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Advanced Industrial Organization: Problem Set 2

CRN 25965 - ECON 485 B Pascal Courty University of Victoria

There is no need to write long answers. I provide suggested length in wordcount to help you practice making clear and concise answers.

Exercise 1  Damaged-good strategy (25%, 40 words per answer on average)

A firm sells a product in a market where there are two types of consumers,high and low-valuation consumers. There are equally many of the two types of consumers, and the total number of consumers is normalized to 1. The producthas value 3 to the high-valuation consumers and value 1 to the low-valuationconsumers. All consumers have unit demand, i.e., they buy either one unit or

do not participate. The product is produced at constant marginal cost equal to0.

1. Find the profit maximizing price and calculate the firm’s profit.

2. The firm considers introducing a damaged version of the product. Thedamaged version is produced at constant marginal cost equal to 1/10. Itresults in a utility of 5/10 to the low-valuation consumers and of 6/10to the high valuation consumers. Find the optimal price of the normaland of the damaged version of the product. Should the firm introduce thedamaged version? What are the welfare consequences of the introductionof the damaged version?

Exercise 2  Bundling (25%, 30 words per answer on average)

Suppose that a monopolist produces two products, product 1 and product2. There is a mass 1 of consumers. A share  λ   of consumers are heterogeneousamong each other and are described by their type   θ. This type is distributeduniformly on the unit interval. The willingness-to-pay for product 1 is assumedto be  r1   =  θ   and  r2   = 1 − θ. A share (1 − λ)/2 of consumers has willingnessto pay   r1   = 2/3 and   r2   = 0. The remaining share (1 − λ)/2 of consumershas willingness to pay  r1  = 0 and   r2   = 2/3. Firms can sell products 1 and 2independently at prices  p1   and  p2, respectively. Alternatively, it may only sella bundle at price  p. This is a situation referred to as pure bundling. A third

possibility is that the firm sells the bundle and the independent products, asituation referred to as mixed bundling.

1. Suppose   λ   = 1. Determine whether independent selling, pure or mixedbundling are profit maximizing. Calculate associated prices and profits.

2. Suppose that λ > 0 and characterize the solution under independent sell-ing for all  λ > 0.

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3. Suppose that λ  = 4/5. Characterize the profit-maximizing solution under

independent selling, pure bundling, and mixed bundling. Show which of the selling strategies is profit-maximizing. Discuss your result.

4. Suppose that λ  = 2/3. Characterize the profit-maximizing solution underindependent selling, pure bundling, and mixed bundling. Show which of the selling strategies is profit-maximizing. Discuss your result.

Exercise 3   Research Article (50%, 40 words per answer on average)

Timothy Bresnahan and Peter Reiss. Entry and Competition in ConcentratedMarkets. Journal of Political Economy, 1991. You should read sections I andII and only what is necessary to understand Figures 3 and 4 in section III (you

can skip IIIC and IV).A local market is populated by   S   consumers. Each consumer has demandd( p) = 100 −  p   for a homogenous product (such as dental care, plumbing).Firms have to invest fixed cost  F   to enter the market and then pay  c(q ) =  q 2

to produce  q  units.

1. (a) Compute the inverse demand curve p(Q) in a local market. (b) Plot p(Q) for   S   = 1,   S  = 2 and   S   = 100. What happens to  p(Q) when thenumber of consumers in the market increases?

2. (a) What is the smallest population size  S  such that a monopolist earnsnon-negative profits? Denote that value   sM . (b) What is the smallestpopulation size such each member of a cartel formed of   n   firms earnsnon-negative profits?

3. Consider a large local market (S   large) with many firms who are pricetaker and earn zero profits. How many consumers does each firm serve?Denote that value  s∞.

4. (a) Show that sM  and s∞ are positive if and only if  F sn)? (b) Why should the ratiosn+1/sn converge to one as  n  increases?

6. How would you derive  sM ,  s2 and s∞ from Figure 3?

7. From looking at Figure 4, which markets would you think are the leastcompetitive? What could explain differences in plots across markets?

8. Would the approach presented in the paper work for other markets suchas retailing, food industry, restaurants?

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