From Growth to Monetization: Managing Freemium Services

Abstract

Motivated by the recent rapid growths of freemium services, we study freemium service providers’ dynamic operating policies to maximize their lifetime profits. We adopt a hybrid of the Bass diffusion model and the replicator equation from evolutionary game theory to capture the user base growth, and model the provider’s dynamic decisions as an optimal control problem. We analyze two variants of the freemium business model inspired by two prominent examples, Dropbox and Spotify, which, respectively, adopt the monetization strategies of limiting features and advertising (and its removal). We establish the optimal dynamic operating policies for the Dropbox-inspired ad-free freemium model and the Spotify-inspired ad-supported freemium model and identify their distinctive operational characteristics: the optimal policies as well as the sustainability of the Dropbox model critically depend on the network effect among users, whereas the optimal policies of the Spotify model show that advertising could be a more effective monetization strategy than limiting features. The latter observation is confirmed in a general model allowing both monetization strategies where the optimal policies consistently adopt advertising without limiting features. We then show that the freemium model significantly outperforms the ad-supported free model in weak advertising markets and that offering multiple tiers of premium subscription is unnecessary and confirm our core insights’ robustness under a generalized network effect, customized advertisements, and liquidity constraints. Our study establishes the versatility and value of the freemium model to suit distinct needs of a service in different stages from growth to monetization, and provides guidelines for service providers adopting this business model.

1. Introduction

Freemium, a portmanteau of free and premium, refers to the business model that allows users to enjoy a product or service’s basic or full features for free, and also offers the option for users to pay for an enhanced experience. The freemium business model was first used in the software industry in the 1980s, but grew explosively into a mainstream business model in the 2000s, largely leveraging the similarly explosive growth of the Internet. The logic of the freemium model is to efficiently grow a user base by offering a basic free experience and then monetize the user base with a premium experience. Although the freemium model can be applied to products as well, it is usually associated with services. In fact, a popular strategy of modern manufacturers is to “servicize” their products, namely selling the products’ functionalities as services rather than selling the products themselves. Therefore, in this article, we focus on freemium services.

A typical freemium service model involves a provider offering free service to its users while attempting to monetize the user base. To provide two representative examples, Dropbox, a cloud storage and sharing service, provides free users with 2 GB of cloud storage space whereas premium subscribers receive 2,000 or more gigabytes of cloud storage space and other perks such as file encryption and recovery (Dropbox, 2022a); and Spotify, a music streaming service, provides free users with unlimited streaming of its entire music library with advertisements whereas premium subscribers can stream music ad-free. Both businesses prove highly successful. Within 4 years after its launch, Dropbox hit the milestone of 100 million users in 2012 (Blacklinko, 2023). Similarly, Spotify, launched in 2008, now serves 551 million monthly active users, with 220 million being premium subscribers (BusinessofApps, 2023). Interestingly, these examples respectively represent the two most important freemium monetization strategies—limiting features and advertising (and its removal). In this article, we focus our study on these two monetization strategies. ¹

A freemium service provider faces a myriad of operational decisions such as the free service and included advertisements, the premium subscription price, and the promotion efforts to grow its user base. Furthermore, as a business model depending heavily on growing its user base, the freemium operating characteristics in early stages may differ significantly from late stages, because the provider’s early decisions not only determine its immediate revenue but may also strongly influence the user base’s growth trajectory and thus the future profitability. The complex decisions and their dynamic nature make managing the freemium model highly challenging for the service provider.

To study a freemium service provider’s dynamic operational decision-making throughout its lifetime, we adopt a hybrid of the Bass diffusion model and the replicator equation from evolutionary game theory to capture the user base growth, and model the provider’s dynamic decisions as an optimal control problem. We analyze two variants of the freemium business model inspired by the two prominent examples, Dropbox and Spotify, which, respectively, adopt the monetization strategies of limiting features and advertising (and its removal). We establish the optimal dynamic operating policies for both variants. In both cases, we find that the optimal operating policies exhibit a threshold structure such that the service provider prioritizes growth in early stages and may not immediately introduce premium subscription, and gradually shifts the focus to monetization in later stages after amassing a critical user base.

We also identify the Dropbox- and Spotify-inspired models’ distinctive operational characteristics. The sustainability of the Dropbox-inspired ad-free freemium model relies on a sufficiently important network effect among users, and interestingly, the optimal free service and premium subscription price may be non-monotonic over time. In the Spotify-inspired ad-supported freemium model, we establish that the provider should always offer full free service and include the maximum number of advertisements, establishing that advertising is a more effective monetization strategy than limiting features. We show that the insights from the Dropbox and Spotify models are respectively retained with a generalized network effect and customized advertisements. We then evaluate a general model encompassing the Dropbox and the Spotify models to confirm that advertising (and its removal) is a more effective monetization strategy than limiting features, and recover key results such as that the optimal operating policies exhibit a threshold structure and that the optimal free service and premium subscription price may be non-monotonic with a strong network effect. Finally, we show that the freemium model significantly outperforms the ad-supported free model in weak advertising markets and that offering multiple tiers of premium subscription is unnecessary, and confirm our core insights’ robustness under liquidity constraints.

Our paper shows that freemium service providers should be aware of the growth and monetization trade-off as well as the key features of their services as they may heavily impact the optimal operating policies. The providers should prioritize the advertising monetization strategy if possible, whereas limiting features offers an alternative monetization strategy when advertising is unavailable or unsuitable. Overall, the freemium model excels in the versatility to suit different needs of a service in different stages from growth to monetization. These insights justify the adoption of the freemium business model and provide guidelines for its adopters.

In the rest of this article, we review the related literature in Section 2 before analyzing the Dropbox freemium model in Section 3, the Spotify freemium model in Section 4, and a general freemium model in Section 5. We then perform additional analyses and derive further insights in Section 6 before summarizing the paper in Section 7. All proofs are relegated to the E-Companion.

2. Related Literature

A business practice related to the freemium model is free trials. The free-trial model traditionally refers to a service being offered free-of-charge for a limited time before users need to pay for continued use; see, for example, Foubert and Gijsbrechts (2016) and Wang and Özkan-Seely (2018). The freemium model is distinguished from the free-trial model by offering base features forever free (some modern free-trial services offer unlimited free trials which makes them essentially freemium services).

