Differentiated Product Oligopoly

1. Differentiated Product Oligopoly

2. Product Characteristics • Goods characterization revisited: • Goods are never perfect substitutes • Distinguishing features = Product Characteristics • Chamberlin/Lancaster approach: Model a good as a bundle of characteristics: • Models: • Vertical differentiation -- quality choice • Issues of adverse selection and moral hazard • Horizontal differentiation -- location models • Issues of search and information aggregation • Multi-characteristic models

3. Quality and Information • Search goods versus experience goods • Warranty goods are pure search goods • Incomplete or absent warranty systems together with durability of the good experience good • Moral Hazard • Adverse Selection • We examine some simple models of these two phenomena (known collectively as asymmetric information).

4. Asymmetric Information • Monopoly firm with quality dimension choice. • Quality choice s=0,1. Quality s=0 is low quality, while s=1 is high quality. Quality is costly: cost of low quality c0=0, while high quality cost c1>0. • Buyers value goods of different quality differently. Specifically, we assume U=s-p, where s is the quality level and p is the price paid. Obviously, if s=0, then the buyer is not willing to pay anything for the good. We also assume that >c1 so that the provision of quality is socially useful. • Buyers are not informed beforehand of quality. • Equilibrium • Firm won’t produce high quality, since it achieves a profit differential of c1 by producing only low quality, without changing demand • Equilibrium involves p=c0=0

5. Asymmetric Information • Modify model to permit signaling. • Some fraction  of buyers do research and become informed about the quality of the good on the market. These buyers will pay  if quality is high and 0 if it is low. The remaining fraction (1- ) of buyers are uninformed as before. • Monopolist offers a price p in [0, ]. Informed buyers purchase the good only if it is high quality, yielding a profit of (p-c1).

6. Asymmetric Information • Consider uninformed buyers: • If they don’t buy, demand only from informed, monopolist produces high quality and sells at p. In this case, uninformed should buy. • If uninformed buy, then monopolists profit will be p-c1 if he produces high quality, and (1-)p if he produces low quality. Hence, he will produce high quality if p-c1(1-)p or  p  c1

7. Asymmetric Information • Interpretation • Notice that when only part of the market is informed, the monopolist will produce high quality only if the price is sufficiently high. This is because when the price is high, switching to low quality will cause the monopolist to lose the high profit margin he makes on informed buyers. • Given this, uninformed agents can infer from the high price that they are in fact getting the high quality good. In fact, if   c1 then the monopolist will charge p= and produce only high quality.

8. Asymmetric Information • This is an example of prices signaling quality. • Role for buyers’ guides (or online search) in ensuring that at least some fraction of the market is informed. • Note role of information externality here: even a relatively small number of informed buyers can induce the firm to produce high quality, thus providing a free benefit to agents who are not informed. • Potential paradox: Endogenous decision to become informed If buyers must choose to become informed and becoming informed is costly, there may be incentives to “free ride” on the information externality embodied in the price signal. But if everyone chooses not to be come informed, the externality disappears.

9. Asymmetric Information • Example: Trial Versions • Buyers are allowed to download a more or less functional version of a particular software application for free, sometimes limited to a trial period (sometimes enforced or sometimes not) accompanied by so-called “nag screens” which degrade loading times. • The free download and evaluation provides the information the buyer needs to ensure quality. At the end of the trial period, the buyer can purchase the fully functional version by paying the full purchase price. • Versioning is also used to segment a market (selling different quality levels at different prices). We will discuss this when we examine price discrimination.

10. Asymmetric Information • Market for Lemons • When quality is not an inherent choice, but rather a feature of the good, we characterize the information problem as one of adverse selection, since buyers on the market must try to distinguish between which goods are low quality and which are high quality. (Obviously, if differences are directly observable, no information asymmetry exists.) • A simple model • Robinson Crusoe is selling a goat on Ebay. The goat will produce milk given by a parameter s. If Robinson does not sell the goat, his utility is 1s; otherwise, if he sells the goat for price p 1s, this is his utility

11. Asymmetric Information • Friday is bidding for goats on Ebay. If he buys a goat with milk parameter s for a price p, his utility payoff will be 2s-p. We assume that 2> 1, so that it is optimal for Robinson and Friday to trade, no matter what the milk parameter turns out to be. • Friday’s problem, then is what to offer to pay for the goat. Robinson has experience with the goat and hence knows s. Friday knows only that s is randomly distributed (with uniform distribution) with s[0,smax]. • Note that if Robinson is willing to sell the goat at price p, the quality s must be such that p 1s

