Stickiness and the Monetization of Apps

Transcription

1 Stickiness nd the Monetiztion of Apps Gil Appel Mrshll School of Business, University of Southern Cliforni Brk Libi Arison School of Business, Interdisciplinry Center, Herzliy Eitn Muller Stern School of Business, New York University Arison School of Business, Interdisciplinry Center, Herzliy Ron Shchr Arison School of Business, Interdisciplinry Center, Herzliy September 06 We thnk Eyl Biylogorsky, Dri Dzybur, nd Oded Koenigsberg for number of helpful comments nd suggestions.

2 Stickiness nd the Monetiztion of Apps Abstrct Though free pps dominte mobile mrkets, firms struggle to monetize such products nd mke profits, relying on revenues from two sources: pying consumers, nd pying dvertisers. Previous studies of such monetizing decisions hve focused on sttic setting i.e., one-period model. However, evidence suggests tht retention (lso referred to s pp stickiness, or the degree of utility tht might be still experienced beyond the first period) is significnt. Accordingly, we introduce two-period model in which firm offers n pp in two versions: Consumers cn downlod free version tht includes ds, or pid version without ds. While consumers hve some prior knowledge bout their fit with the pp, they remin uncertin bout their exct mtch-utility unless they re using it. We show tht s stickiness increses, so do prices nd d intensity, nd firms ern more of their profits from pying customers thn they do from dvertising. Specificlly, we find tht when stickiness increses, the firm s erning from the pid version increses monotoniclly. However, its ernings from dvertising initilly increse, then drop. Furthermore, we demonstrte tht in dynmic setting, firm cn profit from offering free version with ds even if dvertisers re not pying for these ds. In other words, the firm benefits from offering version of the pp tht includes ds even if the consumers re not pying for the pp nd the dvertisers re not pying for the ds. Finlly, we lso consider the dilemm fced by some firms of whether to offer two versions of the pp (free nd pid), or only one. Of course, when operting costs re ignored, offering two versions is more profitble. However, our nlysis cn identify the cses in which the dditionl profit is miniml. In such cses, tking costs into ccount, offering just one version might be more ppeling. Indeed, we find, for exmple, tht when the stickiness level is high, the firm might benefit by focusing on the pid version nd voiding the free version. Keywords: dvertising; freemium; mobile pps; online strtegy; pricing; retention; stickiness

3 . Introduction Consistent with ssertions in the business literture, the prevlence of digitl products tht re provided to customers for free hs risen drmticlly in recent yers, creting new business models tht re ltering mrkets for digitl products (Anderson 009, Kumr 04). In contemporry digitl mrkets, it my become inescpble for firms to offer free product due to mrket norms. In the rpidly growing mobile pp mrkets in prticulr, industry reports indicte tht more thn 90% of the mobile pps strt s free, more thn 90% of the profits of mobile pps come from products tht begn s free, nd tht the shre of free products is only expected to grow in the coming yers (AppBrin 06; Tube 03). At the sme time, the number of pps offered to consumers continues to rise rpidly, nd by mid-06, consumers could choose mong more thn two million pps in either the Google or Apple stores (Sttist 06). Provision of products for free chllenges firms bility to ern revenue, thus firm s success depends on finding wys to monetize these products. Two pproches, not necessrily mutully exclusive, hve risen s essentil to erning money from free digitl products: The first is selling dvertising spce within the free product; nd the second, for-py version (sometimes lbeled freemium or in-pp purchse strtegy), which entils selling product enhncements in forms such n d-free version, or offering dditionl fetures to subset of users (Needlemn 06). While such products begin s free, mrket size cn be very lrge. It is reported, for exmple, tht mobile gmes lrgely begin s free to ply nd bse their profits on There might be other wys to monetize digitl products, such s selling user informtion to third prty, or the cretion of user community, which my not be profitble in the short run, yet tht cn be lter sold to third prty interested in such informtion. These re beyond the scope of our discussion here.

4 combintion of dvertising nd pying for product enhncements: In 06, the worldwide revenue from mobile gmes is expected to rech $37 billion, surpssing income from either video console gmes or PC gmes (Needlemn 06, Sttist 06b). Yet longside the high stkes comes vgueness regrding the bility of mny of the mrket plyers to profit from these strtegies. There re persistent concerns over whether free-bsed business models re indeed sustinble, s free product cretors, from medi sites to mobile pps, struggle to remin profitble (Mrks 0; Zhng 05). Prt of the issue is the need for cler view of the vrious monetiztion tools effectiveness. Indeed, the business literture describes the question of monetiztion model choice nd the level of co-existence of the min tools s plguing the industry (Ntnson 06). An emerging body of cdemic work hs thus exmined consumer nd firm decisions in the context of monetiztion, iming to understnd how to ern money from free digitl products (Hlbheer et l. 04; Knnn 03; Lmbrecht et l. 04). However, previous efforts to exmine the issue of ds versus py hve lrgely ssumed one-shot gme. In prctice, where consumers sty with these products for more thn one period, we should consider dynmic setting tht tkes into ccount customer retention. The issue of retention is of prticulr importnce given tht monetiztion of free pps cn depend hevily on durtion of sty. App retention my hence significntly ffect decision mking by consumers nd firms, the equilibrium in such mrkets, nd generlly how pps re monetized. Indeed the issue of pp retention is ttrcting incresing ttention in the pp industry. Given the nture nd voltility of these mrkets, it is observed tht pp retention rtes re lower thn the observed retention rtes in clssicl products nd services, with reports suggesting tht cross ll ctegories, 75% of ll pp users churn within 90 dys (Perro 06). Businesses often

5 relte in this regrd to mesure of pp stickiness tht represents the tendency of users to continue to use the online product (O Connell 06). Given tht most pps re offered initilly for free, nd future profit lrgely depends on users future interctions with the product, prctitioners incresingly cite the importnce of stickiness for pp success (Perro 06; Yloz 05). Interestingly, stickiness vries widely cross product types: A given user is likely to engge with diverse pps in widely differing wys, using some with high frequency while using others only few times. For exmple, retention rtes for ctegories such s wether, news, nd helth nd fitness pps cn be more thn twice nd three times those ssocited with music, photogrphy, nd sports (Klotzbch 06). Wht we im to show here is tht beyond its expected contribution to success, stickiness lso plys n essentil role in how free pps re monetized. Towrd this explortion, we use stylized two-period gme in which single firm offers free product with two monetiztion sources: pying consumer, nd pying dvertisers. In other words, consumers cn downlod free version tht includes ds, or pid version tht excludes ds. Offering n d-free version s premium lterntive represents slient, free product business model tht is widely used by suppliers such s Spotify nd other music services, s well s virtully ll mobile gmes. While consumers hve some prior knowledge of their fit with the pp, they remin uncertin bout their exct mtch-utility until they re using it. We show tht s stickiness increses, so do prices nd d intensity, nd firms ern more of their revenues from pying customers thn they do from dvertising. Specificlly, we find tht s stickiness increses, the firm s ernings from the pid version increse monotoniclly. However, Consistent with industry terminology free product here is one tht provides the option to consume version of it for free. Some consumers my of course prefer to py for enhncements such s no dvertising 3

6 its ernings from dvertising first increse, then drop. Accordingly, the shre of profit coming from the pid version increses with the stickiness level throughout. Furthermore, we demonstrte tht in dynmic setting, firm cn profit from offering free version with ds even if dvertisers re not pying for these ds. In other words, the firm benefits from offering version of the pp tht includes ds even if the consumers re not pying for the pp, nd the dvertisers re not pying for the ds. The logic behind this result is the following: In dynmic setting, the free version is kind of smple tht enbles consumers to lern their fit with the pp. The firm would rther dd ds to this version (even if they re not pid for) in order to keep the consumers who hve high vlution of the pp wy from the smple nd push them towrd the py version. We lso consider the dilemm fced by some firms over whether to offer two versions of the pp (free nd pid), or only one. Of course, when operting costs re ignored, offering two versions is more profitble. However, our nlysis cn identify cses in which the dditionl profit is miniml. In such cses, tking costs into ccount, offering just one version might be more ppeling. Indeed, we find, for exmple, tht when the stickiness level is high, the firm might benefit by focusing on the pid version nd voiding the free version.. Relted literture Our work is prticulrly relevnt to incresing reserch efforts iming t understnding optiml firm behvior in free digitl mrkets. Reserch in this venue hs lrgely focused on the choice between content nd dvertising in the context of medi mrkets, where the bsic trdeoff is tht moving from n dvertising-only revenue model to chrging for content my reduce viewership nd thus hurt dvertising revenues (Lmbrecht et l. 04). Empiricl results 4

