when acquisition spoils retention: direct selling vs. delegation...
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When Acquisition Spoils Retention:
Direct Selling vs. Delegation under CRM*
Yan Dong
R. H. Smith School of Business
University of Maryland
College Park, MD 20850
Yuliang Yao
College of Business and Economics
Lehigh University
Bethlehem, PA 18015
Tony Haitao Cui
Carlson School of Management
University of Minnesota
Minneapolis, MN 55455
* All authors contribute equally to the paper. Yan Dong is Assistant Professor of Logistics, Business and Public
Policy at the R. H. Smith School of Business, University of Maryland. Yuliang Yao is Associate Professor of
Management at the College of Business and Economics, Lehigh University. Tony Haitao Cui is Assistant
Professor of Marketing at the Carlson School of Management, University of Minnesota. Email correspondence:
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When Acquisition Spoils Retention: Direct Selling vs. Delegation under CRM
Abstract
The widespread implementation of customer relationship management (CRM) technologies in
business has allowed companies to increasingly focus on both acquiring and retaining customers. The
challenge of designing incentive mechanisms that simultaneously focus on customer acquisition and
customer retention comes from the fact that customer acquisition and customer retention are usually
separate but intertwined tasks that make providing proper incentives more difficult. The present study
develops incentive mechanisms that simultaneously address acquisition and retention of customers with
an emphasis on the interactions between them. The main focus of this study is to examine the impact of
the negative effect of acquisition on retention, i.e., the spoiling effect, on firm performance under direct
selling and delegation of customer acquisition.
Our main finding is that the negative effect of acquisition on retention has a significant impact on
acquisition and retention efforts and firm profit. In particular, when customer acquisition and retention
are independent, the firm’s profit is higher under direct selling than under delegation; however, when
acquisition spoils retention, interestingly, the firm’s profit may be higher under delegation. Our analysis
also finds that the spoiling effect not only reduces the optimal acquisition effort but may also reduce
retention effort under both direct selling and delegation. Comparing the optimal efforts under direct
selling and delegation, the acquisition effort is always lower under delegation regardless of the spoiling
effect, but the retention effort may be higher under delegation with the spoiling effect. Furthermore,
when customer antagonism effect from price promotions is considered, our main results hold regarding
the firm’s preferences between direct selling and delegation, which demonstrates the robustness of our
model.
Keywords: customer acquisition; customer retention; customer value; customer relationship
management; incentive mechanism
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1. Introduction
For decades, firms have focused their marketing strategies on acquiring new customers to enhance their
market share. Since the 1980s, however, firms have gradually realized the importance of retaining
existing customers.1 They have therefore begun to measure customer-defection rates and to identify high-
value customers—with a view to preventing the defection of such customers (Coyles and Gokey 2005).
These efforts have been strengthened by recent developments in the field of customer-relationship
management (CRM), of which customer acquisition and customer retention are at the heart (Bowman and
Narayandas 2004; Gupta, Lehmann, and Stuart 2004; Musalem and Joshi 2009; Verhoef 2003).2 CRM
improves a firm’s knowledge and management of individual customers through the gathering, processing,
and sharing of consumer information and thus enhances the acquisition of new customers and the
retention of existing customers. In the retail sector, for example, most retailers have established call
centers that support their CRM efforts and have implemented data-gathering CRM software and analytics.
Using the subsequent analyses of customer’s buying habits, retailers can thus segment their customer
bases and channel special offers and incentives to specific individuals (Collett 2004).
Although customer acquisition and customer retention are separate tasks, they are nonetheless related
— in that both activities should work together to increase a firm’s market share (McGahan and Ghemawat
1994; Thomas 2001). Efforts made in customer acquisition and retention must be applied in a team
fashion across functional areas such as marketing, sales, and customer service (Verhoef 2003). Because
of the cross-functional nature of these areas and the overlapping job responsibilities of the personnel
involved, efforts in one activity are likely to have a substantial effect on the outcome of the other activity.
More specifically, effort made to increase customer acquisition may inadvertently reduce effectiveness of
customer retention; that is, a spoiling effect. This spoiling effect may be caused by aggressive pursuit of
new customers with attractive, non-price deals unavailable to current customers,3 as observed in the cable
1 Reichheld, Markey, and Hopton (2000), for instance, find that small changes in loyalty and retention can lead to
large changes in profitability. 2 Thomas (2001) defines customer acquisition as ―part of the customer–firm relationship that begins with the
consumers’ first interaction with the firm and proceeds through the first purchase until the first repeat purchase‖.
McGahan and Ghemawat (1994) argue that customer retention occurs when price-sensitive switchers (defined as
new customers and disloyal former customers) are retained by a firm’s investment in customer service. Bendoly et
al. (2005) study a multiple-channel structure in which customers can be retained by an alternative channel when a
product or service is unavailable in one channel. Others have defined customer retention more generally as activities
that prolong relationships between firms and customers—such as loyalty programs, direct mailing, and other
programs that enhance the perception of a relationship (Hauser, Simester, and Wernerfelt 1994; Reinartz, Thomas,
and Kumar 2005; Thomas 2001; Verhoef 2003). 3 Acquisition efforts are non-price activities that directly increase demand for a given price, such as advertising and
special services offered only to new customers. Note that such activities are different from promotions, which is a
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industry, for example, ―the acquisition marketing was increasing customer defection rates‖ (Novo 2005).
Similarly, in the banking industry, while investment in digital services such as online new account
opening ―will go a long way toward getting more low-cost deposit accounts,‖ such customer acquisition
effort may actually reduce customer satisfaction (Decastro 2009) and thus reduce customer retention. In
fact, a study of the UK financial services finds customer acquisition strategies undermine the attempts at
customer retention (Farquhar 2005).4
In carrying out customer acquisition and retention tasks, firms can choose to control and perform the
tasks in a centralized setting, or alternatively, to delegate some of these tasks to customer representatives
(Bhardwaj 2001; Lal 1986; Mishra and Prasad 2004, 2005). For example, companies such as cell phone
service providers, cable companies, and commercial banks, may centralize efforts to attract new
customers with national advertising plans (i.e., customer acquisition) while leaving retail stores with the
responsibility of service related issues (i.e., customer retention). That is, the firm sells directly to new
customers but leaves customer retention to retail stores. Or, the firm could encourage employees at the
retail stores to actively engage potential customers in order to convert them into future new customers; 5
in which case the firm delegates customer acquisition to retail stores. The firm’s choice between direct
selling and delegation of customer acquisition often affects customer retention and firm performance,
which may be complicated by the existence of the spoiling effect.
The challenge the retail banking industry is faced is a case in point. While some argue that Internet
banking such as HSBC Advance, ING Direct, etc. offers great growth opportunities as direct selling,
others believe that delegated customer acquisition at bank branches provides face-to-face communication,
one stop shopping, and localized marketing that are essential for new customers (Durkin et al. 2003;
Viveiros 2007; Campbell and Frei 2010). On one hand, Internet Banking centralizes such customer
acquisition activities as branding and advertising that create broad and effective awareness of the firm and
its products, particularly for banks focusing on savings and mortgages (Farquhar and Panther 2008). On
the other hand, centralized customer acquisition may have complicated effect on customer retention. For
example, when the CEO of a bank in UK was seen to directly ―drive the product‖, i.e., selling direct, the
management ―were paying lip service to retention,‖ leading to roughly 10% of effort being spent to retain
existing customers while 90% to acquire new customers (Farquhar 2005).
price-based approach to increase demand (without shifting the demand function). Acquisition efforts incur direct
costs while promotions do not. 4 Retail banks offer various introductory offers, such as point awards and free air tickets, to new customers, which
often makes existing customers unhappy. 5 For example, a national wireless communication carrier uses advertising on local billboards, sponsors local youth
sports teams, sends brand ambassadors to shopping malls, etc. for customer acquisition.
