Score out of 100 NAME Midterm 2 November 17, 2004 Prof. Mark Long All answers require explanation and credit will be based on these explanations. Partial credit is available feel free to use graphs if they help with your explanation fully label all graphs used. You have been hired as a consultant to a small business, Exacta. Exacta produces financial reports (Q). Many other firms produce very similar financial reports and the market price is $5. Exacta has already purc hased ten computers (K=10), and they are determined to use these computers next week to produce financial reports. Computers rent for $20 per week. Exacta s worker s earn $200 per week. Exacta has done a study and found the following relationship between number of workers and number of financial reports: K L Q 10 0 0 10 3 60 10 8 260 10 10 420 10 16 660 10 20 740 a) Exacta wants to know how many workers they should hire for the upcoming week, how many financial reports they should produce, and the price they should charge. Fill-in the following tables, and use this information to answer Exacta s questions. Show all formulas used and explain your conclusions. (30 Points) K L Q APL MPL FC VC TC 10 0 0 10 3 60 10 8 260 10 10 420 10 16 660 10 20 740 L=Number of Workers for One Week, APL=Average Product of Labor, MPL=Marginal Product of Labor, VC=Variable Cost, TC=Total Cost, MC=Marginal Cost, AFC=Average Fixed Cost, AVC=Average Variable Cost, ATC=Average Total Cost. 1
K L Q MC AFC AVC ATC Profit 10 0 0 10 3 60 10 8 260 10 10 420 10 16 660 10 20 740 2
b) If Exacta follows your advice in part a, will they be earning a profit? (2 Points) c) With only the information in the tables above, what is your long-run (i.e. for the week after next) advice? (4 Points) d) If Exacta asked for your advice on the optimal number of computers to use, explain in detail how you would make that decision. What additional information would you need? (10 Points) 3
e) Suppose Exacta had only one competitor. If both Exacta and their rival determine their own quantity, and let the market determine the equilibrium price, how should Exacta determine its quantity? (7 Points) THIS IS NOT MATERIAL WE HAVE COVERED YET I.E., NOT RELEVANT FOR THIS TEST f) Suppose Exacta had only one competitor. If both Exacta and their rival determine their own prices, and let the market determine the equilibrium demand for their product, how should Exacta determine its price? (7 Points) THIS IS NOT MATERIAL WE HAVE COVERED YET I.E., NOT RELEVANT FOR THIS TEST 4
2) The city council of Smallburg is considering auctioning the rights for a cable company to provide cable TV service to the all of the residents of Smallburg. All cable companies have the same costs of production: To install the cable lines throughout Smallburg will cost $100,000. In addition, each household will cost $10 to run a line to their house. Demand for cable is given by the following demand curve: 1 P = 110 - Q 200 The winning cable company will be required to charge one price to all of its customers (i.e., price discrimination will be banned). a) If you ran a cable company that won the right to be the monopolist cable company in Smallburg, what price would you charge? How many households would get cable services? What would your profit be? (10 Points) 5
b) What is the most that any cable company would be willing to bid to win this auction? (3 Points) c) What is the socially efficient price and quantity? Explain. (7 Points) d) If Smallburg required cable companies to charge the socially efficient price, explain why no cable company would bid on this right to be the monopolist (at least, they wouldn t bid an amount > $0). (5 Points) 6
3) You run a monopoly called Perpetua. A rival firm is considering entering your market. The following table shows your profit and your rival s profit given your potential strategies: Perpetua's Strategies High Price Low Price Rival's Strategies Enter Stay out Perpetua's Profit = 55 Perpetua's Profit = 95 Rival's Profit = 45 Rival's Profit = 0 Perpetua's Profit = 20 Perpetua's Profit = 70 Rival's Profit = -15 Rival's Profit = 0 a) Does your rival have a dominant strategy? (5 Points) THIS IS NOT MATERIAL WE HAVE COVERED YET I.E., NOT RELEVANT FOR THIS TEST b) Does this game have a Nash Equilibrium? (5 Points) THIS IS NOT MATERIAL WE HAVE COVERED YET I.E., NOT RELEVANT FOR THIS TEST c) How could eliminating one of your strategies actually raise your profits? (5 Points) THIS IS NOT MATERIAL WE HAVE COVERED YET I.E., NOT RELEVANT FOR THIS TEST 7
