has consumer surplus of $8 - $8 = $0). Compared to the situation before the imposition of the tax, where the equilibrium price was $6, consumer surplus has been reduced by $5 (from $6 to $1). Similarly, producer surplus is now $1 (one producer who sells a pizza at $4 has cost $3, so that the producer surplus is $4 $3 = $1, and the other producer has producer surplus of $4 - $4 = $0), so producer surplus has decreased by $5 (from $6 to $1). c. Chicago earns a tax of $4 per pizza sold, which is a total tax revenue of $8. d. Total surplus has been decreased by $10. Of that $10, the town earns $8 in revenue, but $2 of surplus is lost. That is the deadweight loss from this tax. 24

25 Answer to Question 4: Rounds to End of Game Offer by Total Gain to Divide A's Gain Offered B's Gain Offered 1 A B A B A To consider all possible offers to split the gains from an agreement on splitting the cost of the triangle route, consider a bargaining payoff table. The game ends if an offer is accepted or if the five months end without an accepted agreement, and gains are measured as a percentage of the gain from using the triangle route for all five months. Starting from the end of the bargaining game and rolling back to the beginning, Albuquerque s best acceptable offer leaves Albuquerque with 60 percent of the gains from trade, and Boston with 40 percent. Recall, the airfares each month are: Triangle $1200, Chicago-Albuquerque roundtrip $800, Chicago-Boston roundtrip $600. In particular, the gain from five triangle trips is 5x( ) = Albuquerque s initial offer should be for Albuquerque to keep 60 percent of the $1000 gain, or $600. So Albuquerque pays 5x = $3400 for the five trips. Boston should accept that offer, and gain $400 and pay 5x = $2600 for the five trips. 25

26 Answer to Question 5: The Price Competition Game has a dominance solution for each player: First, eliminate $80 because it is weakly-dominated; then, choose $70 because it is weakly dominate. Conclusion: Both should choose $60. Sam's Costco $60 $70 $80 $60 400, ,0 800,0 $70 0, , ,0 $80 0,800 0, ,300 To define the normal form for the Modified Price Competition Game, at Sam s price $70 and Costco price $60, Sam s reduces price to $60 and splits the market demand of 80; hence, both make $(60-50)x40 = $400. And so on. Sam's Costco $60 $70 $80 $60 400, , ,400 $70 400, , ,500 $80 400, , ,300 The Price Competition Game modified by The Low Price Guarantee has a $70 as a weakly dominate strategy for each player. Conclusion: The Low Price Guarantee guarantees high prices and profits. 26

27 Answer to Question 6: To begin, fill out the normal form for each month for this game of simultaneous moves, with payoffs in thousands of dollars. For example, if Reynolds advertises and Philip does not, Reynolds pays $20,000, then takes $60,000 profit from Philip. Hence, Reynolds makes $40,000 and Philip looses $60,000. Reynolds (Payoffs are in thousands of dollars.) Philip Ad No Ad Ad -20,-20 40,-60 No Ad -60,40 0,0 On the one hand, what strategies (A One,B One ) should each player choose if they expect this game to last only one time period? In that one-shot game, each player should choose Advertise since it is the dominate strategy for each player. Each player thus earns -20. On the other hand, if the game continues indefinitely, then each player should consider the Grim Strategy. The Grim Strategy has two components. 1) The Cooperative action of No Advertise, which is mutuallybetter than the non-cooperative strategy of Advertise. 2) The Punishment action of Advertise, which gives the other player the worst payoff after that player chooses his best response to (makes the best of) his punishment. The Grim Strategy is thus, in each month, Cooperate and choose No Advertise, as long as the other player has Cooperated and chosen No Advertise in every previous month. But if the other player ever chooses to Not Cooperate and so to Advertise, then you punish by choosing Advertise in the next month and in every month thereafter --- forever. 27

28 Suppose Player B followed the Grim Strategy. Would Player A cooperate each period and choose No Advertise? On the one hand, if Player A cooperated each period and chose No Advertise, then the Grim Strategy says Player B will also cooperate each period and choose No Advertise, and so Player A earns 0 each period. On the other hand, if Player A cheated in any period, then consider the first period when he cheats. In that first period, the Grim Strategy says Player B will still cooperate and choose No Advertise. Player A s best response to cooperation is Advertise, which earns 40 in that period, rather than earning 0 if he had continued to cooperate. So the one period gain from cheating is 40. But starting in the next period and continuing forever, the Grim Strategy says Player B will punish by choosing Advertise. Player A s best response to Advertise is to Advertise, which earns -20 in each punishment period, rather than earning 0 if he had continued to cooperate. So the eventual loss from cheating is 20. Summing up, if Player B followed the Grim Strategy, then Player A would cooperate each period exactly if the one period gain of from cheating of 40 does not compensate for the eventual losses of 20 starting the next period. Use the formula that $1 starting next month and continuing for each subsequent period is worth $(1/r) today. Since the interest rate r = 20% = 0.20, the eventual losses of 20 is the same as loosing 20/0.20 = 100 today. Therefore, the one period gain of from cheating of 40 does not compensate for the losses of 100 (since 40 < 100), so Player A would cooperate and would choose No Advertise each period. 28