4
Alternatively, as a case of delegating customer acquisition in retail banking, front-line employees at
local branches play an important role in customer acquisition, and are given sales targets and provided
sales incentives (Farquhar 2005). Furthermore, decisions of selling processes are often delegated to
branch managers, who then receive more incentive based pay as a result of increased authority (Nagar
2002). The value of delegation may come from increased coordination between tasks and potential
efficiency gains when transferring tasks to capable and skilled customer representatives, but these gains
will need to be traded off with higher costs from the tasks being performed by customer representatives
under delegation. Empirical results (e.g., Slade 1996) show that such relationships between tasks may
directly affect incentives and efforts associated with the tasks. In fact, delegation may create synergy by
allowing different tasks to be coordinated under the control of customer representatives, but a
multitasking representative may require a more costly and higher powered incentive than a single tasking
representative (Slade 1996). Such tradeoffs become more complicated when acquisition effort spoils
retention as the incentives allocated between tasks and the way the firm assigns acquisition tasks (e.g.,
under direct selling and delegation) need to fully reflect the spoiling effect.
Customer acquisition and retention tasks may also interact with each other at a pricing level. It is
common for firms to use price promotions to acquire customers from competition (Gupta 1988;
Narasimhan 1988; Raju, Srinivasan, and Lal 1990). Such an acquisition approach, however, may come at
the cost of ―antagonizing customers‖ (Anderson and Simester 2010). For example, the promotions used
by a cellular phone company to attract new customers can increase dissatisfaction among certain existing
customers as they may feel they are not being treated fairly. Through a large-scale 28-month randomized
field experiment involving over 50,000 customers, Anderson and Simester (2010) find that existing
customers make fewer purchases of both the same and other products by a firm subsequent to the firm
reducing prices.
Although customer acquisition and retention are nevertheless one of the most important components
of CRM, previous literature on CRM has mostly focused on assessment of CRM performance (Bowman
and Narayandas 2004; Crosby and Stephens 1987; Lewis 2004; Mittal and Kamakura 2001; Reinartz et
al. 2005; Thomas, Blattberg, and Fox 2004), evaluation of drivers of customer satisfaction and retention
(Gounaris 2005; Heim and Sinha 2001; Shankar, Smith, and Rangaswamy 2003), allocation of resources
within a CRM system (Reinartz et al. 2005), structural design of a CRM system and impact of customer
value on design and implementation of effective CRM strategies (Blattberg and Deighton 1996; Chen
2005; Chu and Desai 1995; Gupta et al. 2004; Hauser et al. 1994; Kalra and Shi 2001; Kalra, Shi, and
Srinivasan 2003; Lim, Ahearne, and Ham 2009; Venkatesan and Kumar 2004; Villanueva, Bhardwaj, and
Balabsuramanian 2007), and the long-term vs. short-term perspective of CRM under competition
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(Villanueva et al. 2007). Among them, only a few studies have examined customer acquisition and
customer retention issues. For example, Hauser et al. (1994) elegantly show how the precision of
measuring customer satisfaction could affect the design of the incenting system and thus affect customer
satisfaction. Park and Fader (2004) develop a bivariate timing model to empirically examine the
correlation between acquisition and retention, called ―linked propensities‖ in their paper, and Schweidel,
Fader, and Bradlow (2008a, 2008b) examine the implications of such a correlation on the value of
prospects and customers. A very interesting study by Simester and Zhang (2010) considers how a firm
should design the rewarding system when managers, who are rewarded by product success, may choose
to invest in projects that show little potential of success. They show that the firm should appropriately
design the rewarding system in order to solve the tension that rewarding killing bad products may
undermine the rewards for success, and find that the timing for the manager to learn demand is crucial for
the design of the rewarding system. To our best knowledge, however, little research has specifically
studied the development of appropriate sales force incentives with respect to intertwined customer
acquisition and retention, and the delegation of acquisition to customer representatives.
The present study aims to fill these gaps in the literature. We develop incentive mechanisms that
simultaneously address acquisition and retention of customers with an emphasis on the spoiling effect of
acquisition on retention. In particular, we compare incentive designs and the firm’s profit between direct
selling and delegation in the presence of the spoiling effect. Our main finding is that, when customer
acquisition and retention are independent, the firm’s profit is higher under direct selling than under
delegation; however, when acquisition spoils retention, the firm’s profit may be higher under delegation,
suggesting that delegation can be an effective mechanism in mitigating the spoiling effect. The intuition
is that, under delegation, the multitasking agent is able to coordinate the tasks to contain the negative
effect of the conflict, by shifting effort from customer acquisition to retention. As a result, when
acquisition spoils retention to a great degree, the firm may be better off delegating customer acquisition
activities to take advantage of the coordination effect. In addition, our analysis finds that the spoiling
effect not only reduces the optimal acquisition effort, but may also reduce retention effort under both
direct selling and delegation. Comparing optimal efforts under both schemes, the acquisition effort is
always lower under delegation regardless of the spoiling effect, but the retention effort may be higher
under delegation with the spoiling effect. Furthermore, when customer antagonism effect from price
promotions is considered, our main results hold regarding the firm’s preferences between direct selling
and delegation. This demonstrates the robustness of our model.
The present study is distinctive from previous research mainly in the following two ways. First, it is
the first study to develop sales force incentive mechanisms for customer acquisition and customer
6
retention as potentially conflicting CRM activities. Similar models have been adopted to study related
issues, such as customer service and satisfaction, but none for customer acquisition and retention. Hauser
et al. (1994) present a customer incentive scheme to improve customer satisfaction and services by
separating customers into groups according to the marginal effort it takes to acquire or retain them. The
authors noted that customer satisfaction should be measured differently for various groups and that
customer satisfaction among existing customers (leading to retention) should be given a different
weighting from that among non-customers (leading to acquisition). Joseph and Thevaranjan (1998)
examine the role of monitoring and incentives in providing customer services and found that monitoring
allows a firm to decrease the incentive paid to salespersons. Other related research has analyzed the
strategic use of targeted promotions for customer retention and customer acquisition in a dynamic and
competitive environment (e.g., Fruchter and Zhang 2004; McGahan and Ghemawat 1994). The present
study extends this stream of research by specifically modeling customer acquisition and customer
retention, and more importantly, their interactions as the main components of incentive mechanisms.
Second, this study compares two commonly used incentive contracting mechanisms, direct selling vs.
delegation of customer acquisition, with and without spoiling effect. Our study compares two second best
solutions, one from a double moral hazard problem (direct selling) and the other from a multi-tasking
framework (delegation), in terms of efforts and firm profits. By comparing the two mechanisms, this
research highlights a potential benefit of delegating conflicting tasks that may have a broad range of
application within and beyond CRM. To our best knowledge, this research is the first such effort in
marketing to study these issues.
The rest of the paper is organized as follows. Section 2 presents the model setup and development.
Section 3 presents the analyses and results. Section 4 draws conclusions from the research and discusses
managerial implications, limitations, and future research. Proofs of the lemma, proposition, and all
corollaries are provided in the Technical Appendix, which can be found online at
http://mansci.journal.informs.org.
2. The Model
This study models customer acquisition and retention in a principal–agent framework, in which the firm
acts as the principal and the firm’s customer representative as the agent. The risk-neutral firm sells a
single product either directly, or through its customer representative, to customers. The customer
representative is risk-averse with a constant absolute risk-aversion (CARA) utility function given by U()
= 1 – e – r
, where r is the coefficient of absolute risk aversion and is the customer representative’s
income (Bhardwaj 2001; Hauser et al. 1994; Joseph and Thevaranjan 1998; Lal 1986). In the direct
7
selling model, the firm makes efforts to acquire new customers, while in the delegation model, customer
acquisition tasks are delegated to the customer representative (Bhardwaj 2001). In both models, the
customer representative performs the retention task. This assumption is based on the interactive nature of
many customer retention activities that can be better performed by front-line representatives. For front-
line representatives, the existing customer base is known and face-to-face interaction is more effective to
retain the existing customers, particularly when existing customers experience service issues and consider
moving their business elsewhere. (Farquhar 2005). The total demand of the firm’s product consists of
three components: the base demand n, the demand through customer acquisition AD , and the demand
through customer retention RD . The based demand can be equivalently considered as the long-term
demand from established customers of the firm that is not affected by acquisition or retention efforts.
