ECN121A (INDUSTRIAL ORGANIZATION) PROBLEM SET 3 – Consider the market for music distributed via FM radio.

PROBLEM SET 3DUE BEGINNING OF CLASS: NOVEMBER 20, 2015Question 1: [40 points] Consider the market for music distributed via FM radio. Think of the FMradio spectrum as a Hotelling line of length 1, with only two radio stations currently operating:Classical music located at position 0 and Heavy Metal music located at position 1. Listeners areassumed to have listening preferences that are uniformly distributed across the Hotelling line.Since radio stations do not have the ability to charge for their content, they compete for listenersby positioning themselves as pro?tably as possible on the Hotelling line.(a) [10 points] What is the “location” of the consumer exactly indifferent between listening toClassical or Heavy Metal?(b) [10 points] A ?rm is considering entering the radio business and has hired you to ?gureout what sort of music it should play. Where do you suggest the ?rm locates? Does itmatter?(c) [10 points] Unfortunately another ?rm beats you into the market, choosing a location of0.4 corresponding to Top 40 music. What fraction of listeners will choose this new station?(d) [10 points] Despite a third station now in the market, the ?rm you are advising is stilladamant about entering and becoming the fourth. What is/are the location(s) that willgive this ?rm the maximum about of listeners?Question 2: [30 points] Consider the following model of entry deterrence by strategic investmentin capacity. Inverse demand for a homogeneous product is P( Q) = 180 ? Q and ?rms have amarginal cost of 30. Of this cost, 20 is the cost of building capacity and 10 is the cost of production.Firm 1 is the incumbent and can choose to build capacity in the ?rst stage. Both ?rms compete inCournot competition in stage 2. Both ?rms have a ?xed cost of production F.(a) [10 points] What is the equilibrium strategy of Firm 1 when F = 0?(b) [10 points] What is the equilibrium strategy of Firm 1 when F = 2500?(c) [10 points] What is the equilibrium strategy of Firm 1 when F = 961?Question 3: [30 points] Consider a monopolist manufacturer that produces a product at a marginal cost of 20 but must sell to customers through a retailer which it does not own. Inverse retaildemand for the product is P = 80 ? Q. The retailer has no marginal costs aside from the wholesaleprice, w, it must pay the manufacturer for each unit of the product. The retailer has a ?xed cost of50 which you can think of as the cost of leasing retail space from a strip mall.1(a) [10 points] Assume the manufacturer does not own the retailer. What wholesale price wwill it charge? What will the retail price for the good be?(b) [10 points] Suppose the retailer buys the manufacturer so that the retailer can now producethe product at a marginal cost of 20 instead of paying some higher wholesale price forthe good. Will the retailer change its retail price? Who bene?ts and who loses from thisexample of vertical integration?(c) [10 points] Suppose the retailer buys the strip mall so that it no longer has to pay the ?xedcost of 50. Will the retailer change its retail price? Who bene?ts and who loses from thisexample of vertical integration?Question 4: [40 points] Consider a second price auction with 3 bidders, 1,2, and 3 who value somegood at 50, 40, and 30, respectively. Each bidder knows what the other bidders’ valuations for thegoods are so there is no uncertainty.(a) [10 points] Is it a weakly dominant strategy for bidder 1 to bid his true valuation for thegood? Why/why not?(b) [10 points] Is it a Nash equilibrium for each bidder to bid his true valuation for the good?(c) [20 points] Suppose this is an auction for a highway renovation project and the biddersare construction ?rms. Suppose further that bidder 1 has the highest valuation to win theproject because the work site is near bidder 1’s head of?ce. How much would bidder 1 bewilling to pay bidder 2 not to participate in the auction?

 

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