Markets with interested advisors On brokers, matchmakers, and middlemen

Transcription

1 Markets with interested advisors On brokers, matchmakers, and middlemen Marco A. Haan Linda A. Toolsema VERY PRELIMINARY PLEASE DO NOT QUOTE December 27, 2008 Abstract We study markets in which brokers, alternatively known as matchmakers or middlemen, advise consumers which product to buy. The broker may charge a fee to consumers for his services, but also receives a commission from producers for each sale that he generates. This implies that he may not always act in the consumer s best interest. We find that, due to the presence of the broker, consumers will choose a product that better suits their needs. However, as consumers are better informed, firms have more market power, which allows them to raise their prices. The effect of higher prices more than outweighs that of selecting a more suitable product, which implies that the existence of a broker makes consumers worse off. Despite the fact that they pay commissions, firms do benefit from the presence of a broker. Keywords: Intermediation; Oligopoly. JEL classification: D43; D82; L13. ieef, Faculty of Economics and Business, University of Groningen, P.O.Box 800, 9700 AV Groningen, The Netherlands. m.a.haan@rug.nl coelo, Faculty of Economics and Business, University of Groningen, P.O.Box 800, 9700 AV Groningen, The Netherlands. l.a.toolsema@rug.nl. The authors thank José Luis Moraga-González and Bastiaan Overvest for useful comments. 1

2 1 Introduction Consumers who buy a product often have to rely on the information of an interested party. This is particularly clear in the case of financial products. A home buyer often relies on a mortgage broker to advise her on which product and which provider would best serve her financing needs. A consumer that wants to take out insurance often relies on an insurance broker to tell her which insurance company offers the policy with the coverage and conditions that suit her best. But also a person that wants to purchase some consumer durable often relies on the advice of a retailer that tells her which product is best for her. In such cases, there is an obvious principal-agent problem. The consumer would like the advisor to act in her best interest. But often, the advisor has an interest in pushing particular products. A mortgage broker will be inclined to push the mortgage products of the bank that offers him the highest commission. An insurance broker will be inclined to push the products of the insurance company that offers him the highest commission. A durable good retailer will be inclined to push the product on which he makes the highest profit. Regulators are concerned about such conflicts of interest. In the UK, for example, this led to the Insurance Brokers (Registration) Act 1977, which was designed to thwart the bogus practices of firms holding themselves as brokers but in fact acting as representative of one or more favored insurance companies In this paper, we study such markets. A monopolist broker, matchmaker, or middleman (he) advises a client (she) on which product to purchase. In the remainder of this paper, we will for simplicity refer to such an advisor as a broker. Producers set the price that they charge to consumers, but also the commission that they offer to the broker. A priori, the client does not know which product is best for her. She therefore relies on the advice of the broker. Yet, with some probability, the client may find out whether or not the broker has given her the best possible advice. If this is the case, she will not follow the broker s advice, which implies that he will not earn 2

3 any commission. This gives the broker at least some incentive to take the interests of his client into account. The questions that we can address using our model are manifold. What are equilibrium prices and commissions in our model? How are they affected by an increase in competition among producers? What are the welfare effects of the existence of a broker? How does observability of commissions affect the outcome of the model? What is the effect of competition between brokers? We will answer some of these questions in this paper, and plan to answer others in future work. Our work is obviously related to the growing literature on two-sided markets, where an intermediary provides a platform on which buyers and sellers can interact (see e.g. Rochet and Tirole, 2003 or Armstrong 2006). Yet, in that literature, the services that intermediaries provide is mainly the aggregation of information, and the lowering of transactions and search costs. In Yavaş (1992), the broker lowers search costs of both consumers and firms. Yavaş studies why some markets have marketmakers (brokers that buy and sell on their own account) while others have matchmakers (brokers that match buyers to sellers, but do not trade on their own account). Different from our model, he assumes that consumers have private information about their valuation. Other papers in this vein include Gehrig (1993) and Yavaş (1994,1996). Caillaud and Jullien (2003) add network effects. In Biglaiser (1993) middlemen can establish a reputation for providing products of high quality. Hence, this paper comes closer to ours. Crucially, however, we consider horizontal rather than vertical product differentiation, which also makes it infeasible for the broker to establish a reputation. Models similar to Biglaiser (1993) are provided by Biglaiser and Friedman (1994), and Hänchen and Von Ungern-Sternberg (1985). The latter also consider a Salop circle, as do van Raalte and Webers (1998). Another related literature is that on credence goods, see e.g. Nelson (1970), Emons (1997), the survey by Dulleck and Kerschbamer (2005). With credence good, the consumer does know not which product they need. We 3

