Master Thesis
Switching Behavior and Customer Recognition:
Is It Worth to Learn about Customer Loyalty?
Ilia Samarin
Student Number: s2727161
Email: i.samarin@student.rug.nl
Supervisor: dr. M.A.Haan
Rijksuniversiteit Groningen
Faculty of Economics and Business
Department of Economics, Econometrics and Finance
Abstract
This paper examines the welfare effect of customer recognition in the two-period Hotelling setting. In the second period, firms are able to price discriminate between consumers with different loyalty levels, given that those consumers bought from this firm in period one. The model shows that consumer welfare decreases with the possibil-ity of customer recognition, while firms gain additional profits. Using logit estimation, we also analyzed determinants of switching intentions in the liberalizing Dutch energy market. Results suggest that switching intentions decline when customers believe in high companys involvement with its clients. Perceived switching costs prevent switch-ing, however, their importance decreases when the other loyalty-related attitudes are considered.
Contents
1 Introduction 3
2 Related Literature on Price Discrimination 5
2.1 Brand Preferences Approach . . . 5
2.2 Switching Costs Approach . . . 8
3 The Model 11 3.1 Benchmark: No customer recognition . . . 12
3.2 Pricing with Customer Recognition . . . 20
3.3 Effect of Customer Recognition . . . 24
4 Data 31 4.1 Institutional Framework . . . 31
4.2 Data Description . . . 32
4.3 Description of the Survey . . . 33
5 Empirical Analysis 35 5.1 Empirical Framework for Analysis of Customers’ Loyalty . . . 35
5.2 Probability of Switching . . . 36
5.3 Consumer Value and Impact on the Company . . . 42
5.4 Customer Value Subsamples and Weighted Estimation . . . 43
5.5 Heteroscedasticity . . . 46 6 Discussion 48 7 Conclusion 50 8 References 53 9 Appendices 55 9.1 Correlation Tables . . . 55
1
Introduction
The phenomena of consumer switching between different brands and companies is widely spread in many markets, for example in banking (Colgate and Hedge, 2001; Chakravarty et al., 2004), telecommunication (Eshghi et al., 2007; Ascarza et al., 2016) and energy (Damme, 2005; Wieringa and Verhoef, 2007) markets. Since customer switching undoubtedly affects companies performance, it has attracted a lot of attention of numerous economics and mar-keting researchers, who tackled this issue from both theoretical and empirical perspectives.
A wide range of studies examines switching behavior using microeconomic modeling (e.g. Fudenberg and Tirole, 2000; Taylor, 2003; Esteves, 2014). These researchers focus on the ways a company can manage switching. Specifically, the behavior-based price discrimination or dynamic pricing is of the main interest. Observing past purchase behavior as well as certain characteristics of consumers, companies adjust their pricing strategies in such a way that they induce customers of their competitors to switch, yet make their own customers less willing to switch.
Marketing studies, however, focus on customer management and determinants of switch-ing. The empirical framework often involves such concepts as customer loyalty, inertia, satis-faction and switching barriers (e.g. Eshghi et al., 2007; Jones et al., 2002; Kim et al., 2004). This group of studies aims to understand the causal relationships between these factors as well as their impact on customers switching behavior.
Despite a large variety of theoretical and empirical studies investigating switching behav-ior, there seems to exist a disconnection between them. On the one hand, marketing studies do not rely on any theoretical model that could explain the nature of findings obtained in the studies. Empirical studies usually do not take the competitive effects into account and rather consider firms in isolation. On the other hand, only few theoretical studies consider the effect of loyalty heterogeneity on companies activity (e.g. Esteves, 2010; Ouksel and Eruysal, 2011). However, the results derived from those theoretical models often contradict empirical findings. For example, Esteves (2010) found out that it would be more profitable for companies to avoid customer recognition, while the empirical studies clearly demonstrate the importance of learning about customers attitudes towards a company. Thus, we find it very important to develop a study that would consistently bridge the gap between theoretical and empirical frameworks.
aims at answering the following question: what is the effect of consumer loyalty heterogeneity on companies pricing decisions, companies profits as well as social welfare? The model indicates that companies are able to gain more profits if they put some efforts in learning the strength of loyalty of their customers. Since the model also predicts that some consumers do switch in equilibrium, it is also important to analyze the switching behavior of customers. The empirical section of this thesis, therefore, investigates the following question: Does learning about different consumers loyalty attributes help to better understand and predict switching intentions? This question is approached by estimating the effect of numerous loyalty attributes derived from a survey on probability of switching between different electricity suppliers. If the loyalty-associated indicators remarkably contribute to the ability of a model to correctly identify loyal customers and switchers, then a company has more opportunities to target potential switchers and more loyal customers with different offers that may make them to stay or to become even more loyal to the company. The quality of retention management also directly affects companies profits (Neslin et al., 2006).
We first present a theoretical model of a duopoly with switching costs and behavior-based price discrimination. Consumers are heterogeneous in terms of their brand loyalty levels. We consider two cases: the benchmark, when firms cannot distinguish between more and less loyal consumers; and the case with customer recognition, when firms are able to learn about the loyalty levels of their own customers and can target each of the group with different prices. The model shows that the possibility of customer recognition leads to lower consumer and total welfare, however, firms profits increase. Moreover, the profit gain resulted from customers’ targeting increases with the difference between the loyalty levels of more and less loyal customers. However, the profit gain decreases with the share of less loyal consumers if this share is relatively high: when the number of less loyal customers is higher, there are less opportunities to boost profitability by setting higher prices for more loyal customers, as the share of those is too low to provide a remarkable profit increase.
Second, we empirically analyze the benefits of learning about customers loyalty-related attitudes. The data were provided by one of the key players in the Dutch energy market and consist of two datasets: transaction data and the customers survey data. At the time of data collection, the last step of the Dutch energy market liberalization was taking place. Using logit models, we show that if a company does learn about its customers loyalty attitudes, it becomes able to predict switching intention more accurately, which enables a company to better target customers and gain or save additional customer value.
We also consider a difference between customers, who generate positive or negative value to the company. The analysis provides some important implications for companies, because there is a substantial difference between the importance of several loyalty-related parameters across these two groups, which should be taken into account in retention management.
behavior-based price discrimination. Then in section 3 we present the microeconomic model. We start with the benchmark case, when firms cannot target more and less loyal customers. After that, we introduce customer recognition and analyze its welfare effect. In section 4 we discuss the data and the institutional framework. Section 5 investigates the effect of different loyalty-related parameters on probability of switching. In section 6 we discuss results of theoretical and empirical analyses and provide some implications for companies. Section 7 concludes the thesis.
2
Related Literature on Price Discrimination
Behavior-based price discrimination (BBPD) is a pricing strategy, where firms are able to observe the purchase history of consumers and use this information in such a way that different groups of consumers face different prices in future based on their past behavior. For example, when a firm is able to distinguish between customers that bought from this firm in the past and those who bought from a competing company, the firm may offer a different price for the rival’s customers in order to poach them. For this reason, BBPD is sometimes also called dynamic pricing. Esteves (2010) has distinguished two approaches to the analysis of the welfare effect of BBPD within the existing literature. The first is the brand prefer-ences approach, which implies that firms learn some information about consumers’ exogenous brand preferences from the purchase history. The second approach involves learning from the purchase history about exogenous switching costs, which consumers face when they con-sider switching to another supplier. Since the model presented in this paper involves both switching costs and learning about both brand preferences, we will consider each group of studies in more detail. We first start with the brand preferences approach.
2.1
Brand Preferences Approach
buy from another firms located at the other side of the Hotelling line. With the possibility of long-term contracts in period one, firms are able to prevent switching by setting an infinitely high penalty for breaking a contract. Since fewer customers switch in this scenario, long-term contracts prove their ability to mitigate the negative welfare effect of price discrimination. For this reason, even though firms’ profits increase compared to the case with only short-term contracts, the total welfare is higher when long-term contracts are introduced. Even though this models does not feature switching costs, its flexibility makes it a convenient work-horse framework that was used by many researchers.