There is an extensive literature on the freemium business model, primarily in the Marketing and Information Systems areas. Niculescu and Wu (2011, 2014) study the freemium model in the software industry. Runge et al. (2022) investigate the impact of pricing on a freemium service’s conversion rate and revenue via field experiments. Appel et al. (2020) study the retention and monetization of mobile apps adopting the freemium model. Shi et al. (2019) examine the optimality of the freemium model with product differentiation and network externalities. Ascarza et al. (2021) identify a twofold effect of customer retention in freemium settings through field experiments. Kamada and Öry (2020) compare the freemium versus referral programs in terms of generating customer word-of-mouth. Deng et al. (2023) empirically examine the spillover effects between the free and paid versions of a mobile app. Each of these papers focuses on one or few salient elements of the freemium model, including valuation learning, pricing, word-of-mouth, network effect, customer retention, contracting, and spillover. Our paper is distinguished from these papers with a holistic analysis of the freemium model adopting a general dynamic optimal control framework encompassing all of its key elements. An application of the freemium model in video games is the free-to-play model where all gameplay contents are typically offered for free with no advertisements and the games are monetized through sales of in-game cosmetic items (Lam et al., 2020; Mai and Hu, 2022). This unique monetization strategy is distinct from those considered in this article—limiting features and advertising, and accordingly, the aforementioned papers focus on video game-specific mechanics, including in-game digital goods release timing, matchmaking efficiency, and social comparisons among players. By contrast, this article has broad applicabilities to general freemium services adopting the popular monetization strategies of limiting features and advertising.

Our paper adopts a modified Bass diffusion model to capture the user base growth. The Bass diffusion model is a classic model for innovation adoptions introduced by Bass’s (1969) seminal paper; see Meade and Islam (2006) for a comprehensive review of the innovation adoption literature employing this model (there are also papers employing alternative models for innovation adoptions; see, e.g., Niu et al., 2021; Wang et al., 2021). In the Operations Management literature, the Bass diffusion model has been primarily adopted to study the production and inventory decisions for innovative goods undergoing capacity-constrained Bass diffusion; see, for example, Ho et al. (2002), Kumar and Swaminathan (2003), Shen et al. (2011, 2014), and Hu and Sun (2022). Our work differs from this stream of literature by studying services rather than manufacturing, and consequently focusing on decisions such as pricing and advertising rather than production and inventory.

We adopt the optimal control theory to study an Operations Management problem. Sethi (2019) provides a comprehensive review of the applications of the optimal control theory in management science and economics. Some notable papers that apply the optimal control theory to Operations Management problems include Ha (1997a, 1997b, 2000) (make-to-stock production), Berling and Martínez de Albéniz (2011), Yang et al. (2014), Feng et al. (2014), Feng et al. (2020), Xu et al. (2019), Gong and Chao (2013) (inventory control), Wang et al. (2016), Yuan et al. (2018), Xu et al. (2020), Kim and Xu (2024) (environmental and risk management), and Hu and Sun (2022) (self-replicating production). Our paper expands the Operations Management literature adopting the optimal control theory.

3. Dropbox Model: Ad-Free Freemium With Network Effect

We first analyze the Dropbox freemium model. Dropbox, a cloud storage and sharing service, provides free users with 2 GB of cloud storage space whereas premium subscribers receive 2 TB of cloud storage space or more and other perks such as file encryption and recovery (Dropbox, 2022b). Notably, Dropbox does not include third-party advertisements (possibly because advertising is incompatible with a cloud-storage service). Another characteristic of Dropbox’s service is the network effect: Dropbox allows cloud-based file sharing between users, and thus Dropbox users derive utilities not only from individual usage but also all active users’ collective usage of the service.

To capture the Dropbox freemium model, we consider a service provider facing a market of a continuum of potential users with a normalized size of 1; that is, the maximum possible size of the user base for the service is 1. Each potential user derives base utility $u$ from each unit of service. We assume that $u$ follows a distribution $F$ over [0, 1]; that is, $F(u)$ users have base utilities below $u$ . Of all potential users, we denote the amount of active users by $n\in [0,1]$ who are constantly using the provider’s service. The assumption of constant service usage is an abstraction of relatively consistent usage patterns; for example, a Dropbox user stores data with the service all the time. We assume that the provider offers a full unit of service per unit time to each premium user at subscription price $p$ per unit time, and offers $\varphi \in [0,1]$ units of service per unit time to each free user due to potentially limited service (namely the limiting-features monetization strategy; e.g., limited storage space offered by Dropbox), with the cost of service normalized to zero. There is no third-party advertisements.

We allow users to derive utilities from individual usage as well as all active users’ collective usage of the service; that is, the network effect. The usefulness of the Dropbox service depends not only on one’s individual storage space but may also on the size of Dropbox’s active user base and the amount of storage available to free users (because a shared storage involving free users would be limited by the latter’s storage capacity). The network effect has been the subject of study in the Operations Management literature; for example, Shi et al. (2019) and Birge et al. (2021). We denote the relative importance of the network effect in users’ utilities by $\theta$ and assume that a user derives utility $u[1-\theta +\theta w(\varphi ,n)]$ per unit service, where the network effect $w(\varphi ,n)$ is increasing in the free service $\varphi$ and the active user base $n$ (in Section 3.1, we analyze an extension of the Dropbox model with a generalized network effect and find that all key results remain). We also assume $w(\varphi ,n)<1$ to reflect that users primarily derive utilities from individual usage of the service. We respectively express free and premium users’ net utilities per unit time in the Dropbox freemium model given base utility $u$ :

$$\begin{array}{rl}{\mathrm{\Pi }}_F(u)& =u\varphi [1-\theta +\theta w(\varphi ,n)],\\ {\mathrm{\Pi }}_P(u)& =u[1-\theta +\theta w(\varphi ,n)]-p.\end{array}$$

By comparing ${\mathrm{\Pi }}_F(u)$ and ${\mathrm{\Pi }}_P(u)$ , one can immediately see that users with sufficiently high base utilities $u>u^{*}$ will subscribe to the premium service, where $u^{*}$ solves ${\mathrm{\Pi }}_F(u^{*})={\mathrm{\Pi }}_P(u^{*})$ .

Lemma 1 (Dropbox model premium subscription)

The proportion of premium users in the Dropbox freemium model is $1-F(u^{*})$ , where

(i)

$u^{*}=p/[(1-\varphi )(1-\theta +\theta w(\varphi ,n))]$ , if $p<(1-\varphi )(1-\theta +\theta w(\varphi ,n))$ ;

(ii)

$u^{*}=1$ , otherwise.

