Retention Strategies in a Switching Cost Model

Transcription

1 Retention Strategies in a Switching Cost Model ndreia morim University of Minho and NIPE Rosa-ranca Esteves y University of Minho and NIPE May 07 Preliminary version bstract With the developments in technology, rms can gather information about consumers purchase history which can be use to price discrimination accordingly - ehaviour-ased Price Discrimination (PD). Introducing the capacity of rms to implement retention strategies, the aim of this paper is to analyze the e ects of PD when rms apply retention strategies under a switching costs approach. Retention strategies are good for consumers and bad for pro ts. Introduction In markets with repeat purchases, rms can gather and record information about consumers behaviour and quote di erent prices according with their decisions. Huge amounts of data are collect at each second. Data is not only becoming more available but also more understandable by computers. They can measure and communicate location, movement and behaviour of consumers, which can be useful to de ne a customer pro le. Data is the oil of the digital era. Firms can predict more accurately the willingness to pay Corresponding author contact: andreia.amorim@eeg.uminho.pt y Corresponding author contact: rbranca@eeg.uminho.pt The World s most valuable resource is no longer oil, but data, in The Economist, May 6th 07.

2 of customers and set prices in order to get much of the value in a given transaction (especially when the competition between rms is not strong enough). For that reason, rms are increasingly using big data to make predictions about consumers behaviour and use these predictions to implement innovative pricing strategies. ehaviour-ased Price Discrimination (PD) is one of the pricing strategies that rms have been using and its economic and welfare e ects has receive some attention in the recent literature (Chen (997), Corts (998), Villas-oas (999), Fudenberg and Tirole (000), Taylor (003), Chen (005), rmstrong (006), Fundenberg and Villas-oas (006), Stole (007),Esteves (009), Esteves (00), Esteves (04a), Esteves (04b), Esteves and Reggiani (04)). In the digital era, the cost of collecting information about customers decreases, making it easier for rms to identify new customers segments and to target those with customized marketing and pricing strategies. The practice of charging lower prices to new customers is very usual markets such as in the telecommunications markets and in the banking services. It is very common the rival telecommunication rm o ers a lower price to new customers or banks o er advantageous interest rates for new clients. The economics literature o ers important insights on the economic and welfare e ects of PD. This dynamic pricing is analysed under two di erent approaches: the switching costs approach and the brand preferences approach. The rst assume that consumers must incur in some switching costs if they decide to change supplier. Klemperer (987) identi es three di erent switching cost: transaction costs, learning costs and arti cial or contractual costs. Transaction costs occur when the switch is between two identical brands as changing from one bank to another one. When the consumer needs to learn about the new good or service then there is a learning cost associated to the switch. For example, when we change from the Windows software to the Macintosh. rti cial or contractual costs arises entirely at rms discretion. The delity cards in the retail rms rewards the repeated customers or the frequent- yer card in the airlines companies. The second assume that customers have a preference about one rm due to their location along the Hotelling line.

3 s underlined by Chen (005), these pricing practices are employed as an equilibrium strategy of oligopoly rms either in markets where rms o er an ex-ante di erentiated product (Fudenberg and Tirole (000), Esteves (009), Esteves (00), Esteves (04a), Esteves (04b), Esteves and Reggiani (04)) or in markets where rms compete with an ex-ante homogenous good but there is ex-post product di erentiation due to consumer switching costs (Chen (997), Taylor (003)). In both economic approaches, PD tends to lower industry pro ts, but may or may not increase consumer welfare. lthough this type of PD has received some attention in the recent past, some issues remain to be further explored and others need to be explored for the rst time. New features arises in the market. One concern is related with the implementation of retention strategies when rms are able to identify their potential switchers. For a rm it is better to keep a current customers instead of to get a new one. fter make a rst decision purchasing, customers have a switching cost to change supplier. The Ofcom s report makes a reminder to the practice of rms implementing retention strategies as a way to discourage customers to change the current supplier by o ering them a special discount. Under a Losing Provider Led (LPL) 3 process, for the consumers switching process to be completed, customers have to validate a code that has to be requested from the existing rm. In the United Kingdom, for instance, customers who want to switch their mobile telephone service must contact their existing provider and request a Porting uthorization Code (PC) which they then put through to their new provider in order to complete the switching process. So, this code request provides rms with the information that the consumers are willing to switch and allows rms to o er advantageous deals to those customers with the objective of retain them. There are some examples of this practice in the market. There are some customers Ofcom is the UK regulator for the communication markets. 3 n alternative to the LPL process is the Gaining Provider Led (GPL) process. Under the GPL process, customers only need to agree to a deal with their new provider who then contacts the customer s existing provider to complete the switching. In contrast with the LPL process, under the GPL process the switching process is easier but the risks of mis-selling are higher because customers have less information about the implications of the switching process. 3

