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Cited by 48Customer churn and segmentationCustomer Service Quality and LoyaltyConsumer Market Behavior and Pricing

Moving from customer lifetime value to customer equity

Open access
Drèze, Xavier, Bonfrer, André·2009·Quantitative Marketing and Economics
DOI 10.1007/s11129-009-9067-y
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Abstract

We study the consequence of moving from Customer Lifetime Value maximization to Customer Equity maximization. Customer equity has traditionally been seen as the discounted sum of the lifetime earnings from all current and future customers and thus it has been largely assumed that maximizing customer lifetime value would lead to maximum customer equity. We show that the transition from CLV to CE is not that straightforward. Although the CLV model is appropriate for managing a single non-replaceable customer, the application of a CLV model to the acquisition and valuation of customers as an ongoing concern for the firm leads to sub-optimal customer relationship management and acquisition strategies. This leads the firm following a CLV maximization approach to have a smaller and less profitable customer base than one that follows a CE maximization strategy.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper argues that maximizing customer lifetime value (CLV) is not equivalent to maximizing customer equity (CE) and is sub-optimal for long-term firm profitability. Using a customer-equity model that treats customers as a renewable resource, it shows CE-maximizing firms communicate less frequently, retain more customers, and generate higher firm value than CLV-maximizing firms.

Key findings

  • CLV maximization is sub-optimal for long-term customer equity: the paper proves that maximizing CLV and CE lead to the same optimum only when the optimal inter-communication interval is zero, which cannot happen because database value is negative at \(t=0\).
  • In the synthetic comparison (Table 1), CE maximization yields a 13.33% larger optimal communication interval than CLV maximization (0.802 vs. 0.708), a 12.70% larger steady-state customer base (6.734 vs. 5.975), and a 2.19% higher value of the firm (135.898 vs. 132.989), despite a 0.92% lower CLV (8.623 vs. 8.703) and 11.76% fewer communications per year (1.247 vs. 1.413).
  • The optimal acquisition policy is to acquire customers as long as marginal acquisition cost per name is equal to the CLV of the name (Proposition 4), but the optimal communication interval depends on the acquisition rate, not acquisition cost (Lemma 2).
  • Comparative statics show that an increase in acquisition rate decreases optimal \(t^*\) and increases CE; an increase in discount rate increases \(t^*\) and decreases CE; an increase in fixed or variable costs decreases CE and increases \(t^*\).

Methods

  • Theoretical modeling paper: derives a customer equity model where customers are treated as a renewable resource, with contact periodicity \(t\) and acquisition spending as control variables, and retention and spending as functions of time between communications.
  • Uses Little’s Law to derive a steady-state database size \(S = \tau g / (1 - P(\tau))\) (Lemma 1), then derives first-order conditions and comparative statics for optimal \(t^*\) (Propositions 2–3e).
  • Includes a synthetic numerical example using quadratic acquisition costs \(AQ(g)=g^2\), exponential revenue recovery \(R(t)=r_0(1-e^{-r_1 t})\) with \(r_0=5\), \(r_1=10\), log-logistic retention with \(\alpha=2\), \(\lambda=3/4\), and a 20% annual discount rate, solved in Excel; also discusses robustness to observed and unobserved heterogeneity.

Limitations

  • Stated by the paper: assumptions about the relationship between customer retention and communication strategy, both timing and content, could be relaxed in future work; further work is needed to incorporate competitive actions and reactions into customer equity measurement.
  • Evident from the text: the main model assumes homogeneous customers for tractability, though Section 6 relaxes this for observed and unobserved heterogeneity; the synthetic example uses arbitrary functional forms chosen as simple, widely used expressions rather than empirically estimated ones.
  • Evident from the text: the analysis focuses on communication frequency and acquisition spending, not the full range of marketing actions such as pricing, package design, or advertising content.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1007/s11129-009-9067-y

Cites

30 of 30 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 6 cited sources checked · 0 supported · 0 flagged

  • Findingreasoning
    § 4.2 Change in expected profit per contact ( R ( t )) · p. 13

    An intercept-shift in revenue per contact leads to a decrease in t* when t* is small to moderate, and an increase in t* when it is large.