4 have a similar situation in mind. Yet, in the credence goods literature, suppliers can offer product of different qualities, whereas in our set-up, brokers can advise different suppliers. The remainder of this paper is structured as follows. In Section 2, we give the general set-up of our model. Consumers are uniformly distributed on a Salop circle where two firms are located. We assume that consumers are not aware of their own location on the circle. We make this simplifying assumption to reflect the idea that a consumer needs a broker to advise her which firm is best able to suit her needs. In Section 3 we solve two benchmark models. Doing so simplifies the analysis of our general model and allows us to study the effect of a broker. Section 3.1 studies the model for the case in which all consumers are informed of their true location. This boils down to the standard Salop model. In Section 3.2, we study our model in the absence of a broker. Some consumers are informed about their true location, and behave as in a standard Salop model. Yet, the other consumers are uninformed, and simply visit the cheapest firm. This implies that we have a mixed strategy equilibrium in prices. Section 4 introduces a broker. We assume that the broker can observe an informative signal concerning the true location of the broker. Section 4.1 makes the simplifying assumption that this signal is precise. In Section 4.1 we study a much richer model in which the signal is imprecise, but some fraction α of consumers will find out their true location after having visited the broker. We find that consumers are worse off in the presence of a broker. They are now able to find the product that is best for them, but firms do charge higher prices. Firms benefit from a broker. Section 4.3 extends the model by allowing the broker to charge a fee to consumers as well. Section 5 concludes. 2 The model Consider a Salop circular of unit circumference. Firms 1 is located at 0, firm 2 at 1/2. Costs are normalized to zero. A continuum of consumers is uniformly distributed along the circle. Each consumer has unit demand, and 4

5 has a willingness-to-pay for the product that equals v > 0. Transportation costs for consumers are normalized to t per unit of distance. The locations of firms are common knowledge. What we want to capture in our model, however, is that consumers do not know in advance which product best suits their needs, and need the advice of a broker to find out. Therefore, we assume that consumers are unable to observe their own location on the Salop circle, 1 but that the broker can observe some possibly noisy signal about that location. The timing is as follows. First, the two firms set prices p i and referral fees s i, with i {1, 2}. Prices are observable for consumers, but we will initially assume that fees are not. The broker can observe both fees and prices. Second, consumers decide whether or not to visit the broker. If they do, the broker advises them on which firm to buy from. The broker may charge a fee f for his service to the consumer, but for now we assume this fee to be zero. We will relax this assumption in Section 4.2. Third, a fraction α of consumers receive information about their true location. For example, they may run into some additional information in the media, or they may encounter a distant family member on a birthday party that who is able to exactly reveal their true location. We need this assumption to give the broker at least some incentive to be truthful to the consumer. In the fourth stage, a consumer buys from one of the two firms. If they have visited the broker, and they also visit the firm that the broker has advised them to, then the broker receives the fee s i. If the consumer decides to not follow the advice of the broker, the broker does not receive a fee. We assume that firms cannot price discriminate. That is, they have to charge the same price to consumers, regardless of whether or not consumers come via the broker. We look for a Nash equilibrium. Consumers make their decisions (i.e. whether or not to visit the broker, and which firm to purchase from) to maximize their expected utility, given the equilibrium behavior of the broker 1 Alternatively, we could make the assumption that consumers do know their own location, but are uninformed about the exact locations of the two firms. This yields an equivalent model, but greatly complicates our exposition. 5

