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I need help graphing part B). Reference for a SIMILAR question is shown below. 1. A software company sells two applications, noted A and B,
I need help graphing part B). Reference for a SIMILAR question is shown below.
1. A software company sells two applications, noted A and B, that are totally unrelated to one another. The marginal cost of production for each application is constant and is equal to 10. The company faces four categories of potential buyers, which are characterized by a pair of reservation prices as depicted in the following table; it is assumed that each category counts the same mass of consumers, which is set to 1. Application A Application B Category 1 100 30 Category 2 80 80 Category 3 60 60 Category 4 30 100 a. What price should the company set for each application if it decides to sell them separately? What profits will the company achieve in this case and, which categories of consumers will buy which application? Show all your computations b. Suppose now that the company pursues a mixed bundling strategy. Which price should it set for the bundle and for the separate applications? What profits will the company achieve in this case and, which categories of consumers will choose which option? Is mixed bundling more profitable than separate selling? Discuss. Show all your computations c. How would your answers to (1) and (2) change if the marginal cost of production increased from 10 to 407 Redo all the computations in part 'a' and 'b' above a. The two applications have similar demand schedules. It is easily found that for each application the profit-maximizing prices are PA = PB = 60; For application A: At p = 30, all categories would buy => 30*4 - (10*4) = 80 = profit At a p = 60, 3 categories would buy => 60*3 - (3*10) = 150 = profit At p = 80 only 2 categories would buy => 80*2 - (2*20) = 120 = profit At p = 100 only 1 category would buy => 1*100-1*10 = 90 = profit For application A, p = 60 is the profit maximizing price For application B: Go through similar steps to see that p = 60 is the profit maximizing price At these prices, category 1 buys application A, categories 2 and 3 buy both applications, and category 4 buys application B. Total profit n is computed as 3*(60-10) +3*(60-10) = 300. b. The reservation price for the bundle is simply the sum of the reservation prices for the two applications. Hence, the reservation price for the bundle is equal to 130 for category 1 and 4, 160 for categories 2 and 120 for category 3. All categories have a reservation price for each application that is above their marginal cost of production. App A App B Bundle Category 1 LOO 30 130 Category 2 80 80 160 Category 3 60 60 120 Category 4 30 100 130 For pure bundling, compute seller's profit Bundle price Profit 160 160 -20 = 140 (only category 2 buys) 130 3(130-20) = 330 (3 categories buy) 120 4(120 -20) - 400 (all categories buy)Total profit from pure bundling = 4012! = max profit [bundle price of 12m Mixed bundling: The sn'ategy for profit max using mixed bundling is as follows: Charge the higher of the reservation values of consmners with a large differential when setting the price of the individual options as price of App A = 100 and price oprp E'. = 10D and then for those consmners whose reservation values have a smaller differential {e.g. consmners 2 and 3] set the bundle price at the lower of the valuations to encourage both to buy the bundle 11$ a bundle price of 12!}. However, if it prices the bundle at 12fl the consmners in category 1 and 4 will not buy the items individually. At 12f] all 4 consumers will buy the bundle because consmner surplus from buying the bundle will be 1G (for category 1 and 4} greater titan consumer surplus = [I from buying the individual items at ill-f}. The firm will be unable to extract all consumer surplus on individual item from Category 1 and 4. Its max prot will be 44:13] 2b] = 4[I[I, same as pure bundling. Tn extract consumer surplus from Category 1 and 2 on individual items it could try to price then in a way that leaves less surplus than {113} what they would get on the bundle =2! pricing the individual items slightly below Elfl. Consider price of App A = EB and price of App B = BE! and price of the bundle = 12!} The max profit from this mixed bundling strategy will be (BE! ill} + [89: ill] + 21113] 2D} = 353 :1- 3m = profit from selling separately Mixed bundling does better than separate selling but not better than pure bundling for this software company 3. Under separate selling, the optimal prices are 11.1 = Fin = ; at these prices, category 1 buys application A, category 2 buys both applications, category 4 buys application E, and category 3 buys nothing. The corresponding profit is 1T3 = 2*[81] 411]] = Elf}. To see it repeat computations in part 'a' above now with a ME = 29. Show your work Consider now bundling. Willi a marginal cost of 41'}, it appears that categories 1 and 4 value one application below its cost. Redo all computations in [part 'b' above now with MC = Ell Hence, the company has no interest in selling the bundle to them and prefers to apply mixed bundling. As far as the bundle is concerned, the company must set pt, :- 13 to discourage categories 1 and 4 tn buy the bundle. At such prices, only category 2 is willing to buy the bundle; hence, the profit-maximizing bundle price is p, = lfl. The separate applications are then intended to categories 1, 3 and 4. It is easily found that the optimal prices are pr. = [In = ill-f}; at these prices, category 1 buys application A, category 4 buys application E, and category 3 buys nothing. Total profit is equal to no = 1 "' [16G - 30) + 2 "' {l 4E] = Efl :- 11;. Mixed bundling improves profit with respect to separate selling. Question 2 A software company sells two applications, noted A and B. that are totally unrelated to one another. The marginal cost of production for each application is constant and is equal to 4D. The company faces four categories of potential buyers, which are characterized by a pair of reservation prices as depicted in the following table; it is assumed that each category counts the same mass of consumers, which is set to l. Application A Application .3 Category ] Category 2' tCategory 3 Category .1 Let CB denote the cost of the bundle. CE = SD Let Ra and Rh denote reservation values for application A and B respectively and RB denote the reservation value for the bundle. Let CS denote consumer surplus and n denote the lm's prot. Show all computations a. What optimal price should the company set and what prots would it make it' it decides to offer {i} only individual items {no bundling) {ii} only the bundle {pure bundling} {iii} bundle and option to buy individual items {mixed bundling}. Be sure to show which categories of consumers will buy which application? {Hint for the seller to do better with mixed bundling than with pure bundling the bundle price will need to be different in the 2 cases) b. Graph the reservation values and prot-maximizing prices Pa and Pb. Show the mixed bundling prices and shade in the area that indicates reservation values of consumers who will purchase the bundle when the rm practices mixed bundling based with marginal cost of $$4Step by Step Solution
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