Notes from Tirole, ch. 2 Product Selection, Quality, and Advertising

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1 MEMO To: From: File FM Date: October 218 Subject: Notes from Tirole, ch. 2 Product Selection, Quality, and Advertising Defining a market is not easy. Think of examples from Merger Enforcement Guidelines. Difficult when products are differentiated. 1 Product Space 1.1 Vertical Differentiation Consumers agree over the most preferred mix of characteristics and over the preference ordering. They may have different taste in the sense of weighting quality differently. Do example of quasi-linear utility characterization of vertical differentiation. Define a quality index where stands for services. Consider a single quality/good monopolist and a consumer who purchases at most one unit with the following preferences if consumer buys = otherwise where is price, and is a taste parameter distributed with a pdf of ( ) and a support of [ + ). Derive the demand function for this type of utility. Let be the total number of customers (could work with a unit mass of customers in which case =1). This is defined by ( ) = [1 ( )] If there are several qualities in the market, consumers choose among the qualities and whether to buy at all. For example, suppose that there are two qualities such that 1 2

2 and to make the problem interesting 1 2. Suppose that no one commodity dominates in the sense of higher quality per dollar of expenditure so that we can define an interior equilibrium or define a 1 such that 2 2 = 1 1 so that ( 2 1 ) ( 2 1 ) Then the respective demands for the two goods are defined by 2 ( 1 2 )= [1 (( 2 1 ) ( 2 1 ))] and 1 ( 1 2 )= [ (( 2 1 ) ( 2 1 )) ( 1 1 )] 1.2 Horizontal Differentiation Here we represent goods in a spatial model. The example is a linear city where the length of themarketis1. There are two shops located at the ends of the unit market at =(firm 1, say) and =1(firm 2). Consumers have transportation costs of per unit distance and these consumers have unit demands. We denote the fob prices of the two stores by 1 and 2. The delivered price of the good for a consumer at location purchasing from firm 1 is given by 1 + and the corresponding utility is given by = ( 1 + ) where is the consumer s reservation value of the product. If the market is fully covered we may identify an interior consumer who is the object of competition between the two firms who is just indifferent between the two firms. This consumer is given by 1 + = 2 + (1 ) or = ( ) 2 and the total demands are 1 ( 1 2 )= [( ) 2 ]

3 and 2 ( 1 2 )= [1 (( ) 2 )] It is obvious that if there is a symmetric solution so that 1 = 2 =, then = 5. Sometimes these spatial type models (whether the space is vertical or horizontal) are labelled as address models. These have a certain play in models of monopolistic competition. An Example: (2.3 in the text): Consider a market of unit length. Consumers are uniformly distributed, have unit demands and are identical save for their location. Transport costs per unit of distance are and the gross surplus or reservation value for each consumer is given by. On the output side assume that shops are located at and 1; they incur a zero marginal cost and a fixed cost of. Put on a parameter restriction of 2 4 ( 2 makes second site profitable; 4gives welfare effect ) and assume that is sufficiently large that the market is covered even if there is a single location. When is sufficiently large, the monopolist sets a price of so that even the most distant purchase. If there are two sites at ( 1), then the price to cover the market increases to 2. Thisisprofitable provided the incremental profit isstrictlypositiveorif Π = 2, which holds by virtue of the parametric assumption. What is the efficient solution? We have inelastic consumption up to the reservation value, so the number of sites affects transportation costs. This leads to the question of evaluating the increment in welfare from adding the second site. So the second site reduces the total transportation costs and the question is whether this cost saving is warranted given the increment fixed costs associated with this second site. (Notice the role of inelastic demand and thus fixed surplus.) The increment value is the savings in transport costs minus the fixed cost of the second site. This is given by Z 1 Z 1 2 = 2 " 2 1 = = # =, by parametric restriction 4 Thus under this parametric restriction, the efficientsolutionhasonesiteandthemonopolist has 2 sites so there is an inefficient allocation of sites (quality) by the monopolist.

4 Comment: Spatial-type models are useful for purposes of illustration and example but less so for proving general results with spatial models, can never be sure whether the result is driven by the specific parametrization or is a general result. [Option: There is the Becker/Lancaster characteristics approach to demand.] 2 Product Selection: Quality (Follows closely work of Michael Spence in 1975 and 1976) Consider a monopolist who produces a single good characterized by price and quality ; let denote quantity. Write the inverse demand curve as = ( ) and the cost curve as = ( ) where is a vector of factor prices. Let us now investigate whether the monopoly produces the efficient level of quality. First define the efficient level of quality as the solution to Z max = ( ) ( ) [Take a moment to be sure that all understand this.] The two FOC are and Z ( ) = ( ) (1) ( ) = ( ) (2) FOC (1) gives the usual price-equals-marginal-cost condition. FOC (2) can be interpreted as follows: Think of each consumer buying one unit of the good and aggregate demand as just the aggregation over consumers ranked by willingness to pay. The LHS then represents the sum over all consumers of their willingness to pay of one more unit of quality. In other words, the LHS focuses on not just the marginal consumer but the sum of marginal valuations over all consumers. The RHS, of course, is just the marginal cost of quality. Now consider the motives facing the monopolist producer. maximizes profits and his problem becomes Obviously this producer max = ( ) ( )