6 and the prices of the firms. Firm i sets its price and fee to maximize its expected profits π i, given the price and fee of its competitor, the broker s advice behavior, and the behavior of consumers. The broker gives the advice to a consumer that maximizes his expected profits π M, given prices and fees, given the signal that it receives about the true location of the consumer, and given the behavior of consumers. Before turning to the solution of the model, we fist consider two benchmark models. The first is the standard Salop model with full information, and the second is the Salop model with incomplete information, but without the broker. Next, we turn to the solution of the model with a broker. We consider third versions of the model. In the first, we assume the broker to be omniscient for simplicity, and in the second we consider the more realistic case of a broker who obtains only a noisy signal on its clients locations. Finally, we add the possibility that brokers can charge a fee to consumers as well. 3 Two benchmarks 3.1 Full information For comparison, we first solve our model for the case in which consumers are fully informed about their true location. In that case, there is no reason for consumers to visit the broker, and we are back to the standard Salop model. The marginal consumer between firms 1 and 2 on [0, 1/2] is located at ˆx 1 which satisfies so ( ) 1 v p 1 tˆx 1 = v p 2 t 2 ˆx 1, ˆx 1 = p 2 p 1. 2t Total demand faced by firm i is given by D i = ˆx i ˆx j = p j 2p i 2t 6

7 and profit by π i = p i D i. The equilibrium is obtained by maximizing π i with respect to p i. The best-reply function is given by This yields the equilibrium values p 1 = t p 2. (1) p = t 2, π = t Incomplete information, no broker Now consider the case in which not all consumers have perfect information about their own location, but there is no broker to whom consumers can turn. Hence, a fraction α of consumers is informed about its true location, but the remaining fraction 1 α is not. In that case, an equilibrium in pure strategies does not exist. This can be seen as follows. First note that all the informed consumers will behave as they do in the standard Salop model described in the previous subsection. The uninformed consumers, however, obtain the highest expected utility by simply visiting the firm that charges the lowest price. Consider the best-reply function of firm 1. If firm 2 charges a relatively high price, firm 1 has an incentive to slightly undercut that price, thereby capturing the entire fraction 1 α of uninformed consumers. However, if the price that firm 2 charges is sufficiently low, firm 1 has an incentive to set a much higher price, thereby foregoing profits on the uninformed consumers but capturing a much higher profit on the informed consumers with a location close to that of firm 1. It is hard to find an explicit solution for the mixed strategy equilibrium. 2 We can however derive the lower and upper bounds of the support of the equilibrium price distribution. In the previous subsection we defined the best-reply function in the standard Salop model (1). In the current model, 2 The expression for firm profits involves an integral of the price distribution (evaluated in some point) over all values of x for the informed, and the price distribution itself for the uninformed. This combination makes it difficult to solve for the distribution function. 7

8 the best reply to p 2 is p 2 ε if p 2 is sufficiently high, and (1) otherwise. Figure 1 shows the best-reply function of firm 1 (denoted r 1, in bold) and, for completeness, also that of firm 2 (r 2 ). As the figure illustrates, the bestreply function is an increasing function with a downward jump, and the mixed-strategy equilibrium must have firms mixing on prices in the jump interval, which we denote by [p, p]. [INSERT FIGURE 1 ABOUT HERE] To derive p, note that the discontinuity in the best-reply function occurs precisely at p. At this point, the firm is just indifferent between undercutting slightly (by an infinitessimally small ε) or setting the price given in (1), so the profits from these two actions must be equal, i.e. Solving for p we obtain ( ) ( α + 1 α p = αt 4 + p ) 2, 2t p = 1 ( 16 12α 8 ) (4 6α + 2α 8α 2 ) t. Thus, p equals t times some function of α. This function of α is increasing, and equals 0 at α = 0 (where all consumers are uninformed) and 1/2 at α = 1 (where all consumers are informed). Furthermore, we can find p using (1) as p = t + 1 p. From this we observe that for any α (0, 1) we must have 4 2 p < t/2, which is the equilibrium price in the standard Salop model. Any price charged in the mixed strategy equilibrium is strictly below the standard Salop price. This immediately implies that total firm profits in the current model with incomplete information must be lower than total profits in the standard Salop model. Also note that social welfare must be lower in this model than in the standard Salop model. Since the market is entirely covered, the only difference in welfare between both scenarios is due to a difference in total transportation 8