4 paying an expensive subscription to access the Sky TV service in UK market. ut others, with some little tricks, can pay around 0% less for the same service. In the users account there is a option thinking of leaving Sky which gives to customers a discount in the Sky service 4. Since save activity can potentially make more di cult the switching processes, it is important to understand the economic and welfare e ects of this business practice. Esteves (04a) investigates the impact of retention discounts when product di erentiated rms engage in PD. morim (0) revisits the same question in a homogeneous product market with switching costs. In both approaches PD with retention strategies boost consumer surplus and social welfare and decrease industry pro ts. Under the switching costs approach and with retention o ers, we want to investigate the economic impact the existence of a dominant rm in the market. In the digital era, data is used as a barrier to the entry and early-warning systems and can sti e competition. For that reason, it is demanded news approaches from regulators. Giants rms have access to in nite data about consumers: Google can see what people search 5, Facebook what they share, mazon what they buy. Competition uthorities must pay attention to the markets and the use of data by rms. ig rms are also present in others markets. ritish Telecom (T) is the dominant provider of broadband services in UK. nd, in 05 T made an acquisition of the mobile operator Everything Everywhere (EE) creating the UK s biggest telecoms company. The work is organized as follows. In the section is presented the model and in section 3 the results for the benchmark case where rms cannot price discriminate (uniform pricing). Section 4 is the model with PD but without retention strategies; while in section 5 is analysed the retention strategies. Here, the model is extended for the case when both rms apply retention o ers and the case only rm apply retention. In section 6 are the e ects of retention strategies and in section 7 the welfare analysis. Conclusion is presented in section 8. 4 vailable in Manchester Evening News, 3 March ccording to Noam (05), 90.7% of US consumers use Google as internet search engine in 0. 4

5 Model In the market there are two rms, and, that produces a non-durable homogenous good produced at a same and constant marginal cost, c. Without loss of generality it is assumed that c = 0. Each consumer wants to buy one unit of the product, either from rm or rm and have an identical reservation value, v. t the beginning, consumers are indi erent between two rms. The product is homogeneous and consumers choose the rm with lowest price. Market is divided into an unequal size. Firm get a portion of consumers, with ;. and rm gets the remain demand, ( ). The introduction of retention strategies is motivated by the Ofcom report (Ofcom (00)) that analyses the economic e ects of saving activity in the UK telecommunication markets. When rms are able to identify their potential switchers, then they are able to implement retention strategies in order to discourage the switching process. Retention strategy is a new form of pricing strategy that rms use in order to not lose their market share. The game is divided in two stages. In the rst stage, rms are able to price discriminate among customers and set two di erent prices, one for old customers, p o;r i, and another for rival s customers, p r;r i, for i = ;. fter observing the set of prices of each rm, consumers can continue to buy to the same rm (customers with high switching costs) or change supplier (with lower switching costs). Following the Ofcom report and the LPL process, all consumers who want to change supplier must contact their existing provider in order to complete the switching process, giving information about their willingness to switch provider. Given this information, in the second stage, rms are able to implemented retention strategy, giving a discount, d i, i = ;, for all customers who show an intention to switch. If a customer decides to switch from his current provider he has to incur a switching cost s, uniformly distributed on [0; i ]. Here it is consider that customers that buy from rm and from rm have di erent costs of switching, such that s U [0; ] and s U [0; ], with 6=. 5