As explained in Section 1, the logic of the freemium model is to efficiently grow a user base by offering a basic free experience and then monetize the user base with a premium experience. Therefore, we need to model the dynamic growth of user base $n(t)$ for potentially varying operational parameters over time. Since a freemium service can have millions of potential users, it would be unrealistic to assume that all of them have sufficient information and sophistication to make fully rational decisions about using the service. Therefore, instead of modeling each individual potential user’s decision, we model the aggregate-level dynamics of the active user base growth. There are two main drivers for the user base growth. First, the provider can run (costly) promotions to attract users, and we denote the provider’s promotion effort by $\rho$ . Second, existing active users’ word-of-mouth—passing of information from person to person—is also a well-documented driver of user base growth in freemium models (e.g., Kamada and Öry, 2020), and the strength of the word-of-mouth may depend on the active users’ experience. Specifically, we adopt the following model to capture the dynamics of the active user base growth:

$$\mathrm{d}n(t)/\mathrm{d}t=[\rho (t)+\mathrm{\Pi }(p(t),\varphi (t),n(t))n(t)][1-n(t)],$$

(1)

where

$$\begin{array}{rl}\mathrm{\Pi }(p(t),\varphi (t),n(t))& ={\int }_0^{u^{*}(t)}{\mathrm{\Pi }}_F(u,\varphi (t),n(t))\mathrm{d}F(u)\\ & +{\int }_{u^{*}(t)}^1{\mathrm{\Pi }}_P(u,p(t),n(t))\mathrm{d}F(u)\end{array}$$

is all active users’ average net utility, and the provider’s promotion effort $C(\rho (t))$ satisfies $C^{\prime },C^{″}>0$ .

To interpret the user base growth model (1), first note that the provider’s promotion effort converts the $1-n(t)$ potential users into active users at rate $\rho (t)$ . We further assume that the $n(t)$ active users exert a collective influence, magnified by their average net utility, on the $1-n(t)$ potential users and convert the latter into active users at rate $\mathrm{\Pi }(p(t),\varphi (t),n(t))n(t)$ . Combining both effects yields equation (1). Note that this equation generalizes the Bass diffusion model (Bass, 1969) by endogenizing the coefficient of imitation to be proportional to the active users’ average utility $\mathrm{\Pi }(p(t),\varphi (t),n(t))$ . On the other hand, it also generalizes the replicator equation in evolutionary game theory (Weibull, 1997) by adding an exogenous drift term $\rho (t)$ to the original formulation. Therefore, equation (1) can be seen as a hybrid of the two influential models. Such a model is particularly suitable for studying the growth of service systems for the mass market.

With the user base growth dynamics established, we can now investigate the service provider’s optimal decisions. In particular, we allow the provider to dynamically control the promotion effort $\rho (t)$ , the premium subscription price $p(t)$ , and the free service $\varphi (t)$ over time. We assume that the provider leverages these decisions to maximize the service’s lifetime total discounted profit at discount rate $r$ . Throughout this article, we require that the discount rate $r$ is not so large that the optimal policy is always myopic. The specific upper bound of $r$ for each model is included in the proof of the corresponding proposition. Although the premium subscription price $p(t)$ has no intrinsic upper bound, per Lemma 1, if $p(t)>[1-\varphi (t)][1-\theta +\theta w(\varphi (t),n(t))]$ , then $u^{*}(t)=1$ (no premium users). As such, we can impose an upper bound $p^U=[1-\varphi (t)][1-\theta +\theta w(\varphi (t),n(t))]$ for $p(t)$ without loss of generality, because any $p(t)>p^U$ is equivalent to $p(t)=p^U$ which captures not introducing premium subscription. Formally, the provider’s problem is formulated as follows:

$$\begin{array}{rl}\underset{\rho (t),p(t),\varphi (t)}{max}& {\int }_0^{\mathrm{\infty }}[n(t)(1-F(u^{*}))p(t)-C(\rho (t))]e^{-rt}\mathrm{d}t\end{array}$$

(2)

$$\begin{array}{rl}\text{s.t.}& \mathrm{d}n(t)/\mathrm{d}t=[\rho (t)+\mathrm{\Pi }(p(t),\varphi (t),n(t))n(t)][1-n(t)],\\ & \mathrm{\Pi }(p(t),\varphi (t),n(t))={\int }_0^{u^{*}(t)}{\mathrm{\Pi }}_F(u,\varphi (t),n(t))\mathrm{d}F(u)\\ & +{\int }_{u^{*}(t)}^1{\mathrm{\Pi }}_P(u,p(t),n(t))\mathrm{d}F(u),\\ & {\mathrm{\Pi }}_F(u,\varphi (t),n(t))=u\varphi (t)[1-\theta +\theta w(\varphi (t),n(t))],\\ & {\mathrm{\Pi }}_P(u,p(t),n(t))=u[1-\theta +\theta w(\varphi (t),n(t))]-p(t),\\ & {\mathrm{\Pi }}_F(u^{*},\varphi (t),n(t))={\mathrm{\Pi }}_P(u^{*},p(t),n(t)),\\ & n(0)=0,\rho (t)\ge 0,0\le \varphi (t)\le 1,0\le p(t)\le p^U\\ & =[1-\varphi (t)][1-\theta +\theta w(\varphi (t),n(t))].\end{array}$$

Problem (2) is a continuous-time optimal control problem. Following the standard approach, we apply Pontryagin’s maximum principle for the current-value formulation (Sethi 2019) to (2). Let $\lambda (t)$ be the co-state variable for the state variable $n(t)$ . The current-value Hamiltonian is as follows:

$$\begin{array}{rl}& H(n,\rho ,p,\varphi ,\lambda ,t)\\ & =n(t)[1-F(u^{*})]p(t)-C(\rho (t))\\ & +\lambda (t)[\rho (t)+\mathrm{\Pi }(p(t),\varphi (t),n(t))n(t)][1-n(t)].\end{array}$$