Thus, the total demand is given by RA DDnD , in which
( )
A a a
R r a r
D e
D e e n
. (1)
For the demand through customer acquisition, ea refers to the acquisition effort made by either the firm
(in direct selling) or the customer representative (in delegation) and is not contractible. The customer
representative’s retention effort is denoted as er and is not contractible either. So the firm’s demand can
be increased from either acquiring new customers or retaining current customers or both. The term of
r ae e can be considered as customer retention rate (0 1) which is the ratio of the expected
retained customers to the base demand n (Rao 1990).6 Without loss of generality, we assume n = 1.
7
Both a and r are independent with each other and normally distributed with mean zero and respective
variances of 2
a and 2
r , i.e., ),0(~ 2
aa N and ),0(~ 2
rr N . Parameters a and r represent the
accuracy of acquired and retained sales as indicators of customer representative’s respective efforts
(Hauser et al. 1994).8 Parameter captures the spoiling effect of acquisition effort ea on retention and
such an effect is not higher than the direct effect of retention effort er on retention, i.e., 0 ≤ ≤ 1.9 10
6 Another way to model retention is to assume that the retained customer is given by
rAR DnD )( , which will
bring similar insights but the analysis will be much more complicated. The assumed retention demand
rR nD in the model represents the situation where both the principal and agent agree on the base of the
retention (i.e., n). 0 1 can be relaxed without changing the main results. 7 We consider the cases where the retention demand is positive and is smaller than the base demand, i.e.,
0 1r ae e . The explicit expressions of the feasible conditions are given in the online Technical Appendix,
which can be found at http://mansci.journal.informs.org. 8 Hauser et al. (1994) use variance in measure of customer satisfaction as an indicator of employee efforts.
9 This range can be increased to 1 1 without changing the main insights of the following results.
10 The single-period model adopted here renders better tractability given the multitasking feature and the multiple-
level interactions, thereby allowing clearer insights into implications of interactions between customer acquisition
8
Under direct selling, the costs for acquisition and retention efforts are given by 2
2
1aaec and
2
2
1rrec ,
respectively. Under delegation, the total costs for acquisition and retention are given by 2 21 1
2 2a a r rc e c e .
We assume that the two tasks do not present any forms of technological dependency (i.e.,
interdependence between the marginal costs of customer acquisition and customer retention efforts)
(Holmstrom and Milgrom 1991). Since acquiring a new customer usually is more costly than retaining an
old customer, we further assume a rc kc with k > 1.
The firm provides the following linear incentive scheme to the customer representative (Bhardwaj
2001; Hauser et al. 1994; Joseph and Thevaranjan 1998):
delegationinDD
sellingdirectinDy
ra
r
, (2)
in which y is the total payment from the firm to the customer representative. The payment consists of
three components: 1) is a fixed salary that is independent of performance in customer acquisition and
retention; 2) is the commission rate, in the case of delegation, for total acquired demand; and 3) is the
compensation for the total number of retained customers. In the direct selling model, since the customer
acquisition effort is made by the firm, the compensation for customer acquisition is not relevant. If the
customer representative successfully retains a customer, the firm gains the long-term customer value lp
associated with this customer (Bendoly et al. 2005). Such a value is often termed as the ―customer
lifetime value‖ (CLV) (Collett 2004; Dwyer 1989; Fader, Hardie and Lee 2005; Pfeifer and Carraway
2000). The parameter p is the long-term price that is assumed to be fixed in the model, and l is a
multiplier, l > 1. The production or purchase cost of the product is normalized to zero. Therefore, price p
can be considered as the gross margin of the product. CLV increases in the gross margin of the product.
The firm’s profits from direct selling (denoted with superscript DS) and delegation (denoted with
superscript DL) are respectively given by: 11
21( ) [ ( )]
2
DS
a r a r a r aE pe lp e e kc e e e
and customer retention. When purchases are made repetitively and decisions are made in a long-term fashion,
however, it is likely that customer retention effort affects future demand function as well. A multi-period or a
repetitive model would possibly be needed to further explore customer acquisition and customer retention incentive
mechanisms for a more general situation. We recognize the limitation of our model in this regard and leave this
possibility for future research. 11
We only consider CRM related profits for the firm. Incorporating the profit from base demand, pn, will not
change the main results.
9
( ) [ ( )]DL
a r a a r aE pe lp e e e e e . (3)
The first term in the profit functions is the firm’s net sales profits from the new demand generated by
the acquisition effort. The second term is the contribution of the long-term customer value from retained
customers. The third term in direct selling is the firm’s direct cost for customer acquisition effort. The
last term is the incentive payment transferred to the customer representative. Since the firm does not
make direct effort for customer acquisition or customer retention under delegation, the firm’s profit
function contains no effort costs but only the payment for the acquisition and retention activities.
The incentive mechanism in the direct selling model is stated as follows:
21( ) [ ( )]
2
DS
a r a r a r aMax E pe lp e e kc e e e
(4)
Subject to:
IC(A): ( ) arg max[ ( ( , )]r
r a re
e E U e e
IC(P): ( ) arg max[ ( , )]a
DS
a a re
e E e e
IR: [ ( , )] 0a rE U e e ,
where the Certainty Equivalent (CE) of the customer representative’s expected utility is given by:
2 2 21( )
2 2r a r r r
rCE e e c e .
In a similar fashion, the incentive mechanism for delegation is stated as follows:
,( ) [ ( )]DL
a r a a r aMax E pe lp e e e e e
(5)
Subject to:
IC: ,
( , ) arg max [ ( , )]a r
a r a re e
e e E U e e
IR: [ ( , )] 0a rE U e e ,
where the CE of the customer representative’s expected utility is given by
2 2 2 2 2 21 1( ) ( )
2 2 2a r a r a r r a r
rCE e e e kc e c e
The direct selling model is a double moral hazard problem (Demski and Sappington 1991) with
acquisition and retention efforts made by separate parties. The delegation model is a multitasking
problem (Holmstrom and Milgrom 1991; Hauser, et al. 1994), where both customer acquisition and
10
retention efforts are made by the representative. The objective function is the firm’s expected profits over
uncertainties in customer acquisition and customer retention outcomes. The incentive compatibility
constraint (IC) states that the firm and the customer representative will choose the effort level that will
result in their greatest profits and utility, respectively. The individual rationality (IR) constraint reflects
the minimum utility required by the customer representative to accept the incentive contract. The detailed
analyses of both models are given in the online Technical Appendix. In the next section, we will provide
main results and discuss the implications.
3. Analyses and Results
In what follows, we focus our analyses on studying how the spoiling effect of acquisition effort on
retention outcome ( > 0) affects firm profitability and efforts under direct selling and delegation. We
then extend our models to include promotion and consumer antagonism effect.
3.1 The Spoiling Effect of Acquisition ( > 0): Direct Selling vs. Delegation
Under both direct selling and delegation, acquisition and retention tasks are balanced such that the
firm’s profit is maximized. Under direct selling, the balance of tasks is established between the firm and
the representative, whereas under delegation, it is done by the representative under the multitasking
contract designed and offered by the firm. The optimal outcomes under both direct selling and delegation
are presented as follows.
Under direct selling, we have
2 2
(1 )
( )
DS
a
r r r r
p l lpe
kc c k kc r
,
2 2( )
DS
r
r r r
klpe
c k kc r
, and
2 2( )
DS
r r
klp
k kc r
. (6)
Under delegation, we have
2 2 2 2
2 2 2 2
[1 (1 ) (1 )( )]
[ (1 )(1 ) ]
DL r a r r r aa
r r a r r r a
p l kc r l c r c re
c k kc r c r kc r
,
2 2
2 2 2 2
[ (1 ) ( ) ]
[(1 )(1 ) ]
DL r a r ar
r r a r r r a
p l kc r p l c re
c kc r c r c r
,
11
2
2 2 2 2
[1 (1 ) ]
(1 )(1 )
DL r r
r a r r r a
p l c r
kc r c r c r
, and
2 2
2 2 2 2
[ (1 ) ( ) ]
(1 )(1 )
DL r a r a
r a r r r a
p l kc r p l c r
kc r c r c r
(7)
Given the optimal efforts under direct selling and delegation, the following lemma depicts the impact
of the spoiling effect on the optimal efforts.