6 It is identi ed two kind of consumers: the passive and the active consumers. Passive consumers do not show any intention to switch and thus do not receive a discount. In this category is included all the consumers with high switching costs. ctive consumers express an intention to switch and receive a discount by rm. However, within this group of consumers there are some that conclude the switching process (switchers, with lower switching costs) and some that are retain by rm through the discount (saved/retain customers, for which the discount is not su ciently high to make the switching). 3 Uniform Pricing enchmark In this section we present the case when price discrimination is not feasible, either because it is prohibited or rms cannot segment their customers. Then, consider that rms cannot price discriminate between customers and set an uniform price for all consumers p u i, i = ;. ll customers who want to change supplier must incur a switching cost, i :From the initial purchase decisions, there are three possible cases: rm charges a higher price than rm, the price of the two rms is the same and, rm charges a lower price than its rival s. Firms compete a la ertrand, deciding simultaneously the prices. Since >, rm has the weakly higher ertrand price and only customers from rm will switch (those that pay a higher price at the beginning). Given es the level of switching cost such that the consumer is indi erent between buy again from rm and change for rm, v p u = v p u es and es = p u p u : There are a part of consumers from rm that change supplier while consumers from rm does not change. Thus, the demand of rm is Z q u = d = ( es p u + p u ) : 6

7 nd the demand of rm is Z es q u = 0 Z ds + ( ) 0 Each rm wants to maximize their pro ts. Then, max p u p u ( p u + p u ) ds = (p u p u ) + ( ) and max p u p u (p u p u ) + ( ) Solving the rst-order conditions for the maximization problem of each rm and solving for p u and pu, it is obtained the Nash equilibrium prices and corresponding pro ts. Proposition When rms cannot price discriminate between their existing customers and rival s customers, the uniform Nash equilibrium for prices and pro ts is given by: p u = (+) 3 p u ( ) = 3 for all >. u = (+) 9 u ( ) = 9 The pro t advantage of rm (dominant) is u u = 3 ( ) : For any > ; u u > 0: Corollary With = =, pro ts with uniform pricing are given by u = (+) 9 and u = ( ) 9 : Without price discrimination, rms prices depend on the market share: a rm s second-period price is an increasing function of its previous market share. rm with a higher market share will set a higher price. ecause only customers of rm will change supplier, prices of each rm depend only on s switching costs - rm s baseline market share. 7

8 Pro ts and prices at the uniform pricing benchmark are decreasing in rm s market share. The intuition is the following. For rm is indi erent to charge a higher price for its customers in order to exploit them or charge a lower price to capture some of rm s customers. The lower is ( ), less consumers rm has to exploit and lower is the price charged from rm. Given that, lower will be the price of rm : Moreover, pro ts and prices are increasing in switching costs of consumers (in this case, the switching costs of consumers from rm ). Higher is the switching costs for consumers from rm, more di cult is for rm capture these customers and then both rms compete less aggressively. Under the uniform pricing policy, only consumers from rm will switch supplier. In this case, the number of swicthers, q u, are q u = 3 3 The number of switchers depend on market share of rm. Since >, there is always a swicthers in the market and those increase when market share increase as well. 4 No Retention Strategies enchmark In this section it is consider the case where rms can price discriminate among its customers but retention strategies are not feasible. This model is similar to the static analysis presented in Sha er and Zhang (000). In rm s turf the indi erent consumer between buying again from or switching to rm is located at s such that v p o = v p r s where, s = p o p r : The number of consumers who switch to rm, q are those with lower switching costs. q is given by Z s q = 0 ds 8

9 q = (p o p r ): nd, the number of consumers who buy again from rm have the highest switching costs. q, is Z q = ds s q = ( p o + p r ) : Similarly, the intuition is the same when we look at the rm s turf. The number of consumers that change suppliers are q = ( ) (p o p r ) and, the consumers that continue to buy from rm are q = ( ) ( p o + p r ) : Given the results above, the demand of each rm, D i, i = ; is D = ( p o + p r ) + D = ( ) (p o p r ) ( ) ( p o + p r ) + (p o p r ) Each rm wants to maximize its pro ts with each type of consumers. Thus, at the rm s turf: in the rm s turf, each rm wants to maximize their return with each type of consumers. Thus the maximization problem, for rm, is and, for rm max p o max p r p o ( p o + p r ) p r (p o p r ) : nd in the rm s turf, each rm wants to and, for rm max p o max p r ( )p r (p o p r ) ( )p o ( p o + p r ) : Solving the model, it is obtained the following results. 9