9 costs. In the standard Salop model, all consumers visit the firm that is closest. That is no longer the case with incomplete information: the uninformed consumers now pick a firm at random, rather than visiting the nearest firm. That implies that in the case of incomplete information, total transportation costs increase, and hence welfare decreases by (1 α)( t t ) = (1 α)t/ Solving the model In this section, we solve for the equilibrium of our full model, with incomplete information and the presence of a broker. For now, we assume that consulting the broker is costless to consumers, that is, the broker does not charge a fee for its service to customers. In that case, consumers will visit the broker whenever the expected value of buying via the broker exceeds that of buying from a randomly selected firm. For ease of exposition, we first consider the relatively simple case in which the broker can perfectly observe the location of a consumer. In such a setting, although the informed consumers will never visit the broker, the uninformed consumers may find it worthwhile to do so. In Section 4.2, we analyze the more interesting setting where the broker only obtains a noisy signal about a client s location. In Section 4.3, we add the possibility for the broker to also charge a fee to consumers. 4.1 A broker with precise signals Suppose that the broker can perfectly observe the true location of the consumers that consult him. In what follows, we will refer to the broker as M. An uninformed consumer finds it optimal to buy via M if and only if the expected utility from doing so exceeds that from buying from a randomly selected firm. In a symmetric equilibrium, where prices are equal, this condition can be written as E M [min {x i, 1 x i }] 1 4, where E M denotes the expected value given that the consumer buys via the broker. This condition states that the expected travel distance when buying 9

10 through M is smaller than 1/4, which is the expected travel distance when buying at a randomly selected firm. Uninformed consumers only buy via the broker if this is beneficial on average. Demand from informed consumers is the same as in the benchmark model (of course multiplied by the fraction of informed consumers α). Consider a symmetric candidate equilibrium where uninformed consumers buy via the broker, with price p > 0 and referral fee s > 0. For this to be an equilibrium, we need that neither firm wants to change its price p, or its referral fee s, given that its competitor does charge p and pay s. In such an equilibrium, the broker is indifferent about the advice that he gives to consumers: he will make s per consumer, regardless of whether he sends a consumer to firm 1 or firm 2. We make the simplifying assumption that whenever the broker is indifferent, he will be truthful to consumers, which implies that he will send them to the firm that serves them best. In turn, this implies that consumers have an incentive to follow the broker s recommendation. In equilibrium, each firm will serve half of all consumers. A fraction α of these consumers are informed and will come directly to this firm. The profit margin on such a consumer is exactly p. The remaining fraction 1 α comes through the broker. The profit margin on these consumers is p s. Profits of each firm thus equal π = 1 2 (αp + (1 α) (p s )). Suppose that one firm considers a defection to some s = s + ε, for small ε. By assumption, such a defection is unobservable to consumers. The broker will now send all consumers to the defecting firm, as this firm pays a higher referral fee. Profits of the deviating firm then equal π = 1 2 αp + (1 α) (p s ε), which exceeds π if and only if p s > 2ε. 10

11 This implies that the equilibrium necessarily has s = p. 3 Effectively, the firms engage in Bertrand competition in referral fees. By setting a referral fee slightly higher than that of the competitor, a firm attracts all consumers that come through the broker. This implies that the referral fee will be set such that all profits are competed away entirely. This immediately implies that firms make a profit only on the informed consumers. But competition for the informed consumers is identical to that in the standard Salop model the only difference being that we now have a mass of informed consumers that equals α rather than 1. This implies that the equilibrium is given by p = t/2, s = t/2, π = αt/4, π M = (1 α) t/4. Thus, the presence of the broker will drive prices up from the benchmark mixed strategy equilibrium back to the Salop level, as if all consumers were informed. The broker extracts all profits earned on uninformed consumers. Note that with a perfectly informed broker, welfare is also back to the Salop level, as all consumers again buy from the firm that is closest to them. 4.2 A broker with noisy signals We now consider the more interesting case where the broker only obtains a noisy signal about a client s location, and some clients become fully informed only after consulting the broker. This setting more closely describes the situation of (independent) mortgage and insurance brokers. It allows for the possibility that a client finds out that the broker has given him suboptimal advice, which may occur even without explicit cheating by the broker. In this subsection, for expositional convenience we set t = 1. We first assume 3 Note that if s > p the firm would be making a loss on consumers who buy via the broker and would be better off refusing to sell to these clients. 11