7 regrding the consequences of such choice vry (Chiou nd Tucker 03; Puwels nd Weiss 008). Profitbility in such contexts my depend on fctors such s the type of promotions used (Puwels nd Weiss 008), temporl chnges in demnd (Lmbrecht nd Misr 06), nd users bility to bring new business through referrls (Lee et l. 05). Anlyticlly, noticeble effort hs centered on the questions of profit from content vs. dvertising in two-sided medi mrkets such s newsppers (Hlbheer et l. 04). The trdeoff between pid content nd dvertising my depend on competitive intensity (Godes et l. 009), consumer heterogeneity in willingness to py (Prsd et l. 003), or the extent to which consumers dislike dvertisements (Tåg 009). Looking t the use of free product s smpling mechnism, recent work hs suggested tht dvertising effectiveness, coupled with consumers expecttions regrding qulity, cn determine which revenue source firms should focus on in ttempting to enhnce profitbility (Hlbheer et l. 04). Moreover, it hs been shown tht the ppel of the free option is influenced by the effectiveness of word of mouth (Niculescu nd Wu 04), nd tht referrl considertions ffect efforts to move user from free to pying (Lee et l. 05). These reserch efforts, however, do not consider the role of customer retention or long-term customer vlue in generl in the mrket equilibrium tht emerges. As the consumers in our setting lern bout the product, our work ddresses lso the demnd-side literture on consumers lerning (Ackerberg 003; Erdem et l. 999; Erdem nd Kene 996; Iyengr et l. 007). Our lerning structure is not on specific ttributes of the product, but rther on the idiosyncrtic utility tht the consumer cn expect from experiencing the product, similr in spirit to Ackerberg (003). Our work is lso relevnt to the literture brnch tht ddresses customer reltionships, nd in prticulr the role of customer retention (Ascrz nd Hrdie 03; Gupt et l. 004; Libi et 5

8 l. 009; Schweidel et l. 008), nd how optiml retention efforts my differ bsed on mrket chrcteristics (Muslem nd Joshi 009; Shin nd Sudhir 0, Subrmnin et l. 03). In the context of online behvior, reserchers hve considered the ntecedents of users tendencies to stick with website (Chen nd Hitt 00; Lin 007; Li et l. 006) or specificlly with n pp (Hsu nd Lin 06; Kim et l. 05), s well s free digitl product doption s effect on retention rtes (Dtt et l. 05). Yet the dynmics of how retention ffects monetiztion in free digitl mrkets hve not been exmined. 3. The Model We consider digitl product primrily designed for mobile devices, for which such products re lrgely distributed s pplictions on either Google s Ply Store or Apple s itunes. In the rest of the pper, for simplicity, we refer to our product or service s n pp. The term free pp is somewht of misnomer, s the consumer pys for the pp in one of two wys: either s/he pys one-time price to downlod the pp, or else s/he pys with her time by viewing dvertising. However, for convenience, we will refer to the d-supported version s free. A user downloding the pp cn choose insted of downloding the free version to purchse version in which no dvertisements re displyed (Tåg 009). Users re heterogeneous in their mtch with the pp, nd they fce uncertinty with respect to the exct fit of the pp to their preferences. In other words, lthough consumers hve some prior knowledge, they remin uncertin bout the idiosyncrtic utility the consumer cn expect from using the pp. Once s/he uses it, ll uncertinty is resolved. The frmework we use is twostge gme: Specificlly, we ssume tht while consumers experience deprecition in their utility from using the pp, it is only prtil. In other words, consumers might enjoy using the pp 6

9 beyond the first period. The degree of utility tht might be still experienced in the second period, termed here the stickiness fctor, plys key role in this frmework. In ech period, the user cn choose whether to use the pp or not, nd which version of the pp to use (free, or pid). Users decisions in the second period re ffected by their choices in the first period in two wys: Firstly, if s/he chooses to use the pp in the first period, her exct utility mtch with the product is reveled, nd s/he does not fce ny uncertinty in the second period. Secondly, if s/he pid for the pp in the first period, s/he cn use the d-free version in the second period with no dditionl fees. The firm sets the levels of price nd dvertising, given the consumers heterogeneity nd decision rules. Stickiness, s well s uncertinty, should therefore ffect the firm s decision-mking nd the resultnt profits. 3. Consumers Utility We begin by describing the fctors ffecting consumers utility such s uncertinty, dvertising, nd costs; then proceed with the forml utility mximiztion problem; nd conclude with the resultnt demnd nd firm mximiztion. Uncertinty. Mrket reports suggest tht given the bsence of monetry cost to downlod pps, consumer lerning often occurs post doption rther thn pre doption, s in clssicl consumer mrkets, so tht users re more comfortble thn ever before downloding n pp nd giving it try (Klotzbch 06). Yet consumers re not entirely in the drk with respect to their mtch with ny specific pp. For exmple, some consumers know -priori tht they prefer helth nd fitness pps over food nd drink pps, or socil gmes over brin gmes. However, since ech pp is unique, even fter reding n pp s description, consumers re uncertin bout the fit between their preferences nd the pp. 7

10 To cpture this type of uncertinty, we let nture determine the mtch prmeter in two stges: First, ech individul is ssigned with n α (below we ssume tht α is distributed uniformly in the popultion with support 0,). Second, nture either dds or subtrcts εε to α (with probbility of / to ech option). This process is common knowledge, nd ech individul lso knows her own α. However, s/he does not know whether nture dded or subtrcted εε in her cse. Accordingly, from her perspective, the mtch prmeter is rndom vrible, denoted by αα with the following distribution: αα εε with probbility / () αα = αα + εε with probbility / where 0 α, 0 ε. Thus, the prmeter εε represents the degree of uncertinty the individul is fcing with respect to her true bse utility 3. This uncertinty is completely resolved when the consumer is using the pp, irrespective of whether s/he uses its free or pid version 4. For exmple, the source of uncertinty is tht the potentil downloder of mobile gme does not know the level of complexity, fun, nd enggement tht s/he, personlly, will enjoy. Once s/he plys the gme nd relizes her enggement, or lck thereof, this uncertinly is resolved. The intensity of dvertising. The free version of the pp is bundled with dvertising. Exposure to dvertising is nnoying to the consumer, nd cretes discomfort nd irrittion, nd thus the intensity of dvertising, γγ, deprecites the consumer s utility (Wilbur 008). Advertising cretes inconvenience for the consumer in tht it effectively reduces the mount of content tht 3 Due to uncertinty utility my be negtive, which is consistent with rel world possible negtive disposition towrds the pp 4 This type of lerning is consistent with the experientil component of consumption good described in Ackerberg (003). 8

11 the consumer cn enjoy from the pp, in ddition to inflicting other costs, such s distrction nd opportunity cost of time (Tåg 009; Vrtonjic et l. 03). Indeed, previous work hs empiriclly demonstrted tht consumer nnoynce ssocited with online dvertising hs negtive effect on consumer utility nd resultnt retention (Goldstein et l. 04). While firms tend to hve limited control over d content, which is typiclly outsourced to d exchnges tht mtch ds to pps (e.g., Google s Admob, Flurry, Apple s iad), the firm cn select the level of dvertising intensity. Since the bse utility is bounded, we ssume tht 0 γ. Pid version cost. Consumers my choose to eliminte the nnoynce of ds, for price. The firm offers pid version of the pp for price p 0. If consumers choose to py this price, the ds re removed nd the consumers benefit from the full utility of the pp. Thus price is decision vrible of the firm. App holding costs. Although consumers re exposed to lrge number of free pps, they downlod only smll subset, nd use n even smller subset. It is costly for consumer to mintin nother pp in her current collection of pps, becuse of system limittions (such s memory cpcity nd screen cpcity), cost of downloding nd instlling, nd cognitive limittions (such s depletion), privcy issues, nd others (Perez 04; Smith 06). We tke these costs into ccount by hving consumer utility decrese by the per-period cost of holding nd using the pp, c. The holding costs re thus subtrcted from the bse utility t ech period. Since the bse utility is bounded, we ssume tht 0 c. The stickiness fctor. The stickiness of n pp or gme represents consumers tendency to re-use it (Lin 007) or to be precise, the frction of the mtch-utility, αα, tht might still be experienced in the second period. This frction is denoted by δ, where 0 δ, nd lbeled the stickiness fctor. The higher the vlue of δ, the higher the consumer s utility in the second 9