Villas-Boas (1999) considered a model similar to Fudenberg and Tirole (2000), however, they assumed overlapping generations of consumers. Moreover, the key difference is that firms can distinguish between their own and new customers, yet they do not know if new consumers used to be customers of their competitors or they are new totally agents in the market. In the equilibrium, firms do set lower poaching prices to attract new consumers, while the past customers end up paying higher prices. Nevertheless, consumer welfare increases, because customers foresee that a firm will exploit them and they become less sensitive to the future prices. The effect on competition also depends on patience (i.e. value of the discount factor) of firms and customers. Higher consumer patience leads to fiercer competition and lower prices, because consumers become more indifferent between suppliers, and firms have to offer lower prices to attract and retain them.
Chen and Pearcy (2010) modified the model of Fudenberg and Tirole (2000) by allowing brand preferences to be dependent across periods, i.e. consumers draw new location in period two, however, this new drawing is not random and depends on the first-period location. They found that when firms cannot commit to second-period prices, profits decrease with the increase of the dependence parameter. In other words, low intertemporal dependence of preferences motivates companies to set lower poaching price in the second period in order to induce switching. However, it also makes firms to lower prices for the repeat customers. Consumer surplus also decreases with the possibility of price discrimination, because more switching will occur, which implies more utility losses due to additional transportation costs. The situation looks different if firms can commit to the second-period prices for their loyal customers. In this case, when the preference dependence is low, firms engage in the loyalty reward policy and set lower prices for their past buyers. However, when the dependence parameter is high, firms realize that past consumers are less likely to switch, which motivates firms to set lower poaching prices in order to attract rivals’ customers.
cus-tomers, which negatively affects firms profits and their welfare, while is beneficial for consumer welfare. If firms do not know the brand preferences, they set higher prices regardless of loy-alty. However, once they learn about the existence of disloyal customers, they compete for this segment, which drives prices down. As a result, firms’ profits decrease compared to the case of no customer recognition. Hence, firms have incentives to avoid customer recognition when price discrimination is allowed.
A slightly different research question was analyzed by Ouksel and Eruysal (2011), who modified the Hotelling model by assuming that there are customers with different trans-portation costs, who are loyal to either firm A or firm B. An essential feature of this model is the asymmetry of firms: the loyalty levels and the sizes of the most loyal customers’ seg-ments differ across companies. Firms are able to learn a technology in order to segment their customers into m equal segments according to the strength of their loyalty. Learning is costly, yet the market segmentation boosts firm’s profit and allows it to retain most of its customers. As a result of segmentation, price-sensitive customers enjoy lower price, while more loyal customers pay a premium, which leads to higher price for them. The value of the premium increases with the loyalty level. Total consumer welfare, nevertheless, increases. The model, however, does not allow for intertemporal price discrimination.
Esteves (2014) presented a framework that features the possibility of discriminating not only between own and competitor’s customers, but also within own customers based on their switching intention. The author enhanced the Fudenberg and Tirole’s (2000) framework of behavior-based price discrimination by allowing firms to react to the poaching prices of competitors. Specifically, the model assumes that when a consumer is willing to change a service provider, she has to inform the current supplier about her intention before she can finalize switching. The current provider, however, now can attempt to retain these customer from switching by offering them a retention price in form of a price discount. Hence, in this model, firms set three prices in the second period: poaching price, loyalty price to those who will stay with this firm and retention price for switchers. The possibility of retention offers in the model enables firm to keep their market shares, however, this possibility also makes competition fiercer and, as a result, leads to lower industry prices. Even though loyal consumers end up paying higher price than in case of no retention offers, the positive welfare effect of customers, who signal switching intention and accept retention, prevails and leads to higher consumer surplus. Firms, however, are worse off due to lower industry prices.
of switching happens, total consumer welfare may fall due to additional transportation costs incurred by those who switched. Moreover, consumers, who decide to stay, often pay higher loyalty prices. Firms face a trade-off between market share and profits: lower prices enable them to retain the market share, however, very low prices due to fierce competition result in lower profits.
2.2
Switching Costs Approach
We now move to the switching costs approach. We will also see that sometimes two approaches overlap and augment each other. The nature of switching costs differs among customers. For example, Burnham et al. (2003) distinguished between the following types of switching costs: (a). procedural, which include time and effort, (b). financial, for instance, when a customer has to pay administration fee to sign up with a new supplier, and (c). relational switching costs, i.e. emotional discomfort. Theoretical models, however, focus rather on procedural and financial examples of switching costs, while the relational switching costs are more related to the brand preferences.
Klemperer (1987) presented one of the first Hotelling-like models with switching costs. There are two period in the model and three groups of consumers: some of them have fixed preferences, another group has changing preferences, and a share of consumers leaves the market after the first period and is replaced by new consumers in the second period. Firms set different prices in each period, however, they do not price discriminate between their past consumers and rival’s customers. The model shows that firms set higher second-period prices compared to the case with no switching costs. This research introduced the idea of consumers, who are “locked-in” due to switching costs, which allows firms to charge higher prices. First-period prices, however, decrease in the presence of switching costs, because firms are competing more fiercely in order to gain a larger market share, which will result in higher demand in the second period. This result also depends on the type of consumers: when consumers are forward-looking, they foresee switching costs in the second period, which makes them less price-sensitive and enables firms to set higher first-period price. Effect of switching costs on companies’ profits largely depends on the share of consumers with changing tastes. Profits are higher than in the standard model without switching costs if the share of consumers with constant tastes is relatively high. However, the impact on profits is negative when there are many consumers with changing preferences, because their second-period behavior does not depend on their first-period purchase decision.
zero economic profit, because they set a price below production costs for switchers and ask loyal customer to pay a premium. Since consumers now can choose between more than one potential supplier to switch to, it induces competition for switchers. An interesting result of the study is that higher number of firms may lead to worse competitive outcome than a duopoly, because it may result in aggressive pricing, which stimulates more customers to switch, hence to incur switching costs, which are the welfare loss.
Gehrig et al. (2011) investigated the effect of switching cost and price discrimination in the monopolistic market, when an incumbent is faced a potential entrant, who cannot price discriminate because she does not know the purchase history of the incumbents customers. However, the possibility of price discrimination has no impact on the entry decision. It does influence consumer welfare though. Consumer benefit if price discrimination is prohibited, yet total welfare increases with the possibility of price discrimination, as the profit gain exceeds the loss of consumer welfare. Switching cost acts as a strategic advantage for an incumbent firm. Therefore, consumer welfare gain from the non-discrimination policy increases with the switching cost. If the latter equals zero, the welfare gain disappears because the incumbent is able to fully exploit the strategic advantage.
Gnutzmann (2013) examined the model with N ≥ 2 firms producing a homogenous good. In the second period firms simultaneously set loyalty, retention and poaching prices and consumers can decide, which price they choose. However, consumers have to exert certain efforts (switching costs) to secure poaching or retention prices. The difference with the other models with switching costs is that consumer learn their switching costs only in the second period, and firms can only observe the population distribution of switching costs. Since consumers learn their switching costs only in the second period, the first-period prices have no impact on the actions that will be undertaken in the second period. The analysis showed that the possibility of retention offers results in lower prices for all groups of consumers. Firms profit also fall with the retention offers. The social welfare also decreases since loyal consumers opportunistically claim retention offers, which leads to additional dead-weight losses dut to incurred switching costs.
for retention offers, pay higher price than poaching price. Since firms know, that signaling is costly, they set higher retention prices for potential switchers. Although firms profits increase, total welfare decreases due to incurred switching costs and disutility associated with additional transportation costs that a switched consumer faces. Thus, heterogeneous switching costs and the possibility of less loyal customers to solicit a retention offer enable firms to enhance their profitability at the expense of more loyal customers and some of potential switchers.