12 that there is no fee to consumers when consulting the broker (as we did before). This assumption is relaxed later. More precisely, consider a consumer with a true location that equals x. We will assume that the broker observes some signal y U [x δ, x + δ] where 0 < δ < 1 reflects the accuracy of the signal and U represents the uniform 4 distribution. 4 First consider the behavior of the broker. Consider the interval [0, 1/2]. As the model is completely symmetric, the interval [1/2, 1] is a mirror image of [0, 1/2]. The broker will send to firm 1 all consumers for whom he observes a sufficiently low y, say y < y. We will now derive profits of the broker as a function of y, and will then derive the optimal behavior of the broker by taking the derivative of these profits with respect to y. We will do so under the maintained assumption that both firms charge the same price to consumers, i.e. that p 1 = p 2 p. First consider consumers that will turn out to be uninformed. We will show below that these consumers will simply follow the recommendation of the broker. Total profits for the broker from these consumers thus equal [ ( ) ] 1 πm u = 2 (1 α) y s y s 2. Now consider the consumers that will turn out to be informed. The broker will still earn a referral fee on these consumers if the advice he has given them, turns out to indeed be their best option. Given that prices are equal, the optimal choice for an informed consumer is to visit firm 1 whenever x < 1/4. Such a consumer will for sure have received the advice to go to firm 1 whenever x < y δ. Now suppose that x [y δ, 1/4]. In that case, the broker will give this consumer the correct advice whenever it turns out that y < 1/4, which occurs with probability 1 1 2δ (x y + δ). This is illustrated in Figure 2. Figure 2 shows a consumer s true location x on the horizontal axis, and graphs the probabilities that a consumer is sent to firm i by the broker M, i = 1, 2. From this graph, it is easy to see that the broker will 4 Of course, the fact that we operate on a circle implies that if this draw yields a signal y < 0, the true signal should be interpreted as y + 1, whereas if the draw yields a signal y > 1, the true signal should be interpreted as y 1. 12

13 correctly send a consumer to firm 2 whenever x > y + δ. If x [y + δ], he will do so with probability 1 1 2δ (y + δ x). [INSERT FIGURE 2 ABOUT HERE] The discussion above implies that the expected profits to the broker from informed consumers, is given by 1 πm i = 2α [(y 4 δ) s 1 + s 1 y δ ( ) 1 y +δ + 2 y δ s 2 + s Total profits of the broker then equal π M = π i M + π u M. ( 1 1 ) 2δ (x y + δ) dx ( 1 1 ) ] 2δ (y + δ x) dx Note that we require y δ < 1 as well as 4 y + δ > 1. This can be shown to 4 hold for marginal changes in s 1 from the equilibrium that we derive below. From the expression of broker profits we can derive y which satisfies y = s 1 s 2 s 1 + s 2 2 α α δ. For given prices p firm 1 s profits are then given by [ ( 1 ( 1 π 1 = α 2 p 2s 1 y 4 δ ) )] 2δ (x y + δ) dx + 2 (1 α) (p s 1 ) y. y δ Here, the first term refers to profits on informed consumers and the second to profits on uninformed consumers. The latter buy from firm 1 whenever the broker sends them there. With equal prices, exactly half of the informed consumers buy from firm 1. But the firm pays referral fee s 1 only for those informed consumers who were sent to firm 1 by the broker and indeed have a location that is closer to firm 1 than to firm 2. This holds true for sure for 13

14 consumers with location x < y δ, and with probability 1 1 2δ (x y + δ) for consumers with location y δ < x < 1. From the first-order condition 4 (FOC) of firm 1 with respect to s 1, imposing symmetry, it follows that in equilibrium we must have s = p 2 (2 α) (1 α) δ α (1 + α) (1 2δ) + 4δ p k, where it can be verified that 0 < k < 1. Note that k can be interpreted here as the commission percentage received by the broker. Now consider the equilibrium prices p. For given s, firm 1 can deviate by changing its price to p 1. We then have ( 1 π 1 = 2p 1ˆx 1 2s (α 1 4 δ δ ( 1 1 (x 14 )) 2δ + δ dx ) + (1 α) ˆx 1 ) Setting dπ 1 /dp 1 = 0 and imposing symmetry yields p = (1 α) s, so we conclude that p = s = 1 2 (1 (1 α) k), k 2 (1 (1 α) k), π = (1 δ) αs, π M = (1 αδ) s. Comparing this equilibrium to that of the benchmark Salop model with incomplete information, we see that the presence of the broker leads to higher consumer prices. Since k is decreasing in α it takes on its minimum value for α = 1, which is 0, and p takes on its minimum value for α = 1 as well at t/2. Prices are above the standard Salop level for any value of α (0, 1), and are decreasing in α. Recall that both bounds of the support of the equilibrium price distribution in the benchmark model are increasing in α. So, we find that the equilibrium price with a broker, and in particular the price increase as compared to the relevant benchmark, are high especially when there are. 14