12 period. Thus, stickiness cn ffect the decision whether to sty for the second period. Furthermore, with forwrd-looking consumers (s in our setting), this prmeter lso ffects first-period choices. Our model considers stickiness to be chrcteristic of the pp. Vrious pp-bsed fctors my influence n pp s stickiness level, including the qulity of the pp nd its bility to crete consumer commitment nd trust (Li et l. 006). Yet mrket informtion suggests tht stickiness my be highly dependent on the specific type of pp (Klotzbch 06). Some ctegories nd subctegories re clerly stickier thn others, which my be fctor in the pp s long-rnge utility, vriety-seeking nd boredom on the prt of the trget mrket, nd the qulity of the lterntives. Firms tht trget certin ctegory or subctegory my thus be ble to obtin n ssessment of the rnge of stickiness they cn expect to see, nd they my use informtion from similr freemium pps to ssess the extent to which consumers re expected to continue using given pp (Hdiji et l. 04). Setting the individul utility. The forml setting is s follows: In ech period, denoted by tt =,, the individul fces three lterntives, denoted byjj: () not to use the pp (jj = 0); () to use the free version of the pp (jj = ); or (3) to use its pid version (jj = pp). In ech period, the individul mkes choice, denoted by CC tt from mong these 3 options. In other words, CC tt = jj when the individul chooses lterntive jj t time tt. The utility of the individul from these options uu jj,tt is: () uu 0,tt = 0 uu,tt = αα ( γγ)δδ tt cc uu pp,tt = αα δδ tt pp[ II{tt = CC = pp}] cc where αα is the mtch-utility, γγ is the intensity of dvertising, δδ tt is the pp stickiness prmeter (equls in the first period nd δδ < in the second period), cc is the cost ssocited with using 0

13 the pp, nd pp is the price of the pid version. The indictor function I cptures the fct tht the price is pid only once. Next we clculte the individul s expected vlue i.e., the sum of her expected utility in both periods. 3. Consumer s Expected Utility When forming her expecttions, the individul tkes into ccount the consequences of her choices in the first period on her stte in the second. Her ctions in the first period hve two types of effects on the sttes of the second: First, using the pp resolves the uncertinty of αα, nd the individul knows whether her bse utility is αα εε, or αα + εε. This hppens irrespective of whether s/he uses the pp s free or pid version. Second, pying for the pp in the first period mkes it free for use (without ds) in the second. Thus, to clculte the user s lifetime expected utility, we first need to describe her second-period utilities nd choices (conditioned on her firstperiod choice). We begin by considering the cse in which the user chooses the pid version in the first period. In such cse, s/he hs two options in the second period: () continue to use the pid version or (b) not use the pp t ll. The option of using the free version is not ppeling to her, s it contins ds, which decrese her utility, nd s/he hs lredy pid for the d-free version. Her utility would be either (αα εε)δδ cc, or (αα + εε)δδ cc if s/he continues using the pid version, depending on the reliztion of αα, which will be known to her t tht point, or else zero if s/he does not continue using the pp. Therefore, the choice between using the pp or not, which mximizes her utility, cn be chrcterized s follows: (i) if αα < cc εε, s/he will not use the pp in the second period, δδ (ii) if cc εε < αα < cc + εε, s/he will use it only if her relized bse utility is high, nd δδ δδ

14 (iii) if cc + εε < αα, s/he will use the pp in the second period irrespective of the reliztion of her δδ bse utility. We denote these brek points, s they will become hndy lter, s follows: αα pp = cc εε nd αα δδ pp = cc δδ + εε. Accordingly, her lifetime expected utility if s/he pys for the pp in the first period is: (3) UU pp (αα) = αα cc pp + (αααα cc)ii αα pp < αα < αα pp + (αααα cc)ii αα pp < αα Figure depicts the lifetime utility for ech level of the bse utility α. Figure : Expected lifetime utility when choosing the pid option in the first period Next, we consider her lifetime expected utility if s/he chooses the free version in the first period. In such cse, s/he hs three options in the second period: ) stop using the pp, in which cse her utility in the second period is zero; b) keep on using the free version, gining second-

15 period utility of (αα εε)( γγ)δδ cc or (αα + εε)( γγ)δδ cc depending on the reliztion of αα ; or c) py for the premium version with utility of (αα + εε)δδ cc pp 5P. While it is cler tht (αα + εε)( γγ)δδ cc > (αα εε)( γγ)δδ cc, it is unknown whether (αα + εε)δδ cc pp is greter thn both these expressions, greter only thn the one with the low bse utility, or smller thn both. As result, the structure of the lifetime expected utility (i.e., the brek points between the vrious prts of the utility) hs three versions. While in Web Appendix A we present nd describe ll three structures, here we focus on one of them: the one in which the price of the pid version is reltively high. In such cse: (i) if αα < (ii) if cc δδ( γγ) cc δδ( γγ) εε, the consumer will not use the pp in the second period, εε < αα < cc bse utility is high, cc δδ( γγ) + εε, s/he will use the free version of the pp only if her relized (iii) if + εε < αα < pp εε, s/he will use the free version of the pp in the second period δδ( γγ) δδδδ irrespective of the reliztion of her bse utility, nd (iv) if αα < pp εε, s/he will use the free version when her bse utility is low, nd buy the pid δδδδ version if her bse utility is high. We denote these brek points s the following: αα = cc εε, αα δδ( γγ) = cc + εε, nd αα δδ( γγ) 4 = pp δδδδ εε (αα 3 is defined in Web Appendix A, where we present the vrious scenrios tht depend on the reltive vlues of αα jj ). Accordingly, in this cse, her lifetime expected utility if s/he selects the free version in the first period is: 5 It is immedite to show tht if the reliztion of her bse utility is low, s/he will not py for the premium version in the second period, nd thus in (c) bove we consider high bse utility only. 3

16 (4) UU (αα) = αα( γγ) cc + (αα εε)( γγ)δδ cc II{αα < αα} + (αα + εε)( γγ)δδ cc II{ αα < αα < αα 4 } + (αα + εε)δδ cc pp II{αα 4 < αα} Figure depicts the utility level for ech level of the bse utility α. Figure : Expected lifetime utility when choosing the free option in the first period Finlly, consider the cse in which the consumer does not use the pp in the first period. It is esy to show tht in such cse, her lifetime expected utility is zero Consumer s Choice nd Demnd The individul s decision in the first period is quite simple given her bse utility αα, s/he selects the option tht yields the highest utility. In other words, 6 If the consumer does not use the pp in the first period, her expected second-period utilities from using the free nd pid versions re αα( γγ)δδ cc nd αααα cc pp respectively. In both cses, these vlues re lower thn her expected utility in the first period (nd definitely lower thn her ssocited lifetime expected utility). As this individul finds it optiml to not use the pp in the first period, her expected utility from using the pp in the second period is negtive. Thus, s/he would choose to continue bstining from using the pp. 4