10 Proposition 3 When rms cannot implement retention strategies, the Nash equilibria prices and pro ts are given by: p o = 3 p r = 3 p o = 3 p r = 3 = ( ) 9 = 4( ) Corollary 4 With = =, the results are those obtained from Chen (997) for the second period: p o = 3 p r = 3 po = 3 pr = 3. = (3 + ) 9 = (4 3) 9 When rms can price discriminate but retention strategies are not allowed, 3 total consumers will change supplier 6. of the 5 Retention Strategies In this section we analyse the possibility of retention strategies. Following Chen (997) and introducing an asymmetric demand given by the di erences in customers switching costs, the objective is to analyse the impact of retention strategies on welfare, pro ts and consumer surplus. s usual we solve the game by backward induction. 5. Second stage In the second stage, rms can implement a retention strategy by o ering to all potential switchers a discount, d i, i = ;. 6 Total of switchers when there is PD but no retention are q S = ( ) = 3 : 0

11 In rm s turf the indi erent consumer between buying again from at price p o;r or switching to rm at price p r;r + s is located at s such that d p o;r d = p r;r + s where, s = p o;r d p r;r : t s consumers are indi erent between acting as passive and active consumers and d = 0. Thus, s = p o;r p r;r : Given rm s market share,, the number of consumers who bought from rm and switch to rm, q R, is given by Z s q R = 0 ds q R = (p o;r d p r;r ): The number of consumers who are saved and accept the discount d, q s, is given by Z s q s = s q s = d : ds nd, the number of consumers who buy again from rm and do not receive the discount (passive consumers), q R, is Z q R = ds s q R = p o;r + pr;r In the second stage, rm wants to maximize the pro t obtained with saved consumers. Thus, rm solves the following problem: max p o;r d d d :

12 Solving the rst order condition, yields d = po;r The second-order condition is satis ed for this result. The optimal discount for rm is given by d = po;r : Following the same analysis for rm, is straightforward to see that we can get a similar result. Thus, the optimal discount for rm i is given by for i = ;. d i = po;r i 5. First stage In the rst stage rms can price discriminate between their existing customers and rivals customers setting two di erent prices for each group of consumers, p o;r i and p r;r i, i = ;. fter observing prices, consumers choose to stay or switch depending on their switching costs. In rm s turf, each rm wants to maximize their return with each type of consumers. Thus the maximization problem, for rm, is and, for rm max p o;r p o;r ( p o;r max p r;r p r;r + pr;r ) + (p o;r p o;r d p r;r : For the second-stage equilibrium result, d = po;r p o;r = 3 + p r;r d )d the rst-order conditions yields, where, p r;r = po;r 4 p o;r = 4 5 ()

13 and, p r;r = 5 () Looking now for rm s turf, the maximization problem for each rm as in the rm s turf, each rm wants to maximize their return with each type of consumers. Thus the maximization problem, for rm, is and, for rm max p o;r max p r;r ( )p r;r ( )p o;r ( p o;r p o;r d p r + pr;r ( ) ) + (p o;r Solving the rst-order conditions and with d = po;r ; d )d p r;r = 5 (3) and, p o;r = 4 5 (4) Proposition 5 With retention strategies and asymmetric demand, the Nash equilibria prices and pro ts are given by: p o;r = 4 5 p o;r = 4 5 p r;r = 5 p r;r = 5 and, d = 5 d = 5 R = ( ) R ( ) = s Proposition 5 shows, with retention strategies prices do not depend on market share. For any ;, it can be inferred that for rival s customers, the price is lower with retention strategies, while the price for old customers, p o;r i, is higher with retention. However, there is a portion of old customers (saved customers) who receive a discount and pay a lower price. More, there is 0% of consumers 7 that change supplier. 7 Total swicther are q S = = 5 : 3