5 and the corresponding FOC s are given by ( )+ ( ) = ( ) (3) and ( ) = ( ) (4) Define the solutions as ( ). The difference between the monopolist s choice of output and the efficient choice of output is obvious. What about the difference between the monopolist s choice of quality and the efficient choice of quality. The monopolist equates the marginal cost of quality to the marginal valuation of quality as reflect in ( ). So the monopolist cares only about the effect of incremental quality on the marginal consumer while the efficient level of output weighs the impact of marginal quality added up over all consumers. If we define the average marginal valuation for consumers as Z ( ) it is clear that the monopolist worries about the marginal consumer defined by ( ) while the efficient solution is concerned about the average consumer defined by ½ Z ¾ ( ) A caveat: It may be tempting to try to compare these two LHS of respective equations. Butitcannotbedoneasthe will be different. We can say that for a given output, the monopolist undersupplies quality when Z ( ) ( ) and vice versa or the monopolist introduces a bias in product selection at a given level of output. The point here is that if declines with increases in, then the average (LHS) should exceed the marginal and so quality is undersupplied for a given level of output. The above is the direct effect associated with a comparison between the yardstick of the socially optimal quality and that put forth by the sole supplier. If we take as a given the output decision by the firm given by equation ( 3) and solve this for ( ), we

6 may substitute this into the FOC for quality and redo the exercise to ask the second-best question: conditional on the rule by which output is determined, is the quality optimal or not? To proceed, we need to know the sign of. Ifwedefine ( )+ ( ) ( ) Then + = so that = If and are strategic complements then (if local, all that is needed for super modularity), with concavity of the profit function, we have Conditional on a concave welfare function, the welfare question of whether the monopolist produces the optimal quality conditional on its output rule is now equivalent to asking whether? ( ) Under the assumed condition, let s substitute to see = { ( ) ( ( ) ) ½ Z ¾ ( ) } + ( ) = {indirect effect} + {direct effect} = {+} + {±} Theinterpretationforthedirecteffect is as before: if the average marginal evaluation of quality exceeds the marginal evaluation (for example if there is a declining evaluation of quality as quality increases), the direct effect points towards too little quality. There is now a (not surprising) indirect effect and the interpretation is straightforward: as the monopolist produces an inefficiently small output, increasing quality which is a strategic complement to output would encourage the monopolist to increase its output which enhances economic welfare. If quantity and quality are strategic substitutes so that, then

7 = and the indirect effect would promote a reduction in quality as doing so would increase output. [Again this is strongly related to the issue of whether a monopolistic competitor will produce toomuchortoolittle seemwonbuyersgroupsaswell.] [Also could see Glen Weyl s vector extension of Spence s quality result to a world with heterogeneous consumers in both preferences and values: Here is the abstract for the paper: Insurance contracts and other products are designed to attract individuals who are healthy or otherwise particularly valuable. An empirically relevant model of this process requires individuals heterogeneous in both preferences and values. A simple price-theoretic analysis is possible when individual heterogeneity is of high dimension relative to the firm s product design instruments. Necessary conditions for profit and welfare maximization depend on moments of the distribution of individual heterogeneity. Our main result is that the power of an instrument to sort for value is proportional to the covariance, within the set of marginal individuals, between value and marginal utility for the instrument. Existing models assume unidimensional heterogeneity or require restrictive assumptions that imply the absence of sorting. Our analysis applies in settings with non-transferable utility, consumption externalities, non-linear pricing, third-degree discrimination and imperfect competition. We discuss applications to broadcast media, the credit card industry and imperfectly competitive insurance provision.] 3 Quality and Information (including Advertising) There is a classification of goods according to the speed with which consumers can learn about product attributes: (i) the quality of some goods can be verified prior to purchase ( search goods); (ii) other goods require use by consumers first before quality verification ( experience goods); and still other goods can never have their quality verified ( credence goods). (examples of each). Many goods may have attributes that fit into all categories. For search goods the main issues are the ones we discussed above: product selection quality and product diversity. For experience goods, the main issues are how consumers learn about quality and whether firms will have an incentive to supply quality. To no one s