17 (5) CC tt = rg mx jjjj{0,,pp} UU jj (αα ) So fr we hve focused on the decision of one individul with specific αα nd εε, but the firm fces lrge number of individuls with heterogeneous levels of bse utility. To ccount for tht, we ssume, s mentioned bove, tht αα comes from uniform distribution t intervl [0,]. 7 Next, we wish to clculte the resulting demnd. Specificlly, we im to find the shre of individuls in ech option nd in ech period, denoted by ππ jjjj. In other words, we seek to identify the subset of utilities αα who find it optiml to choose option j (jj εε {0,, pp}), in ech period t. The following two Lemms nd the proceeding proposition re useful in the solution of the firstperiod shres. The proofs re in Web Appendices B nd C for Lemms nd respectively. Lemm : UU (0) is lwys greter thn UU pp (0). Lemm : (αα) < pp (αα) These two Lemms led to the following proposition: Proposition : There exists t most one intersection between UU nduu pp. Following the Lemms nd Proposition, we obtin tht () if there is no intersection, the pid version is never selected, nd (b) if there is intersection, the free version yields higher utility for those with low mtch-utility, while the pid version yields higher utility for those with high mtch-utility. Of course, the decision to use the pp depends not only on the reltionship between UU nd UU pp, but lso upon whether they yield positive expected utility. Otherwise, it is 7 This mens tht the support of the ctul bse utility, i.e., αα is [ εε, + εε]. In other words, it is possible tht the individul will lern tht using the pp yields negtive utility, i.e., αα εε < 0, s cn occur in mny rel-world cses. 5

18 optiml for the individuls to refrin from using the pp t ll. To get sense of these reltionships, consider Figure 3. Figure 3: Utility of free pp (UU ), pid pp (UU pp ), nd nonprticiption (UU 0 ) In this cse, consumers with low levels of mtch-utility (αα AA) do not downlod the pp; consumers with intermedite levels of utility (AA αα BB) use the free version in the first period, nd consumers with high mtch-utility (BB αα) use the pid pp. It is immedite to see tht if the line tht represents UU 0 hd been higher, the mrket shre of the free version could hve been zero in the first period. Specificlly, if insted of crossing UU t A, it would hve crossed it t B, the mrket would be split between those who do not use the pp nd those who use the pid version. It is esy to show how in this model, the following cses re possible: () no one uses the pp; () those with low αα do not use the pp, nd the rest buy the d-free version; (3) those with low αα do not use the pp, intermedite αα use the free version, nd those with high αα use the pid 6

19 version; (4) the mrket is split between those who use the free version (low αα) nd those who use the pid version (high αα); (5) the mrket is split between non-users (low αα) nd users of the free version (high αα); nd (6) everyone is using the free version. The Lemms nd proposition enble us to clculte, for ny vlue of {γγ, δδ, εε, pp, cc}, the mrket shres of the first period, i.e., ππ jj (jjjj{0,, pp}). The mrket shres of the second period re more strightforwrd. They re given by the following: ππ 0 = ππ 0 + ππ αα + ππ pp αα (6) ππ = ππ αα 3 ππ pp = ππ αα 4 + ππ pp αα 5 (i) αα is the shre of individuls whose αα, given this reliztion, stisfies: αα < cc δδ( γγ) (ii) αα is the shre of individuls whose αα stisfies the condition αα < cc δδ (iii) αα 3 is the shre of individuls whose αα stisfies pp δδδδ (iv) (note tht it is possible tht pp δδδδ < > αα > cc δδ( γγ) cc δδ( γγ), nd in such cse, αα 3 = 0) αα 4 is the shre of individuls whose αα stisfies the condition αα > pp δδδδ (v) αα 5 is the shre of individuls whose αα stisfies the condition αα > cc δδ Now tht we hve the shre of individuls in ech option in ech period, i.e., ππ jjjj, we cn solve the profit function of the firm nd find the optiml levels of price nd d intensity. This is done in the following subsection. 3.4 The Firm s Objective Function The firm chooses the price nd level of dvertising intensity so s to mximize its profits from the two periods. We normlize the overll mrket potentil to. Note tht in our setting, consumer with low mtch-utility α will not downlod the pp, yet the mrket potentil includes these consumers s well. Therefore, the choices of dvertising intensity nd pricing ffect not 7

20 only the proportion of pying buyers to free downloders, but primry demnd s well. In ddition, since the price is expressed in monetry terms, e.g., $ or, we need prmeter, denoted by k, to convert dvertising intensity γ to the sme monetry term. The dvertising contribution prmeter k thus represents the monetry pyment received by the firm from dvertisers per unit of d intensity. The objective function of the firm is thus: 8 (7) Π(pp, γγ; εε, δδ, cc, kk) = pp(ππ pp + ππ pp ) + kkkk(ππ + ππ ) The profit is function of (i) the two decision vribles of the firm price, nd dvertising intensity, nd (ii) the model s prmeters εε, δδ, cc nd kk. We ssume tht price nd dvertising intensity do not chnge in the second period. This ssumption is consistent with wht we see in the rel pp mrket, where these re embedded in the softwre nd re rrely chnged. For exmple, the business press reports tht chnging the in-pp purchse price of n pp is complicted, resource-intensive process tht cn intimidte developers (Ogg 03). The complexity of price nd dvertising chnges is driven lso by pps reltively short life cycles, nd by the fct tht dvertising contrcts re estblished in dvnce with third-prty entities. 4. Equilibrium Computtions Given the nlysis in the previous subsection, it is immedite to solve the pir of price nd dvertising intensity tht mximizes the firm s profit (pp, γγ ) for ny set of prmeters. While we hve the exct solution for ny set of prmeters, there is no closed-form solution for p nd γγ s function of εε, δδ, cc nd kk i.e., there is no closed-form solution for the functions 8 Consumers who buy the premium version might or might not sty for the second period, yet ttrition of these consumers does not ffect the profit function, s the pying consumers in our model do not generte ny revenues in lter period. Thus, consumers py for the pp in the second period only if they switched from the free version to the pid one in tht period. 8

21 pp (εε, δδ, cc, kk ) nd γγ (εε, δδ, cc, kk ). The lck of such solution is due directly to the existence of brek points in the lifetime expected utility function, UU pp nd UU. Tht sid, one of the min interests of this study is to understnd the effects of stickiness nd uncertinty on both price nd dvertising intensity, nd lso on shre of profits from the pid vs. free versions of the pp. In other words, we seek to be ble to nswer questions such s whether dvertising intensity increses or decreses with stickiness. Despite the bsence of closed-form solution for the functions pp (εε, δδ, cc, kk) nd γγ (εε, δδ, cc, kk), we cn solve these optiml vlues for ny set of prmeters, nd so study these reltionships numericlly. To conduct this nlysis, we solved the mrket equilibrium for levels (from zero to one) on ech of the four prmeters, using full fctoril design resulting in 4 = 4,64 cses. When we exmine these numericl reltionships, we find tht in most cses, price nd dvertising generlly increse stickiness (nd uncertinty). However, this monotonicity breks down for some specific vlues of the model s prmeters. For exmple, for ε = 0.8, c = 0., nd k = 0.5. We find (see Figure 4) generl monotonic behvior of price nd dvertising s stickiness increses. However, if we consider much higher cost, c = 0.8, i.e., ε = 0.8, c = 0.8, k = 0.5, we find (see Figure 4b) non-monotonic behvior. To get sense of the intuition behind these results, we need to gin n understnding of the driving forces in this model. In ll cses, individuls with low αα re more likely thn others to refrin from using the product, those with high αα re more likely to choose the pid version, nd those in the middle re more likely to choose the free version. 9

22 Figure 4: Effect of stickiness on price nd dvertising (ε = 0.8, c = 0., k = 0.5) Advertising nd price Stickiness Advertising Price Figure 4b: Effect of stickiness on price nd dvertising (ε = 0.8, c = 0.8, k = 0.5) Advertising nd price Stickiness Advertising Price Let s strt by considering the cse of one-period model i.e., the cse of δδ = 0. In such cse, the effects of the decision vribles of the firm price, nd d intensity re simple: As price rises, the shre of non-users does not chnge, but the split of users between the pid nd free versions skews towrd free. The higher the d intensity, the shre of non-users nd those who use the pid version increses. When choosing the optiml price nd d intensity, the firm 0