The literature on BBPD is highly extensive. Although, in our view, we have considered the most relevant studies, they represent only the top of the iceberg. The Hotelling framework has been widely used for the welfare analysis of BBPD. The welfare effect largely depends on the model setting and therefore varies across studies. Nevertheless, some common patterns can be derived. For example, once switching costs are introduced to a model, more likely it will lead to higher prices than in case of no price discrimination, because switching costs act as an impediment that makes consumers less willing to switch. The consumer welfare usually falls in the presence of switching costs. Not only switching costs themselves negatively affect the welfare, but also the additional disutility, associated with higher transportation costs incurred when a customer switches to another firm, leads to the worse welfare outcome. Nonetheless, some groups of customers may benefit from the price discrimination, specifically, some of the less loyal customers, who demonstrate switching intentions, may end up paying a lower price and get better off.
the problem investigated by Ouksel and Eruysal (2011). In our model, however, we examine the two-period setting with possibility of price discrimination based on the purchase history, i.e. using the Fudenberg and Tirole’s (2000) framework.
3
The Model
The model presented in this thesis is a simplified version of the model of Fudenberg and Tirole (2000). Two firms, A and B, are located at the ends of the Hotelling line. Firms use identical technology to produce a good and face equal production costs c. The game has 2 periods. The timing will be discussed in detail later in this section. Consumer preferences, Θ, are uniformly distributed on [0, 1] and are fixed over time. If a consumer switches to another firms, she incurs switching cost z. Consumers have unit demand, and each of them would like to buy one unit of a good from either firm A or firm B in each period. The willingness-to-pay ν is high enough, so the purchase happens and the market is fully covered. Firms and consumers are forward-looking and have a common discount factor δ ∈ (0, 1).
Unlike many previous studies on price discrimination, the transportation costs in our model differ across consumers. In terms of the Hotelling line, customer’s location Θ also means customer’s brand preference. Transportation costs are, therefore, a sort of weight attached to the preference. For this reason, transportation costs also represent the consumers’ loyalty. The higher the transportation cost is, the more loyal a customer is and the higher she values her preferences, and it is more costly to her to leave the current provider. Thus, transportation costs or loyalty are important determinants of switching behavior, which can be exploited by a company in order to increase its profitability. Customers, however, are very likely to differ in their loyalty attitudes. It is therefore important to analyze such a framework that allows for investigation of the effect of heterogeneous transportation costs on competition. Specifically, we consider two types of consumers in our model: those with low transportation costs t, and those with high transportation costs αt, where t ≥ 1, α > 1. The share of low types equals λ ∈ (0, 1), and the share of the high types is given by (1−λ). Hence, the parameter α might be interpreted as the loyalty difference between more and less loyal consumers. Higher α makes the difference between two groups of customers more prominent and, as we will show throughout the analysis, provides more profit-enhancing opportunities for companies.
cus-tomer’s loyalty level. One of feasible ways to learn about customers’ loyalty and preferences is to carry out a survey among current customers. A survey might be structured in such a way that it becomes possible to make inferences about customers’ satisfaction or intentions to switch to another supplier. Customer recognition, however, is only possible after the first period. In period 1, none of the firms knows their customers’ loyalty levels. The model im-plies the private information case, which means that each firm is able to learn the loyalty level of its own customers but not of competitor’s ones. Thus, each firm can reach out to different groups of own customers and offer them different prices based on their loyalty. However, the firms can offer only single poaching price to their competitor’s consumers.
The game has the following timing. In period 1, both firms simultaneously set prices p1A and p1
B. Consumers observe these prices and decide, from which company to buy in the first period. A fraction ˆΘ1
i of type i ∈ 1, 2 : t1 ≡ t, t2 ≡ αt buys from firm A and the rest 1 − ˆΘ1i buys from firm B. In period 2, two cases are considered. In the benchmark, where companies cannot target specific groups of customers based on their loyalty, firms simultaneously set loyalty prices p2
AA and p2BB to customers that bought from the same firm in the first period and poaching prices p2
AB and p2BA if a customer bought from firm B in the first period and then switched to firm A and vice versa, respectively. In the second case, firms can offer different prices to their own different customers based on the loyalty level. For example, firm A will simultaneously set a loyalty price p2AA to the customers with higher brand loyalty αt, a retention price pR
A to customers with lower loyalty t, since they feel less related to this company and are more willing to switch, and a poaching price p2
ABto former customers of firm B. Firm B, respectively, simultaneously sets prices p2
BB, pRB and p2BA. Hence, each firm can price discriminate between 3 groups of consumers: rival’s former customers, own more loyal customer (with transportation cost αt) and own less loyal customers (with transportation cost t).
Before we proceed with the analysis, we need to impose some parameter restrictions, which will prevent corner solutions. For any value of λ, we want some but not all less loyal customers to get poached in the second period. We also want some but not all more loyal consumers to get poached. As we will show later throughout the analysis, this requires the following restrictions:
z < 1 (1)
α < 3 + z
t (2)
We start our analysis with the case where the customer recognition is impossible. In the first period, firms simultaneously set prices p1
A and p1B. A fraction ˆΘ1i of consumers of type i buys from firm A, and they form segment A. The remaining consumers comprise the turf of firm B. In the second period, firms can poach the competitor’s customers by setting poaching prices p2
AB and p2BA. Loyal customers, i.d. those who bought in period one from a certain firm and stayed with that firm in period one, are charged prices p2
AA and p2BB, respectively. Second period. We start with the second period pricing decisions. In segment A, some of the consumers will be attracted by poaching prices of the competing firm B and switch. Hence, in period 2 a fraction ˆΘ2Ai < ˆΘ1i will again1 choose firm A, and the remaining fraction
ˆ
Θ1i − ˆΘ2Ai will switch to firm B. A consumer of type i in the segment A, who is indifferent between staying with firm A and switching to the firm B is located at:
ν − tiΘˆ2Ai− p 2 AA= ν − ti(1 − ˆΘ2Ai) − p 2 BA− z ˆ Θ2Ai= 1 2ti (ti+ p2BA− p 2 AA+ z) (3)
Indifferent consumer in segment B is located at:
ˆ Θ2Bi = 1 2ti (ti+ p2BB− p 2 AB− z) (4)
Demand expressions (3) and (4) are strictly between 0 and relevant ˆΘ1
i. While the latter holds for both types of consumers and for all values of λ as long as restriction (1) is satisfied, the former one is satisfied only for more loyal customers with transportation cost αt. In case of less loyal consumers with the loyalty level equal to t, we need to derive an additional restriction. Without the loss of generality, we do it for segment A. The second-period demand of less loyal customers is given by:
ˆ Θ2A1= 1 2t(t + p 2 BA− p 2 AA+ z) = 1 2+ 1 2t 1 3z − 1 6γ = = 3tαλ + 3t(1 − λ) + zαλ + z(1 − λ) − αt 6t(αλ + 1 − λ)
This expression needs to be strictly bigger than 0. The denominator is always positive. The numerator is always strictly positive for λ = 1, however might turn negative for λ = 0:
1With a symmetric equilibrium, we have the following condition:
λ ˆΘ2A1+ (1 − λ) ˆΘ2A2<1 2
From which it follows that γz < 12, where γ is defined by (6). Since γ ∈ (2αt1 ;12), we obtain the restriction (1):
z < 1 When the restriction (1) holds, ˆΘ2
t(3 − α) + z vs. 0. Hence, we need to impose the restriction (2):
α < 3 + z t
Figure 1: Market segmentation. Benchmark
Figure 1 depicts the market segmentation in the benchmark. In period 1, consumers located to the left of ˆΘ1 ≡ λ ˆΘ1
A1+ (1 − λ) ˆΘ1A2 will buy from firm A, and those to the right will buy from B. In the second period, consumers of type 1 located to the left of ˆΘ2
A1 will buy from firm A again and pay the loyalty price p2
AA, while those located to the right of ˆ
Θ2
A1but to the left of ˆΘ1 will switch to firm B and pay the poaching price p2BA. Similarly, consumers of type 2 located to the left of ˆΘ2
A2 will buy from firm A and pay the loyalty price p2
AA, and those located to the right of ˆΘ2A2 but to the left of ˆΘ1 will switch to firm B and pay the poaching price p2BA. Something similar holds for segment B. Since t < αt, we have that2 Θˆ2A1< ˆΘA22 and ˆΘ2B1< ˆΘ2B2. As type 1 consumers are less loyal, more of them will be poached in the second period.