Since Problem (2) contains constraints on the control variables $\rho (t)$ , $p(t)$ , and $\varphi (t)$ , we need to define a Lagrangian for the Hamiltonian incorporating such constraints. We let ${\mu }_{\rho }^L$ , ${\mu }_p^{L/U}$ , and ${\mu }_{\varphi }^{L/U}$ be the respective Lagrange multipliers for the constraints $\rho (t)\ge 0$ , $0\le p(t)\le p^U$ , and $0\le \varphi (t)\le 1$ . The Lagrangian for the current-value Hamiltonian is

$$\begin{array}{rl}& L(n,\rho ,p,\varphi ,\lambda ,{\mu }_{\rho }^L,{\mu }_p^{L/U},{\mu }_{\varphi }^{L/U},t)\\ & =H(n,\rho ,p,\varphi ,\lambda ,t)+{\mu }_p^{L}p(t)+{\mu }_p^U[p^U-p(t)]\\ & +{\mu }_{\varphi }^L\varphi (t)+{\mu }_{\varphi }^U[1-\varphi (t)]+{\mu }_{\rho }^L\rho (t).\end{array}$$

Pontryagin’s maximum principle requires the following conditions for any $t$ at optimality:

First-order condition:

$$\begin{array}{rl}& n(t)-n(t)[F^{\prime }(u^{*})\frac{\mathrm{\partial }{u}^{*}}{\mathrm{\partial }p(t)}p(t)+F(u^{*})]\\ & +\lambda (t)n(t)[1-n(t)]\frac{\mathrm{\partial }\mathrm{\Pi }(p(t),\varphi (t),n(t))}{\mathrm{\partial }p(t)}\\ & ={\mu }_p^U-{\mu }_p^L-{\mu }_p^U\frac{\mathrm{\partial }{p}^U}{\mathrm{\partial }p(t)},-n(t)p(t)\mathrm{d}F(u^{*})\frac{\mathrm{\partial }{u}^{*}}{\mathrm{\partial }\varphi (t)}\\ & +\lambda (t)n(t)[1-n(t)]\frac{\mathrm{\partial }\mathrm{\Pi }(p(t),\varphi (t),n(t))}{\mathrm{\partial }\varphi (t)}\\ & ={\mu }_{\varphi }^U-{\mu }_{\varphi }^L-{\mu }_p^U\frac{\mathrm{\partial }{p}^U}{\mathrm{\partial }\varphi (t)},C^{\prime }(\rho (t))-\lambda (t)[1-n(t)]={\mu }_{\rho }^L.\end{array}$$

Complementary slackness:

$$\begin{array}{rl}& {\mu }_{\rho }^L\rho (t)=0,{\mu }_p^{L}p(t)=0,{\mu }_{\varphi }^L\varphi (t)=0,{\mu }_p^U[p^U-p(t)]=0,\\ & {\mu }_{\varphi }^U[1-\varphi (t)]=0,{\mu }_{\rho }^L,{\mu }_p^{L/U},{\mu }_{\varphi }^{L/U}\ge 0.\end{array}$$

Adjoint condition:

$$\begin{array}{rl}{\lambda }^{\prime }(t)& =r\lambda (t)-\frac{\mathrm{\partial }}{{\mathrm{\partial }}_n}L(n,\rho ,p,\varphi ,\lambda ,{\mu }_{\rho }^L,{\mu }_p^{L/U},{\mu }_{\varphi }^{L/U},t)\\ & =r\lambda (t)-[[1-F(u^{*})]p^{*}(t)+\lambda (t)(-{\rho }^{*}(t)\\ & +\mathrm{\Pi }(p^{*}(t),{\varphi }^{*}(t),n^{*}(t))-2\mathrm{\Pi }(p^{*}(t),{\varphi }^{*}(t),n^{*}(t))n^{*}(t))].\end{array}$$

Transversality condition:

$$\underset{t\to \mathrm{\infty }}{lim}{e}^{-rt}\lambda (t)\ge 0,\underset{t\to \mathrm{\infty }}{lim}{e}^{-rt}\lambda (t)n^{*}(t)=0.$$

For analytical tractability, from now on, we focus on the case where the users’ base utility $u$ follows a uniform distribution over $[0,1]$ ( $F(x)=x$ ), and the network effect function is $w(\varphi ,n)=\varphi \sqrt{n}.$ This network effect formulation implies a network effect proportionally increasing in the free service level and concavely increasing in the user base (we investigate a generalized network effect formulation in Section 3.1). By analyzing the necessary conditions holding at optimality as required by Pontryagin’s maximum principle, we can characterize properties of the provider’s optimal dynamic operating policies. The following proposition summarizes these properties and structurally describes the provider’s optimal policies.

Proposition 1 (Dropbox model optimal policies)

The optimal dynamic operating policies of the Dropbox model satisfy the following:

(i)

The promotion effort ${\rho }^{*}(t)$ decreases over time and converges to 0 as $t\to \mathrm{\infty }$ .

(ii)

The provider does not offer premium subscription until a finite threshold time (which can be 0).

(iii)

The free service ${\varphi }^{*}(t)$ and premium subscription price $p^{*}(t)$ may be non-monotonic over time.

(iv)

As $t\to \mathrm{\infty }$ , ${\varphi }^{*}(t)$ converges to ${\varphi }^{*}(\mathrm{\infty })=max\{1-1/(2\theta ),0\}$ , whereas $p^{*}(t)$ converges to $p^{*}(\mathrm{\infty })=1/(8\theta )$ if $\theta \ge 1/2$ or $p^{*}(\mathrm{\infty })=(1-\theta )/2$ if $\theta <1/2$ .

Corollary 1 (Dropbox model sustainability)

The Dropbox freemium model is sustainable in the long run ( ${\varphi }^{*}(\mathrm{\infty })>0$ ) if and only if $\theta >1/2$ .

Proposition 1 shows that the service provider’s optimal dynamic decisions can be complex and non-monotonic. The optimal promotion effort should decrease over time as the user base grows and word-of-mouth becomes increasingly crucial in driving user base growth. The introduction of premium subscription has a threshold structure. In early stages of the service, the provider should maximize user base growth, and may offer full service to all users free of charge until after amassing a critical user base, when it starts to limit service to free users and introduce premium subscription. As the service reaches maturity, the free service and premium subscription price converge to myopic revenue-maximizing levels. In particular, Corollary 1 shows that the Dropbox freemium model is only sustainable in the long run with a sufficiently important network effect; otherwise, the freemium model would eventually become a regular subscription model with no free service. This finding provides an important guideline for services that intend to adopt the Dropbox freemium model and monetize users through limiting features: the long-term sustainability of the Dropbox freemium model requires a sufficiently important network effect.