LEMMA 1. The spoiling effect of acquisition on retention ( > 0) reduces the acquisition and retention
efforts under direct selling. It reduces the acquisition effort and may reduce (increase) the retention
effort when λ is sufficiently small (large) under delegation.
The spoiling effect of acquisition leads to a lower acquisition effort under both direct selling and
delegation because the firm naturally tries to reduce acquisition effort to mitigate the negative impact on
retention. But interestingly, a lower retention effort can also be a result of the spoiling effect under direct
selling, and even under delegation when λ is sufficiently small. As the firm becomes reluctant to allocate
its compensations toward acquisition with the concern of the spoiling effect, conventional wisdom may
suggest that the firm shift compensations toward retention, leading to a higher level of effort regardless of
who performs the retention task. This is possible under delegation when the spoiling effect is sufficiently
large, such that acquisition becomes highly inefficient and retention becomes very effective in protecting
the firm’s long-term profit. In this case, the firm rebalances the two tasks to adjust to the more expensive
tasks and indeed more is allocated toward retention. However, when the spoiling effect is not as
overwhelming, and such an adjustment is mild, the total reduction of compensations allocated to both
tasks, due to the higher marginal costs of the tasks with the spoiling effect, dominates the adjustment of
compensation allocation between the tasks and the optimal retention effort can be lower. The ability of
the firm to make such adjustment under delegation is a result from the role of the multitasking
representative to coordinate the conflicting tasks and absorb the negative effect of the conflict, which,
when the spoiling effect is intense, may have a significant impact on firm profit.
Given the above discussion, the role of the spoiling effect in the total compensations committed to the
acquisition and retention tasks and the allocation of compensations between the tasks that has direct
implications to firm profit. How this role differs between direct selling and delegation is critical in
understanding the impact of the spoiling effect on the firm’s profit under direct selling and delegation.
Under delegation, the firm pays a risk premium to the risk-averse representative for the acquisition
task, which is performed by the representative under delegation. With the more expensive acquisition, the
firm reduces its corresponding compensation leading to a lower acquisition effort. When the tasks are
12
independent, delegating acquisition to the representative only causes acquisition activities, which are
separate from retention activities, to be carried out differently to account for the risk-averseness of the
customer representative. The unchanged retention effort under delegation is very much expected, due to
the independence between the two tasks. The allocation of compensations by the firm between the tasks
remains the same under direct selling and delegation, and the reduction in acquisition effort is entirely the
result from the increase in acquisition cost due to the risk premium the firm has to pay under delegation.
With the spoiling effect, however, acquisition task becomes even more expensive under delegation,
because of the additional risk premium to induce the task as well as the negative effect of acquisition on
retention. More importantly, the balance in compensations allocated to acquisition and retention is
different under the spoiling effect, as the firm is less efficient in inducing acquisition effort than retention
under delegation. When is sufficiently large, the acquisition effort becomes so expensive to the firm
that it is more efficient for the firm to increase compensations allocated to retention to balance the
reduced acquisition effort. However, when is sufficiently small, the retention effort may be greater
under direct selling than that under delegation, which is consistent with the findings in Campbell and Frei
(2010) that the use of online banking, which is a form of direct selling, is associated with greater
retention.
This shift of balance between acquisition and retention under delegation and with the spoiling effect
helps establish our main result—the impact of λ on firm profit, which is summarized as the following.
PROPOSITION 1. The firm profit under direct selling is higher than that under delegation without the
spoiling effect ( 0 ). However, the firm profit under delegation is higher than that under direct selling
when the spoiling effect is present ( > 0) and sufficiently large.
When the tasks are independent (i.e., no spoiling effect), the firm prefers direct selling to delegation.
With both tasks performed by the risk-averse customer representative under delegation, the firm is less
efficient overall due to the higher compensation required to induce the best acquisition effort. Under
direct selling, however, the risk neutral firm faces only the single-tasked customer representative, while
enjoying the leverage of controlling the acquisition effort. Therefore, the firm loses in transferring
customer acquisition to the representative under delegation because of the risk premium required by the
representative to perform the additional task. Combining the independent tasks of acquisition and
retention under delegation, the representative gains little in efficiency against the higher total risk
premium. As a result, the firm has a lower profit under delegation due to both the loss in control of the
acquisition effort and the associated risk premium necessary to induce the effort. This finding is in line
13
with marketing and economic literature of delegation (Bhardwaj 2001; Joseph 2001; Lal 1986; Mishra
and Prasad 2004, 2005).
Surprisingly, for > 0 the firm may prefer delegation to direct selling. The negative effect of
acquisition on retention reduces the optimal acquisition effort under both direct selling and delegation, but
the spoiling effect impacts the retention effort differently under direct selling and delegation when > 0
(Lemma 1). Furthermore, as discussed above, when is sufficiently large, retention effort under
delegation becomes greater than it is under direct selling. This indicates that the relationship between
acquisition and retention under direct selling is fundamentally different from that under delegation, and
this difference may allow the firm to actually gain from delegation. From a theoretical point of view, the
firm and the customer representative make effort in a double moral hazard fashion under direct selling,
while the firm contracts with the representative as a multitasking agent who could coordinate the two
tasks under delegation. Therefore both direct selling and delegation represent a second best solution for
the firm.12
The firm assumes control of acquisition under direct selling but the balance between the tasks
is not coordinated; whereas under delegation, the firm pays a higher cost for acquisition when losing the
control but may benefit from the representative’s ability to coordinate the tasks.
More specifically, when the tasks are independent, = 0, delegating the acquisition task has little
direct impact on the retention task, and therefore the risk-neutral firm only needs to trade off between
efficiency loss to the double moral hazard scheme (under direct selling) and loss of control plus added
risk premium to the risk-averse representative for customer acquisition (under delegation). Direct selling
dominates because of the firm’s risk neutrality that limits the loss to moral hazard. When the tasks are
conflicting, > 0, however, the tradeoff in acquisition is spilled over to retention. Under direct selling,
since inducing retention effort is relatively more expensive with the risk premium, compared with
acquisition effort, the firm may expend more effort directly into acquisition, leading to less effective
customer retention due to the effect of . Under delegation, the role of is neutralized to a certain degree
by the customer representative, who could better allocate resources between the tasks to optimize the
efforts since both tasks are under the control of the representative. The representative may not expend the
acquisition effort to the level the firm would under direct selling, because some of the acquisition benefits
will be offset by the reduction in retention due to the spoiling effect. Under delegation, the tradeoff
between the added risk premium in inducing acquisition effort and the efficiency gains from coordination
of the two tasks determines whether the firm benefits from delegation. This result contributes to the
marketing literature by identifying an important benefit of task delegation with multitasking agents; that
12
We thank an anonymous reviewer for this point.
14
is, the coordination of conflicting tasks could minimize the negative effect from the conflict, leading to
better firm performance.
While the spoiling effect of customer acquisition, , is the same between direct selling and delegation
as assumed in this research, it is possible that the spoiling effect is greater under delegation, because the
multitasking representative is the focal point of customer encounter. In such cases, the benefit from the
coordination between customer acquisition and retention under delegation may be reduced by the
increased negative spoiling effect under delegation.
In the next section, we extend our base model to study a problem that involves an alternative way to
acquire new customers through promotions and the likely antagonism effect from the existing customers.
3.2. Model Extension: Promotions and Customer Antagonism
Although long-term pricing decisions are usually outside the responsibilities of CRM programs, firms
routinely use short-term price promotions to acquire new customers (Anderson and Simester 2004, 2010;
Farquhar and Panther 2008). Price promotions may be effective in attracting price conscious customers
but may also have a negative effect on the existing customers who are not covered by the promotions—an
effect called Customer Antagonism (Anderson and Simester 2010). The role of promotions, in acquiring
new customers and discouraging existing customers, resembles that of the spoiling effect, except that the
decision authority of promotions is controlled by the firm and is not delegated. In this section, we extend
our model to include promotions and the customer antagonism with acquisition and retention tasks. Our
focus remains on the comparison in firm profits between direct selling and delegation of acquisition.