2Using (3), in equilibrium we have:
First, we will do the analysis for firm’s A turf. In this segment, firm A extracts profits from its loyal customers, who stayed with this company and paid price p2
AA. Firm B earns profits from poached customers, who preferred price p2
BA and switched from firm A. Firm’s A second-period profit from its loyal customers is as follows:
Π2AA= (p2AA− c)(λ ˆΘ2A1+ (1 − λ) ˆΘ2A2) = = (p2AA− c)λ 2t(t + p 2 BA− p 2 AA+ z) + (p 2 AA− c) (1 − λ) 2αt αt + p 2 BA− p 2 AA+ z (5) Maximizing (5) with respect to p2AA gives us the following FOC:
∂Π2 AA ∂p2 AA = λ 2t t + p 2 BA− 2p 2 AA+ z + c + (1 − λ) 2αt αt + p 2 BA− 2p 2 AA+ z + c = 0
Rearranging the terms, we have:
2p2AA λ 2t + 1 − λ 2αt = p2BA λ 2t+ 1 − λ 2αt + (z + c) λ 2t + 1 − λ 2αt + 1 2 For the ease of exposition, we define γ as:
γ ≡ λ 2t +
1 − λ
2αt (6)
Using (6), we obtain the following best-response function:
p2AA = 1 2p 2 BA+ 1 4γ + 1 2(z + c) (7)
The second-period profit of firm B from the poached customers is:
Π2BA= (p2BA− c)[λ( ˆΘ11− ˆΘ2A1) + (1 − λ)( ˆΘ12 − ˆΘ2A2)] = = (p2BA− c)λ[ ˆΘ11− 1 2t(t + p 2 BA− p 2 AA+ z)] + (p 2 BA− c)(1 − λ)[ ˆΘ 1 2− 1 2αt(αt + p 2 BA− p 2 AA+ z)] (8) Maximizing (8) with respect to p2BA, using (6) and denoting the weighted average of the first period demand ˆΘ1 = λ ˆΘ1
1+ (1 − λ) ˆΘ12, we obtain FOC:
2γp2BA= ˆΘ1+ p2AAγ −1
2 + (c − z)γ Hence, the best reply of firm B is:
p2BA= 1 2p 2 AA− 1 4γ + ˆ Θ1 2γ + 1 2(c − z) (9)
p2BA= c − 1 6γ + 1 3 2 ˆΘ1 γ − z ! (10) And p2AA = c + 1 6γ + 1 3 ˆΘ1 γ + z ! (11)
Then we have the second-period demand:
ˆ Θ2Ai= 1 2ti [ti+ 1 3 ˆΘ1 γ + z − 1 γ ! ] (12)
And the second-period profit is:
Π2AA = 1 9γ ˆΘ1 γ + 1 2γ + z !2 (13)
We repeat the same analysis for segment B. The second-period profit of firm B from the loyal customers is:
Π2BB = (p2BB− c)[λ(1 − ˆΘ2B1) + (1 − λ)(1 − ˆΘ2B2)] = = (p2BB− c)λ[1 − 1 2t(t + p 2 BB− p 2 AB− z)] + (p 2 BB− c)(1 − λ)[1 − 1 2αt(αt + p 2 BB− p 2 AB− z)] (14) Maximizing (14) with respect to p2BB gives us the following FOC:
∂Π2BB ∂p2 BB = λ[1 − 1 2t(t + 2p 2 BB− p 2 AB− z − c)] + (1 − λ)[1 − 1 2αt(αt + 2p 2 BB− p 2 AB− z − c)] = 0
Rearranging the terms and using (6), we obtain the best-response function:
p2BB = 1 4γ + 1 2p 2 AB+ 1 2(z + c) (15)
The second-period profit of firm A from the poached customers is:
Π2AB = (p2AB− c)[λ( ˆΘ2B1− ˆΘ11) + (1 − λ)( ˆΘ2B2− ˆΘ12)] = = (p2AB−c)λ 1 2t(t + p 2 BB− p 2 AB − z) − Θ 1 1 +(p2AB−c)(1−λ) 1 2αt(αt + p 2 BB− p 2 AB− z) − Θ 1 2 (16) Maximizing (16) with respect to p2
AB, using (6) and denoting the weighted average of the first period demand ˆΘ1 = λ ˆΘ1
p2AB = 1 2p 2 BB+ 1 4γ − ˆ Θ1 2γ + 1 2(c − z) (17)
Combining (15) and (17), we obtain the following second-period prices in the segment B:
p2AB = c + 1 2γ − 1 3 2 ˆΘ1 γ + z ! (18) And p2BB = c + 1 2γ − 1 3 ˆΘ1 γ − z ! (19)
Thus, the second-period profit is:
Π2AB = 1 9γ 3 2γ − 2 ˆΘ1 γ − z !2 (20)
First period. Now we move to the first period. Consumers are forward-looking and they take into account events that will happen in the second period. The indifferent consumer of type i is located at ˆΘ1 i and has: ν − tiΘ1i − p 1 A+ δ(ν − ti(1 − Θ1i) − p 2 BA− z) = ν − ti(1 − Θ1i) − p 1 B+ δ(ν − tiΘ1i − p 2 AB − z) The left-hand side represents the total utility of choosing firm A in the first period and then switching to firm B, while the right-hand side expresses the total utility of choosing firm B first and switching to firm A in the second period. Rearranging the terms, we obtain the following expression: ˆ Θ1i = ti(1 − δ) − δ(p 2 BA− p 2 AB) + p 1 B− p 1 A 2ti(1 − δ) (21)
Using (10) and (18), we have:
p2BA− p2 AB =
2( ˆ2Θ1− 1)
3γ (22)
Hence, the total first-period demand of firm A is as follows:
ˆ Θ1 = 1 2 + 3γ (3 + δ)(p 1 B− p 1 A) (23)
In period 1, firm A sets price p1A in order to maximize the total discounted profit ΠA:
ΠA= (p1A− c) ˆΘ 1 + δΠ2AA+ δΠ2AB = = (p1A− c) ˆΘ1+ 1 9δγ ˆΘ1 γ + 1 2γ + z !2 + 1 9δγ 3 2γ − 2 ˆΘ1 γ − z !2 (24)
Taking the derivative of (24) with respect to p1
A yields: ∂ΠA ∂p1 A = (p1A− c)∂ ˆΘ 1 ∂p1 A + ˆΘ1+2 9δ ˆΘ1 γ + 1 2γ + z ! ∂ ˆΘ1 ∂p1 A − 4 9δ 3 2γ − 2 ˆΘ1 γ − z ! ∂ ˆΘ1 ∂p1 A = 0 From (23) we have ∂ ˆ∂pΘ11 A
= (3+δ)−3γ . Imposing symmetry, i.d. p1A = p1B, we have ˆΘ1 = 12. Then the FOC becomes:
∂ΠA ∂p1 A = (p1A− c)(−3γ) (3 + δ) + 1 2 − 2γδ 3(3 + δ)[z + 1 γ + 4δγ 3(3 + δ) 1 2γ − z ] = 0
Rearranging, we obtain the first-period price:
p1A= c + 1 2γ + δ 3 1 2γ − 2z (25)
Theorem 1. In the benchmark model without customer recognition, the equilibrium prices are as follows:
pbm1 = c + 1 2γ + δ 3 1 2γ − 2z pbmloyal = c + 1 3 1 γ + z pbmpoach = c + 1 3 1 2γ − z
And the equilibrium profits are given by:
Πbm = 1 4γ + 2δ 9 1 γ + z(γz − 1)
higher price in the second period than those poached by the other company (pbmloyal > pbmpoach). The loyalty price is, however, lower than the price in the standard model (ph > pbm
loyal), which indicates higher competition in the presence of possibility to price discriminate. The effect in the first period is ambiguous. The outcome depends on the size of switching costs z and loyalty parameters t and α. With higher switching costs and lower loyalty (which implies higher value of parameter γ, since ∂γ∂t < 0 and ∂γ∂α < 0), the first-period price is lower (pbm
1 < ph), while it is higher than the standard model price in case of lower switching costs and higher loyalty levels (pbm1 > ph). On the one hand, when switching costs are higher, firm will set lower prices in the first period in order to gain a more extensive customer pool, since firms know that in the second period it will be more costly for customers to switch. On the other hand, when the loyalty levels (i.e. the transportation costs) are lower, firms know that in the second period customers will be less willing to stay. Therefore, competing firms will charge lower first-period prices in order to maximize their total profits.