15 many uninformed consumers. Of course, the presence of the broker does reduce transportation costs for uninformed consumers. The profits of the broker simply equal the equilibrium referral fee s times the number of consumers that visit a firm via the broker. In equilibrium, the broker is truthful in the sense that he will give the advice that is consistent with the signal that he has received. Again consider consumers on the interval [0, 1/2]. For any x / [1/4 δ, 1/4 + δ], the broker will definitely receive the correct signal. For x [1/4 δ, 1/4 + δ], it is easy to derive that he will receive the correct signal in 3/4 of the cases. That implies that a total of 1 δ of all consumers will be sent to the correct firm, which in turn implies that a total of αδ of all consumers will receive the wrong advice and, moreover, will become informed about that. Hence the equilibrium number of consumers that visit a firm through a broker exactly equals 1 αδ. The equilibrium profits of firms are harder to interpret. Note that in the standard Salop model total firm profits equal 1/2. In our model with a broker, total firm profits fall short of this by an amount (1 δ)αs, which is the equilibrium referral fee multiplied by the number of consumers that become informed, but that follow the advice of the broker anyway. We now consider the effect of the broker on consumer surplus. Total profits of the firms and the broker together equal 1 +(1 α) 2 s, which exceeds 1/2, the total profits in the standard Salop model, which itself exceeds profits in the benchmark Salop model with incomplete information but without a broker. The latter profits cannot be higher than α/2. This can be seen by noting that if a firm sets p = p, it will only get informed consumers and earn at most α/4, which is what it earns in the most optimistic case if the other firm would set price just slightly below p. Total welfare increases by (1 α) /8 after the introduction of the broker because of the better match obtained for uninformed consumers. The change in consumer surplus must 15

16 therefore be CS = (1 α) /8 (π 1 + π 2 + π M ) < (1 α) /8 (1 α) (s + 1/2) = (1 α) (s + 3/8) < 0, so consumer surplus decreases upon the introduction of the broker. In our set-up, the introduction of a broker thus has the following effects. First, prices increase, as consumers are better informed. If uninformed consumers do not have any information on which product best suits their needs, they will simply visit the firm that charges the lowest price. Yet, as consumers visit a broker, they become better informed, and differentiation between products increases, which implies that each individual has more market power. Consumers also benefit from the fact that they now consume a product that is closer to their true preference. Still the adverse effects of higher prices more than outweigh the positive effects of a better match. Interestingly, despite the fact that an individual consumer would be strictly better off visiting the broker, consumers as a whole are hurt by the existence of a broker. For a given consumer, her individual decision whether or not to visit the broker has no effect on prices. But if all consumers go through the broker, there is such an effect. Consumers thus face a prisoners dilemma, and would like to be able to commit no to go through the broker, but visit a firm at random. At the same time, firms benefit from the existence of a broker, as their profits are higher in the presence of one. 5 broker is better off. Naturally, the 5 Equilibrium profits of the broker equal (1 αδ)s, which implies that a fraction αδ of consumers does not follow the advice of the broker. The average profit margin that firms receive in the model with a broker is thus given by p a = (1 αδ) (p s ) + αδp. It can be shown that this is decreasing in δ. Hence, the worst case scenario for firms would be if δ = 1/4. If that is the case, then p e = α2 3α α 2 12α But this always exceeds the upper bound on the probability distribution of prices in the 16

17 4.3 A fee for consumers Finally, we consider the possibility for the broker to charge a fee to consumers. We assume that firms set referral fees before the broker sets its fee f. Note that equilibrium prices, referral fees, and firm profits all remain the same; the only change is in the level of the fee f (and therefore in broker profits and consumer surplus). The fee that a monopolist broker can charge to consumers simply equals the difference between a consumer s net surplus in the case with a broker and that without one, given the prices that are set by the firms. If your true location is x, then the probability that the broker sends you to the closest firm is ρ ( 1 4 x) /2δ. Expected utility for a consumer buying via the broker is EU = v p α/8 ( 1 4 δ (1 α) xdx δ ( ( )) ) 1 ρx + (1 ρ) 2 x dx The only term which is affected by whether or not the consumer buys via the broker is the transportation cost in case he does not become informed, i.e. the last term in brackets. This term can be simplified to t 96 (1 α) (3 + 16δ2 ). The equilibrium fee equals the consumer s willingness to pay for the broker s service, f = (1 α) /4 (1 α) ( δ 2) /96 = (1 α) ( 21 16δ 2) /96, which is strictly positive since δ < 1 4. Note that df /dδ < 0 and df /dα < 0. As the broker s signal becomes more precise (so δ decreases), his advice becomes more valuable, hence he can charge a higher price. As consumers are better informed (so α is higher), the broker s advice is less likely to be valuable, and hence the broker has to charge a lower price. model without a broker, which is given by Hence, firms are better off with a broker. p = ( 16 12α 8 ) (4 6α + 2α 8α 2 ) /2. 17