12. Asymmetric Information • We assume next that Friday is risk-neutral, and hence evaluates the utility of obtaining the goat as 2sa-p Here, sa is the value of s that Friday anticipates getting. • What milk value should Friday anticipate? Conditional on Robinson being willing to sell, Friday can anticipate that s will be uniformly distributed in the interval [0,p/1]. • Under the risk-neutrality assumption, then we have

13. Asymmetric Information • Note how the average quality of goats on the market is biased downward by the decision to put the goat on the market. This is the so-called adverse selection problem. • Friday will buy the goat if and only if 2sa p • From the definition of sa, this tells us that Friday will make a purchase only if 2  21. Clearly, if preferences are similar in the sense that 2 is close to 1 (though larger), then there cannot exist any price at which trade will occur.

14. Asymmetric Information • Implications • Information makes markets. • In the moral hazard example, more informed buyers lead to lower prices and larger markets, even in the case of a monopoly. • In the adverse selection example, more information about product quality allows emergence of separate markets for different qualities of good. • Positive role of the internet in making better search possible. • Potential negative role in making it easier to market faulty products.

15. Price Competition • Price Wars • The Bertrand model of price competition • 2 firms, homogeneous product, common marginal cost of production. • Because each firm’s product is a perfect substitute for the other’s, consumers always buy from the firm charging the lowest price. Hence

16. Price Competition • Equilibrium in a one-shot, non-cooperative pricing game will have both firms charging marginal cost and making zero economic profits. • We can show this result formally by showing that if firms charge different prices, the one charging the higher price has an incentive to at least match that of its rival. If both charge the same price but this price is in excess of marginal cost, then by undercutting its rival slightly, either firm can steal the other’s market share and increase profit. The only price at which this incentive is no longer active is when p=c. • Note that in the absence of mechanisms to prevent undercutting, the Bertrand mechanism leads to price instability and the phenomenon of price wars.

17. Non-Price Competition • Avoiding the Bertrand paradox • With capacity constraints • Cartel formation (Explicit collusive monopolization) • Illegal under most domestic antitrust laws • Can be difficult to enforce if cheating is hard to detect • Dynamic price competition (Implicit collusion) • Repeated game structure using mutual punishment strategies to enforce cooperation • Can also be difficult to enforce if cheating is hard to detect • Without capacity constraints • Commodity product  competitive outcome • Product differentiation • Monopolistic competition

18. Product Differentiation • Modeling product differentiation • Modeling product characteristics • Characteristics space • Spatial location models of competition • Spatial competition • The circular model • Two dimensional characteristic space, with products located around a circle. • Example: Image processing software. One dimension of the characteristics space specifies the number of photo versus video formats the product can process. The second dimension specifies the complexity and sophistication of functionality, ranging from complex but sophisticated to easy to use but not very powerful.

19. Spatial Model

20. Spatial Model • Consumers in the model wish to purchase one unit of product, and are uniformly distributed around the circle (whose circumference is normalized to 1). A consumer’s location on the circle represents her most preferred combination of product characteristics. • Consumer’s incur transportation costs in the amount t if they purchase a good which is t units from their most preferred location. The consumer’s surplus if she gets her most preferred product is s. • There are n products located (exogenously) uniformly around the circle. We can interpret the products as arising from the entry of new firms (or of new brands put forward by existing firms) drawn from a large pool of potential entrants to the market.

21. Spatial Model • Each product has price pi for i=1,…,n. We illustrate this in the diagram below.

22. Spatial Model • With firms and consumers located symmetrically around the circle, it makes sense to look for an equilibrium where every product sells for the same price: pi=p. Since there are no barriers to entry in the model (other than low fixed costs) we will have an equilibrium when the number of firms is such than no firm earns a positive profit. • Firm’s pay a fixed cost to enter in the amount f, and a marginal cost c for each unit sold. Thus, firm i’s profit is given by i=(pi-c)Di-f where Di is the demand firm i is facing. • To determine the demand firm i faces, we note that firm i will attract customers only from the segment of the circle on either side of its own location.