14 Corollary 6 With = =, the pro ts with retention strategies are R = ( + ) 5 and R = 5 ( ). From Corollary 6, R is greater than R for any >. While prices do not depend on market share, pro t of each rm does depend on market share and the relative switching costs ( and ). The higher is the market share and/or the switching costs of each type of consumers, the higher is the pro t of each rm. Thus, it is important to analyse the e ects of market share,, and relative switching costs on the pro ts and the demand of each rm. The demand of rm (dominant rm) with retention strategies, D R, is given by D R = q + q s + q D R = The total demand of rm without retention strategies, D, is D = With PD the demand of rm does not depend in switching costs level, even when it is consider retention strategies and when retention strategies are not allowed. The demand of rm after implement PD only depend on its baseline of consumers from the beginning of the period,. Without loss of generality it is consider that rm is the dominant rm in the market, such that >. The bigger rm will always lose its dominance with and without retention strategies. However, rm (dominant rm) will continue with the high demand in the market. Let us suppose that rm departs with an initial market share of 75% of the market, = 0:75. PD with retention strategies reduce the market share to 65%, D R = 0:65: PD with no retention reduce market share to 58%, D = 0:58: Firm loses dominance but still have the higher market share of the market. ecause of the retention o ers, rms can retain some consumers and allow rms to not lose so much market share. 4

15 Let us look at the pro ts of each rm. Remember that R = 5 + R = ( ) 5 ( ) Depending on the values of switching costs, and, it is important to analyse the behaviour of pro ts with market share,. For that, let us take the derivative of pro ts in order to : and, From the above = = If <, pro ts for rm and rm are decreasing in If < decreasing); < pro t of rm is increasing in (while pro t of rm is nd, if > both pro ts are increasing in. Pro ts of each rm is a weighted of their market share and the switching costs of each group of consumers: the losses in market share can be compensated by the relative switching costs. Imagine, for example, that rm increases its market share,, which can be translated in a pro t gain of rm if >. However, rm can gain as well. With > this means that the switching costs of rm s customers are relative smaller than rm s customers. In this case if the market share of rm decreases this can be compensated by the larger relative switching costs: gain in the per-unit pro t with the old customers given by the higher price than rm. Thus, retention strategies are a good tool for the dominant rm ( rm ) to maintain its dominance in the market. The e ect of an increase in on each rm s pro t depends on the level of switching costs. Over a large region of parameter values an increase in will bene t rm and 5

16 harm rm. However, if is extremely high compared to ; rm can bene t from an increase in : Moreover, with retention strategies, the pro t of rm is higher than the pro t of rm, i.e., >, i > ( ) : s by de nition > as long as > it is always true that >. When is large enough compared to the smaller rm can earn the higher pro t. Since rm has more locked-in customers less customers change supplier and rm have a higher proportion of consumers that charge a higher price. Then, rm can have a higher pro t even with a lower market share. 5.3 Only rm can implement retention strategies In this section we analyse the e ects of retention strategies when only the dominant rm () implements retention strategies. Firm is the biggest rm in the market and have more information about their customers. This advantage could be from the technology used for rm that allows rm to gather more and better information about consumers and their willingness to switch. Firm because is small or new in the market could be a di cult to retain customers. The model is solved by backward induction. Second stage cannot do this. In the second stage rm can apply retention strategies while rm In rm s turf the indi erent consumer between buying from rm or switching for rm is located at s such that p o d = p r + s s = p o d p r 6

17 The indi erent consumer between acting as passive or active consumer is located at s and s = p o The number of consumers that switch from rm to rm (those that do not accept the discount), q ; is q = p r : p o d p r The number of saved consumers, q s, which receive the discount, is q s = d nd, the number of passive customers, q, is q = ( p o + p r ) In the second stage, rm wants to maximize the return with saved consumers. Then, the maximization problem for rm is max s = p o d d d Solving the problem, we get the following result for the discount: d = po Firm cannot apply retention strategies. So, in the second stage there is no saved consumers neither the discount. Thus, q s = 0 and d = 0. First stage In rm s turf each rm wants to maximize the return with each type of consumers. Firm wants to maximize the pro ts with old and saved consumers, and rm with the switchers. Then, the maximization problem for each rm in the rm s turf is the following: max p o = p o ( p o + p r ) + p o p o p o 7