Figure 1 illustrates the optimal operating policies of the Dropbox freemium model for varying importance of the network effect $\theta$ and cost of promotion $c$ (assuming $C(\rho )=c{\rho }^2$ ). In these examples, we evaluate the model in a sufficiently long finite horizon ( $t\in [0,20]$ ) to simulate an infinite horizon. Case (a) is a combination of low network effect importance and low promotion cost; both point to less need for free users (who can generate the network effect and word-of-mouth). As a result, the freemium model in this case degenerates into a regular subscription model where no free service is offered and all users are premium users. The promotion effort decreases and the subscription price increases over time; both are reasonable given that the provider gradually shifts the priority from user base growth to profitability. Case (b) has low network effect importance and high promotion cost. Therefore, in early stages, the provider offers free service for all to maximize word-of-mouth instead of solely depending on promotion to grow the user base. After amassing a critical user base, the provider introduces premium subscription and gradually reduces the free service, eventually transitioning into a regular subscription model. The behavior of the promotion effort and the premium subscription price is similar to Case (a). These cases are not examples of a sustainable Dropbox freemium model because free service is either never offered or only offered in early stages to stimulate growth.

Figure 1.

Optimal operating policies of the Dropbox model. (a) $\theta =0.3$ , $c=0.6$ , (b) $\theta =0.3$ , $c=1.8$ , (c) $\theta =0.7$ , $c=0.6$ , and (d) $\theta =0.7$ , $c=1.8$ . Notes: This example is generated with $C(\rho )=c{\rho }^2$ and $r=0.05$ .

Case (d) is similar to Case (b), but the high network effect importance means that free users provide significant value for premium users. As a result, the provider continues to offer free service even when the user base approaches 1. Perhaps the most interesting one is Case (c), where the optimal premium subscription price $p^{*}$ and free service ${\varphi }^{*}$ are non-monotonic over time. In this case, the low promotion cost means that the provider does not need to depend on free users’ word-of-mouth to drive initial user base growth (at which time the network effect is also negligible), and can focus on monetization in the earliest stage. Therefore, at $t=0$ , no free service is offered and a relatively high subscription price is charged similar to Case (a). However, the high network effect importance means that, as the user base grows after the service launch, free users increasingly drive the user base growth, and thus the provider offers increasing levels of free service (while generally reducing the subscription price to prevent premium users from unsubscribing). This is true until the user base reaches a critical mass when monetization again overtakes growth as the provider’s priority, and Case (c) begins to behave similarly to Case (d) in that the provider gradually reduces the free service and increases the premium subscription price, but eventually still offers free service. In short, Case (c) can be seen as an amalgam of Cases (a) and (d), which explains the non-monotonic premium subscription price and free service. Cases (c) and (d) are examples of a sustainable Dropbox freemium model where free service is offered throughout the service’s lifetime.

Figure 1 demonstrates how the Dropbox freemium model suits different needs in different stages of the service’s life time. In early stages, the free users generate word-of-mouth to drive user base growth, which can substitute conventional promotion when the latter is costly. In later stages, the freemium model adds value to premium users through the network effect by continuing to attract free users, thus enhancing the limiting-feature monetization strategy. Such versatility is a highlight of the Dropbox freemium business model.

3.1. Generalized Network Effect

We have thus far adopted the network-effect formulation $w(\varphi ,n)=\varphi \sqrt{n}$ . The idea was that the service’s network effect (e.g., a group’s shared storage space) should be limited by the free service (e.g., the free storage space) and concavely increasing in the active user base $n$ . This formulation, however, contains simplifications for tractability; for example, a group may or may not contain a free user, and the likelihood depends on the group size and the overall proportion of free users. In this section, we derive a generalized network-effect formulation by considering the $M$ members of a group where $M$ is a random variable. Recall that the proportion of free users equals $u^{*}$ assuming uniformly distributed base utilities. Therefore, the likelihood that a group of size $M$ contains at least one free member is $1-(1-u^{*}{)}^M$ , yielding the network-effect formulation $w(\varphi ,u^{*},n)={\mathbb{E}}_M[\varphi (1-(1-u^{*}{)}^M)+(1-u^{*}{)}^M]\sqrt{n}$ . We assume that $M$ follows an exponential distribution with a variable parameter $\lambda (u^{*})>0$ , which implies that the group size distribution may depend on the proportion of free users. The exponential distribution has a long right tail that is consistent with naturally formed group sizes, and yields the relatively simple expression

$$w(\varphi ,u^{*},n)=\varphi \sqrt{n}+\frac{(1-\varphi )\lambda (u^{*})\sqrt{n}}{\lambda (u^{*})-\log (1-u^{*})}.$$

One can see that the network-effect formulation $w(\varphi ,n)=\varphi \sqrt{n}$ adopted in model (2) is part of this generalized formulation. We rewrite $\lambda (u^{*})=g(u^{*})\log (1-u^{*})$ (where $\lambda (u^{*})>0$ requires $g(u^{*})<0$ ) to yield an algebraic formulation $w(\varphi ,u^{*},n)=\varphi \sqrt{n}+(1-\varphi )\sqrt{n}g(u^{*})/(g(u^{*})-1).$ As such,

$$\begin{array}{rl}{\mathrm{\Pi }}_F(u)& =u\varphi [1-\theta +\theta w(\varphi ,u^{*},n)],\\ {\mathrm{\Pi }}_P(u)& =u[1-\theta +\theta w(\varphi ,u^{*},n)]-p.\end{array}$$

Note that ${\mathrm{\Pi }}_F(u^{*})={\mathrm{\Pi }}_P(u^{*})$ defines users’ premium subscription equilibrium. The following lemma further specifies a sufficient condition for a unique premium subscription equilibrium.

Lemma 2

There is at most one solution $u^{*}\in [0,1]$ to ${\mathrm{\Pi }}_F(u^{*})={\mathrm{\Pi }}_P(u^{*})$ if $g^{\prime }(u^{*})\le 0$ .

The Dropbox model is analytically intractable with the generalized network effect. Therefore, we let $g(u^{*})=-u^{*}$ based on Lemma 2 and perform numerical experiments. Four representative examples are offered in Figure 2. These examples well replicate the four cases of Figure 1, showing that the insights revealed by the Dropbox model (2) are robust with the generalized network effect.

Figure 2.