23 blnces these effects. When there re two periods, i.e., the cse of δδ > 0, there re two mjor chnges: From the consumers perspective, the product is more ppeling, s they cn enjoy it lso in the second period. From the firm s perspective, there is nother source of income: sles of ds in the second period. These new forces might hve opposing effects on the choices of price nd d intensity. Consider the choice of price. When stickiness increses, s the product is becoming more ppeling nd consumers willingness to py increses, the firm tends to chrge higher prices. However, the pid version is now becoming more ppeling lso to consumers who did not consider it in the pst nd downloded the free version. To cpture these potentil consumers, the firm tends to lower the price of the pid version. Of course, the finl decision depends on the reltive sizes of these two mrket shres, nd lso on the initil price nd d intensity. A similr pttern exists regrding the choice of d intensity: On the one hnd, given tht the product is more ppeling, the firm cn fford to dopt higher d intensity strtegy. On the other hnd, the free version cn now become ppeling to consumers who erlier did not consider using it t ll; nd to cpture them, the firm might opt to lower the d intensity. With these ptterns in mind, let s return to Figure 4 nd focus on the effect of stickiness on price. As we will illustrte shortly, price generlly increses with stickiness level, nd thus Figure 4 represents its effect better thn does 4b. Tht sid, understnding the drop in price tht we see in the middle of Figure 4b cn shed some light on the dynmics in the model. In Figure 4b, the cost of using the pp is very high, c = 0.8, nd thus most of the individuls do not use the product. This is especilly the cse when δδ is low (nd thus the individul cnnot relly enjoy the product in the second period). As δδ increses, some of these individuls re beginning to find the pp ppeling, nd re drwn to the free version. When δδ is round 0.5, the mss of consumers

24 who use the free version builds up sufficiently, nd the firm finds it optiml to shift some of them to the pid version. To chieve this, it does two things: It lowers the price of the pid version, nd increses the price of the free version (i.e., d intensity). This is the reson for the drop in price tht we see in this figure. Now compre Figure 4b with Figure 4. The first difference tht comes cross is tht price nd d intensity re much higher in 4. The reson is simple: The cost of using the pp is much lower in 4, nd thus the firm cn chrge higher rtes. The second difference is tht the price never drops in 4. The logic behind this result reltes to the discussion in the previous prgrph: The min reson to lower prices is to move consumers from the free version to the pid version. However, in 4, there is lredy mss of consumers who buy the pid version, nd the forementioned strtgem is therefore irrelevnt. While the discussion bove sheds some light only on two specific cses (Figures 4 nd 4b), nd is fr from comprehensive, it should give sense of the driving forces in the model, nd provide rtionle for the fct tht price does not hve to move monotoniclly with stickiness level. Similr rguments cn be mde with respect to the effect of uncertinty; see Appendix D for some dditionl insights. Now tht we hve estblished tht the effect of stickiness depends on the other prmeters of the model, we wish to identify its common role, e.g., which is more frequent: n increse, or decrese in price when stickiness increses? We do this in two wys: First, we verge the effect over ll prmeters vlues in our numericl clcultions, i.e., over ll 4,64 cses. Second, we regress our vribles of interest (e.g., price nd the shre of revenues from the pid versus the free version) over ll the prmeters of the model (e.g., stickiness nd cost). These results re reported in the next section.

25 5. Min Results Tble presents the outcome of OLS regressions where the explntory vribles re stickiness δ nd the other three prmeters of the model, which re used s controls (ε, c, nd k), while the DVs re given in the heding of the tble. Tble : Effects of model s prmeters on price, dvertising, nd profits 9 Profits Price Advertising intensity Shre of profits from pid version ε Uncertinty ns δ Stickiness c Holding cost k Advertising contribution Adj. R 58.%.7% 69.% 50.4% AIC -8 5,50-0,90 4,750 BIC -83 5,565-0,858 4,795 All coefficients re stndrdized nd significnt t the 0.00 level except for the one mrked with ns. Recll tht higher stickiness implies tht the individuls cn enjoy higher levels of utility from the pp lso in the second period. Thus, it is not surprising tht higher stickiness leds to higher price nd higher dvertising intensity, s well s higher profits. The estimtes imply tht the two decision vribles of the firm, price nd d intensity, increse with stickiness level. In other words, while we find some specific cses (i.e., specific vlues of εε, cc nd kk) for which pp nd γγ might decrese in δδ, these re the exceptions to the 9 in,9 cses out of totl of 4 = 4,64 cses, the firm did not find it optiml to enter the mrket (i.e., with the optiml choice of price nd dvertising, profits turned out to be zero), nd thus we hve N =,4 for ll of the following regressions nd grphs. 3

26 rule. Controlling for the vrious vlues of εε, cc nd kk, while regressing the optiml price nd d intensity on δδ, we find positive coefficient. Also, the sme holds for the effect of εε on γγ. The rtionle behind the incresing effect of stickiness δδ on pp is the following: The higher the stickiness, the higher the utility the individul cn derive from the pp in the second period, ergo her willingness to py increses. The rtionle behind the incresing effect of εε on pp is bit different: At first glnce, it looks s if the role of εε is symmetric, s it ppers s α ε or α + ε in the utility of the consumer. This is misleding, s if the reliztion of the utility isα ε, then the consumer might not use the pp t ll in the second period, while if the reliztion is α + ε, the consumer might either continue to use the free pp, or switch to the pid version. Therefore, n increse in uncertinty hs n symmetric effect; indeed, it pushes some consumers out of the mrket, but on the other hnd it shifts enough consumers from free to pid version in the second period. It lso implies tht the effect of uncertinty will be smller thn tht of stickiness: While n increse in stickiness implies tht the utility of the pp in the second period is lrger ergo the incresed demnd nd profits n increse in uncertinty increses both the number of consumers who stop using the product s well s the number of consumers who switch to the pid version. These conflicting effects of uncertinty re reflected in the fct tht uncertinty follows the direction of stickiness, yet by lower mgnitude (see Tble ). If one wnts to consider the effect of uncertinty on the shre of profits from the monetiztion tools, we will lso see similr pttern, yet with lower mgnitude. 5. Stickiness nd the profitbility of monetiztion tools The lst column in Tble ddresses one of the centrl issues of this study: the impct of stickiness on the monetiztion of pps. It turns out tht the higher the stickiness, the higher the shre of profit from the pid version. To get better sense of this result, consider Figure 5. In 4

27 Figure 5, we plot the reltive shres of the pid nd free versions over stickiness. It is evident tht s stickiness increses, the reltive shre in profits of the pid version goes up, nd, of course, tht of the free version goes down. In Figure 5b, we see the brekdown of the profit into these two monetiztion tools. It turns out tht the profit from the pid version goes up sizbly with stickiness, yet tht of the free version goes up nd then dips. Figure 5: Effect of stickiness on shre of profits from free nd pid versions of the pp Shre of profits 80% 70% 60% 50% 40% 30% 0% 0% 0% Stickiness Shre of profits from free version Shre of profits from pid version Figure 5b: Effect of stickiness on profits from free nd pid version of the pp Profits Stickiness Profits from free version Profits from pid version Totl profits 5

28 To understnd the rtionle of these results, recll tht individuls who do not use the pp re chrcterized by low mtch-utility; those who use the free version hve medium level of αα, nd those who buy the pid version hve high level. As pointed out bove, when stickiness increses, consumers willingness to py increses s well. This pushes some of the non-users towrd the free version, nd some of those who re using the free version towrd the pid version. As result, if price nd d intensity do not chnge, the shre of the non-users decreses, while the shre of individuls who use the pid version increse. At the sme time, the shre of those using the free version might either increse or decrese. Indeed, it is likely tht for low levels of stickiness, the mss of individuls who move from being non-users to users of the free version would be higher thn of those who re moving from the free to the pid; while for high stickiness, the opposite will hppen. And this might explin the rise nd then the fll in the profit from the free version. However, in the optimum, prices nd d intensity do chnge nd intervene in this process. Specificlly, s we hve shown bove, when stickiness levels increse, both vribles, pp nd γγ, increse (s the firm cptures some of the increse in consumers willingness to py). Figure 5 demonstrtes tht, even when the increse in pp nd γγ re tken into ccount, the profit from the pid version increses with δδ, while the role of dvertising s source of profit increses, nd then decreses. This is summrized in the following results: Result. With n increse in stickiness, shre of profits decreses in the free version, nd increses in the pid version. Result b. Profits from the pid version of the pp increse with stickiness, while profits from the free version first increse, nd then decrese with stickiness. Level of uncertinty, i.e., εε, lso contributes to the firm s profit, but to lesser degree, s demonstrted in the second column of Tble. As mentioned bove, higher εε mens higher 6