    “It also leads to a decrease in t * when t * is small to moderate, and an increase in t * when it is large.”
    Quote in the paperSubstantial claim
  • Findingreasoning
    § 3.1 Finding the optimal periodicity ( t *) · p. 11

    The optimal inter-communication interval (t*) is found when the sum of elasticities is equal to 0.

    “The optimal inter-communication interval ( t *) is found when the sum of elasticities is equal to 0.”
    Quote in the paperSubstantial claim
  • Findingreasoning
    § 2.3 Customer equity · p. 8

    Given an acquisition stream, the marketing actions that maximize CE depend on the rate of acquisition, but are separable from the cost of acquisition.

    “Lemma 2 Given an acquisition stream, the marketing actions that maximize CE depend on the rate of acquisition, but are separable from the cost of acquisition.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Acquisition expenses are an ongoing expenditure that the firm recognizes on a periodic basis (e.g., monthly) while communications expenses and revenues are recognized at the time of the communication.
    • The authors state this as an assumption: Acquisition efforts are constant over time and produce a steady stream of names; there is no free production of names and the cost of acquisition increases with the size of the name stream.
    • The authors state this as an assumption: Fixed and variable communications costs are constant across communications.
    • The authors state this as an assumption: Communications are identical in nature, if not in actual content, and customers' reaction to the communications depends only on their frequency, such that A_i(t)=A(t) and P_i(t)=P(t).
  • Findingreasoning
    § 2.3 Customer equity · p. 7

    For any given constant marketing actions, there exists a steady state such that the database is constant in size; the steady state size is S = t*g / (1 - P(t)).

    “Lemma 1 For any given constant marketing actions there exists a steady state such that the database is constant in size. The steady state size is S ¼ t : g 1 P t ð Þ :”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Acquisition efforts are constant over time and produce a steady stream of names; there is no free production of names and the cost of acquisition increases with the size of the name stream.
    • The authors state this as an assumption: Fixed and variable communications costs are constant across communications.
    • The authors state this as an assumption: Communications are identical in nature, if not in actual content, and customers' reaction to the communications depends only on their frequency, such that A_i(t)=A(t) and P_i(t)=P(t).
    • The authors state this as an assumption: A(t) is monotonically increasing in t, with A(0)=0 and A(∞) finite.
    • The authors state this as an assumption: P(t) is inverted-U shaped and dependent on A(t) such that ∂P(t)/∂A(t) > 0.
  • Findingnone given
    § 3 Customer equity and customer lifetime value · p. 10

    t* is always strictly greater than zero.

    “But, as we will show in the next section, t * is always strictly greater than zero.”
    Quote in the paperNot a substantial claim
  • May combine two claims. 31
  • Classified as probably not a substantial claim. 16
  • The quote only partly states this claim. 1

  • May combine two claims.

    Findingreasoning
    § 4.1 Change in retention rate ( P ( τ )) · p. 12

    A level-shift increase in retention leads to an increase in t* when t* is small, and a decrease in t* when it is large.

    “It also leads to an increase in t * when t * is small, and a decrease in t * when it is large.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: P(t) is inverted-U shaped: increasing at a decreasing rate for small t, then decreasing after some threshold.

  • May combine two claims.

    Findingreasoning
    § Proof See Appendix C. · p. 17

    Maximizing CE leads to a higher value of the firm (+2%) despite fewer opportunities to generate revenues (-12% contacts per year).

    “This leads to a higher value of the firm (+2%) despite the fewer opportunities to generate revenues (-12% contacts per year).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § 5 Acquisition policy · p. 15

    Acquisition spending is separable from the optimization of t, and only the acquisition rate matters for the derivation of the optimal intercommunication interval.