Optimal operating policies of the Dropbox model with generalized network effect. (a) $\theta =0.3$ , $c=0.6$ , (b) $\theta =0.3$ , $c=1.8$ , (c) $\theta =0.9$ , $c=0.6$ , and (d) $\theta =0.9$ , $c=1.8$ . Notes. This example is generated with $C(\rho )=c{\rho }^2$ and $r=0.05$ .

4. Spotify Model: Ad-Supported Freemium Without Network Effect

We next analyze the Spotify freemium model. Spotify, a music streaming service, interlaces third-party advertisements between songs for free users, whereas premium users can enjoy the music ad-free (among other perks; see Spotify 2022). Notably, Spotify’s music streaming service does not exhibit a significant network effect (e.g., a user’s experience is not significantly enhanced by a growing user base). Therefore, Spotify offers a natural contrast with Dropbox by incorporating advertising that is incompatible for the latter as a monetization strategy, while not exhibiting a significant network effect that is important for the latter.

To capture the Spotify freemium model, we modify the Dropbox freemium model of Section 3 as follows. First, reflecting the nature of Spotify, we remove the network effect by setting $\theta \equiv 0$ and include third-party advertisements. We further note that advertisements may induce disutility. Consider a free user with utility $u$ per unit service and disutility $d$ per unit advertisement; their net utility with $\alpha$ amount of advertisement per unit service would be $u-\alpha d$ . This formulation is widely adopted in the literature; for example, DeValve and Pekeč (2022). Recall that $u$ is heterogeneous among all users; it is conceivable that $d$ is also heterogeneous and may be correlated with $u$ ; that is, users who enjoy the content more are less tolerant toward advertisements. In this model, we make a simplifying assumption for tractability that $u$ and $d$ are perfectly correlated and $d=\beta u$ . Under this assumption, a free user’s net utility with $\alpha$ amount of advertisement per unit service $u-\alpha d$ becomes $u(1-\alpha \beta )$ . We further define $a=\alpha \beta$ and write the net utility as $u(1-a)$ . Effectively, we convert the provider’s absolute advertising decision $\alpha$ into a relative advertising decision $a$ . The intuitive requirement that $\alpha$ should not be so large as to reduce free users’ net utilities below zero becomes $a\le 1$ . Note that in this model, the utilities of users with different $u$ are reduced to zero at the same relative advertising level $a=1$ (absolute advertising level $\alpha =1/\beta$ ); this property significantly simplifies the analysis by eliminating the need for customized advertisements. In Section 4.1, we study a variant of the Spotify model with non-perfectly correlated utility from service and disutility from advertisements that justifies customized advertisements, and show that our main insights are preserved.

We denote the amount of revenue the provider receives from third-party advertisers per advertisement impression (or “eyeball”) by $q^{\prime }$ . In order to be consistent with the utility model, we define $q=q^{\prime }/\beta$ so that the advertising revenue from displaying $\alpha$ (absolute) advertisements, $\alpha q^{\prime }$ , equals $aq$ (recall that $a=\alpha \beta$ ), where $q$ can be understood as the advertising revenue per relative advertising level. Recall that a user receives at most 1 unit of utility from a unit of service. Therefore, we further require $q<1$ to ensure that a user generates less advertising value than the utility they can derive from the service; otherwise, the provider can simply pay users to receive advertisements.

Although Spotify provides free users with unlimited streaming of its entire music library, limiting free service remains a viable option; therefore, we allow $\varphi <1$ to reduce a free user’s per-unit-time service to $u\varphi$ . Their disutility from advertisements remain $\alpha d=ua$ for relative advertising level $a$ . As such, the free and premium users’ net utilities per unit time in the Spotify freemium model given base utility $u$ are

$${\mathrm{\Pi }}_F(u)=u(\varphi -a),{\mathrm{\Pi }}_P(u)=u-p,$$

where we require $\varphi \ge a$ to ensure free users to have non-negative utilities. Comparing ${\mathrm{\Pi }}_F(u)$ and ${\mathrm{\Pi }}_P(u)$ yields the following lemma:

Lemma 3 (Spotify model premium subscription)

The proportion of premium users in the Spotify freemium model is $1-F(u^{*})$ , where

(i)

$u^{*}=p/(1+a-\varphi )$ , if $p<1+a-\varphi$ ;

(ii)

$u^{*}=1$ , otherwise.

The rest of the model, including the user base growth dynamics, remains unchanged. Accordingly, the provider’s problem is formulated as follows:

$$\begin{array}{rl}\underset{\rho (t),p(t),\varphi (t),a(t)}{max}& {\int }_0^{\mathrm{\infty }}[n(t)[(1-F(u^{*}))p(t)+F(u^{*})a(t)q]\\ & -C(\rho (t))]e^{-rt}\mathrm{d}t\end{array}$$

(3)

$$\begin{array}{rl}\text{s.t.}& \mathrm{d}n(t)/\mathrm{d}t=[\rho (t)+\mathrm{\Pi }(p(t),\varphi (t),a(t))n(t)][1-n(t)],\\ & \mathrm{\Pi }(p(t),\varphi (t),a(t))={\int }_0^{u^{*}(t)}{\mathrm{\Pi }}_F(u,\varphi (t),a(t))\mathrm{d}F(u)\\ & +{\int }_{u^{*}(t)}^1{\mathrm{\Pi }}_P(u,p(t))\mathrm{d}F(u),\\ & {\mathrm{\Pi }}_F(u,\varphi (t),a(t))=u[\varphi (t)-a(t)],\\ & {\mathrm{\Pi }}_P(u,p(t))=u-p(t),\\ & {\mathrm{\Pi }}_F(u^{*},\varphi (t),a(t))={\mathrm{\Pi }}_P(u^{*},p(t)),\\ & n(0)=0,\rho (t)\ge 0,0\le \varphi (t)\le 1,0\le a(t)\le \varphi (t),\\ & 0\le p(t)\le p^U=1+a(t)-\varphi (t).\end{array}$$

Similar to Problem (2), we apply Pontryagin’s maximum principle for the current-value formulation (Sethi, 2019) to Problem (3). Let $\lambda (t)$ be the co-state variable for the state variable $n(t)$ . The current-value Hamiltonian is as follows:

$$\begin{array}{rl}& H(n,\rho ,p,\varphi ,a,\lambda ,t)\\ & =n(t)[1-F(u^{*})]p(t)+n(t)F(u^{*})a(t)q\\ & -C(\rho (t))+\lambda (t)[\rho (t)+\mathrm{\Pi }(p(t),\varphi (t),a(t))n(t)][1-n(t)].\end{array}$$