Proof. pbmloyal− pbm poach = c + 1 3 1 γ + z − (c +1 3 1 2γ − z ) = 1 6 1 γ + 4z > 0 ph− pbm loyal = c + 1 2γ − (c + 1 3 1 γ + z ) = 1 3 1 γ − z > 0 since z < 1 and γ ∈ (2αt1 ;12). ph− pbm 1 = c + 1 2γ − (c + 1 2γ + δ 3 1 2γ − 2z ) = −δ 3 1 2γ − 2z thus, ph > pbm1 if γz > 14 and ph < pbm1 if γz < 14.
Corollary 1. Consumers are better off compared to the standard Hotelling model. The total discounted price payed by all groups are consumers are lower. Firms are worse off due to lower profits. The total welfare decreases.
Proof. For the loyal customers, the effect on total discounted price is as follows:
∆Ployal = pbm1 + δp bm loyal − c + 1 2γ (1 + δ) = −δz 3 < 0 For the poached consumers, we have:
∆Ppoach = pbm1 + δp bm poach− c + 1 2γ (1 + δ) = −δ 6( 1 γ + 6z) < 0
∆Π = Πbm− 1 4γ(1 + δ) = − δ 36γ + 2δz 9 (γz − 1) < 0
We can see that consumers are better off, yet firms are worse off, since their total profits are lower than in case of no price discrimination and no switching costs. However, since in equilibrium some of the customers get poached and switch to another firm, they incur switching costs as well as disutility associated with additional transportation costs: those who get poached have to travel to another firm. From the welfare point of view, this disutility and switching costs are a loss. As a result, since prices are transfers between economic agents, incurred switching costs and disutility lead to lower total welfare.
In this subsection, we analyzed the benchmark case, when firms can price discriminate between their past customer and those, who used to buy from a competing firm. Firms, however, are not aware of each customer’s transportation cost (loyalty level). The model showed that in the second period poached consumers pay lower price than those, who decide to stay. We compared this case with the standard Hotelling model without switching costs and price discrimination. All second-period prices are lower when price discrimination is possible. Effect on the first-period prices, however, depends on the value of switching and transportation costs. Even though consumers end up paying lower total discounted prices than in the standard model, the total welfare decreases when price discrimination is possible. The welfare loss occurs due to switching costs and additional transportation costs paid by those customers, who get poached by competitors in the second period.
3.2
Pricing with Customer Recognition
We now consider the case when the customer recognition is possible. In this paper, customer recognition implies learning about each consumer’s transportation cost. In other words, in the second period firms can price discriminate between the two types of consumers with different transportation costs, provided that they were their customer in period 1. Con-sumers that have lower transportation cost t are less loyal, hence, they are more inclined to get tempted by lower poaching prices offered by a competitor. Thus, the firms offer retention prices pR
A and pRB to less loyal customers in order to retain them. More loyal customers with higher transportation cost are offered the loyalty prices p2
AA and p2BB. However, firms are not able to offer different poaching prices to the competitor’s customers, since firms are able to identify only their own customers’ loyalty levels. As before, we first perform the analysis for segment A starting with the second period and using backward induction.
B. Indifferent consumers in segment A are located at: ˆ Θ2A1 = 1 2t(t + p 2 BA− p R A+ z) (26) And ˆ Θ2A2 = 1 2αt(αt + p 2 BA− p 2 AA+ z) (27)
Firm A’s second-period profit from segment A equals:
Π2AA = λ(pRA− c) ˆΘA12 + (1 − λ)(p2AA− c) ˆΘ2A2 = = (pRA− c)λ 2t(t + p 2 BA− p R A+ z) + (p 2 AA− c) (1 − λ) 2αt (αt + p 2 BA− p 2 AA+ z) (28)
Maximizing (28) with respect to pR
A and p2AA gives: pRA = 1 2(t + p 2 BA+ z + c) (29) And p2AA = 1 2(αt + p 2 BA+ z + c) (30)
Firm B’s profit from poached customers is as follows:
Π2BA = λ(p2BA− c)( ˆΘ11 − ˆΘA12 ) + (1 − λ)(p2BA− c)( ˆΘ12− ˆΘ2A2) = = λ(p2BA− c)[ ˆΘ11− 1 2t(t + p 2 BA− p R A+ z)] + (1 − λ)(p 2 BA− c)[ ˆΘ 1 2− 1 2αt(αt + p 2 BA− p 2 AA+ z)] (31) Maximizing (31) with respect to p2
BA and using (6) and ˆΘ1 = λΘ11+ (1 − λ)Θ12, we obtain the following best reply of firm B:
p2BA = ˆ Θ1 2γ − 1 4γ + λ 4tγp R A+ (1 − λ) 4αtγ p 2 AA− 1 2(z − c) (32)
Using (30) and (29) yields the following poaching price:
p2BA= c + 2 ˆΘ 1 3γ − 1 6γ − 1 3z (33)
Then the retention and the loyalty prices are given by:
pRA= c + ˆ Θ1 3γ − 1 12γ + 1 3z + 1 2t (34) And p2AA = c + ˆ Θ1 3γ − 1 12γ + 1 3z + 1 2αt (35)
Π2AA = λ 2t ˆΘ1 3γ − 1 12γ + 1 2t + 1 3z !2 + (1 − λ) 2αt ˆΘ1 3γ − 1 12γ + 1 2αt + 1 3z !2 (36)
We repeat the analysis for segment B. The poaching price and profit of firm A are as follows: p2AB = c + 1 2γ − 2 ˆΘ1 3γ − 1 3z (37) And Π2AB = 1 9γ 3 2γ − 2 ˆΘ1 γ − z !2 (38)
First period. The indifferent consumer is again given by (21). Using (33) and (37) we also have:
p2BA− p2 AB =
2(2 ˆΘ1− 1) 3γ The first-period weighted average demand is given by:
ˆ Θ1 = 1 2 + 3γ (3 + δ)(p 1 B− p 1 A) (39)
In period 1, firm A sets price p1
A in order to maximize the total discounted profit ΠA:
ΠA= (p1A− c) ˆΘ1+ δΠ2AA+ δΠ2AB
Essentially, the first-period analysis does not change in case of customer recognition. After taking derivative of the total discounted price, imposing symmetry p1A= p1B and using ∂ ˆΘ1
∂p1
A =
−3γ
(3+δ), we have the first-period price:
p1A= c + 1 2γ + δ 3 1 2γ − 2z (40)
pcrretent= c + 1 2t + 1 3 1 2γ + z
And the equilibrium profits are given by:
Πcr = 1 2( 1 2γ + δ 3 1 2γ − 2z ) + δγ 9 1 2γ − z 2 + +δ[λ 2t 1 12γ + 1 2t + 1 3z 2 + (1 − λ) 2αt 1 12γ + 1 2αt + 1 3z 2 ]
Prices and profits comparison. In case of customer recognition, pcr
loyal > pcrretent > pcr
poach (see the proof below). Hence, more loyal customers pay higher price than in case if they switched to another firm. The current provider is aware of high loyalty of this group of customers and knows that in case of switching they would incur high disutility due to their “break-up” with a preferred brand, thus, a provider sets higher price for them.