    “We were able to do this since Lemma 2 shows that the actual spending on name acquisition is separable from the optimization of t , and therefore only the acquisition rate matters for the derivation of the optimal intercommunication interval.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § Proof See Appendix C. · p. 18

    Even with uneven retention, the database size is still equal to the sum of the cohort size over its life, and the revenues generated by the database in one period are still equal to the revenues generated by a cohort over its life.

    “However, as is demonstrated by Figure 2b, the database size in this case is still equal to the sum of the cohort size over its life, and the revenues generated by the database in one period are still equal to the revenues generated by a cohort over its life.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § Proof See Appendix C. · p. 17

    Maximizing CE leads to smaller acquisition budgets (-2%) and fewer new customers acquired every year (-1%).

    “And thus smaller acquisition budgets (-2%) and fewer new customers acquired every year (-1%).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Proof See Appendix C. · p. 17

    Maximizing CE leads to a slightly larger retention rate and larger revenue per communication per customer, but a lower CLV (1% smaller).

    “This leads to a slightly larger retention rate and larger revenue per communication per customer, but as expected a lower CLV (1% smaller).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Findingown data
    § Proof See Appendix C. · p. 18

    In the cohort profile shown in Fig. 2a, retention is not constant over the life of its members: it is low in the first year, high for the next 4 years, then steady for the remaining years.

    “Indeed, looking at Fig. 2a we see a cohort profile where retention is not constant over the life of its members. Retention is low in the first year, high for the next 4 years, then steady for the remaining years.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning
    § 3 Customer equity and customer lifetime value · p. 10

    The multiplier e^{rt} P(t) / (e^{rt} - 1) is greater than 1, accounting for the fact that customers are renewable and lost customers are replaced.

    “In this equation, the multiplier e r t P t ð Þ e r t 1 > 1 accounts for the fact that customers are renewable and lost customers are replaced.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Customers are renewable and lost customers are replaced.

  • Probably not a substantial claim: may not pass S4 (based).

    Findingreasoning
    § 3 Customer equity and customer lifetime value · p. 10

    The value of the database as a whole is the value of its names minus the costs associated with extracting profits from these names.

    “The value of the database as a whole is the value of its names minus the costs associated with extracting profits from these names.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning
    § Moving from customer lifetime value to customer equity · p. 1

    Firms that optimize CLV have lower profits and retain fewer customers than firms that optimize CE.

    “This leads the firm following a maximization approach to have a smaller and less profitable customer base than one that follows a CE maximization strategy.”
    • Also stated in: § 1 Introduction · p. 2 · plain
      “We find that firms that optimize CLV generate lower profits and retain fewer customers than firms that optimize CE.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Proof See Appendix C. · p. 17

    t*CLV produces a higher CLV than t*CE, but produces lower non-discounted lifetime revenues (by 0.42%), which coupled with a smaller steady state customer base yields a lower value for the firm.

    “Referring back to Table 1, we can see that although the t * CLV produces a higher CLV than t * CE , it does produce a lower non-discounted lifetime revenues (by 0.42%) which, coupled with a smaller steady state customer base, yields a lower value for the firm.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § 3.1 Finding the optimal periodicity ( t *) · p. 11

    If P(t) is not too convex, then there are no local maxima and the maximum is unique.

    “Further, if P ( t ) is not too convex then there are no local maxima and thus the maximum is unique.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: P(t) is not too convex (typically concave over the domain of interest).

  • May combine two claims.

    Findingreasoning
    § A.1 Proof of Lemma 1 · p. 26

    Maximizing CLV and CE lead to the same optimal only when t*=0, which cannot happen because at t=0 the database value is negative.

    “Hence, this shows that it will only be for t =0 that @ @ t S e r t p t ð Þ e r t 1 . And thus, maximizing the Vclv and the Vce lead to the same optimal only when t *=0, which cannot happen since at t =0 the database value is negative ( Vce ð 0 Þ ¼ 1 ð Þ ). QED”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: We look at the equilibrium conditions so that Si = S.

  • May combine two claims.

    Findingown data
    § 5.2 The path to steady state · p. 18

    In the synthetic example starting with no customers at time 0, the CE approach grows the customer base faster and to a higher level than the CLV approach; revenues follow a similar pattern.