We let ${\mu }_{\rho }^L$ , ${\mu }_p^{L/U}$ , ${\mu }_{\varphi }^{L/U}$ , and ${\mu }_a^{L/U}$ be the respective Lagrange multipliers for the constraints $\rho (t)\ge 0$ , $0\le p(t)\le p^U$ , $0\le \varphi (t)\le 1$ , and $0\le a(t)\le 1$ . The Lagrangian for the current-value Hamiltonian is

$$\begin{array}{rl}& L(n,\rho ,p,\varphi ,a,\lambda ,{\mu }_{\rho }^L,{\mu }_p^{L/U},{\mu }_{\varphi }^{L/U},{\mu }_a^{L/U},t)\\ & =H(n,\rho ,p,\varphi ,a,\lambda ,t)\\ & +{\mu }_p^{L}p(t)+{\mu }_p^U[p^U-p(t)]+{\mu }_{\varphi }^L\varphi (t)+{\mu }_{\varphi }^U[1-\varphi (t)]\\ & +{\mu }_a^{L}a(t)+{\mu }_a^U[\varphi (t)-a(t)]+{\mu }_{\rho }^L\rho (t).\end{array}$$

Pontryagin’s maximum principle requires the following conditions for any $t$ at optimality:

First-order condition:

$$\begin{array}{rl}& n(t)[1-F^{\prime }(u^{*})\frac{\mathrm{\partial }{u}^{*}}{\mathrm{\partial }p(t)}p(t)-F(u^{*})]+n(t)a(t)\frac{\mathrm{\partial }F(u^{*})}{\mathrm{\partial }p(t)}q\\ & +\lambda (t)n(t)[1-n(t)]\frac{\mathrm{\partial }\mathrm{\Pi }(p(t),\varphi (t),a(t))}{\mathrm{\partial }p(t)}\\ & ={\mu }_p^U-{\mu }_p^L,-n(t)p(t)F^{\prime }(u^{*})\frac{\mathrm{\partial }{u}^{*}}{\mathrm{\partial }\varphi (t)}+n(t)a(t)\frac{\mathrm{\partial }F(u^{*})}{\mathrm{\partial }\varphi (t)}q\\ & +\lambda (t)n(t)[1-n(t)]\frac{\mathrm{\partial }\mathrm{\Pi }(p(t),\varphi (t),a(t))}{\mathrm{\partial }\varphi (t)}\\ & ={\mu }_{\varphi }^U-{\mu }_{\varphi }^L-{\mu }_a^U-{\mu }_p^U\frac{\mathrm{\partial }{p}^U}{\mathrm{\partial }\varphi (t)},\\ & -n(t)p(t)F^{\prime }(u^{*})\frac{\mathrm{\partial }{u}^{*}}{\mathrm{\partial }a(t)}+n(t)[a(t)\frac{\mathrm{\partial }F(u^{*})}{\mathrm{\partial }a(t)}+F(u^{*})]q\\ & +\lambda (t)n(t)[1-n(t)]\frac{\mathrm{\partial }\mathrm{\Pi }(p(t),\varphi (t),a(t))}{\mathrm{\partial }a(t)}\\ & ={\mu }_a^U-{\mu }_a^L-{\mu }_p^U\frac{\mathrm{\partial }{p}^U}{\mathrm{\partial }a(t)},\\ & C^{\prime }(\rho (t))-\lambda (t)[1-n(t)]={\mu }_{\rho }^L.\end{array}$$

Complementary slackness:

$$\begin{array}{rl}& {\mu }_{\rho }^L\rho (t)=0,{\mu }_p^{L}p(t)=0,{\mu }_{\varphi }^L\varphi (t)=0,{\mu }_a^{L}a(t)=0,\\ & {\mu }_p^U[p^U-p(t)]=0,{\mu }_{\varphi }^U[1-\varphi (t)]=0,\\ & {\mu }_a^U[\varphi (t)-a(t)]=0,{\mu }_{\rho }^L,{\mu }_p^{L/U},{\mu }_{\varphi }^{L/U},{\mu }_a^{L/U}\ge 0.\end{array}$$

Adjoint condition:

$$\begin{array}{rl}{\lambda }^{\prime }(t)& =r\lambda (t)-\frac{\mathrm{\partial }}{\mathrm{\partial }n}L(n,\rho ,p,\varphi ,a,\lambda ,{\mu }_{\rho }^L,{\mu }_p^{L/U},{\mu }_{\varphi }^{L/U},{\mu }_a^{L/U},t)\\ & =r\lambda (t)-[[1-F(u^{*})]p^{*}(t)+F(u^{*})a(t)q+\lambda (t)(-{\rho }^{*}(t)\\ & +\mathrm{\Pi }(p^{*}(t),{\varphi }^{*}(t),a^{*}(t))-2\mathrm{\Pi }(p^{*}(t),{\varphi }^{*}(t),a^{*}(t))n^{*}(t))].\end{array}$$

Transversality condition:

$$\underset{t\to \mathrm{\infty }}{lim}{e}^{-rt}\lambda (t)\ge 0,\underset{t\to \mathrm{\infty }}{lim}{e}^{-rt}\lambda (t)n^{*}(t)=0.$$

We once again focus on the case of $F\sim \text{Uniform}[0,1]$ . By analyzing the necessary conditions holding at optimality as required by Pontryagin’s maximum principle, we can characterize properties of the provider’s optimal dynamic operating policies. The following proposition summarizes these properties and structurally describes the provider’s optimal policies.

Proposition 2 (Spotify model optimal policies)

The optimal dynamic operating policies of the Spotify model satisfy the following:

(i)

The promotion effort ${\rho }^{*}(t)$ decreases over time and converges to 0 as $t\to \mathrm{\infty }$ .

(ii)

The provider does not include advertisements or offer premium subscription until a finite threshold time (which can be 0).

(iii)

The provider always offers full free service ${\varphi }^{*}(t)\equiv 1$ and always includes maximum advertisements $a^{*}(t)\equiv 1$ for free users after introducing premium subscription.

(iv)

The premium subscription price $p^{*}(t)$ increases over time and converges to $p^{*}(\mathrm{\infty })=(1+q)/2$ as $t\to \mathrm{\infty }$ .