We can see that poaching prices decrease in switching costs both in the benchmark and in case of customer recognition, as it becomes more difficult for firms to attract new customers if it is more costly for those to switch. The loyalty prices, however, increase in switching costs, because firms know that due to higher switching impediment, past customers become less willing to switch. It allows firms to exploit the non-switchers by charging higher loyalty prices. First-period prices also decrease in switching costs, since firms know that in the second period consumers will be less inclined to switch and it is profitable for firms to gain a larger customer base in the first period by offering lower price. When switching costs are high, higher first-period demand leads to relatively higher second-period demand compared with the situation when switching costs are low.
Proof. pcrloyal− pcrretent= c + 1 2αt + 1 3 1 2γ + z − (c + 1 2t + 1 3 1 2γ + z ) = 1 2t(α − 1) > 0 pcrretent− pcr poach(= p bm poach) = c + 1 2t + 1 3 1 2γ + z − (c + 1 3 1 2γ − z ) = 1 6(3t + 4z) > 0 Corollary 2. Customer recognition leads to higher firms’ profits compared to the bench-mark case. Proof. ∆Π ≡ Πcr−Πbm= −1 + 2γλt + 2γ(1 − λ)αt 16γ = λ(1 − λ)(α + α1 − 2) 16γ = λ(1 − λ)(α − 1)2 16αγ > 0 From the comparison of profits we can see that it may be profitable for companies to obtain the information about the loyalty levels of their customers and set differentiated prices based on the strength of loyalty. If we introduce the cost of learning S, then it is beneficial for companies to incur costs in order to learn the loyalty levels and enable the price discrimination based on loyalty as long as the learning cost do not exceed the profit gain, i.e. ∆Π ≥ S.
The profit gain increases in the loyalty parameters: ∂∆Π ∂t > 0,
∂∆Π
∂α > 0. Higher trans-portation costs allow companies to exploit customers to a greater extent by charging them higher prices. Therefore, learning about customer loyalty when the loyalty levels are higher would unleash greater profitability opportunities for a firm. Higher difference in loyalty (α) also boosts the profit gain, since it implies higher premium paid by more loyal customers. However, the effect of the customers’ shares is ambiguous, since the sign of ∂∆Π∂λ varies with different values of λ: ∂∆Π∂λ > 0 for lower values of λ and ∂∆Π∂λ < 0 for higher values of λ. Essentially, the profit gain from learning the loyalty levels decreases when the share of less loyal customers is high, because it becomes less reasonable for a company to spend resources to learn about the loyalty levels and set special prices for more loyal customers, since their share is low.
3.3
Effect of Customer Recognition
Theorem 3. When firms are able to recognize the loyalty levels of their own customers, we have the following results:
1. First period prices do not change compared to the benchmark
3. Retention prices are higher than poaching prices
4. New loyalty prices are higher than loyalty prices in the benchmark
Table 1: Effect of customer recognition on total discounted prices Pbm
poach Ployalbm Ppoachcr = < Pretcr > ? Ployalcr > >
Proof. The proof is based on the comparison of equilibrium total discounted prices.
Ppoachcr − Pbm loyal = − δ 6 1 γ + 4z < 0 Pretcr − Pbm loyal = δ 6 3t − 1 γ ?0 Ployalcr − Ployalbm = δ 6 3αt − 1 γ > 0
For λ = 0, we have Pretcr − Pbm loyal =
tδ
6(3 − 2α), sign of which is ambiguous and depends on the value of α: for α > 32, Pretcr − Pbm
loyal < 0, while when α < 32, P cr
ret− Ployalbm > 0. For λ = 1, however, Pcr
ret− Ployalbm = tδ6 > 0.
Thus, the possibility of customer recognition leads to higher total discounted prices. There are, however, two exceptions. The first is the case when a consumer would be loyal in the benchmark, but would get poached in the case of customer recognition. Such consumer pays lower total discounted price when the recognition is possible. The second exception is the case, in which a loyal consumer in the benchmark gets a retention price. In such a case, a consumer pays higher price when λ is high enough or when λ is low and the difference in loyalty levels α is low enough, namely α < 32.The total discounted price paid by this consumer is, however, lower, when the share λ is low yet the value of α is high (α > 32).
Effect on Consumer Welfare. We will follow the logic of Haan and Siekman (2015) in order to assess the effect of the customer recognition on consumer welfare. For each consumer, there are 6 possible outcomes for comparison, based on a price she faces in the benchmark scenario and in the case of customer recognition. All possible options are summarized in Table 2. Note that more loyal customers, i.e. those having αt, can get the price pcr
loyal, while only less loyal obtain the retention price pcr
retent.
Table 2: Possible options for a consumer
Benchmark Scenario Customer Recognition Scenario Notation
Poached Poached PP
Loyal Gets Loyalty Price LL
Poached Gets Loyalty Price PL
Loyal Poached LP
Loyal Gets Retention Price LR
Poached Gets Retention Price PR
prices. Since the first-period prices are equal in both scenarios, we consider only the effect of the second-period prices. We are going to consider each of 6 options.
PP. The difference in disutilities is equal to the difference in total discounted prices: Pcr
poach = Ppoachbm , hence Dcrpoach= Dbmpoach.
LL. The difference in disutilities is equal to the difference in total discounted prices: Pcr
loyal > Ployalbm , hence Dloyalcr > Dbmloyal.
PL. Since a consumer pays the poaching price in the benchmark scenario, Dbm
poach < Dbmloyal. As Dloyalcr > Dloyalbm , Dbmpoach < Dloyalcr .
LP. Since a consumer pays the loyalty price in the benchmark scenario, Dbmloyal < Dpoachbm . As Dpoachbm < Dpoachcr , Dloyalbm < Dcrpoach.
LR. ∆D ≡ Dcr
retent−Dbmloyal = Pretentcr −Ployalbm . From the price comparison that we have done before, we have the following: for λ = 0, ∆D = Pcr
ret− Ployalbm = tδ
6(3 − 2α), which is negative with α > 32 and positive with α < 32. For λ = 1, however, ∆D = Pcr
ret− Ployalbm = tδ
6 > 0. Thus, the net effect is ambiguous.
PR. ∆D ≡ Dcr
retent − Dbmpoach(Θ) = Pretentcr − Ppoachbm − δz − δm(Θ), where m(Θ) is the utility mismatch (Haan and Siekman, 2015) that a consumer located at Θ ≤ 12 incurs when she chooses the poaching price: instead of transportation costs tΘ she now faces the costs t(1 − Θ). Hence, the utility mismatch is given by: m(Θ) = t(1 − 2Θ). The difference in disutility is hence equal to:
∆D = δ1 2t − 1 3z − t(1 − 2Θ) = − δ 6[t(3 − 12Θ) + 2z] the sign of which is ambiguous.