    “As one can see in Fig. 3, the CE approach grows the customer base faster and to a higher level than the CLV approach. Revenues follow a similar pattern.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Findingnone given
    § 7 Managerial implications and conclusion · p. 24

    Customer equity has a unique maximum.

    “This is simplified by the fact that customer equity has a unique maximum.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Findingnone given
    § 7 Managerial implications and conclusion · p. 24

    The model is robust to unobserved heterogeneity.

    “We show that our model is robust to unobserved heterogeneity.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given
    § 3 Customer equity and customer lifetime value · p. 10

    Allocating a portion of campaign costs (FC) to each name does not affect the substance of the findings.

    “This allocation does not affect the substance of our findings.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § 5.1 Optimal acquisition policy · p. 15

    A higher customer acquisition rate leads to greater database size and larger revenues, but these benefits must be offset against the cost of acquiring these customers.

    “We found in Section 4.3 that a higher customer acquisition rate leads to greater database size, and larger revenues, but these benefits must be offset against the cost of acquiring these customers.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § Proof See Appendix C. · p. 18

    Lemma 1 still holds under uneven retention: there is a fixed long-term size to the database, though the actual size is not t g / (1 - P(t)) because P is not constant over time.

    “Thus, Lemma 1 will still hold in that there is a fixed long-term size to the database (the actual size will not be t g 1 P t ð Þ as P is not constant over time, but it can still be calculated, we show an example of this in Section 6.1).”
    Quote in the paperSubstantial claim

  • May combine two claims. The quote only partly states this claim.

    Interpretationreasoning
    § 4.4 Change in discount rate (r) · p. 14

    As a firm grows from a start-up to a large legitimate company, its discount rate diminishes, and by Proposition 3d it will decrease its inter-communication time.

    “Proposition 3d states that in such case, the firm will decrease its inter-communication time as it grows.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: A start-up has a high implicit discount rate, and as a firm grows its future becomes less uncertain and its discount rate diminishes.

  • Classified as probably not a substantial claim.

    Interpretationcitation
    § 2.3 Customer equity · p. 9

    Lemma 2 formalizes Blattberg and Deighton's (1996) suggestion that, when maximizing customer equity, the acquisition and customer equity management tasks are very different and should be treated separately.

    “Further, this Lemma formalizes Blattberg and Deighton ' s (1996) suggestion that, when maximizing customer equity, the ' acquisition ' and the ' customer equity ' management tasks are very different, and should be treated separately.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Blattberg and Deighton (1996)
    • The authors state this as an assumption: Acquisition expenses are an ongoing expenditure that the firm recognizes on a periodic basis (e.g., monthly) while communications expenses and revenues are recognized at the time of the communication.
    • The authors state this as an assumption: Acquisition efforts are constant over time and produce a steady stream of names; there is no free production of names and the cost of acquisition increases with the size of the name stream.

  • May combine two claims.

    Interpretationreasoning
    § 4.3 Change in acquisition rate (g) · p. 13

    When the resource (customers) is plentiful (g is high), the firm can harvest it by setting a low t*; when scarce (g is low), the firm must conserve it by setting a high t*.

    “When the resource is plentiful ( g is high) the firm can harvest it; setting a low t *. When the resource is scarce ( g is low), the firm must conserve it; setting a high t *.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 2.1 Customer flow: acquisition and retention process · p. 3

    Economists consider three types of resources: depletable, renewable, and expendable.

    “Economists (Sweeny 1992) consider three types of resources: depletable, renewable, and expendable.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Sweeny 1992

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationreasoning
    § 4.5 Changes in costs · p. 15

    In the CE framework, database growth is achieved by reducing communication frequency (increasing t), while database harvesting is achieved by reducing the inter-communication interval (decreasing t), except when t is very small, in which case both objectives are achieved by increasing t.