Midterm 2 Answers November 17, 2004 Prof. Mark Long All answers require explanation and credit will be based on these explanations. Partial credit is available feel free to use graphs if they help with your explanation fully label all graphs used. You have been hired as a consultant to a small business, Exacta. Exacta produces financial reports (Q). Many other firms produce very similar financial reports and the market price is $5. Exacta has already purc hased ten computers (K=10), and they are determined to use these computers next week to produce financial reports. Computers rent for $20 per week. Exacta s worker s earn $200 per week. Exacta has done a study and found the following relationship between number of workers and number of financial reports: K L Q 10 0 0 10 3 60 10 8 260 10 10 420 10 16 660 10 20 740 a) Exacta wants to know how many workers they should hire for the upcoming week, how many financial reports they should produce, and the price they should charge. Fill-in the following tables, and use this information to answer Exacta s questions. Show all formulas used and explain your conclusions. (30 Points) L=Number of Workers for One Week, APL=Average Product of Labor, MPL=Marginal Product of Labor, VC=Variable Cost, TC=Total Cost, MC=Marginal Cost, AFC=Average Fixed Cost, AVC=Average Variable Cost, ATC=Average Total Cost. K L Q APL MPL FC VC TC MC AFC AVC ATC Profit 10 0 0 200 0 200-200 10 3 60 20.0 20 200 600 800 10.00 3.3 10.00 13.3-500 10 8 260 32.5 40 200 1,600 1,800 5.00 0.8 6.15 6.9-500 10 10 420 42.0 80 200 2,000 2,200 2.50 0.5 4.76 5.2-100 10 16 660 41.3 40 200 3,200 3,400 5.00 0.3 4.85 5.2-100 10 20 740 37.0 20 200 4,000 4,200 10.00 0.3 5.41 5.7-500 Since they are a competitive firm, they should charge $5 per report. They should produce where P = MC (and MC is increasing) i.e., they should produce 660 units. To produce 660 units, they should hire 16 workers. Note that P>AVC, so they should operate in the short-run. 8
b) If Exacta follows your advice in part a, will they be earning a profit? (2 Points) No, their profit will equal -$100. c) With only the information in the tables above, what is your long-run (i.e. for the week after next) advice? (4 Points) Assuming they could not change their capital stock, they should shut-down in the longrun. d) If Exacta asked for your advice on the optimal number of computers to use, explain in detail how you would make that decision. What additional information would you need? (10 Points) They would choose capital and labor such that: MPL/MPK = w/r. (This answer needs a full explanation of why). e) Suppose Exacta had only one competitor. If both Exacta and their rival determine their own quantity, and let the market determine the equilibrium price, how should Exacta determine its quantity? (7 Points) Cournot Model discussed on page 373. f) Suppose Exacta had only one competitor. If both Exacta and their rival determine their own prices, and let the market determine the equilibrium demand for their product, how should Exacta determine its price? (7 Points) Bertrand Model not discussed in Browning and Zupan 9
2) The city council of Smallburg is considering auctioning the rights for a cable company to provide cable TV service to the all of the residents of Smallburg. All cable companies have the same costs of production: To install the cable lines throughout Smallburg will cost $100,000. In addition, each household will cost $10 to run a line to their house. Demand for cable is given by the following demand curve: 1 P = 110 - Q 200 The winning cable company will be required to charge one price to all of its customers (i.e., price discrimination will be banned). a) If you ran a cable company that won the right to be the monopolist cable company in Smallburg, what price would you charge? How many households would get cable services? What would your profit be? (10 Points) MR = 110 (1/100)*Q MC = 10 Maximize profit where MR = MC 110 (1/100)*Q = 10 100 = (1/100)*Q Q = 10,000 P = 110 (1/200)*10,000 = 60 Profit = Revenue Cost = P*Q (100,000 + 10*Q) = 60*10,000 (100,000 + 10*10,000) = 600,000 (100,000 + 100,000) = 400,000 b) What is the most that any cable company would be willing to bid to win this auction? (3 Points) They would be willing up to, but not greater than, $400,000. c) What is the socially efficient price and quantity? Explain. (7 Points) Socially efficient quantity is where MB = MC. MB = 110 (1/200)*Q MC = 10 110 (1/200)*Q = 10 10
100 = (1/200)*Q Q * = 20,000 The socially efficient price is $10. d) If Smallburg required cable companies to charge the socially efficient price, explain why no cable company would bid on this right to be the monopolist (at least, they wouldn t bid an amount > $0). (5 Points) At this price, demand would equal 20,000. Profit = Revenue Cost = P*Q (100,000 + 10*Q) = 10*20,000 (100,000 + 10*20,000) = 200,000 (100,000 + 200,000) = -100,000 3) You run a monopoly called Perpetua. A rival firm is considering entering your market. The following table shows your profit and your rival s profit given your potential strategies: Perpetua's Strategies High Price Low Price Rival's Strategies Enter Stay out Perpetua's Profit = 55 Perpetua's Profit = 95 Rival's Profit = 45 Rival's Profit = 0 Perpetua's Profit = 20 Perpetua's Profit = 70 Rival's Profit = -15 Rival's Profit = 0 a) Does your rival have a dominant strategy? (5 Points) No they should enter if you charge a high price, but stay out if you charge a low price. b) Does this game have a Nash Equilibrium? (5 Points) (High Price, Enter) is a Nash Equilibrium, as neither firm can do better by unilaterally deviatiating. c) How could eliminating one of your strategies actually raise your profits? (5 Points) If you could eliminate your high price strategy and commit to setting a low price, your rival will not enter. In this case, your profit is 70 which is higher than the Nash Equilibrium profit of 55. 11