Thus, we have the following result: possibility of customer recognition makes the most loyal consumers (i.e. those, whose transportation costs equal αt) worse off, while the less loyal ones may benefit from the retention prices that they are offered.
Effect on the total welfare of the less loyal customers is more difficult to analyze. If we focus of segment A in the benchmark, the total disutility of less loyal consumers, who stay with the firm equals ˆΘbmA1 · Dbm
first two components can be written as (12 − ˆΘbmA1)(Ppoachbm + δz). The total utility mismatch for all less loyal consumers is equal to:
MA1bm= Z 1/2 ˆ Θbm t(1 − 2Θ)dΘ = t 1 2− ˆΘ bm A1 2
From which we have the total disutility in the benchmark:
Dbm1 ≡ 2 ˆΘbmA1· Pbm loyal+ 2 1 2 − ˆΘ bm A1 (Ppoachbm + δz) + 2t 1 2− ˆΘ bm A1 2
And the total disutility in case of customer recognition is as follows:
Dcr1 ≡ 2 ˆΘcrA1· Pcr retent+ 2 1 2− ˆΘ cr A1 (Ppoachcr + δz) + 2t 1 2 − ˆΘ cr A1 2
Although we know that Pcr
poach = Ppoachbm and ˆΘcrA1 = 1 4 + z 6t, ˆΘ bm A1 = 1 2 + z 6t − 1 12tγ, hence ˆ
ΘbmA1 − ˆΘcrA1 = 121(3 − tγ1) < 0, it is impossible to compare these two expressions analytically. For this reason, we use numerical analysis. For all values of λ ∈ [0; 1], we calculated the lower and the upper bounds of the net welfare effect (D1cr − Dbm
1 ) of customer recognition for less loyal customer group (i.e. for those whose transportation cost is t), for all admissible values of z ∈ (0; 1), t > 1 and α > 1. Figure 2 presents the results in case of α < 3/2, and Figure 3 for α > 3/2. The analysis was performed using MATLAB. The discount factor δ was assigned the value of 1, since it does not affect the qualitative analysis (Haan and Siekman, 2015). 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lambda 0 0.1 0.2 0.3 0.4 Effect of Customer
Recognition on Disutility of Less Loyal Consumers
Figure 2: Effect of customer recognition on disutility of less loyal customers. α < 3/2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lambda -0.4 -0.2 0 0.2 0.4 Effect of Customer
Recognition on Disutility of Less Loyal Consumers
Figure 3: Effect of customer recognition on disutility of less loyal customers. α > 3/2
hand, lower share of less loyal customers also implies lower number of switchers, which leads to lower disutility caused by extra transportation costs. Hence, for some low values of λ the positive effect of lower disutility outweighs the negative effect of higher poaching prices due to higher α. For this reason, when the share of less loyal customers is low enough, yet the loyalty parameter α is high enough, less loyal customers may get better off in case of customer recognition compared to the benchmark case.
Figures 4 and 5 were constructed in the similar way, however, they show the effect of customer recognition on the total consumer surplus. Regardless of values of λ and α the total consumer welfare decreases with the possibility of customer recognition. More loyal customers end up paying higher price than in the benchmark regardless of the parameters’ values. This negative welfare effects outweighs the positive effect of some less loyal customers resulting in lower total consumer surplus.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lambda -0.8 -0.6 -0.4 -0.2 0 Effect of Customer Recognition on Consumer Welfare
Figure 4: Effect of customer recognition on consumer welfare. α < 3/2
Effect on Profits. Although we analytically compared profits with and without cus-tomer recognition and found that the cuscus-tomer recognition results in higher profits, we also provide results of numerical analysis in order to visualize the effect of customer recognition on profits. This examination might be interesting because not all the customers end up paying higher price in case of customer recognition compared to the benchmark: of those who were loyal in the benchmark, get poached or offered a retention price in the other scenario, they may pay lower price.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lambda -1.5 -1 -0.5 0 0.5 Effect of Customer Recognition on Consumer Welfare
Figure 5: Effect of customer recognition on consumer welfare. α > 3/2
Higher average price automatically implies higher profits in case of uni mass of consumers who buy in equilibrium. Again focusing in segment A, we have the following average price paid in the benchmark:
¯ Pbm≡ 2λ ˆΘbmA1· Pbm loyal+ 2λ 1 2− ˆΘ bm A1 Ppoachbm + +2(1 − λ) ˆΘbmA2· Ployalbm + λ 1 2− ˆΘ bm A2 Ppoachbm
Similarly, in case of customer recognition, the average price is given by:
¯ Pcr ≡ 2λ ˆΘcrA1· Pretentcr + 2λ 1 2− ˆΘ cr A1 Ppoachcr + +2(1 − λ) ˆΘcrA2· Pcr loyal+ 2(1 − λ) 1 2 − ˆΘ cr A2 Ppoachcr 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lambda -0.05 0 0.05 0.1 0.15 0.2 Effect of Customer Recognition on Average Price
Figure 6: Effect of customer recognition on average price. α < 3/2
Figures 6 and 7 present the results of the numerical analysis performed in the same way as in case of consumer welfare. The plots depict the upper and lower bound of the effect of the customer recognition, i.e. ¯Pcr− ¯Pbm. The results show that for all values of λ and α the average price paid increase with possibility of retention offers resulting in higher profits.
Effect on Total Welfare. Finally, figures 8 and 9 present the effect on total welfare. Clearly, the possibility of customer recognition results in lower total welfare.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lambda -0.1 0 0.1 0.2 0.3 Effect of Customer Recognition on Average Price
Figure 7: Effect of customer recognition on average price. α > 3/2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lambda -6 -4 -2 0
Effect of Customer Recognition on Total Welfare
Figure 8: Effect of customer recognition on total welfare. α < 3/2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lambda -15 -10 -5 0
Effect of Customer Recognition on Total Welfare
Figure 9: Effect of customer recognition on total welfare. α > 3/2
using the Hotelling setting. In period 1, each firms sets one price. In period 2, however, firms learn about the loyalty levels (transportation costs) of their past consumers and set three different prices: poaching prices targeted at rival’s consumers, loyalty prices for their own more loyal customers and retention prices for their own less loyal customers. Not only brand preference, but also switching costs act as impediments in period 2 if a consumer considers switching to another supplier. Since firms become able to target more and less loyal consumers with different prices, they retain a higher number of less loyal customers as well as exploit their more loyal consumers by charging them higher prices. It results in higher profits compared to the benchmark case, where firms cannot recognize customer loyalty. Consumer welfare decreases in case of customer recognition: more loyal customers end up paying higher price, and poached customers incur switching costs and additional transportation costs. The latter two terms are also a reason for the fall in total welfare.
switching. In business practice, churn management plays an important role (Neslin et al., 2006), since it allows companies to identify potential switchers and approach them with retention offers. The model also shows that it is essential to target the group of more loyal customers in order to exploit their loyalty and gain additional profits. Furthermore, more accurate identification of loyal customer prevents from the losses associated with wrong targeting (Lemmens and Gupta, 2013). Therefore, a natural way to connect the theoretical framework and empirical application is to investigate the loyalty-related determinants of the switching probability as well as the impact of those factors on the model’s accuracy of prediction. In other words, in the empirical section of this thesis we will be analyzing the following aspects: (a). the relationship between loyalty-related attitudes and switching intentions; (b). the effect of learning about customers’ attitudes on predictive power of models estimating the probability of switching.
4
Data
4.1
Institutional Framework
We are analyzing switching behavior of consumers using data provided by one of the key Dutch energy suppliers. Due to confidentiality matters, we will refer to this company as company X. The data are a cross-section for the year 2004. At that time, however, the Dutch energy market was being restructured, which means that the market featured some characteristics that may influence our analysis and, therefore, have to be discussed. This subsection mostly follows Damme (2005) and Wieringa and Verhoef (2007).