    “In the CE framework this can be achieved by reducing the communication frequency (i.e., increasing t ). On the other hand, when the objective is to harvest the database, marketing actions need to be adjusted so as to increase short-term revenues. This can be achieved by reducing the inter-communication interval (i.e., decreasing t -except in some occasions when t is very small, in which case both”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § 1 Introduction · p. 2

    CLV and CE are not interchangeable when optimizing marketing decisions; maximizing CLV does not maximize CE.

    “The theoretical development we conduct in this paper shows that the answer to these two questions is a resounding No.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation
    § 2.3 Customer equity · p. 7

    Little's Law states that an inventory reaches a steady state size L, which is a product of the arrival rate of new stock (λ) and the expected time spent by any single unit of stock in the inventory (W), or L=λW.

    “This is analogous to Little ' s Law , which states that an inventory reaches a steady state size, L , which is a product of the arrival rate of new stock ( l ) and the expected time spent by any single unit of stock in the inventory ( W ) or L= l W (Little 1961).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Little 1961 source

  • May combine two claims.

    Interpretationreasoning
    § 4.4 Change in discount rate (r) · p. 14

    An increase in r leads to a decrease in the discount multiplier (D), which decreases the value of each name and the database; this decrease must be offset by increasing t.

    “What actually happens is that an increase in r leads to a decrease in the discount multiplier ( D ). This decrease means that, holding everything else constant, the value of each name decreases, and so does the value of the database. This decrease must be offset by either an increase in database size ( S ) or an increase in expected profit per name per communication ( R ). Both are accomplished by”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § 4.5 Changes in costs · p. 15

    Whenever a change beneficial to the firm occurs (e.g., higher return from acquisition, better retention rate, lower interest rate), the firm can adjust actions to favor harvesting at the expense of growth (decrease t); conversely, detrimental changes lead the firm to lean toward growth (increase t).

    “Whenever there is a change in the firm ' s performance or in the environment that is beneficial to the firm (e.g., higher return from acquisition, better retention rate, lower interest rate), the firm can adjust its actions in a way that favors harvesting at the expense of growth (i.e., decrease t ). Conversely, if the change is detrimental (e.g., lower return per campaign, higher costs), the firm”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § 2.2 The impact of marketing actions on customer retention and expenditure · p. 4

    Periodicity affects the value of names in two ways: more frequent contact leads to more opportunities to earn money, and more frequent contact provides customers with more opportunities to defect.

    “Thus, periodicity affects the value of names in two ways. On the one hand, more frequent contact leads to more opportunities to earn money. On the other hand, more frequent contact provides customers with more opportunities to defect.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § 2.1 Customer flow: acquisition and retention process · p. 4

    New cohorts of customers are recruited over time, but each cohort will eventually become extinct.

    “New cohorts of customers are recruited over time, but each cohort will eventually become extinct (Wang and Spiegel 1994).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Wang and Spiegel 1994 source

  • May combine two claims.

    Interpretationreasoning
    § 1 Introduction · p. 2

    Maximizing CLV is sub-optimal from a CE perspective; it leads to the wrong marketing actions and the wrong acquisition policy.

    “Maximizing CLV is sub-optimal from a CE perspective, it leads to the wrong marketing actions and the wrong acquisition policy.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisenone given
    § 7 Managerial implications and conclusion · p. 23

    The lifetime value of a firm's customer base depends both on the acquisition process used by the firm and the marketing actions targeted at these customers.

    “The lifetime value of a firm ' s customer base depends both on the acquisition process used by the firm and the marketing actions targeted at these customers.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § Proof See Appendix C. · p. 18

    Proposition 4 still applies under uneven retention, and the maximum acquisition spending can be computed by computing the CLV of each cohort.

    “Finally, proposition 4 still applies, and we can compute the maximum acquisition spending by computing the CLV of each cohort.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § 5.2 The path to steady state · p. 18

    These two benefits (less acquisition investment and less capital needed) should make raising capital easier for the start-up firm.

    “These two benefits should make raising capital easier.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § 7 Managerial implications and conclusion · p. 24

    Firms are attempting to balance two conflicting objectives: database growth and database harvesting.