Define z as the price promotion for the firm to acquire customers. The new demand becomes
A a aD e z , where > 0 measures the customer reaction to the promotion. Further denote > 0,
which captures the customer antagonism effect (i.e., the negative effect of price promotion on customer
retention) (Anderson and Simester 2010). In addition, it is assumed that > , meaning that the price
promotion z has a larger positive effect on acquiring new customers than its antagonism effect on
retaining existing customers. Therefore, we have ( )R r a rD e e z .
Most of our base models remain the same, except that the firm’s profit functions are modified to
incorporate the promotion and its antagonism effect on retention:
21( )( ) ( ) [ ( )]
2
DS
a r a r a r aE p z e z lp e e z kc e e e z
( )( ) ( ) [ ( ) ( )]DL
a r a a r aE p z e z lp e e z e z e e z . (8)
15
The first term of the equations is the revenue from the newly acquired customers, with a reduced margin
due to the promotion. The second term is the long-term value from the retained customers, after
accounting for the spoiling effect and the antagonism effect of the promotion. The rest of the profit
functions are the same as in the base model. Note that the long-term value of retained customer does not
reflect the short-term promotion. This is because the promotion is applied only to the new customers who
understand that this promotion does not have a long lasting effect to their future purchases.
We first analyze how promotions and customer antagonism affect acquisition and retention efforts for
any 0.
COROLLARY 1. When the firm uses promotions, the acquisition effort is higher with customer antagonism
( > 0) than that without antagonism ( = 0) under both direct selling and delegation. The retention
effort is the same under direct selling with and without customer antagonism, but is lower with customer
antagonism under delegation.
Since promotions can be used alongside the acquisition task and the customer antagonism negatively
affects retention as does the spoiling effect, promotions can function as a substitute to the acquisition
effort. When the customer antagonism is present, promotions become less efficient compared to the
acquisition effort due to the negative effect of the antagonism to retention. Increasing acquisition effort to
balance the promotions and the antagonism, even with the spoiling effect, allows coordination between
these two ways of generating new customers. This coordination between promotions and customer
acquisition is fully capitalized by the firm under direct selling because the firm internalizes and controls
both promotions and customer acquisition task. As a result, the customer antagonism has little impact on
the optimal effort level in customer acquisition—the negative effect of promotions is completely absorbed
by the increase in customer acquisition task. However, under delegation, the representative’s ability to
coordinate acquisition and retention tasks enables the representative to make a quick adjustment to the
antagonism effect of promotions, that is, to lower retention effort while increasing acquisition effort.
In order to examine the robustness of our main result (Proposition 1), we next consider the impact of
promotion z on the firm’s profit under direct selling and delegation when promotions are used. We first
consider the case where the spoiling effect is absent ( = 0), which focuses on the effect of promotions
and the related antagonism without spoiling effect. We then consider the general case where the spoiling
effect is present ( > 0), which combines both the effect of promotions and antagonism and the spoiling
effect. The following corollary summarizes the results.
COROLLARY 2. When the firm uses promotions in the absence of the spoiling effect ( = 0), its profit is
higher under direct selling than that under delegation, regardless of customer antagonism ( > 0).
16
However, when the firm uses promotions in the presence of the spoiling effect ( > 0), its profit may be
higher under delegation than that under direct selling.
The results show that using promotions with the acquisition task but without the spoiling effect does
not change the firm’s preference of direct selling to delegation. More importantly, the firm prefers direct
selling even when customer antagonism of the promotion exists. This result indicates that promotions
provide an alternative to customer acquisition, and customer antagonism creates a negative impact on
customer retention, similar to the spoiling effect. However, this alternative way of generating new
customers does not change how the customer acquisition task interacts with the retention task. The firm’s
choice between direct selling and delegation still depends on the spoiling effect that directly connects the
tasks. When the tasks are independent, promotions, as effective as they are in generating new customers,
do not change the firm’s choice of direct selling, with or without customer antagonism. This result is
consistent with the main finding in Proposition 1.
When promotions are used with antagonism and spoiling effects, the comparison between firm profit
under direct selling and delegation is more complicated. The result depends on the effectiveness of the
promotions in generating new customers, the intensity of the customer antagonism, and the degree of the
spoiling effect. However, since the addition of promotions and the existence of customer antagonism do
not change the ability of the multitasking representative to coordinate conflicting acquisition and retention
tasks, the fundamental tradeoff between the benefit from the coordination and the higher risk premium
due to the delegation of the acquisition task remains unchanged. This shows that our main results with
regard to the firm’s choice between direct selling and delegation with spoiling effect are robust when
promotions are included as another measure to acquire new customers, and with negative effect on
retention due to customer antagonism.
Although adding promotions and customer antagonism to the model does not change our main
results, this is not to suggest that promotions and customer antagonism have no impact on the comparison
between firm profit under direct selling and delegation. In fact, in this case the condition under which the
firm may prefer delegation for a higher level of profit is different. Specifically, when promotions and
customer antagonism are not considered, the firm prefers delegation when λ is sufficiently large such that
1 – λl is sufficiently small. However, when promotions and the customer antagonism are included, the
effectiveness of the promotions (φ) and the intensity of the customer antagonism (η) may both be so
strong that controlling and managing both promotions and acquisition effort under direct selling provides
a different type of coordination whose value may outweigh the value from coordinating the two tasks
under delegation. Therefore, for the firm to have a higher profit under delegation, not only does the
17
spoiling effect have to be sufficiently large, but the effects of promotions and customer antagonism need
to be at a level such that the benefit from coordination of the two tasks still dominates.
4. Conclusion
Most of the previous research on customer acquisition and customer retention has studied acquisition and
retention as independent tasks (Hauser et al. 1994; Joseph and Thevaranjan 1998) or has been of an
empirical nature (Reinartz et al. 2005; Schweidel, et al. 2008a, 2008b; Thomas 2001), while recognizing
that customer acquisition and customer retention can be related in different ways (Blattberg and Deighton
1996; Hauser et al. 1994; Venkatesan and Kumar 2004). In addition, although customer acquisition and
retention activities are sometimes both performed by customer representatives who interact directly with
customers, customer acquisition may be centralized at the firm level in a direct selling fashion. Thus,
customer acquisition and retention are sometimes conflicting to each other — increasing one may lead to
lower performance of the other — and such conflicts are further complicated by who performs the tasks,
the firm or the representative. Different interests and incentives by customer representatives and firms
make managing customer acquisition and retention complicated and challenging.
However, it remains unclear in the marketing literature how firms should structure their sales force
and efficiently allocate incentives to carry out customer acquisition and retention based on the interactions
between both activities. Specifically, how does the spoiling effect of customer acquisition affect firm
decisions and performance? Should a firm centralize its acquisition or delegate it to a multitasking
customer representative? And does the spoiling effect have any impact on the firm’s such choice? These
are significant questions to marketing researchers as well as practitioners. Our research investigates these
issues by applying a principal-agent framework that allows for direct interactions between customer
acquisition and retention and by modeling two commonly used governance schemes, direct selling and
delegation of customer acquisition. We also extend our model to examine promotions and customer
antagonism and their effects on firm profit under direct selling and delegation.
We find that the interdependency between customer acquisition and customer retention has
significant impacts on the incentive contracts and the corresponding decisions in acquisition and retention
efforts. The nature and degree of this interdependency determine the firm’s choice between keeping
acquisition in house (i.e., direct selling) or delegating it to customer representatives. When the
acquisition and retention tasks are independent, the firm chooses direct selling by controlling its customer
acquisition program. When the acquisition effort has a spoiling effect on the outcome of customer
retention, the firm may prefer delegation. In addition, the presence of the spoiling effect reduces
acquisition effort and leads to a lower level of effort under delegation than under direct selling. However,
18
the reduction of acquisition effort does not necessarily translate to an increase in retention effort; rather
the spoiling effect may also reduce the optimal retention effort under both direct selling and delegation.