29 vlue from using the pp in the first period, nd thus higher willingness to py. Furthermore, higher εε lso leds lrger proportion of individuls using the free version in the first period to switch to the pid version in the second. These two effects (higher willingness to py in the first period, nd lrger proportion of switchers to the pid version in the second period) contribute to the profit of the firm. However, higher εε lso hs some negtive effect on profit, s lrger proportion of users of the free version stop using the pp in the second period. As result, the contribution of εε to profit is lower thn tht of δδ. To further understnd the interctions between stickiness nd uncertinty, observe Tble, which shows the firm s profitbility t vrious levels of stickiness nd uncertinty. Tble : Profits s function of stickiness nd uncertinty levels Stickiness Uncertinty If the gme lsts only single period (zero stickiness), or if stickiness is low, it is esy to see tht there is no effect (or little effect) of uncertinty: Consumers downlod the pp, nd whtever they lern in the first period cnnot be used, s there is no second period; or else the benefit in the second period is negligible. In prticulr, we show tht stickiness cn ffect the difference between the cses: When nlyzing elsticities in Tble, we find tht the interction between stickiness nd uncertinty is non-symmetric: Stickiness hs pronounced effect on 7

30 sensitivity of profits to uncertinty, while uncertinty hs smller effect on sensitivity of profits to stickiness. 5. The role of dvertising s contribution In one-period model, i.e., δδ = 0, the only contribution of the free version to profits is vi dvertising revenues. In this subsection, we show tht in two-period model, i.e., δδ > 0, the free version cn increse profits in nother wy. To illustrte this point, consider the cse of kk = 0: In one-period model, the firm s objective function (Eqution 7) is not function of d intensity t ll, nd the optiml decision of the firm is to offer pid version only, s free version cnnot increse its profits in ny wy, nd thus will not be offered. However, in model with stickiness, the firm s objective function depends on d intensity even when kk = 0. Furthermore, the free version with ds cn yield profits even if dvertisers re not pying for these ds. In two-period model, the free version contributes to the profit of the firm not just vi dvertising revenues, but lso by cting s sort of smple. Specificlly, some individuls who would otherwise not use the pp (s the pid version is too costly for them) downlod nd use the free version to lern bout their fit with the pp. Some of these re likely to switch in the second period to the pid version. Thus, even if dvertisers do not py for ds, the firm cn benefit from offering free version with ds. However, offering this version lso hs some costs: Some individuls who would otherwise buy the pid version, might be ttrcted to the free version. Thus, the optiml level of dvertising blnces between two incentives. To exmine this ide tht the free version with ds cn yield profits even if dvertisers re not pying for these ds we focused our nlysis on ll cses in which kk = 0. Indeed, we find in our numericl cses tht when kk = 0, it is still optiml for the firm to offer the free 8

31 version, nd the optiml level of dvertising therein is 0 < γγ <. The firm hs two sources of income: the consumers who downloded the pid version in the first period; nd the consumers who chose to downlod the free version in the first period, then switch to the pid version in the second period. The firm does not relize ny revenues from the ltter segment in the first period (s k = 0), but does relize some profits from these consumers in the second period. This sitution might ber some similrity to producing n imperfect product (e.g., Fornell nd Wernerfelt 988), except tht the firm constructs this imperfect product knowing full well tht it will not obtin ny direct benefit from it, its min motivtion being to get some consumers to downlod it for the ske of lerning bout its fit to their preferences. The firm mkes money only from the pid version of the pp, despite setting n optiml level of dvertising for the free version, from which it erns no revenues. This is summrized in the next sttement: Result. When dvertising s contribution to the firm s profits is zero, the firm still dvertises, despite the fct tht it sees no revenues from these ds. We conclude this subsection by noting nother interesting finding on dvertising intensity: In the fourth column of Tble, we find tht n increse in k leds to decrese in γγ. Recll tht the dvertising contribution prmeter k converts the dvertising intensity vrible (γγ) into monetry terms comptible with price, such s $. In other words, we find tht when dvertisers py more for dvertising, the firm decreses its dvertising intensity. This result is not s strnge s it sounds first. When k increses, the firm fces two conflicting forces: On the one hnd, it wishes to increse d intensity in order to directly benefit from the higher py. On the other hnd, n increse in d intensity (which nnoys consumers) would decrese the shre of individuls who will choose the free version, nd thus might eventully decrese the income from dvertising. Thus the finl decision of the firm of whether to increse or decrese d 9

32 intensity depends upon the model s elsticities, nd in our cse, it is optiml to decrese d intensity. 5.3 The interctions between the monetiztion tools The previous discussion leds to question of specil interest to prctitioners: While some firms re offering both versions of the pp, pid nd free, others offer only one, nd there re questions in the industry whether the two should co-exist (Ntnson 06). From strightforwrd economic point of view, disregrding progrm opertion costs, hving the bility to use two monetiztion tools should improve profits over using one tool only. Thus, the only wy our nlysis cn provide some insights to prctitioners is by () shedding light on the dynmics resulting from hving the two versions versus only one, nd (b) identifying the conditions under which hving two versions is especilly ppeling. We begin by solving three cses: ) the joint free/pid versions re vilble; b) only the free version is vilble; nd c) only the pid version is vilble. We then compre the three results in terms of price, dvertising, nd profits. While verge dvertising nd price for the joint cse re 0.50 nd 0.70 respectively, in the seprte cses, these re much lower, given by 0.4 nd 0.44 respectively. This points to cler price discrimintion in the joint cse, leding obviously to higher profits. In other words, by hving high γγ, the firm is pushing the high-αα individuls wy from the free version nd into the pid version; while hving high pp ensures tht the medium-αα individuls re pushed wy from the pid version nd into the free version. If only the pid version is vilble, prices hve to be lower in order to ttrct more users, especilly some medium-αα individuls. The reson for the lower γγ in the cse of the two versions (versus one) is more interesting: Consider the cse of firm tht hs only the free version nd is bout to dd the pid version. In order to gin the most from hving both options, 30

33 it must mke the pid version especilly ppeling for the high-αα individuls, nd one wy of doing so is by mking the free version less ppeling vi higher d intensity. Indeed, it is likely to lose some users those with reltively lower αα re now likely to void the pp ltogether but our nlysis shows tht this risk is worth tking. Next, we wish to identify the conditions under which offering both free nd pid is especilly ppeling to the firm. We do this by looking t the correltion between the stickiness level nd the difference in profits between joint progrm nd one-tool progrms. We find positive correltion between stickiness nd the difference in profits between joint nd free version only (r = 0.4; p < 0.0), nd negtive correltion between stickiness nd profits difference between joint nd pid only progrm (r = 0.; p < 0.0). This result is closely relted to Result b, which demonstrtes tht s stickiness increses, the shre of profits from the pid version of the pp increses. Wht we find now, vi those correltions, is tht when stickiness is high, the gin in profit from hving both options versus offering the pid version only is reltively low. In other words, when stickiness is high, the ppel of dding free version is the lowest. Thus, tking into ccount cost considertions, this would be one of the cses in which it might be better for the firm to refrin from dding free version. The following sttement summrizes this result. Result 3: The gin in the firm s profits due to price discrimintion when both versions exist decreses in stickiness when compred to the pid-only version, nd increses in stickiness when compred with the free-only version. 6. Discussion The significnce of the ongoing customer reltionship for profitbility hs been demonstrted in numerous studies nd business writings in the lst two decdes (Gupt et l. 004; Reichheld nd Tel 996). App cretors who trditionlly hve focused on customer 3