18 and to p r max p r = p r p o Maximizing the equation above with respect to p o yields the following reaction functions p o p r and the other equation with respect p o = 3 ( + p r ) and, p r = po 4 Joining the two previous reaction equation, yields: p o = 4 5 (5) and, p r = 5 (6) Looking now to rm s turf. Here, rm wants to maximize the return only with the loyal customers, while rm wants to maximize the pro t with switchers consumers. Then, and ( ) max = p o p o ( p o + p r ) ( ) max = p r p r (p o Solving the model, we obtain the following results: p r ) p o = ( + p r ) p r = po nd the results are p o = 3 (7) p r = 3 (8) 8

19 Proposition 7 When only rm implements retention strategies, the Nash equilibrium is: p o = 4 5 p o = 3 p r = 3 p r = 5 and, d = 5 d = 0 = ( ) = 4( ) s the results with PD (with and without retention strategies), prices do not depend on market share. Corollary 8 With = =, the pro ts when only implements retention strategies are = (83 + 5) and 5 = (00 9). 5 When only applies retention strategies, the number of switchers are q s = 3 5 : Higher is the market share of rm, less consumers will switch under this pricing policy. If rm was a higher market share, higher is the locked-in consumers and then, less consumers change supplier. 6 E ects of Retention Strategies So far we investigate the results of PD with and without retention strategies. Now, we analyse the e ects of retention strategies under the di erent pricing policies when there is a dominant rm in the market. Pro ts The pro ts for rm, for = = = are given by: u = (+) 9 = (3 + ) 9 R = ( + ) 5 = (83 + 5) 5 9

20 Profit of firm 0.50 Uniform pricing 0.45 Only oth retention No retention Only Market share of firm For a higher market share, rm is better when only she apply retention strategies (for ' 0:9) or both apply retention o ers (for ' 0:9). The pro ts for rm, for = = = are given by: u ( ) = 9 = (4 3) 9 R = 5 ( ) = Firm 's profit Uniform pricing 0.3 Only Only No retention oth retention Market share 0

21 Let s assume that rm (small rm) has a xed cost to keep in the market, f. If f < b f, then rm remains in the market; otherwise, rm left. The values for the xed costs for the di erent pricing strategies are presented bellow: f u ( ) 9 f 4 9 f R f For = 0:75 f u 0:3 f 0:9 f R 0:5 f 0:4 If rm has a lower cost to remain in the market ( b f ' 0:4) she can be excluded if the market share of rm is very high ( = 0:75). Demand The demand of rm in each di erent pricing strategies are D u = D = D R = D = Second market share of oth retention Uniform princing = No retention Only 0.6 Only Initial market share of Firm, in each policy pricing, loses market share. However, the loss is lower when retention strategies are allowed, specially when only rm can implement retention

22 strategies. If rm starts with a market share of 75% ( = 0:75), the market share reduces to approximately 68% when only implement retention strategies and to 65% when both apply retention o ers. However, when retention is not possible, rm s market share is approximately 58%. In each case, rm keeps its dominance in the market. Firm can loses its dominance if only rm apply retention strategies and for a weakly dominance ( < 0:643). 7 Welfare nalysis In this section it is analysed the welfare e ects of retention strategies with asymmetric demand under switching costs model. ecause some customers change supplier, PD can lead to some ine cient switching. However, the goal is compared the case when retention strategies are not allowed with the case when rms are able to implement retention strategies and compared the results in terms of welfare. Overall pro t, R, with retention strategies is given by R = 3 5 ( + ( ) ) When rms cannot implement retention strategies, the overall pro t,, is = 5 9 ( + ( ) ) In this way, it can be inferred that with retention strategies the overall pro t of industry is lower when compared with the case when retention is not allowed. verage prices decreased because rms o er a discount in order to retain customers and industry pro t decreases. nd, the overall pro t when rms practice an uniform pricing, u, is u = When only implement retention strategies, the pro t of industry,, is given by = ( )

