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

Question 1: [40 points] Consider the market for music distributed via FM radio. Think of the FM
radio 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 are
assumed 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 listeners
by 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 to
Classical or Heavy Metal?
(b) [10 points] A ?rm is considering entering the radio business and has hired you to ?gure
out what sort of music it should play. Where do you suggest the ?rm locates? Does it
matter?
(c) [10 points] Unfortunately another ?rm beats you into the market, choosing a location of
0.4 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 still
adamant about entering and becoming the fourth. What is/are the location(s) that will
give this ?rm the maximum about of listeners?

Question 2: [30 points] Consider the following model of entry deterrence by strategic investment
in capacity. Inverse demand for a homogeneous product is P( Q) = 180 ? Q and ?rms have a
marginal 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 in
Cournot 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 retail
demand for the product is P = 80 ? Q. The retailer has no marginal costs aside from the wholesale
price, w, it must pay the manufacturer for each unit of the product. The retailer has a ?xed cost of
50 which you can think of as the cost of leasing retail space from a strip mall.
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(a) [10 points] Assume the manufacturer does not own the retailer. What wholesale price w
will 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 produce
the product at a marginal cost of 20 instead of paying some higher wholesale price for
the good. Will the retailer change its retail price? Who bene?ts and who loses from this
example of vertical integration?
(c) [10 points] Suppose the retailer buys the strip mall so that it no longer has to pay the ?xed
cost of 50. Will the retailer change its retail price? Who bene?ts and who loses from this
example of vertical integration?
Question 4: [40 points] Consider a second price auction with 3 bidders, 1,2, and 3 who value some
good at 50, 40, and 30, respectively. Each bidder knows what the other bidders’ valuations for the
goods are so there is no uncertainty.
(a) [10 points] Is it a weakly dominant strategy for bidder 1 to bid his true valuation for the
good? 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 bidders
are construction ?rms. Suppose further that bidder 1 has the highest valuation to win the
project because the work site is near bidder 1’s head of?ce. How much would bidder 1 be
willing to pay bidder 2 not to participate in the auction?