34 cquisition re incresingly reminded of the power of stickiness (Perro 06; Yloz 05). Recent reports show tht mngers my be indeed listening: A sizeble increse in pp retention in 05 is prtly ttributed to pp cretors bilities to engge customers by providing vlue without sking for too much informtion (Shul 06). Here we looked beyond the mere effect of stickiness on profitbility to explore how stickiness my drive monetiztion. We focused on the tension between the min monetiztion sources: pying consumers versus pying dvertisers. While the tension between the monetiztion options is recognized s fundmentl to pp success (Pozin 04), in-depth nswers s to the drivers of the use of ech re lcking. Furthermore, to the best of our knowledge, no previous studies hve nlyzed this issue in customer durtion dynmic setting. Here we show tht such setting, i.e., stickiness level, leds to some importnt insights on price levels, dvertising intensity, profitbility, nd profitbility sources. We show tht s stickiness increses, prices nd d intensity increse, nd firms ern more of their profits from pying customers thn they do from dvertising. Specificlly, we find tht when stickiness increses, the firm s erning from the pid version increses monotoniclly. However, its ernings from dvertising first increse, then drop. Accordingly, the shre of profit ccruing from the pid version increses with the stickiness level throughout. Furthermore, we demonstrte tht in dynmic setting, firm cn profit from offering free version with ds even if dvertisers re not pying for those ds. In other words, the firm benefits from offering version of the pp tht includes ds even if the consumers re not pying for the pp nd the dvertisers re not pying for the ds. The logic behind this result is the following: In dynmic setting, the free version cts s sort of smple tht enbles consumers to lern their fit with the pp. The firm would rther dd ds to this version (even if 3

35 they re not pid for) in order to keep the consumers who hve high vlution of the pp wy from the smple nd buying the py version. We lso consider the dilemm fced by some firms bout whether to offer two versions of the pp (free nd pid) or only one version. Of course, when operting costs re ignored, offering two versions is more profitble. However, our nlysis cn identify the cses in which the dditionl profit is miniml. In such cses, tking costs into ccount, offering just one version might hve more consumer ppel. Indeed, we find, for exmple, tht when the stickiness level is high, the firm might benefit by focusing on the pid version nd voiding the free version. It hs yet to be seen how increse in stickiness will ffect mrkets, yet recent reports on the incresing importnce of in-pp purchses in pp cretors profitbility re t lest consistent with the reported increse in stickiness (Needelmn 06). Our nlysis elucidtes the combined role of uncertinty nd stickiness in creting the mrket dynmics of pps. Specificlly, the role of uncertinty is complex, s overll higher uncertinty, nd in prticulr under high levels of stickiness, cn led to higher profits. This finding deprts from the conventionl wisdom regrding digitl products, which sys tht mrketers should seek to decrese the level of the uncertinty of fit to individuls (Mtt nd Hess 06). However, for free digitl products where product tril is prt of the business cycle, nd where the firm profits from dvertising during tril, higher uncertinty reflects lso the bility to ttrct customers who otherwise would not hve downloded the pp, s they do so if they believe the upside is lrge enough to ber the costs of trying the product in the first plce. Our ttempt to cpture complex mrket sitution with reltively prsimonious model clerly hs number of limittions. One issue is the lck of explicit modeling of competitive ctivity, beyond the pp holding cost, which tkes into ccount lterntive spce, time, nd 33

36 competitive pps. The dded complexity thereof is beyond our scope here. It should lso be mentioned tht it is not trivil to model explicit competition, due to the complex mening of wht constitutes competitor in this mrket. Mny free products compete in generl sense for users ttention nd time, nd not necessrily with products to which they re very similr. However, there my be specific ctegories in which cler, direct competitors emerge. We exmined specific freemium model in which the premium version of the product hd no dvertising. There re more complex free business models in which, for exmple, people purchse in-pp dditions tht chnge the product s utility in vrious wys. Modeling ech of these scenrios would dd complexity tht we felt is unneeded t this stge, yet cn of course be done in future explortions. In the sme vein, we ssumed fixed price for the pid version. This ssumption is supported by mrket observtions nd interviews with mngers, which suggest tht given the short time periods, the pid version price is lrgely fixed. Chnging this ssumption dds significnt complexity to the model, yet cn be n interesting venue for future reserch. More generlly, we believe our results to hve brod implictions beyond the specific freemium model discussed here. In recent yers, much ttention hs been devoted to how the online ecosystem hs led to fundmentl chnges in business ctivities such s dvertising (Goldfrb 04), competitive strtegy (Csdesus-Msnell nd Zhu 00), nd product pricing nd design (Knnn 03). Most nlyses of these topics hve not explicitly tken into ccount the role of retention in the emergence of mrket strtegies. Yet in online mrkets, retention is not only importnt, but is lso more esily trceble thn in most offline businesses. We suggest tht more ttention should be pid to this issue s bsic prt of nlysis of firms optiml behvior in these emerging mrkets. 34

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41 Web Appendices Web Appendix A: Three scenrios for the utility of free pp We define the following: lifetime expected utility from the three options 0 : U (WA) U = α ( γ ) c + mx( 0, ) + mx( 0, b, d ) U = α c p + mx( 0, e) + mx( 0, f ) 0 p = 0 where UU 0, UU, nd UU pp re the expected utility from the no-use, use free, nd use pid options, respectively; nd (WA) = b = d = e = f = ( α ε ) ( γ ) ( α + ε ) ( γ ) ( α + ε ) δ c ( α ε ) δ c ( α + ε ) δ c δ c δ c p Let α be the threshold when expression (b) of Eqution equls zero ( α = c ( γ ) ε ) δ. Similrly α - the threshold when Expression () equls zero ( α = ε γ δ + ), c 3 3 c + p α s the threshold when Expression (d) equls zero ( α = ε ). δ We define the following utility equtions: U - the utility when, b, d < 0, α( ) c U = γ ( ) U - the utility when b > 0 nd d, < 0, = α( γ ) c + [( α + ε )( γ ) δ c] 3 U 3 U - the utility when b, > 0 nd d < 0, U ( )( ) c 4 U - the utility when d > b > 0 nd > 0 4 = γ c + α ε γ δ c + α + ε δ U = α γ + δ ( ) [( )( ) ] [( ) c p] α 0 Note tht Equtions WA nd WA re equivlent to Equtions nd 3; however, we use the extended version here, s the multiple expressions in Eqution WA llow for smoother discussion of this web ppendix. 39

42 5 U - the utility when d > 0 nd b, < 0, = ( γ ) c + [( α + ε ) δ c p] 5 The reltive loctions ofα, α, nd U α 3 α define the possible scenrios for U. Since α > for α 3 3 ll α, the only three possible scenrios re defined when: α > α > α, α > α > α, nd α > α > α. As result of the following scenrio nlyses, the scenrios lso differ s per the 3 reltive size of the price: high, intermedite, nd low. 3 Scenrio : α > α > α - high price In the first scenrio, price is reltively high, so only customers with high α will consider moving to the pid version in the second period. In the second period, s α increses, first the consumers with positive reliztion of ε will use the free version (Expression (b)), then those with negtive reliztion of ε will lso use the free version (Expression ()), nd finlly, those with positive 3 reliztion of ε will move to the pid version (Expression (d)). In this scenrio, α > α > α. Note tht positive vlue for brek point α requires c > ε ( γ )δ, or we begin with section rther thn with U. Furthermore, once α is lrge enough so tht Expression (b) is greter thn zero, the consumer will move to the pid version only when her utility from pying is greter thn her utility from the free version, where Expression (d) = Expression (b), given by α = p 4 3 ε, nd not in threshold α (in this cse γδ α >, or 4 3 α c p > ). In ddition, for this γ 4 4 scenrio to hold, we needα > α > α ; while α > is lwys true, α > is described by the following limittion, defining the lrge p: α p Lrge ( γ ) α ε δγ + cγ >. Also note tht if εε is γ lrge enough, α is negtive, nd this scenrio begins with the second segment of Figure WA rther thn the first segment. U The slopes of the utility segments of Figure WA re given by the following equtions: (WA3) U = α γ for α < α δ ( γ )( + ) for α < α < α 4 ( )( ) ( )( ) γ + δ for α < α < α δ δ 4 γ + + for α < α 40