Interestingly, retention effort is the same under direct selling as under delegation when the tasks are
independent, but it may be higher under delegation than under direct selling when the spoiling effect
exists.
By extending the model and analysis to include promotions and customer antagonism, we find that,
despite the similarity of the customer antagonism to the spoiling effect, using promotions without the
spoiling effect, regardless of customer antagonism, does not alter the firm’s preference to favor direct
selling. This suggests that using promotions when the spoiling effect is absent, with or without customer
antagonism, does not lead the firm to choose delegation. In other words, the firm prefers direct selling
when the spoiling effect is not present regardless of customer antagonism effect, but may prefer
delegation only when the spoiling effect is present. This interesting result indicates that the key role of
the spoiling effect in determining the firm’s preference between direct selling and delegation is consistent
with or without the introduction of promotions.
Our results have important managerial implications to customer relationship managers. Marketing
managers should recognize and understand the existence of the spoiling effect between customer
acquisition and retention, thus taking it into their decision making process. The existence of the spoiling
effect poses a challenge to maintaining a balance in marketing resources allocated to compensate between
customer acquisition and retention. As it may be a first response to move marketing dollars away from
acquisition toward retention, our results show that it is best to reduce marketing spending in both areas in
response to the spoiling effect. In the cases where such effect is severe, delegation of acquisition to the
customer representative may actually increase retention effort than under direct selling. More
importantly, the spoiling effect directly influences the firm’s design strategy in sales force and customer
services. When the spoiling effect is nonexistent, the firm should use a direct selling approach to control
the acquisition task; whereas, when such effect is sufficiently strong, the firm should delegate the
acquisition task to the customer representative to benefit from the coordination of the acquisition and
retention tasks. Our extended results also indicate that the existence of customer antagonism from
promotions does not change the firm’s preference to use direct selling in the absence of the spoiling
effect. However, the firm may prefer delegation when the spoiling effect exists.
This research has several limitations that can be addressed in future research. First, the effects of
customer acquisition and customer retention can be studied under competitive conditions (McGahan and
Ghemawat 1994; Villanueva et al. 2007). For example, Villanueva et al. (2007) indicate that price
competition may shift the long-term focus of customer value to a period-by-period basis in managing
19
CRM programs. The model could therefore be extended to include competing firms—such that decisions
on customer acquisition and retention are determined strategically in a competitive context.
Second, the model assumes the same cost efficiency for direct selling and delegation. We made such
an assumption in order to directly compare the efficiency between the two governance frameworks
beyond cost efficiency. Relaxing the assumption, however, may allow the model to capture a wider range
of acquisition and retention activities. In addition, the tasks of customer acquisition and retention are
assumed technologically independent to each other. That is, increasing one task does not increase or
decrease the marginal cost of the other task. Allowing technologically dependent tasks, which
significantly increases the complexity of the problem, may create additional insight of this research.
Third, as discussed, the model can be extended to a multi-period or repetitive model of decisions of
customer acquisition and retention to further examine the dynamic aspects of such decisions. By doing
so, retention effort can also be extended to cover newly acquired customers.
Fourth, the current model analyzes the optimal effort allocation for customer acquisition and
retention, assuming a given governance framework, direct selling or delegation. Although it makes sense
to consider a fixed governance framework since the decision on direct selling or delegation is usually a
long-term strategic decision for firms, endogenizing such a decision may provide additional insights. It is
also important to recognize that, although the main issues discussed in this research apply to many
industries, they are not necessarily universal—there might be industries where no spoiling or customer
antagonism effects exist. In these industries, as our results indicate, direct selling outperforms delegation
of customer acquisition. All of these issues are worthy of deliberate considerations for marketing
managers, and we leave the analyses of these issues for future research.
20
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1
When Acquisition Spoils Retention: Direct Selling vs. Delegation under CRM
Online Technical Appendix
The Technical Appendix is organized in the following way. We construct our base model with
only the spoiling effect of customer acquisition. We derive and prove our main results for the
cases of direct selling and delegation. We then extend the base model by adding promotions and
customer antagonism. We examine the additional results and present the proofs of the corollaries.
The Base Model with the Spoiling Effect: The Main Results
Direct Selling
Under direct selling, the firm solves a double moral hazard problem as follows:
21( ) [ ( )]
2a r a r a r aMax E pe lp e e kc e e e
subject to:
IC(A): ( ) arg max[ ( ( , )]r
r a re
e E U e e
2 2 21
argmax ( )2 2
r
r a r r re
re e c e
IC(P): ( ) arg max[ ( , )]a
a a re
e E e e
= 21
arg max ( ) [ ( )]2
a
a r a r a r ae
pe lp e e kc e e e
IR: [ ( , )] 0a rE U e e .
Although two tasks are involved, only customer retention is performed by the agent. We have
2 2 21( )
2 2r a r r r
rCE e e c e , and solving for re leads to
r
r
ec
. Similarly,
solving IC(P) leads to ( )
a
r
p lpe
kc
. Given the optimal efforts as functions of , the firm’s
profit function becomes:
2 22 2( )1 1
[ (1 )]2 2
r r
r r r
p lp lpMax E k c r
kc c kc
.
2
The first order condition (FOC) leads to 2 2(1 ) 0r rklp k c r . The optimal retention
compensation, , is solved as 2 2( )
DS
r r
klp
k kc r
< lp. The optimal efforts can then be
solved accordingly and are given by:
2 2( )
DSDS
r
r r r r
klpe
c c k kc r
,
2 2( )
DS
a
r r r r
p lp lpe
kc c k kc r
.
For the retention rate to satisfy
2 2 2 2
2 2
( )( )1
( )
DS DS r rr a
r r r
k lp k p p lp kc re e
kc k kc r
, a
sufficient condition is 2
1(1 )
DS DS
r a
r r r
lpe e
c c r
when = 0. That is, the long-term
customer value is sufficiently small so that 2(1 )r r rlp c c r . Similarly, when = 1, the
retention rate is greater than zero when
2
2
( ) ( )(1 )0
(1 )
DS DS r rr a
r r r
k klp p p lp kc re e
kc k kc r
.
Given 1k , a sufficient condition of 2( ) ( )(1 ) 0r rk klp p p lp kc r , or
2( ) ( )(1 ) 0r rk klp p lp p kc r , is given by 1l . The optimal profit can be shown as
2 2
2 2
( ) ( )1 1 1
2 2 ( )
DS
r r r r
p lp k lpE
kc c k kc r
. When 0 , we have:
2 2
2
( )1 1 1
2 2 1
DS
r r r r
p lpE
kc c c r
,
DS
a
r
pe
kc and
2(1 )
DS
r
r r r
lpe
c c r
.
Delegation
Now we consider the scenario of delegation. Under delegation, the firm solves a problem as
follows:
,max ( ) [ ( )]a r a a r aE pe lp e e e e e
Subject to
IC: ,
( , ) arg max( ( , ))a r
a r a re e
e e U e e
3
IR: ( , ) 0a rU e e .
We have 2 2 2 2 2 21 1
( ) ( )2 2 2
a r a r a r r a r
rCE e e e kc e c e . Solving IC for
' ( , )a re e e leads to a
r
ekc
and
r
r
ec
. The firm’s optimization problem is given by:
2 2 2 2 2 2
,
1 1max ( ) ( )
2 2 2a r a r a r r a r
rE pe lp e e kc e c e
.
Solving the problem, we have the following FOCs:
21{ (1 ) ( )} 0r a
r
kc r p lpkc
,
2 2 21{ [ (1 )] ( )} 0r r
r
k c r p lp kkc
.
Or,
2
22 2
2 2 2 2
( )(1 )
( )[ (1 )]
(1 )(1 ) 0
r a
r r
r r r a r a
p lpkc r
p lp kk c r
H k c r kc r kc r
.
When 0 , we have 2 2(1 )(1 )r r r aH k c r kc r . The optimal
DL and DL are solved in
closed form as follows:
2[ ( ) ]DL
r r
kp p lp c r
H ,
2 2[ (1 ) ( ) ]DL
r a r a
klp kc r p lp c r
H .