Since 1998 the Dutch energy market had been going through the liberalization process in line with two EU Electricity Directives. Before the process started, the energy market had been served by 23 licensed suppliers owned by municipalities. Each of those companies were tied to a certain geographical segment, which they had to serve. Such market conjuncture implied that all those providers were local monopolists and consumers had no possibility to choose between suppliers and switch from one to another. After a new energy law had been passed, privatization became possible, which eventually resulted in three biggest players in the Dutch energy market: Essent, Eneco and Nuon.
as new market entrants, for example, Shell. The liberalization of the market was a serious challenge for yesterday’s monopolists. According to Damme (2005) the switching activity was prominent. For example, within 18 months since the liberalization of the middle segment, 60% of customers had switched at least once. However, in case of the green energy, only about 18% of users switched from their original supplier 3 years after the liberalization had taken place. Thus, despite the opportunity to change a supplier, the consumer inertia played high role in the liberalized market.
4.2
Data Description
The data used for the analysis were collected by the company X before the final step of total energy market liberalization (July 2004). The final dataset was constructed using two data sources: the company’s data on transactions and the customer survey carried out by the company. The dataset covers 7115 customers. Apart from supplying electricity and gas, the company also provides such services as a cable TV and maintenance services and equipment. The study, however, mostly revolves around the electricity supply.
4.3
Description of the Survey
Table 3: Survey
Questions and notations Possible responses
1. What is your opinion about:
v1 1. The prices of the products and services of X?
1=very bad, 10=excellent v1 2. The quality of the products and services of X?
v1 3. The service quality of X?
3. To what extent do you agree with the following statements? v3 1.X is reliable
1=fully agree, 5=fully disagree, 6=do not know v3 2. X is sympathetic
v3 3. X is involved with its customers
v4. What is your overall grade for X? 1=very bad, 10=excellent
v7. Would you recommend X to other people as an energy supplier? 1=definitely recommend, 5=definitely not recommend 10. Imagine that you would like to switch to another energy supplier.
To what extent do you expect problems with the following aspects? v10a. The continuity of supply
1=many problems, 5=no problems, 6=do not know v10b. Solving issues and malfunctions
v10c. Payments
v10d. Answering questions v10e. Response to complaints
11. To what extent do you agree with the following sentences?
v11a. There is not much differences between products and services of different energy suppliers
1=fully agree, 5=fully disagree, 6=do not know v11b. There is not much difference between the service quality of different energy suppliers
v11c. There is not much difference between prices of different energy suppliers v11d. It is very difficult to switch to another energy supplier
The variable of interest, churn, was constructed in the following way. The customers were presented a list of 11 suppliers and were asked to pick one, from which they would like to buy. If the answer was different than the company X, then the value of 1 was assigned to churn, meaning a potential switch. If the company X was chosen, the variable equals 0. The survey indicates 23% of potential switchers, which is a substantial value.
The data on transactions include such indicators as the yearly projected usage of elec-tricity, the margin made on each customer for different groups of services utilized by the customers, the total (for all kinds of services) number of contracts held by a customer within the company. Due to confidentiality matters, we do not present the summary statistics in this version of the thesis. The transactions data contain variables that may also provide some insights on customers’ loyalty and switching behavior. For example, the total number of contracts held with the company and the margin made from all services that a customers buys from the company are potentially correlated with the loyalty, because a customer who has been buying multiple products and services may feel more related to the company. They may be also be less willing to switch to another supplier, because it would cost them more time and efforts associated with paper work. The data on the electricity usage may also con-tribute to predicting the switching intentions. According to Wieringa and Verhoef (2007), high energy use implies high energy savings, resulting in potential gains of switching for high users.
Table 4: Definition of variables
Variable Definition
lnelectro Logarithm of the projected electricity consumption in 2004
customer value Company’s estimate of the value of a customer contributed in 2004 margin without electricity Margin made from a customer for all
products and services minus electricity margin contracts Total number of contracts held
with the company
churn Switching intention
Things looks slightly different, however, in case of question 3. While the vast majority of customers agreed that the company X is reliable, the “neutral” reply prevails in the other sub-questions asking about the company’s customer relations. Nevertheless, only a small fraction of customers expressed their disagreement with the statements.
The patterns for questions 10 and 11 look substantially different. Although the distri-butions within the questions again are very similar, the higher share of customers chose the answer “I do not know”. There might be two potential reasons for such distributions of answers. First, respondents might have been reluctant to spend time and effort to answer these questions and the option “I do not know” was a natural way to avoid thinking and move on to the next question. The second reason is related to the market structure existed at the moment. The questions 10 and 11 imply some consumers’ awareness of the market and the competing companies. So far customers had to deal with only one monopolist. Although they may have formed some anticipations (Rust et al., 1999) through their experience with the company, they might have little knowledge about the other companies operating in the market (Wieringa and Verhoef, 2007). Hence, the high fraction of the “I do not know”answer might reflect the true unawareness of customers of the market conjuncture.
Since the answer “I do not know” is not very informative, we exclude it throughout the empirical analysis. If we consider the distribution of answers to questions 10 and 11 without this option, we see that most of the customers do not expect many issues after switching. Moreover, the majority of customers do not see big differences in prices, products and quality of services across different suppliers. However, rather many of them consider switching as a difficult and costly process (question 11D).
5
Empirical Analysis
5.1
Empirical Framework for Analysis of Customers’ Loyalty
The theoretical model presented in the previous section promises higher profitability to companies that invest in learning the loyalty level of their customers. The idea of loyalty, however, is somewhat blurred in the theoretical framework. When it comes to the empirical investigation of the loyalty-related components and their effect on the customers’ behavior, the concept of loyalty is complex, which makes its measurement very difficult (Yang and Peterson, 2004).
1987). From the behavioral perspective, loyalty is determined by the past purchase behavior (Neal, 1999). The integrated approach, consequently, combines the attitudinal and behav-ioral approaches. In other words, the integrated approach considers loyalty as a combination of the repurchase behavior and customers’ attitudes. In this study we tackle loyalty from the integrated perspective.
Customer loyalty is also very closely related with the concepts of customer satisfaction and switching barriers (Kim et al., 2004). Edvardsson et al. (2000) provide a concise and comprehensive definition of the satisfaction: “customers’ overall evaluation of the purchase and consumption behavior”. Even though higher satisfaction implies lower propensity of churn and, consequently, higher loyalty (Lee and Cunningham, 2001), switching barriers were introduced in the loyalty-related framework (Jones et al., 2002) as an additional factor that influences switching behavior. Previous studies have shown that switching barriers affect the relationship between loyalty and satisfaction (Colgate and Lang, 2001; Lee and Cunningham, 2001).
The complexity of the concept of loyalty resulted in a variety of empirical approaches used to analyze it. Three methodological frameworks, however, are particularly popular. Those are exploratory and confirmatory factor analysis (Kim et al., 2004; Jones et al., 2002), binary choice models (Neslin et al., 2006; Wieringa and Verhoef, 2007) and Structural Equations Models (Eshghi et al., 2007). Although each of these techniques provide valuable insights about the relationship between switching barriers, customers’ loyalty and satisfaction, we believe that the binary choice models are capable of giving results that can be directly used by companies in order to adjust their operations in order to improve their profitability and customers’ experience with a company.
5.2
Probability of Switching
The empirical analysis consists of two main steps. First, we estimate the logistic model of probability of switching using the transaction and survey data. The probability of switching itself has been used as a proxy for loyalty by some researchers (Methlie and Nysveen, 1999). We will consider the contribution of additional survey items and different loyalty-signaling variables to the more accurate identification of switchers and non-switchers. After that, we use the results to investigate the implications of correct classification and misclassification for the company in terms of potentially gained/lost customer value. After that, we will explore the potential unobserved heterogeneity across the customers.