43 Figure WA: Utility of free pp, high price scenrio 3 Scenrio : α > α > α - intermedite price In Scenrio, price is t n intermedite level, so customers with lower α thn in Scenrio will consider moving to pid version in the second period. In the second period, s α increses, first the consumers with positive reliztion of ε will use the free version (Expression (b)), then those with positive reliztion of ε will move to the pid version (Expression (d)), nd finlly, those with negtive reliztion of ε will use the free version (Expression ()). In this scenrio, α > α > α. Note tht positive vlue for brek point α requires c > ε ( γ )δ, or we strt 3 with section U rther thn withu. Similr to Scenrio, the threshold for moving from free to 4 pid version is given byα. In ddition, for this scenrio to hold, we needα > α > α ; while α α > is lwys true, we need to limit α to be inα > α > α. α > is described by the 4 ( ) α ε γ δγ + cγ 4 following limittion (the opposite of Scenrio s limit): p <, nd α > α is γ 4

44 cγ described by the following: p >. Thus, the intermedite p is defined by: γ ( γ ) cγ ε δγ + cγ < pinter < γ γ Figure WA: Utility of free pp, intermedite price scenrio The slopes of Figure WA s utility segments re given by the following equtions: (WA4) U = α γ for α < α δ 4 ( γ )( + ) for α < α < α ( ) ( )( ) δ 4 γ + for α < α < α δ δ γ + + for α < α 3 Scenrio 3: α > α > α - low price In the third scenrio, price is reltively low, so customers with lower α thn in Scenrio will consider moving to the pid version in the second period before even considering the free version. In the second period, s α increses, first the consumers with positive reliztion of ε will move to the pid version (Expression (d)), nd then those with negtive reliztion of ε 4

45 3 will use the free version (Expression ()). In this scenrio, α > α > α. Recll tht 3 c + p α = ε. Also, once α is lrge enough tht Expression (d) exceeds Expression (b), this δ inequlity will hold for ny lrger α. Thus, in this scenrio, α is not used, s consumers with positive reliztion of ε will use the pid rther thn the free version in the second period. The slopes of the utility segments of Figure WA re given by the following equtions: U 3 γ for α < α δ 3 (WA5) = ( γ ) + for α < α < α α δ δ ( )( ) γ + + for α < α Note tht positive vlue for brek pointα requires c + p > εδ, or we strt with section rther thn withu. Note tht for this scenrio to hold, we needα > cγ the following limittion, defining the smll p: p Smll <. γ Figure WA3: Utility of free pp, low price scenrio 3 α 5 U, which is described by 43

46 Web Appendix B: Proofs of Lemm In this web ppendix, we show tht for ll p, γ, δ, ε, nd c, when α = 0, U(0) > Up(0). Notice tht when α = 0, from Eqution we get: U U p ( 0) = c + mx[ 0, ε ( γ ) δ c, εδ c p] ( 0) = c p + mx[ 0, εδ c] There re two cses to consider: Cse WB: > εδγ In this cse, we get tht: U ( ) U ( 0) p (i.e., ( γ ) δ c > εδ c p p p 0 p = εδ + c p ε ) εγδ for < ε ( γ ) ( γ ) δ < c for ε for εδ < c δ c < εδ The first line is non-negtive, since in this cse (i.e., Cse WB), we know tht p > εδγ, nd thus certinly p > εδγ. The third line is non-negtive, s p 0. For the second line, s c > ε ( γ )δ, we know tht ( -γ ) δ = p εγδ 0 p (becuse in Cse I, p > εδγ ). c εδ + > p > εδ + ε Cse WB: p < εδγ In this cse, we get tht: U p ( 0) U p( 0) = εδ + p for c < εδ p c for εδ p < c p for εδ < c < εδ The first nd third lines re non-negtive, s p 0. The second line is for c > εδ p, thus we know tht p > εδ c, nd s c < εδ, we cn write tht p > εδ c > 0, nd it is immedite tht p > ( εδ c), which leds to p εδ + c > 0. Notice tht U(0) = Up(0) only when p = 0, s if p > 0, then U(0) > Up(0). 44

47 Web Appendix C: Proofs of Lemm In this ppendix, we show tht for ll p, γ, δ, ε, nd c; nd for ech α, the slope of Up is greter thn tht of U. Recll the slopes of Up: for α < α p U p δ = + for α p < α < α p α + δ for α p < α We now compre these slopes to tht of the three scenrios of U from Web Appendix A. 3 Scenrio : α > α > α - high price γ for α < α δ ( )( ) U The slopes of U in scenrio re: γ + for α < α < α =. 4 α ( γ )( + δ ) for α < α < α δ δ 4 γ + + for α < α Since α < p α when α α < either ( γ ) p α p ( )( ), when α <, the slope of Up = nd the slope of U = γ. As α <, α p <, the slope of Up = ( δ δ + ) nd the slope of U ( γ )( + ) δ or ( γ )( + ) vlue of ll of the slopes bove. p α, tht is, it cn be. Finlly, when α p < α, the slope of Up = + δ, which is the highest 3 Scenrio : α > α > α - intermedite price The slopes of U in scenrio re : U = α γ for α < α δ 4 ( γ )( + ) for α < α < α δ 4 ( γ ) + for α < α < α ( )( ) δ δ γ + + for α < α When α <, the slope of Up = nd the slope of U = γ (recll tht α < α p when α α < <, the slope of Up = ( + δ ) nd the slope of U ( γ ) + p α p. δ p α ). Asα <,. Finlly, when α p < α, the slope of Up = + δ, which is the highest vlue of ll of the slopes bove. p α 45

48 3 Scenrio 3: α > α > α - low price δ 3 The slopes of U in scenrio 3 re: = ( γ ) + for α < α < α α δ δ ( )( ) γ + + for α < α U 3 γ for α < α 3 When α <, the slope of Up = nd the slope of U = γ (since α < ). When α α < α p <, the slope of Up = ( + δ ) nd the slope of U ( γ ) + p α p δ p α, sα <. Finlly, p α whenα p < α, the slope of Up = + δ, which is the highest vlue of ll of the slopes bove. U Thus, in ll of the three cses, we get U p < α α nd Up intersect, it hppens only once. for ll α, leding to the conclusion tht if U Web Appendix D: The joint effects of stickiness nd uncertinty In the text we hve shown tht the effect of stickiness nd uncertinty depend on the model s prmeters. Here we provide some dditionl insights on this. To understnd the intricte effects of the interply between stickiness nd uncertinty on demnd nd profits, observe Figure WD tht depicts the choices of consumers in both periods, for prticulr set of prmeters (c = 0., k = 0.5). The res in Figure WD re mrked ccording to the differing levels of stickiness nd uncertinty nd their effects on the consumers behvior in both periods. Note tht this figure ws computed so tht price nd dvertising re t their optiml levels for the firm. In the three A res in Figure WD, the stickiness level is low so tht even with high level of uncertinty (which dds to the utility level in Period in the cse of positive εε), consumers who downloded the free pp in the first period re out of the mrket in the second. Consumers who downloded the pid version in the first period, re either out of the mrket in Are A, or remin with the pid version in Are A for positive εε, or with positive nd negtive εε in Are A3. Likewise, the stickiness is just high enough in the Ares B for the free downloders to sty for the second period for positive εε only, while the pid downloders sty for nother period, except for negtive εε in Are B. In the two res denoted by C, when εε is positive, some free consumers switch to pid, while others keep the free version. Moreover, negtive εε users sty out of the mrket. Similr to Ares B, the pid downloders sty for nother period, except for negtive εε 46

49 in Are C. In Are D, the uncertinty is so low nd stickiness reltively high, so tht consumers of free nd pid pps stick to their decisions in the second period. Figure WD: Stickiness nd uncertinty regimes (c = 0., k = 0.5) Uncertinty Stickiness The following tble summrizes the consumers behviors in ech re of Figure WD: Tble WD: Stickiness nd uncertinty regimes Are st period s pp version nd period usge low vlution (negtive εε) nd period usge high vlution (positive εε) 47 Price (on verge) Advertising (on verge) A free (low) 0.70 (med) pid - - A free (low) 0.70 (med) pid - Pid A3 free (low) 0.70 (med) pid pid pid B free - free 0.7 (med) 0.67 (low) pid - pid B free - free 0.80 (med) 0.69 (low) pid pid pid C free - free or pid* 0.9 (high) 0.75 (high) pid - pid C free - free or pid* 0.9 (high) 0.74 (high)