8 surprise, repeat purchases by offering consumers the opportunity to punish firms in the future by withholding their business from firms offers consumers some disciplinary power over firms. Credence goods where quality can never be accurately measured by the user face severe informational problems. Warranties on goods can be signals by the producers who are knowledgeable about the quality embodied in a product. However, when this quality can be influenced by the care taken by the consumer/users of the product, there is the reverse moral hazard problem of consumer neglect. This means that warranties would have to unload onto consumers some of the risk. In a world with variation in the warranties, there can be an adverse selection problem that high-risk consumers self-select into full or more complete warranties while less risky users self-select into more limited warranties. This skews the results for the producers who may have set their prices and warranties on the assumption that they were getting representative samples of consumers. To understand some of these issues, let s proceed to a world without warranties and consider experience goods. Suppose at the outset that consumers purchase the product only once and that there is no word-of-mouth communication among consumers. 3.1 One-Shot Relationships: Moral Hazard and Lemons Any manufacturer who sells an experience good to one-time consumers and neither offers a warranty nor bears any legal burden for faulty quality (false claims), has an incentive to chisel on quality. Consider our previous specification of consumer welfare (consumers buy one unit) defined by if consumer buys = otherwise Consider the following simple specification for the firm: A monopolist chooses a price and a quality. Thereare2typesofqualityasfollows: high quality: =1costs 1 low quality: =costs where [ 1 ]

9 Let there be a unit mass of consumers and assume that 1 (so that producing the high quality is efficient). The monopolist s profit isthen =[ ] If the consumers do not observe quality before purchasing, then each firm would have an incentive to reduce its quality should it start out with the high quality for it would believe that it could save 1 by shaving quality as doing so would not dilute demand (firms are Nash players wrt to consumer demands). But if quality is zero, consumers should rationally anticipate this and would not pay a positive price for zero quality. That is, if =,the equilibrium consists of =and =.If, the market disappears as no one would pay a positive price under our utility for =. Horizontal Externalities With informed Consumers: Suppose that some consumers are informed. Suppliers know this but exactly which consumers are informed is private information. The presence of informed consumers, however, drives up the quality of the monopolist s product. Suppose in our previous set-up that some fraction of consumers are perfectly informed. These consumers will pay if the product is high and zero otherwise. Suppose that the monopoly price [ ]. The informed consumers buy if quality is high which yields a profit of [ 1 ]. Consider uninformed consumers (1 ) whoobservequalityonlyexpost. Suppose that they do not buy. Then demand is from only the informed folks and the monopolist s choice is high quality. Then uninformed types should expect this and should thus purchase. So there is a contradiction. Suppose that uninformed consumers do purchase. The monopolist s profit is 1 if =1, and (1 )( ) if =. What are the monopolist s incentives? The monopolist provides high quality iff. 1 (1 )( ) or 1 (1 ) In fact if 1 (1 )

10 the monopolist in equilibrium charges = andprovideshighquality. What to make out of this? 1. The monopoly will supply the high quality only if the price is sufficiently high. This tells us that the monopolist might loose a high profit marginoninformedconsumers. The claim is that high prices could signal high qualities to uninformed consumers. 2. The condition above is more likely to be satisfied the larger is. Soincreasingthe number of informed customers favors efficiency. 3. If becoming informed is costly this market will undersupply becoming informed as the informed customers generate benefits for the uninformed if high quality prevails. The question is who are the more informed consumers? Are they those with lower search costs? [Discuss a bit] Exercise 2.4 (on pages 18) is insightful. This asks what happens if 1 (1 ) The answer appears on page 127. If 1 (1 ), not all uninformed consumers can buy because otherwise the monopolist would cut quality. Some uninformed consumers must buy because otherwise the monopolist would offer the high quality. Let ( 1) denote the fraction of uninformed consumers who buy. The claim is that the monopolist randomize between the two qualities (otherwise would be or 1). The monopolist must be indifferent between the two so that [ + (1 )] ( 1 )= (1 )( ) or = 1 (1 )[(1 ) 1 + ] This equation defines. (Note that grows with.) The uninformed consumers must be indifferent between buying and not buying. Let denote the probability that the monopolist provides the high quality. Then =

11 or = 3.2 Lemons Problem In an important paper, George Akerloff showed that similar issues arise when the quality of the goods available for the market is not a choice variable but exactly which goods get put on the market is a matter of choice. Consider a used car that is characterized by the level of service or quality that the car produces in some period of time. If the seller keeps the car, it yields a surplus of 1 and the seller receives if he/she sells it. The buyer receives a surplus of 2 if the buyer purchases the car for and otherwise. Assume that 2 1 so that the exchange should be completed. But trading is voluntary. The seller knows perfectly the remaining service or quality level of the vehicle but the buyer is uncertain, knowing only that is distributed onthesupportof[ max ]. Both parties are risk neutral. The buyer s expected pay-off is 2 ( offered for sale). The seller sells if 1 or if 1 or the seller sells iff belongs to the interval [ 1 ].But is uniformly distributed so that the average quality offered for sale is ( offered for sale) = 5 1 The average quality is biased downwards by the decision to sell the car ( ( offered for sale) 5 max for 1 max ). This is the adverse selection or lemons problem. The buyer agrees to purchase the car iff, his/her expected surplus is positive, i.e. iff 2 ( offered for sale) = or iff Iftastesdonotdiffer too much in the sense that 2 2 1, there exists no price at which seller is willing to sell and buyer is willing to buy the market breaks down. The rationale for this results is this: Suppose that the price is high and the seller is willing to sell but the buyer is unwilling to buy. Normally, the price falls and the market may clear. This mechanism does not work here: a decrease in price reduces the average quality on the market the fact that the good is still being sold is a bad news signal; the actual quality that clears is in fact endogenous. This may also occur in insurance markets where only bad risk wish to buy, yet conventionally premia are set with a random draw in mind.