23. Spatial Model • To determine demand explicitly, consider a buyer located at x(0,1/n) (i.e. at a distance no more than 1/n from i’s location). This buyer will be indifferent between buying from i or from i’s nearest neighbor if pi+tx=p+t(1/n-x) • Firm i’s demand is given from the equation above by solving for 2x (since i attracts buyers from either side symmetrically). Note that p is the price charged by either neighboring firm. Solving for demand yields

24. Spatial Model • Firm i’s profit maximization problem is then one of choosing a price to maximize • The taking first-order conditions with respect to the price, and then setting pi=p (the symmetry assumption on prices), we find

25. Spatial Model • Interpretation: • Mark-up over marginal cost is >0 firms have some monopoly power in the market. • Mark-up is decreasing in n; as more firms put similar products on the market (filling in the circle), price approaches marginal cost. • Equilibrium number of firms: With no barriers to entry, firms will enter until profit is zero:

26. Spatial Model • What is the optimal number of firms? • Don’t need to worry about consumer surplus, since each consumer ends up purchasing one unit of her most preferred good, and her utility is just the surplus s minus the price, plus the transportation cost. • The problem of computing the socially optimal number of firms, then, reduces to simply choosing n to minimize the sum of the aggregate fixed costs plus aggregate transportation costs:

27. Spatial Model • Taking first-order conditions and solving for n, we find • From the perspective of an omniscient social planner, then, the equilibrium in the location model has too many firms! • Potential role for copyrights and trademarks as welfare enhancing by limiting entry. • Issues with the model: • Location choice • Sequential entry • Brand proliferation

28. Advertising • Role of advertising in non-price competition: two polar views • Advertising fosters product differentiation directly by persuading consumers of differences in product which don’t actually exist • Creates barriers to entry • Enhances market power • Advertising can communicate information to consumers about product characteristics and quality. • Facilitates matching of consumers with products • Efficient use of information resources

29. Efficient Advertising • A model of informative advertising • Monopolistic competition: many firms, all producing a homogeneous product using constant returns technology, with unit cost $c. • Each consumer in the market has unit demand for the product and receives utility U=S-p if she buys a unit of the good at price p. • Consumers are uninformed about the existence of the good or the price charged by a firm. The firm can inform consumers using advertising. For simplicity, we assume that ads are sent to consumers at random. Each ad provides a characterization of the good and a price quote.

30. Efficient Advertising • With N consumers, each consumer receives an ad with probability 1/N. Consumers can thus receive no ads, one ad, or more than one ad. If a consumer receives no ads, she makes no purchases. If she receives one ad, she buys from the firm sending the ad as long as the price p is less than S. If she receives several ads, she buys from the firm advertising the lowest price, as long as this price is less than S. (If more than one firms offers the same price, consumers select a firm at random.) • Let A denote the total number of ads sent by all firms in the market. Let  be the probability that an individual consumer receives at least one ad. Then the probability that she receives no ads is (for large N)

31. Efficient Advertising • If the marginal cost of sending out an ad is c’, then (assuming constant marginal ad costs), the total cost of advertising is • The advertising cost per consumer is then • We assume that S>c+c’ (so trade will take place).

32. Efficient Advertising • Free-entry equilibrium: firms pay no cost to enter (no fixed costs of production). • Let x(p) be the probability that a consumer makes a purchase at price p (i.e. she receives no additional ads for a price lower than p). • Note trade-off between higher price (which increases firm profit) and lower probability of acceptance • Zero profit condition for equilibrium: for any price, the expected profit must be zero or new firms will enter the industry and send ads at that price until the probability of acceptance drops sufficiently to restore equilibrium (p-c)x(p)-c’=0 • Note that when p=c+c’, we have x(c+c’)=1. When p=S, we have

33. Efficient Advertising • x(S) must be equal to 1-, since the only time a consumer will buy at price S is if she receives no other ads except the one at price S. But this occurs with probability 1-. Hence, in equilibrium, we have • Now, consider the social welfare problem. Since all possible prices such that c+c’  p  S are possible in equilibrium, the only thing that matters from a social welfare perspective is the cost of providing advertising relative to its effectiveness in promoting trade. • Positive effect in generating trade • Negative effect if some consumer’s don’t receive information.

34. Efficient Advertising • The central planner’s problem, then, is to choose  to maximize • The first-order condition for this problem is • Hence, the competitive outcome is socially optimal.

35. Efficient Advertising • Issues • Failure of prices to converge in the competitive setting • Result of the one-shot game assumption in the model • Need to examine richer models in which prices, industry structure, and advertising a determined simultaneously • Special nature of assumptions on the ad probabilities • Memory-less distribution function • No targeting of ads at particularly consumers or consumer types • Importance of targeting and ability to set differential prices in ecommerce