18-Daytime2023ME.OA04.q

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MGRECON - Fall 2023 Online Assignment 4 due by Wed, 09/20, 11:59 pm

MGRECON - Fall 2023 ⋄ Online Assignment 4 1. Dupont invented and patented Kevlar, a superstrength synthetic fiber. It has a number of end use applications including tire belts, bullet-resistant vests, cables, aircraft components, and so on. Dupont charged different prices to different end users and contractually prohibited resale. There are no capacity constraints. Suppose that at the profit-maximizing prices, the elasticity of demand for Kevlar (Market 1) for end use in aircraft components is − 1 . 3 and for end use in tire belts (Market 2) is − 5. Marginal cost for Dupont is constant at 5 per unit output. What prices did Dupont charge for each end use? A. P 1 = $31 . 45 and P 2 = $9 . 1 B. P 1 = $13 . 7 and P 2 = $8 . 26 C. P 1 = $21 . 67 and P 2 = $6 . 25 D. none of the above page 2 of 11

MGRECON - Fall 2023 ⋄ Online Assignment 4 For questions 2 - 4 use the following information. You have been hired by the software company Bug-Free Solutions (BFS) to provide advice for their pricing. The company’s best selling application currently comes in 3 levels of quality: basic , medium and best . After much legwork, you have determined that BFS has three types of customers, whose willingness to pay for each quality increment is listed in the following table: MWTP Units 1 2 3 Group size Type 1 125 50 20 22 000 Type 2 100 30 5 54 000 Type 3 70 20 0 30 000 The last column indicates the number of buyers of each type. The first 3 columns indicate the willingness to pay for each quality increment . For example, each buyer of type 2 is willing to pay a total of $100+$30+$5 = $135 for the best quality version of the application. The buyers’ types are not observable; therefore all BFS can do is offer a menu of price-quality pairs and let each buyer select one that the buyer likes best. The cost of developing the application is sunk, thus you should aim to maximize BFS’s revenue. 2. What quality levels should BFS offer, and at what prices? A. basic at $70, medium at $100 and best at $120 B. medium at $130 and best at $150 C. best only, at $195 D. basic only, at $90 page 3 of 11

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MGRECON - Fall 2023 ⋄ Online Assignment 4 For questions 2 - 4 use the following information. You have been hired by the software company Bug-Free Solutions (BFS) to provide advice for their pricing. The company’s best selling application currently comes in 3 levels of quality: basic , medium and best . After much legwork, you have determined that BFS has three types of customers, whose willingness to pay for each quality increment is listed in the following table: MWTP Units 1 2 3 Group size Type 1 125 50 20 22 000 Type 2 100 30 5 54 000 Type 3 70 20 0 30 000 The last column indicates the number of buyers of each type. The first 3 columns indicate the willingness to pay for each quality increment . For example, each buyer of type 2 is willing to pay a total of $100+$30+$5 = $135 for the best quality version of the application. The buyers’ types are not observable; therefore all BFS can do is offer a menu of price-quality pairs and let each buyer select one that the buyer likes best. The cost of developing the application is sunk, thus you should aim to maximize BFS’s revenue. 3. Suppose that an advertising campaign would increase the number of type 3 customers (the group with the lowest WTP) to 50 000. The sizes of the other two groups remain unchanged. If the campaign takes place, what quality levels should BFS offer, and at what prices? A. basic at $70 and best at $150 B. basic at $70, medium at $130 , and best at $150 C. medium at $130 and best at $150 D. medium at $90 and best at $110 page 4 of 11

MGRECON - Fall 2023 ⋄ Online Assignment 4 For questions 2 - 4 use the following information. You have been hired by the software company Bug-Free Solutions (BFS) to provide advice for their pricing. The company’s best selling application currently comes in 3 levels of quality: basic , medium and best . After much legwork, you have determined that BFS has three types of customers, whose willingness to pay for each quality increment is listed in the following table: MWTP Units 1 2 3 Group size Type 1 125 50 20 22 000 Type 2 100 30 5 54 000 Type 3 70 20 0 30 000 The last column indicates the number of buyers of each type. The first 3 columns indicate the willingness to pay for each quality increment . For example, each buyer of type 2 is willing to pay a total of $100+$30+$5 = $135 for the best quality version of the application. The buyers’ types are not observable; therefore all BFS can do is offer a menu of price-quality pairs and let each buyer select one that the buyer likes best. The cost of developing the application is sunk, thus you should aim to maximize BFS’s revenue. 4. What is the maximum amount of money that BFS should be willing to pay for this campaign? A. 1 460 000 B. 1 000 000 C. 250 000 D. 0 because the campaign will not change the profit-maximizing menu page 5 of 11