    “This exercise shows how firms are attempting to balance two conflicting objectives: database growth and database harvesting.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationreasoning
    § 7 Managerial implications and conclusion · p. 24

    Conversely, if the change is detrimental (e.g., lower return per campaign, higher costs), the firm must counteract this change by leaning more toward growth rather than harvesting.

    “Conversely, if the change is detrimental (e.g., lower return per campaign, higher costs), the firm must counteract this change by leaning more toward growth rather than harvesting.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § 6.2 Observed heterogeneity · p. 23

    In CRM applications, the set of rules or models used to generate offers is identical for all customers, even though the output differs; the costs of creating the rules and communication templates are shared across all individuals rather than borne individually.

    “Nevertheless, the set of rules or models that are used to generate these offers will be identical for all frequent flyers, or all Amazon customers. The output will be different, but the process will be identical. Further, the costs of creating the rules and communication templates will be shared across all individuals rather than borne individually.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § 5.2 The path to steady state · p. 18

    A start-up firm using the CE approach will need to raise less capital and provide a larger ROI than if it followed a CLV maximization strategy.

    “Thus, it will need to raise less capital and provide a larger ROI than if it were to follow a CLV maximization strategy.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationreasoning
    § 7 Managerial implications and conclusion · p. 24

    The first-order condition derived in Proposition 2 is easy to optimize empirically; the firm can run a series of tests to estimate the various elasticities and infer from them if it should increase or decrease its communication periodicity.

    “The strength of the first-order condition derived in Proposition 2 is that it is easy to optimize empirically. The firm can run a series of tests to estimate the various elasticities and infer from them if it should increase or decrease its communication periodicity.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § 6.2 Observed heterogeneity · p. 22

    Increasing the number of segments should increase revenues because marketing communications can be better customized as segments become more homogeneous, but communication costs will also increase because different communications must be created for different segments.

    “The trade-off one makes when increasing the number of segments is that revenues should increase with the number of segments as one can better customize the marketing communications when the segments become more homogenous; but, communication costs will also increase as different communication must be created for different segments.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 6.2 Observed heterogeneity · p. 23

    CRM in practice proposes to develop a set of rules or models that, when applied to information known about the firm's customer, yield a customized marketing message.

    “What CRM proposes to do in practice is to develop a set of rules or models that, when applied to the information known about the firm ' s customer, yield a customized marketing message (Winer 2001).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Winer 2001 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § 6.2 Observed heterogeneity · p. 22

    If CRM promises were realized and segments were of size one, then a CLV model would be more appropriate than a CE model, because segments would be depletable and newly acquired customers would constitute their own segments rather than replenishing pre-existing segments.

    “If this promise were realized, one could argue that a CLV model is more appropriate than a CE model. Indeed, if segments are of size one then they truly are depletable. When the segment member defects; the segment is depleted. Newly acquired customers constitute their own segments rather than replenishing pre-existing segments.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given
    § 7 Managerial implications and conclusion · p. 24

    The first-order condition lends itself well to static comparisons (Propositions 3a to 3d).

    “The first-order condition also lends itself well to static comparisons (Propositions 3a to 3d).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § 7 Managerial implications and conclusion · p. 24

    The model allows derivation of the optimal actions for the firm and the long-term steady-state size of a firm's customer base (Lemma 1).

    “This allows us to derive the optimal actions for the firm, and we derive the long-term steady-state size of a firm ' s customer base (Lemma 1).”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Interpretationreasoning
    § 7 Managerial implications and conclusion · p. 24

    The first-order condition for the maximization of customer equity (Proposition 2) shows that a firm should adapt its marketing actions to changes in the critical factors that impact database value.

    “Our first-order condition for the maximization of customer equity (Proposition 2) shows that a firm should adapt its marketing actions to changes in the critical factors that impact database value.”
    Quote in the paperSubstantial claim
45 of 45

  • The authors state this as an assumption.