12 So insurers loose money because of the selection problem, raise premia, but this discourages some better risk and so there is a sample selection bias towards even poorer risks and so on. One way around this, for example, in insurance markets is to use deductibles where the better risks in a separating equilibrium will self-select into the correct item on the menu. 3.3 Repeat Purchases: Quality Premia To repeat the set-up: There are two potential qualities: low or =, and high or =1. The unit cost of producing low quality is and the unit cost of producing high quality is 1 where 1. Consumers are identical and have per period (this is a multiple period set up) surplus of if consumer buys = otherwise Assumptions: 1. Thereisamonopolisticproducerwhochoosesqualityineachperiod. 2. There is an infinite number of periods: =1. Define the discount factor to be =(1) (1 + ). 3. All consumers learn at the beginning of period +1 the quality chosen by the monopolist at date, for example, there is superefficient word-of-mouth communication. If only one period, the set-up is extreme lemons and producer would choose =regardless of the price and the consumer would not purchase. But we have an multiple-period model. Consider the following equilibrium. consumers base their expectation of quality on the firm s reputation where at this reputation is measure by the quality chosen by the monopolist at 1: = 1. Assume that 1 =1 consumers have a favorable prior. the monopolist starts with a price 1 and keeps on charging the same price; he also provides the high quality. If the monopolist were to deviate and provide the low

13 quality in some period, then he would keep providing a low quality from then on and charge =; the consumers would then cease to purchase. For a judicious choice of 1, the strategies form an equilibrium. We examine the choices open to the monopolist and then invoke an incentive compatibility condition. If the monopolist follows the suggested policy he/she obtains a present value of profits of ( 1 1 )( ) = 1 1 µ 1 1+ = ( 1 1 ) If instead he/she were to deviate and sell a low quality, the produce would capture a one-period only gain from chiselling on quality and then earn profits forever. Incentive compatibility requires µ 1+ ( 1 1 ) 1 or 1 1 ( 1 ) In order for the monopolist not to cut quality, the high-quality price must command a premium that exceeds marginal cost ( 1 1 )by ( 1 ). The rationale is straightforward: by cutting quality, the monopolist saves on production cost now but looses his reputational rent in the future which is ( 1 1 )( ) =( 1 1 ) Next 1 must be such that the monopolist would not want to rebuild his reputation if he lost it. To do this, he could sell for one period at a zero (or slightly negative) price and high quality. This would cost the monopolist 1 in the short run and would bring the reputation rents ( 1 1 ). To knock out this we need or We also need 1 for consumers to purchase the good. Comments

14 1. The message is that the producer has an incentive to produce a high-quality product only if high quality implies a rent that the producer is afraid of loosing if quality is cut. If there were open entry into the model then Klein and Leffler postulate the existence of some fixed costs such that returns from the quality premium should be zero. If this were an initial once-for-all sunk advertising expenditure of reputation, say denoted by, then with minimum quality the entry condition would be ( 1 )=, the amortized value of the initial sunk investment. Alternatively, if there were introductory offers with prices below unit production costs, then the future return would be sufficient to earn present value profits of zero. Somehow, though, my empirical sense is that these initial losses from introductory offers that I see don t seem to be large enough to support much in the way of future profits. (Although a branch of a fancy up market mini food chain opened near my home; the renovation of a commercial site took about 8 months and I was told that the forecast was that the chain would loose money for from 2 to 3 years. hmm.) 2. The minimum quality premium ( 1 ) increases with the rate of interest. If the time lag between periods lengthened so that consumers took longer to observe past quality, then the interest rate per period would grow with the information lag. In this case, the monopolist would be more tempted to cut quality as such a cut takes longer to be detected. The corresponding quality premium must increase to keep the monopolist from cutting quality. 3. Note that this is a bootstraps equilibrium. Reputation matters because consumers believe that it does. If this commitment comes through sunk advertising then ok but why this vehicle. Think about holes in the ground where a larger hole signals a larger amount of sunk capital. 4. If horizon is finite get the chain-store paradox.