23 Industry profits Uniform pricing No retention Only 0.5 oth retention Market share of When we look at the consumer surplus with retention strategies, CS R, we need to consider the consumers of type and the consumers of type. surplus, CS R, is given by CS R = v nd s consumer surplus, CS R, is The s consumer CS R = v With retention strategies, consumer surplus, CS R, is given by CS R = v Similarly, with no retention, consumer surplus, CS, is CS = v 3 3 Comparing the results it is inferred that consumers are better o with retention strategies. There are a higher proportion of consumers who pay a lower price - switchers and saved consumers. In general, consumers pay a lower price under retention strategies and consumer surplus boosts. Consumer surplus with uniform pricing, CS u, is given by 3

24 CS u = v ( + ) 3 nd consumer surplus when only rm implement retention o ers, CS ; is CS = v Graphically, Consumer surplus. Uniform pricing Only = Only oth retention No retention Market share of firm The overall welfare, W R, is the sum of industry pro ts, R, and consumer surplus, CS R. Then, with retention the welfare is given by W R = v : Without retention strategies, the overall welfare, W, is W = v : It is straightford that welfare with retention strategies is higher than the welfare without retention strategies. The decrease in industry pro t is compensated by an increase in consumer surplus and social welfare increases. lso, because less consumers make the switching, the deadweight loss due to the decrease in ine cient switching. 4

25 The overall welfare under uniform pricing, W u, is W u = v 3 ( + ) : nd, the overall welfare when only rm apply retention o ers, W, is given by W = v : Overall welfare.0 Uniform pricing.5 Only No retention.0 oth retention Market share of firm 8 Conclusion The economic literature on PD in oligopolist markets is relatively new. The main literature on this topic analysis the PD under two di erent approaches - the switching costs approach (Chen (997) and Taylor (003)) and the exogenous brand preferences approach (Fudenberg and Tirole (000), Esteves (009), Esteves (00), Esteves (04a), Esteves (04b) and Esteves and Reggiani (04)). In both economic approaches, PD tends to lower industry pro ts, but may or may not increase consumer welfare. This work aims to extend the existing literature by introducing retention strategies and the dominant position of one rm in the market. Retention strategies is a pricing strategy used to discourage consumers to switch supplier o er to all consumers that show an intention to switch a special discount. 5

26 The main conclusions of this work is that retention strategies (i) decreases the pro ts of rms because some proportion of consumers pay a lower price - customers who really change supplier and customers who are saved; (ii) increases the consumer surplus because more customers pay a lower price; and (iii) decreases the deadweight loss is lower under retention activity because less consumers change supplier in the second period (less ine cient switching). ppendix. Only rm can implement retention strategies Here are presented the results for the case when only the rm can implement retention strategies. Second stage In rm s turf the indi erent consumer between receive the discount or switching for rm is located at s such that p o s d = p r + s = p o d p r The indi erent consumer between acting as passive or active consumer is s = p o p r The number of switchers, q, are q = ( ) p o d p r The number of saved consumers, q S, are given by q S ( ) = d nd, the number of passive consumers, q ; are q = ( ) ( p o + p r ) 6

27 is Firm wants to maximize the pro t with saved consumers, then the problem of rm max S d = p o d ( ) d Taking the derivative of S with respected to d yields, d = po For rm, because she is not allowed to retain consumers, the discount will be zero. Then, d = 0: First stage each rm is and In the rst stage and in the rm s turf the maximization problem for max p o = p o max p r = p r ( (p o p o Solving each of the maximization problems, we get + p r ) p r ) p o = ( + p r ) and, p r = po Joining the two above equation, yields p o = 3 p r = 3 In rm s turf, the maximization problem for each rm is ( ) max = p o p o ( p o + p r ) + (p o p o ) p o )( 7

28 and ( ) max = p r p r p o p o p r Following the intuition for the results on rm s turf, we obtain the following p o = 4 5 and, p r = 5 Given the above results, the pro ts for rm and for rm are presented below: = = 9 + ( ) 5 ( ) 5 Welfare The consumer surplus when only rm applies retention, CS, are CS = v The overall pro ts,, are = ( ) nd, the overall welfare, W ; are given by W = v

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