29 Answer to Question 7: Since the market is perfectly competitive, the sellers price is $1.50 per unit. Assuming there are no taxes or subsidies, consumption = 4, producer surplus = 0, consumer surplus = = $3.80, and external effects are - 3x0.25x4 = - $3.00, so total surplus is $0.80 Assuming the government imposes the optimal tax = marginal external effect = 3x0.25 per unit, the buyers price is = $2.25 per unit, so 3 units are consumed. Assuming the government imposes the optimal tax, consumption = 3, producer surplus = 0, consumer surplus = = $1.45 Since the tax revenue balances the external effect, the optimal tax increased total surplus from $0.80 to $

30 Answer to Question 8: First, complete the normal form below for the Work-Shirk Game. For example, if the employee chooses to work and the employer chooses to monitor, then the employee loses $130 of happiness from the effort of working but is paid $210, and the employer gains $500 from his employee but pays $50 for monitoring and pays $210 to his employee. Employee Monitor Trust Work 80,240 80,290 Shirk 0, ,-210 To predict actions or recommend actions, since the game has simultaneous moves, first look for dominate or dominated actions. There are none. Then look for a Nash equilibrium in pure strategies. There is none. If the Employee were known to Work, the Employer Trusts. But if the Employer were known to Trust, the Employee Shirks. But if the Employee were known to Shirk, the Employer Monitors. But if the Employer were known to Monitor, the Employee Works. So there is no Nash equilibrium in pure strategies. Since the game is repeated, actions need to become unpredictable because predictable actions can be exploited. The Nash equilibrium strategy for the Employee is the mixed strategy for which the Employer would not benefit if he could predict the Employee s mixed strategy. Suppose the Employer predicts p and (1-p) are the probabilities the Employee chooses Work or Shirk. The Employer expects 240p - 50(1-p) from playing Monitor, and 290p - 210(1-p) from Trust. The Employer does not benefit if those payoffs equal, 30 Employer

31 240p - 50(1-p) = 290p - 210(1-p), or p = p, or p = 160/210 = The Nash equilibrium strategy for the Employer is the mixed strategy for which the Employee would not benefit if he could predict the Employer s mixed strategy. Suppose the Employee predicts q and (1-q) are the probabilities the Employer chooses Monitor or Trust. The Employee expects 80q + 80(1-q) from playing Work, and 0q + 210(1-q) from Shirk. The Employee does not benefit if those payoffs equal, 80q + 80(1-q) = 0q + 210(1-q), or 80 = q, or q = 130/210 =

32 Answer to Question 9: Value/Cost Consider finding an appropriate integer number N so the Employer should accept a wage demand of $140K per year for workers that have completed at least N courses, and a wage demand of $70K per year to the other workers. There are two constraints on N, incentive compatibility and participation. Incentive compatibility constrains the number N of courses to be high enough so Type B workers do not bother to meet it, and low enough so Type A workers will meet it. Incentive compatibility for Type B requires $70,000 > $140,000 - $10,000 x N, or N > 7. The Worker is a Type A Type B to Employer $140K $70K of Self $60K $50K of Courses $2K $10K Incentive compatibility for Type A requires $140,000 - $2,000 x N > $70,000, or N < 35. Participation constrains the number N of courses so Type B and Type A workers both accept the job offers of $70,000 to Type B workers and $140,000 to Type A workers. Participation for Type B requires $70,000 > $50,000, which is true regardless of N. Participation for Type A requires $140,000 - $2,000 x N > $60,000, or N <

33 Putting it all together, the Employer should pick any number N between 7 and 35 and accept a wage demand of $140K per year for workers that have completed at least N courses, and accept a wage demand of $70K per year for the other workers. Comment: Those acceptances separate Type A from Type B workers, but it comes at the communication cost of $2,000 x N per year paid by the Type A workers. Even if the smallest number of courses were picked (N = 7), the cost of the information asymmetry is $2,000 x 7 = $14,000 per year. 33