When 0 , we have 2(1 )
DL
r a
p
kc r
and
2(1 )
DL
r r
lp
c r
. The optimal efforts can be
derived accordingly as follows:
2 2 2 2(1 ) ( ) ( )DL r a r r aa
r
p lp kc r p lp c r re
c H
,
2 2{ (1 ) ( ) }DL
r r a r a
r
ke lp kc r p lp c r
c H .
When 0 , we have 2(1 )
DL
a
r r a
pe
kc kc r
and
2(1 )
DL
r
r r r
lpe
c c r
.
Given the results above, we now proceed to provide proofs of the lemma, proposition and
corollaries in the paper.
4
LEMMA 1. The spoiling effect of acquisition on retention ( > 0) reduces the acquisition and
retention efforts under direct selling. It reduces the acquisition effort and may reduce (increase)
the retention effort when λ is sufficiently small (large) under delegation.
Proof of Lemma 1. Comparing the optimal efforts for = 0 and > 0 under direct selling, we
have:
( 0) ( 0)DS DS
a ae e 2 2
2 2 2 2
( )0
( ) ( )
r r
r r r r r r r r
lp kc rp lp lp p
kc c k kc r kc kc k kc r
,
( 0) ( 0) 0DS DS
r re e .
Comparing the optimal efforts for = 0 and > 0 under delegation, we have:
2 2 2 2 2( 0) ( 0) {(1 )[ (1 ) ( )]} 0DL DL ra a r a r a r r r a
kce e kc r lp kc r lp c r c r
H
,
2 2[ ( ) ]( 0) ( 0)DL DL r r r a
a a
r
p p lp c r c re e
c H
.
We thus have ( 0) ( 0) 0DL DL
a ae e if 2( ) 0r rp p lp c r , or
2
21
1
r r
r r
c rl
c r
.
This is satisfied for 1l , or when λ is sufficiently small. Q.E.D.
PROPOSITION 1. The firm profit under direct selling is higher than that under delegation without
the spoiling effect ( 0 ). However, the firm profit under delegation is higher than that under
direct selling when the spoiling effect is present ( > 0) and sufficiently large.
Proof of Proposition 1. The optimal profit under delegation can be shown as
2 2 2 2 2 21 1( ) ( )
2 2 2
DL
a r a r a r r a r
rE pe lp e e kc e c e
2 2 2 2
2 2 2 2
( ) (1 ) ( ) [ ( )][ (1 ) ( ) ]1 1
2 (1 ) [ (1 )]
r r r a r a
r r r r a r r
p lp c r lp p lp lpk p lp lp kc r p lp c r
kc c r c r k c r
When 0 , we have
2 2
2 2
( )1 1[ ]
2 1 1
DL
r r a r r
p k lpE
kc kc r c r
.
Under direct selling, the optimal profit of the firm is given by:
2 2
2 2
( ) ( )1 1 1
2 2 ( )
DS
r r r r
p lp k lpE
kc c k kc r
.
5
When 0 , we have
2 2
2
( )1 1[ ]
2 1
DS
r r r
p lpE
c k c r
. Therefore, for 0 , we have
DL DSE E .
When 0 , the optimal profit under delegation can be rewritten as
2 2 2 22
2 2 2 2
( ) (1 ) ( ) [( )(1 ) 2 ]1 1 1 1( )
2 2 (1 ) [ (1 )]
DL r a r a r r
r r r r r a r r
lp kc r p lp c r p lp c r lpE p lp
kc c c r c r k c r
.
Since
2 2
2 2
( ) ( )1 1 1
2 2 ( )
DS
r r r r
p lp k lpE
kc c k kc r
, the sign of the profit comparison
between delegation and direct selling is same as the sign of the following term:
2 2 2 2 2
2 2 2 2 2 2
2 2 2 2 2 2
2 2 2 2
( ) (1 ) ( ) [( )(1 ) 2 ] ( )
(1 ) [ (1 )] ( )
( ) ( ) [( )(1 ) 2 ]( )
{(1 ) [ (1
r a r a r r
r r r a r r r r
r a r r r r
r r r a r r
lp kc r p lp c r p lp c r lp k lp
c r c r k c r k kc r
lp p lp c r p lp c r lp k kc r
c r c r k c r
2 2)]}( )r rk kc r
When (1 )p l is sufficiently small, or when and l are sufficiently large, the term above is
positive, i.e., delegation can be more profitable than direct selling, or DL DSE E . Q.E.D.
Promotions and Consumer Antagonism: Extension
We first consider the case of 0 , i.e., there is no spoiling effect of acquisition, and derive the
results for 0 . Based on such analysis, we show the proofs of both corollaries. When 0 ,
we have the following analysis.
Under direct selling, the firm solves a double moral hazard problem as follows:
21( )( ) ( ) [ ( )]
2,a r r a rMax E p z e z lp e z kc e e z
z
subject to:
IC(A): ( ) arg max[ ( ( , )]r
r a re
e E U e e
2 2 21
argmax ( )2 2
r
r r r re
re z c e
IC(P): ( ) arg max[ ( , )]a
a a re
e E e e
= 21
arg max( )( ) ( ) [ ( )]2
a
a r r a re
p z e z lp e z kc e e z
6
IR: [ ( , )] 0a rE U e e .
Again, r
r
ec
and
a
r
p ze
kc
; and therefore we have profit for the firm:
2 2 2 21 1( )( ) ( )
2 2 2a r r a r r r
rE p z e z lp e z kc e c e .
Solving the FOCs leads to:
21( ) 0r r
r
lp c rc
,
2( )(1 ) ( ) 0r r rp z kc kc p p z lp kc .
21
DS
r r
lp
c r
, and
( )
2 1
DS r
r
p l kcp z
kc
, or
[ ( ) 1]
(2 1)
DS r
r
p kc lz
kc
(Note: for 0,p z 2 1 0rkc )
( )
2 1
DS
a
r
p le
kc
, and
2(1 )
DS
r
r r r
lpe
c c r
.
2 2 21 1 1[( )( ) ( ) (1 )]
2 2
DS
r r r r
r
E p z p z kc z klp kc lp z p z k c rkc
2 22
2
( )1 1{ }
2 (2 1) 2 (1 )
r
r r r r
kc l lp l
kc c c r
Under delegation: the firm solves a problem as follows:
, ,max ( )( ) ( ) [ ( ) ( )]a r a r
zE p z e z lp e z e z e z
Subject to
IC: ,
( , ) arg max( ( , ))a r
a r a re e
e e U e e
IR: ( , ) 0a rU e e .
We have 2 2 2 2 2 21 1
( ) ( ) ( )2 2 2
a r r a r r a r
rCE e z e z kc e c e . Solving
for efforts leads to a
r
ekc
and
r
r
ec
. The profit function is then given by:
2 2 2 2 2 2
, ,
1 1 1max [( )( ) ( ) ( )]
2 2 2r r r a r
zr
rE p z kc z lp k kc z k kc
kc
7
The FOCs are given by:
2( ) (1 ) 0r ap z kc r ,
2(1 ) 0r rklp k c r ,
2 ( ) 0r rkc z pkc l ,
2
2
2 2
(1 ) 0 1
0 (1 ) 0
1 0 2 ( )
(1 )[2 (1 ) 1]
r a
r r
r r
r r r r a
kc r p
k c r klp
kc z pkc l
H k c r kc kc r
,
0,H because 22 (1 ) 1 0r r akc kc r .
Solving the F.O.C.s leads to:
2
2
( )(1 )
2 (1 ) 1
DL r r a
r r a
pkc l kc rp z
kc kc r
, or
2
2
[1 ( )(1 )]
[1 2 (1 )]
DL r r a
r r a
p kc l kc rz
kc kc r
,
2
( )
2 (1 ) 1
DL r
r r a
pkc l
kc kc r
, and
2(1 )
DL
r r
lp
c r
.