MGRECON - Fall 2023 ⋄ Online Assignment 4 For questions 5 - 6 use the following information. CzechAir (CA) offers a daily round-trip flight from Lisbon to Prague. There are two types of travelers: 50 Business travelers (B types) and 50 Leisure travelers (L types). CA can offer two types of tickets: Economy class (E-class) and Premium class (P-class). CA has information about the willingness to pay of its customers, but cannot directly observe whether any customer is a B-type or an L-type. Assume that all costs are zero, and the plane used on this route has more than 100 seats. 5. On any weekday, there are 50 Business travelers (B types) and 50 Leisure travelers (L types), and their WTP is as in the following table: WTP group size B types 300 400 50 L types 120 150 50 E-class ticket P-class ticket To maximize its profit, CA should sell A. E-class tickets at $120 each, and P-class tickets at $150 each B. E-class tickets at $120 each, and P-class tickets at $220 each C. E-class tickets only at $120 D. P-class tickets only at $400 page 6 of 11

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MGRECON - Fall 2023 ⋄ Online Assignment 4 For questions 5 - 6 use the following information. CzechAir (CA) offers a daily round-trip flight from Lisbon to Prague. There are two types of travelers: 50 Business travelers (B types) and 50 Leisure travelers (L types). CA can offer two types of tickets: Economy class (E-class) and Premium class (P-class). CA has information about the willingness to pay of its customers, but cannot directly observe whether any customer is a B-type or an L-type. Assume that all costs are zero, and the plane used on this route has more than 100 seats. 6. On any weekend day, the numbers of Business travelers and Leisure travelers become 10 and 90 respec- tively. In this case, what are the prices for the E-class ticket ( P E ) and for the P-class ticket ( P P ) that maximize CA’s profit? A. E-class tickets at $300 each, and P-class tickets at $120 each B. P-class tickets only at $400 C. P-class tickets only at $150 D. E-class tickets at $120 each, and P-class tickets at $400 each page 7 of 11

MGRECON - Fall 2023 ⋄ Online Assignment 4 For questions 7 - 8 use the following information. “Piaccio” is an Italian company that rents mopeds in a large Spanish city. Demand consists of two types of customers: residents who rent mostly to move around town without getting stuck in traffic, and tourists who rent mainly for sightseeing. The following table shows the estimated marginal willingness to pay of each customer type for each hour of usage in a normal day. hours 1 2 3 4 5 6 Group size Tourists 30 25 20 15 7 3 300 Residents 25 12 5 0 0 0 1200 As the last column indicates, the numbers of daily customers are: 300 tourists and 1200 residents. Piaccio has more than 1500 mopeds available for rental (thus enough for the highest possible demand 300+1200). Assume that renting mopeds entails no costs. 7. What are the rental packages that Piaccio should offer in order to maximize its profit? A. 3 hours at 75; and 6 hours at 96 B. 3 hours at 42; and 6 hours at 67 C. 6 hours at 100 D. 3 hours at 42 page 8 of 11

MGRECON - Fall 2023 ⋄ Online Assignment 4 For questions 7 - 8 use the following information. “Piaccio” is an Italian company that rents mopeds in a large Spanish city. Demand consists of two types of customers: residents who rent mostly to move around town without getting stuck in traffic, and tourists who rent mainly for sightseeing. The following table shows the estimated marginal willingness to pay of each customer type for each hour of usage in a normal day. hours 1 2 3 4 5 6 Group size Tourists 30 25 20 15 7 3 300 Residents 25 12 5 0 0 0 1200 As the last column indicates, the numbers of daily customers are: 300 tourists and 1200 residents. Piaccio has more than 1500 mopeds available for rental (thus enough for the highest possible demand 300+1200). Assume that renting mopeds entails no costs. 8. In the month of August all residents move out of town, and thus only tourists will rent mopeds. In other words, the residents’ group size becomes 0. What are the rental packages that Piaccio should offer in this case in order to maximize its profit? A. 3 hours at 42; and 6 hours at 67 B. 6 hours at 100 C. 3 hours at 75; and 6 hours at 96 D. 3 hours at 42 page 9 of 11

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MGRECON - Fall 2023 ⋄ Online Assignment 4 For questions 9 - 10 use the following information. The company “Alternative Drugs” (AD) based in Northlandia sells the antidepressant Omega Fish Oil (OFO) both in its own country and abroad. The inverse demand in the domestic market is p 1 = 210 − q 1 , while the (inverse) demand in the foreign market is p 2 = 100 − 1 2 q 2 . AD can produce any number of antidepressant bottles at constant marginal cost $10. 9. The quantities that maximize AD’s profit are: A. q 1 = 70, q 2 = 30 B. q 1 = 50, q 2 = 50 C. q 1 = 60, q 2 = 80 D. q 1 = 100, q 2 = 90 page 10 of 11

MGRECON - Fall 2023 ⋄ Online Assignment 4 For questions 9 - 10 use the following information. The company “Alternative Drugs” (AD) based in Northlandia sells the antidepressant Omega Fish Oil (OFO) both in its own country and abroad. The inverse demand in the domestic market is p 1 = 210 − q 1 , while the (inverse) demand in the foreign market is p 2 = 100 − 1 2 q 2 . AD can produce any number of antidepressant bottles at constant marginal cost $10. 10. Suppose now that AD cannot produce more than 100 units of OFO. The quantities that maximize AD’s profit now are: A. q 1 = 70 , q 2 = 30 B. q 1 = 100 , q 2 = 0 C. q 1 = 50 , q 2 = 50 D. q 1 = 0 , q 2 = 100 page 11 of 11

18-Daytime2023ME.OA04.q

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