    Acquisition expenses are an ongoing expenditure that the firm recognizes on a periodic basis (e.g., monthly) while communications expenses and revenues are recognized at the time of the communication.

    “Consistent with Venkatesan and Kumar (2004), we assume that acquisition expenses are an ongoing expenditure that the firm recognizes on a periodic basis (e.g., monthly) while communications expenses and revenues are recognized at the time of the communication.”

  • The authors state this as an assumption.

    Acquisition efforts are constant over time and produce a steady stream of names; there is no free production of names and the cost of acquisition increases with the size of the name stream.

    “First, we assume that the acquisition efforts are constant over time and produce a steady stream of names (i.e., g i t ð Þ ¼ t : g ; AQj ¼ AQ g ð Þ ). There is no free production of names and the cost of acquisition increases with the size of the name stream such that: AQ ð 0 Þ ¼ 0 ; @ AQ ð g Þ =@ g > 0.”

  • The authors state this as an assumption.

    Fixed and variable communications costs are constant across communications.

    “Second, we assume that the fixed and variable communications costs are constant across communications (i.e., VCi ¼ VC ; FCi ¼ FC ).”

  • The authors state this as an assumption.

    Communications are identical in nature, if not in actual content, and customers' reaction to the communications depends only on their frequency, such that A_i(t)=A(t) and P_i(t)=P(t).

    “Third, we assume that the communications are identical in nature, if not in actual content, and that customers ' reaction to the communications depends only on their frequency such that: Ai t ð Þ ¼ A t ð Þ and Pi t ð Þ ¼ P t ð Þ .”

  • The authors state this as an assumption.

    A(t) is monotonically increasing in t, with A(0)=0 and A(∞) finite.

    “Further, we assume that A( t ) is monotonically increasing in t , with A (0)=0 and A( ∞ ) finite (i.e., the more time the firm has to come up with a new offer, the more attractive it can make it -up to a point)”

  • The authors state this as an assumption.

    P(t) is inverted-U shaped and dependent on A(t) such that ∂P(t)/∂A(t) > 0.

    “and that P ( t ) is inverted-U shaped (i.e., retention is lowest when the firm sends incessant messages or when it never contacts its customers and there is a unique optimal communication periodicity for retention purposes) and dependent on A ( t ) such that @ P t ð Þ =@ A t ð Þ > 0 (i.e., the better the offer, the higher the retention rate).”

  • The authors state this as an assumption.

    Customers are treated by the firm as homogeneous entities; there is no observed heterogeneity the firm can use to derive different t for different individuals.

    “We assume, for now, that customers are treated by the firm as homogenous entities; i.e., there is no observed heterogeneity the firm can use to derive different t for different individual.”

  • The authors state this as an assumption.

    P(t) is inverted-U shaped: increasing at a decreasing rate for small t, then decreasing after some threshold.

    “If we assume that P ( t ) is invertedU shaped (increasing at a decreasing rate for small t -@ VCE @ P > 0 ; @ 2 P t ð Þ @ t 2 < 0 ; 8 t < t p -then decreasing after some threshold -@ P t ð Þ @ t < 0 ; 8 t < t p )”

  • The paper relies on this without support.

    A start-up has a high implicit discount rate, and as a firm grows its future becomes less uncertain and its discount rate diminishes.

    “Indeed, a start-up is a risky venture and its implicit discount rate will be high. As the firm grows, its future becomes less uncertain and its discount rate diminishes.”

  • The paper relies on this without support.

    Acquisition costs correspond to a stream of payment over time, rather than a one-time transaction.

    “It is critical, for this analysis, to understand that the acquisition costs correspond to a stream of payment over time, rather than a one-time transaction.”

  • The authors state this as an assumption.

    It is possible for the firm to make some profits (there exists t such that Vce(t) is positive).

    “This is not a restrictive condition, as it only assumes that it is possible for the firm to make some profits.”

  • The authors state this as an assumption.

    P(t) is not too convex (typically concave over the domain of interest).

    “Further, if P ( t ) is not too convex then there are no local maxima and thus the maximum is unique. This, again, is not restrictive, as P ( t ) will typically be concave over the domain of interest.”