The firm’s profit function is thus given by:
2 2 2 2 2 2
2 2 22
2 2
1 1 1[( )( ) ( ) ( )]
2 2 2
( ) (1 )1 1{ }
2 2 (1 ) 1 2 (1 )
DL
r r r a r
r
r r a
r r a r r r
rE p z kc z lp k kc z k kc
kc
kc l kc r lp l
kc kc r c c r
.
Now we consider the case where 0 . For 0 , the retention demand becomes
r ae e z . Following the above process, we solve the problems as follows.
Under direct selling, the solutions are given by:
2 2
DS
r r
kpl
k kc r
,
[ ( ) ]
2 1
DS r
r
p kc l lp z
kc
.
And optimal efforts can be solved accordingly:
8
2 2( )
DS
r
r r r
kple
c k kc r
,
2 2
[( ) 2 ]
2 1 ( )
DS
a
r r r r
p l l ple
kc c k kc r
.
The optimal profit can be shown as
2 2 2 22
2 2
[ ( ) ]1 1{ }
2 (2 1) 2 ( ) 2
DS r
r r r r r r
kc l l kl lE p l
kc kc c k kc r kc
.
Under delegation, the analysis leads to:
32 2 2
2 2
{ (1 )( ) (1 ) (1 )
[ ( )]}
DL rr r r r a r r
a r r r
pkcp z c r l kc kc r l c r
H
r c kc l kc k
,
32 2 2{ (1 )( ) [ (1 ) (2 1) ]}DL r
r r r r r r r r
pkcc r l kc l c r kc lc r
H ,
32 2 2{ [2 (1 ) 1] [ ( 2 )]}DL r
r r a r a
pkcl kc kc r kc r l
H ,
32 2 2{(1 )[2 ( )] [2 ( ) ( )] }DL r
a r r r a
pkce c r l l l k l c r
H , and
22 2 2{ [2 (1 ) 1] [ ( 2 )]}DL r
r r r a r a
pkce l kc kc r kc r l
H .
We have 3 2 2 2 2{(1 )[2 (1 ) 1] (2 1)} 0r r r r r a r a rH kc c r kc kc r c r kc and the
profit is given by:
2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2
2 2 2
{( 2 )[(1 )(1 ) ] }1
2 [(1 )(1 ) ]{(2 1)[(1 )(1 ) ] (1 )}
{2 [( )][(1 )(1 )1
2
DL r a r r r a a
r a r r r a r r r r a r a r a r r
r r a r r
p l l kc r c r c r l rE
kc r c r c r kc c r kc r c r kc r c r
p c l l l kc r c r
2 2 2 22
2 2 2 2
] (1 )}
[(1 )(1 ) ]
r a r a
r r r r a r a
c r l kc rl p
c c r kc r c r
.
Based on the analyses, we prove both corollaries as follows.
COROLLARY 1. When the firm uses promotions, the acquisition effort is higher with customer
antagonism ( > 0) than that without antagonism ( = 0) under both direct selling and
delegation. The retention effort is the same under direct selling with and without customer
antagonism, but is lower with customer antagonism under delegation.
Proof of Corollary 1. We first consider the comparison of acquisition efforts. The acquisition
efforts are given by:
9
2 2
[( ) 2 ]
2 1 ( )
DS
a
r r r r
p l l ple
kc c k kc r
, and
32 2 2{(1 )[2 ( )] [2 ( ) ( )] }DL r
a r r r a
pkce c r l l l k l c r
H .
It is easy to show that both efforts are increasing in η. Therefore, for 0 , the acquisition effort
is greater than that for 0 , under both direct selling and delegation.
Now consider the comparison of retention efforts. The effort under direct selling is given by
2 2( )
DS
r
r r r
kple
c k kc r
, which does not contain η. That is, the retention effort is the same
regardless of η under direct selling. The retention effort under delegation is given by:
22 2 2{ [2 (1 ) 1] [ ( 2 )]}DL r
r r r a r a
pkce l kc kc r kc r l
H , which is decreasing in η.
That is, for 0 , the retention effort is less than that of 0 under delegation. Q.E.D.
COROLLARY 2. When the firm uses promotions in the absence of the spoiling effect ( = 0), its
profit is higher under direct selling than that under delegation, regardless of customer
antagonism ( > 0). However, when the firm uses promotions in the presence of the spoiling
effect ( > 0), its profit may be higher under delegation than that under direct selling.
Proof of Corollary 2. First, when 0 , the firm’s profit under direct selling is given by:
2 22
2
( )1 1{ }
2 (2 1) 2 (1 )
DS r
r r r r
kc l lE p l
kc c c r
.
When 0 , or there is no consumer antagonism, the firm’s profits are given by:
2 2 2
2{ }
2 (2 1) (1 )
DS r
r r r r
p kc lE
kc c c r
, and
2 22 2
2 2
[ (1 )]{ }
2 [2 (1 ) 1] (1 )
DL r r a
r r a r r r
kc kc rp lE
kc kc r c c r
2 2 2
2
2
{ }12 (1 )[2 ]
(1 )
r
r r rr
r a
p kc l
c c rkckc r
.
Clearly, it is easy to show that DL DSE E .
10
When 0 , rewrite the optimal profit under delegation:
2 22
2
2
( )1 1{ }
12 2 (1 )2
(1 )
DL r
r r rr
r a
kc l lE p l
c c rkc
kc r
DSE .
The same result as 0 is retained. This is different from the impact of the spoiling effect
when the firm may be better off with delegation.
Now consider the case where 0 . We have the firm’s profits as:
2 2 2 22
2 2
[ ( ) ]1 1{ }
2 (2 1) 2 ( ) 2
DS r
r r r r r r
kc l l kl lE p l
kc kc c k kc r kc
and
2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2
2 2 2
{( 2 )[(1 )(1 ) ] }1
2 [(1 )(1 ) ]{(2 1)[(1 )(1 ) ] (1 )}
{2 [( )][(1 )(1 )1
2
DL r a r r r a a
r a r r r a r r r r a r a r a r r
r r a r r
p l l kc r c r c r l rE
kc r c r c r kc c r kc r c r kc r c r
p c l l l kc r c r
2 2 2 22
2 2 2 2
] (1 )}
[(1 )(1 ) ]
r a r a
r r r r a r a
c r l kc rl p
c c r kc r c r
.
Note that 2 2 2 2 2 2 2 2(1 )(1 ) (1 ) ( )r r r a r a r r r r r ac r kc r c r c r k kc r c r . Let’s
first look at the first term in the profits. If λ is large enough, such that ( ) 0rkc l l , or λ
is sufficiently large, the first term in the profit function under direct selling is zero. Since
2 (2 1)( )rl l kc l , the first term under delegation becomes
2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2
1 {(2 1)( )[(1 )(1 ) ] }
2 [(1 )(1 ) ]{(2 1)[(1 )(1 ) ] (1 )}
r r a r r r a a
r a r r r a r r r r a r a r a r r
p kc l kc r c r c r l r
kc r c r c r kc c r kc r c r kc r c r
,
which is greater than zero.
Now comparing the 2nd
terms, we have
2 2 2 2 2 2 2
2 2 2 2
2 2 2 2 2
2 2
1 {2 [( )][(1 )(1 ) ] (1 )}
2 [(1 )(1 ) ]
1 1
2 2 ( )
r r a r r r a r a
r r r r a r a
r r r r
p c l l l kc r c r c r l kc r
c c r kc r c r
p l kp l
kc c k kc r
2
2 2 2
2 2 2 2 2 2
1 [2 ( ) ]
2
1
2 ( )[(1 ) ( ) ]
r
r
r r r r r r r r a
p l kc l l l
kc
p l
c k kc r c r k kc r c r
,
which can be written as
2
2 2 2 2 2 2
( ){ (2 1)}
2 ( )[(1 ) ( ) ]r
r r r r r r r a
p l l kkc
k kc r c r k kc r c r
.
11
When 2 1rbkc is sufficiently small, and/or λ and η, are sufficiently large, the second term of the
profit function is greater under delegation than it is under direct selling. Note that when 0 ,
the 2nd
terms are identical. Q.E.D.