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NAME_______________________________________________________________ FE461 Practice Problem Third Problem Set Due March 6th 1. (50 points) Most wireless packages include cell phone minutes and text messages. Suppose AT&T wireless (the wireless provider previously known as Cingular, that was previously known as AT&T) has determined that six people purchase cell phone minutes and text messages (you can interpret them as six equally represented types). The following table represents the willingess to pay for cell phone minutes and the willingness to pay for text messages for the six different people (Bob, Bill, Tom, Sue, Julie, and Mary). The marginal cost to AT&T for cell phone minutes is 3; the marginal cost to AT&T for a text message is 2. Person Willingness to pay Willingness to Combined WTP for telephone pay for a text minutes message Bob 10 15 25 Bill 5 10 15 Tom 20 0 20 Sue 18 2 20 Julie 11 9 20 Mary 10 10 20 a) (10 points) What price will AT&T charge for cell phone minutes if it can only set a uniform price (and it does not bundle)? P = 20, Q = 1 and profits = 17 (P – MC)Q (20 – 3)1 P = 18, Q = 2 and profits = 30 P = 11, Q = 3 and profits = 24 P = 10, Q = 5 and profits = 35 Optimal price is P =10 b) (10 points) What price will AT&T charge for text messages if it can only set a uniform price (and it does not bundle)? P = 15, Q = 1 and profits = 13 (P – MC)Q (15 – 2)1 P = 10, Q = 3 and profits = 24 P = 9, Q = 4 and profits = 28 P = 2, Q = 5, and profits = 0 Optimal price is P = 9 Combined profits with uniform prices are 63 (35 + 28) (or if Pmin = 18 58 (30 + 28). c) (10 points) What price will AT&T charge for a pure bundle (cell phone minutes and text messaging)? Possible bundle prices are Pbundle = 25, Pbundle = 20, and Pbundle = 15 Pbundle = 25, Qbundle = 1, profits = 20 (P – MCtext – MCphone)Q Pbundle = 20, Qbundle = 5, profits = 75 Pbundle = 15, Qbundle = 6, profits = 60 Optimal Pbundle = 20, profits = 75 d) (10 points) What price will AT&T charge for a mixed bundle (cell phone alone, text messaging alone, and bundling cell phone minutes and text messaging)? Key idea is to get those with WTP < MC to not buy the buy. Also – want to find a way to get Bill to buy at least texting. One option: Ptelephone = 19.99, Tom only buys minutes. Q = 1, so profits(telephone) = (19.99 – 3)1 = 16.99 Ptext = 10 (Bill buys) Q = 1 so profits(text) = (10 – 2) = 8 Pbundle = 20, Q bundle = 4 profits(bundle) = 60 Combined profits are 84.99 (60 + 8 + 16.99) Another option: Ptelephone = 5, Tom and Bill only buy minutes. Q = 2, so profits(telephone) = (5 – 3)2 = 4 Ptext = 10 (Bill buys) Q = 1 so profits(text) = (10 – 2) = 8 Pbundle = 20, Q bundle = 4 profits(bundle) = 60 Combined profits are 72 (60 + 8 + 4) Go with option One NOTE: you have to make sure no one gets consumer surplus and switches to buying the product and not the bundle. If Ptelephone = 19.99 everyone else but Tom has WTP less than 19.99 so they would buy the bundle. If Ptext = 10, Bill will buy text and not be out of the market, Mary is indifferent (she has CS = 0 regardless of buying the bundle or not); likewise Bob is indifferent (he has CS = 5 regardless of buying the bundle or not) e) (10 points) Which is more efficient, no bundling (parts a and b), the pure bundle (part c), or the mixed bundle (part d)? Explain. Efficiency requires Q increases. With no bundling, Q = 5 for phone, Q = 4 for text. With pure bundling Q = 5 for both phone and text, so this increases efficiency. With mixed bundle, Q = 5 for both phone and text so improvement from pure bundling occurs with leaving out the person who values less than it costs to produce. Steerage 2. (15 points) The following game has two players, Steerage and Drydock. On a Tuesday night, King Hall is serving meatloaf. Most Mids don’t like meatloaf, so no one is planning to eat in King Hall. Steerage and Drydock realize the consequences of bad King Hall food, and each plan to start cooking food early in order to manage the huge, disgusted crowd. Assume Steerage and Drydock will each only prepare one menu item in advance, and will offer a special deal to get Mids to choose that item over the rest of the menu. They can choose one of the three most popular menu items: Pizza, Mike Schwobs, or Wraps. The payoffs are listed below. Identify all Nash pure strategy Equilbria. Drydock Pizza Mike Schwobs Wraps Pizza 7500, 7500 11000, 10000 10000, 7000 Mike Schwobs 13000, 9500 10500, 6500 14000, 5500 Wraps 2500, 9250 6250, 9000 6500, 6500 Nash equilibria: (Mike Schwobs, Pizza) and (Pizza, Mike Schwobs) 3. (10 points) In your own words, what makes a static game a “prisoner dilemma” game? Dominant strategy leads to pareto inferior outcome. 4. (25 points) Two firms face a market demand of P = 300 – 10Q. Firms face identical marginal costs equal to 60. a) (5 points) Find each firm’s best response function – be sure to solve for these through profit maximization. MC = 60 TR1 = (300 – 10(q1 + q2))q1 MR1 = dTR1/dq1 = 300 –20q1 –10q2 Profit max MC = MR 60 = 300 –20q1 –10q2 Finding firm 1’s best response function (solving for q1): q1 = 240 – 10q2 20 Since this is symmetric: we can easily find firm 2’s best response function q2 = 240 – 10q1 20 b) (10 points) Graph the best response functions – indicating the axis (so you need qmonopoly and qperfect competition) q2 240/10 =24 q1 = R1(q2) =240 – 10q2 20 240/(2*10)=12=q2m 240/(3*10)=8=q2c q2 = R2(q1)= 240 – 10q1 20 8=q1c q1m=12 24 q1 c) (10 points) Find the profit maximizing (Cournot-Nash equilibrium) quantities for each firm. To find the Cournot-Nash equilibrium – we simultaneously solve the two equations q2 = 12 1 q1 2 (plugging in q1 = 12 q2 = 12 1 q2 2 1 1 1 * (12 q 2 ) = 6 q 2 q2 = 8 2 2 4