  • The paper relies on this without support.

    Customers are renewable and lost customers are replaced.

    “In this equation, the multiplier e r t P t ð Þ e r t 1 > 1 accounts for the fact that customers are renewable and lost customers are replaced.”

  • The authors state this as an assumption.

    The acquisition efforts yield a stream of customers whose retention rate has a Beta distribution B(a, β) with β >1.

    “For instance, if we assume that the acquisition efforts yield a stream of customers whose retention rate has a Beta distribution, B( a, β ) with β >1, 3 then we have:”

  • The paper relies on this without support.

    Customers are a renewable resource.

    “Our contention is that customers are a renewable resource and hence marketing actions directed at acquiring and extracting revenues from customers should take a long-term value-maximization approach.”

  • The authors state this as an assumption.

    The optimal database value is positive (otherwise the firm would not engage in database driven marketing).

    “If we restrict ourselves to cases where the optimal database value is positive (otherwise the firm would not engage in database driven marketing) then we have R ( t )>0 and R t ð Þ S t ð Þ FC > 0 and thus, at the maximum, the following first-order condition needs to be satisfied:”

  • The authors state this as an assumption.

    We look at the equilibrium conditions so that Si = S.

    “Assume that we look at the equilibrium conditions so that Si ¼ S .”

  • The authors state this as an assumption.

    The firm currently acquires g customers per period for a cost of AQ(g) and is considering acquiring one more.

    “Let us assume that the firm currently acquires g customers per period for a cost of AQ ( g ) and is considering acquiring one more.”

  • The authors state this as an assumption.

    Any impact of g on t* is ignored.

    “Ignoring any impact of g on t *, the increase in revenue comes from the increase in database size:”
19 of 19

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Retention derivative has conflicting signs for small intervals

    Minor

    The description of the inverted-U retention function says its derivative is negative for intervals below the threshold. Appendix B.2 instead says that the derivative is positive for small intervals.

1 of 1

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Authors
Drèze, X., & Bonfrer, A.
Affiliations
  • University of California, Los Angeles (US)
  • Singapore Management University (SG)
Corresponding author
Drèze, Xavier
ORCID
Bonfrer, André
Venue
Quantitative Marketing and Economics
Publisher
Springer Science and Business Media LLC
Published
2009-07-31
Volume
7
Issue
3
Pages
289-320
ISSN
  • 1570-7156 (ISSN-L)
  • 1573-711X
DOI
10.1007/s11129-009-9067-y
OpenAlex
W2121586327
Semantic Scholar
f4a409acf41cb0e15adb114c122faf718c49b72e
Cited by
48
References
29
Citations by year
2026: 1 · 2025: 1 · 2024: 1 · 2023: 2 · 2022: 1 · 2021: 1 · 2020: 3 · 2019: 1 · 2018: 2 · 2017: 3 · 2016: 3 · 2015: 1 · 2014: 13 · 2013: 2 · 2012: 1
FWCI
4.16
Type
journal article
Language
en
Open access
Licence
cc-by-nc
Locations
  • Quantitative Marketing and Economics (publishedVersion, cc-by-nc)
  • eScholarship (California Digital Library) (submittedVersion, other-oa)
  • Singapore Management University Institutional Knowledge (InK) (Singapore Management University) (submittedVersion, other-oa)
  • RePEc: Research Papers in Economics (submittedVersion)
  • Own your potential (DEAKIN) (submittedVersion)
  • eScholarship (California Digital Library) (submittedVersion)
Funders
Singapore Management University
Topics
  • Social Sciences › Business, Management and Accounting › Marketing › Customer churn and segmentation
  • Social Sciences › Business, Management and Accounting › Organizational Behavior and Human Resource Management › Customer Service Quality and Loyalty
  • Social Sciences › Business, Management and Accounting › Marketing › Consumer Market Behavior and Pricing
Keywords
customer lifetime value, customer equity, customer relationship management, customer acquisition, customer valuation, customer profitability

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