18 When comparing consumer surplus in this model with a fee to that in the benchmark model of Section 3.2, note that the fee paid to the broker by the consumer equals exactly the reduction in his expected transportation cost. So, the expected change in consumer surplus equals minus the price change, and we have argued above that the price will increase. Consumers will therefore be worse off. With competition among brokers, we expect f to become 0. For the brokers, it is impossible to compete on the quality of their advice, so competition will be purely Bertrand. This is exactly what we often observe in practice. 5 Conclusion In this paper, we studied markets in which brokers advise consumers which product to buy. The broker may obtain a fee for his services from consumers, but also receives a referral fee from producers for each consumer that he convinces to buy from them. In the equilibrium of our model, the existence of the broker has the following effects. Consumers obtain a better match with the product that they consume. In equilibrium, the broker does give honest advice to consumers, in the sense that he informs consumers as to which product best serves their needs. Moreover, firms charge higher prices. As consumers are better informed, firms have more market power, which allows them to raise their prices. The effect of higher prices more than outweighs that of having a better match, which implies that consumers are worse off. Despite the fact that they do pay referral fees, firms are better off with the presence of a broker. The higher price that they can charge more than makes up for the referral fees they have to pay. In future work, we plan to extend our model in the following directions. First, we will extend the model to study the effects of observability of referral fees. If consumers can exactly observe the referral fees that firms offer to the broker, they may be less inclined to follow an advice of the broker to buy from the firm that pays him the highest referral fee. As noted, in our current model observability of referral fees has no bearing on the equilibrium, but in 18

19 a richer model there would be such an effect. Second, we will study the effect of an increase in competition among firms, and also the effects of competition among brokers. Throughout this paper, we assumed that consumers either are completely uninformed about their location, or can perfectly observe it. It would be interesting to have a model in which consumers have at least some prior information with respect to their true location. In such a model, consumers would also receive an imprecise signal about their true location. Alternatively, one could imagine a situation in which consumers can observe their true location, but only at a cost. Consumers then have to choose whether to visit the broker, or to invest in learning their location themselves. Such a set-up would allow us to study the effect of increased transparency, i.e. a decrease in costs for the consumer to become informed. References Armstrong, M. (2006): Competition in Two-Sided Markets, RAND Journal of Economics, 37, Biglaiser, G. (1993): Middlemen as Experts, RAND Journal of Economics, 24, Biglaiser, G., and J. W. Friedman (1994): Middlemen as Guarantors of Quality, International Journal of Industrial Organization, 12, Caillaud, B., and B. Jullien (2003): Chicken & Egg: Competition among Intermediation Service Providers, RAND Journal of Economics, 34(2), Dulleck, U., and R. Kerschbamer (2005): On Doctors, Mechanics and Computer Specialists - The Economics of Credence Goods, Journal of Economic Literature, 44,

20 Emons, W. (1997): Credence Goods and Fraudulent Experts, RAND Journal of Economics, 28, Gehrig, T. P. (1993): Intermediation in Search Markets, Journal of Economics and Management Strategy, 2(1), Hänchen, T., and T. von Ungern-Sternberg (1985): Information Costs, Intermediation and Equilibrium Price, Economica, 52, Nelson, P. (1970): Information and Consumer Behavior, Journal of Political Economy, 78, Rochet, J.-C., and J. Tirole (2003): Platform Competition in Two- Sided Markets, Journal of the European Economic Association, 1(3), van Raalte, C., and H. Webers (1998): Spatial competition with intermediated matching, Journal of Economic Behavior and Organization, 34, Yavaş, A. (1994): Middlemen in Bilateral Search Markets, Journal of Labor Economics, 12, (1996): Search and Trading in Intermediated Markets, Journal of Economics and Management Strategy, 5,