Proposition 2 for the Spotify freemium model replicates several properties of Proposition 1 for the Dropbox freemium model, including the decreasing promotion effort, the threshold for introducing premium subscription, and the convergence to the myopic revenue-maximizing premium subscription price (see Figure 3); by contrast, the Spotify freemium model’s premium subscription price is always increasing as opposed to possibly being non-monotonic in the Dropbox freemium model.

Figure 3.

Optimal operating policies of the Spotify model. Notes: This example is generated with $q=0.5$ , $C(\rho )=2{\rho }^2$ , and $r=0.05$ .

The most crucial new operating characteristic of the Spotify freemium model is that the provider should always offer full free service and always include maximum advertisements for free users after introducing premium subscription. Notably, this finding is consistent with practice: Spotify’s free users indeed have access to its entire music library and regularly complain about “ads after every song” (PiunikaWeb, 2022). To understand this policy, one only needs to understand that more advertisements improve the freemium service provider’s profitability from both free and premium users: free users generate more advertisement impressions (“eyeballs”), and premium users are willing to pay more to remove all advertisements. Therefore, the provider includes maximum advertisements for free users (without driving them away). The finding that the provider always offers full free service and maximum advertisements shows that advertising is a more effective monetization strategy than limiting features for Spotify-like services: advertisements generate revenue from both free and premium users, whereas limiting features only generates revenue from premium users.

4.1. Customized Advertisements

Thus far, we have assumed perfectly correlated utility $u$ per unit service and disutility $d$ per unit advertisement. This assumption simplifies the analysis. Particularly, when $d=\beta u$ and by defining $a=\alpha \beta$ , a free user’s net utility $u-\alpha d=u(1-a)$ . This means that we can include the same maximum relative advertisements $a=1$ (equivalently, the same maximum absolute advertisements $\alpha =1/\beta$ ) for users of different utilities $u$ . In this case, there is no need for customized advertisements. It is however necessary to check if the key findings of the Spotify model; that is, the provider always offers full free service and always includes maximum advertisements, remain robust without the simplification.

To do so, in this section, we assume potentially independent user utility from the service and disutility from advertisements, and assume that the provider can discover users’ dis/utility through their consumption patterns and customize their advertisements accordingly; that is, including potentially different amounts of advertisements for different users. In fact, YouTube has recently introduced a new advertisement frequency management strategy that allows the system to adjust the amounts of included advertisements “specifically tailored to video content consumption patterns (Rijo, 2025).” In particular, we assume that four different types of users with respective utilities from the service and disutilities from advertisements $(u_l,d_l)$ , $(u_l,d_h)$ , $(u_h,d_l)$ , and $(u_h,d_h)$ exist, where $u_h\ge u_l\ge d_h\ge d_l$ . We denote the users with dis/utility $(u_i,d_j)$ by type $ij$ , denote their proportion by $x_{ij}$ , $\sum x_{ij}=1$ , and denote the absolute amount of advertisements included for them by ${\alpha }_{ij}$ . Recall that $\varphi \in [0,1]$ denotes the amount of offered free service per unit time. A free/premium type $ij$ user’s net utilities per unit time are, respectively,

$${\mathrm{\Pi }}_F^{ij}=\varphi u_i-{\alpha }_{ij}{d}_j,{\mathrm{\Pi }}_P^{ij}=u_i-p,$$

whose comparison determines whether type $ij$ users subscribe to the premium service. We require $\varphi u_i\ge {\alpha }_{i,j}{d}_j$ , $i,j=h,l$ to ensure free users to have non-negative utilities. Let $I_{ij}$ be the indicator for $\{{\mathrm{\Pi }}_P^{ij}>{\mathrm{\Pi }}_F^{ij}\}$ (i.e., premium subscription). The provider’s problem becomes

$$\begin{array}{rl}\underset{\rho (t),p(t),\varphi (t),{\alpha }_{ij}(t)}{max}& {\int }_0^{\mathrm{\infty }}[n(t)\sum _{i,j}{x}_{ij}[I_{ij}p(t)+(1-I_{ij}){\alpha }_{ij}{q}^{\prime }]\\ & -C(\rho (t))]e^{-rt}\mathrm{d}t\end{array}$$

(4)

$$\begin{array}{rl}\text{s.t.}& \mathrm{d}n(t)/\mathrm{d}t=[\rho (t)+\mathrm{\Pi }(p(t),\varphi (t),{\alpha }_{ij}(t))n(t)]\\ & \times [1-n(t)],\\ & \mathrm{\Pi }(p(t),\varphi (t),{\alpha }_{ij}(t))=\sum _{i,j}{x}_{ij}[I_{ij}{\mathrm{\Pi }}_P^{ij}+(1-I_{ij}){\mathrm{\Pi }}_F^{ij}],\\ & {\mathrm{\Pi }}_F^{ij}(\varphi (t),{\alpha }_{ij}(t))=\varphi (t)u_i-{\alpha }_{ij}(t)d_j,\\ & {\mathrm{\Pi }}_P^{ij}(p(t))=u_i-p(t),\\ & n(0)=0,\rho (t)\ge 0,p(t)\ge 0,0\le \varphi (t)\le 1,\\ & 0\le {\alpha }_{ij}(t)\le \varphi (t)u_i/d_j.\end{array}$$

This model is too complex to analyze in general and we resort to numerical experiments. We illustrate an example in Figure 4 where the included advertisements for different types of users are presented separately for clarity.

Figure 4.

Optimal operating policies of the Spotify model with customized advertisements. Notes: This example is generated with $x_{ij}=0.25$ , $i,j\in \{h,l\}$ , $u_h=1$ , $u_l=0.6$ , $d_h=0.5$ , $d_l=0.1$ , $q^{\prime }=0.5$ , $C(\rho )=10{\rho }^2$ , and $r=0.05$ .

Comparing Figure 4 with Figure 3, one can see in Figure 4(a) that the structures of the optimal promotion ${\rho }^{*}$ , offered free service ${\varphi }^{*}$ , and user base $n^{*}$ are preserved. In particular, the provider always offers full free service ( ${\varphi }^{*}=1$ ). The gradual increase of the premium subscription price $p^{*}$ in Figure 3 is replaced with a fixed price in Figure 4(a) because the provider can now more effectively balance growth versus monetization via customized advertisements.

Figure 4(b) presents the respective optimal levels of included advertisements for type $ij$ users with utility $u_i$ from the service and disutility $d_j$ from advertisements, where $i,j=h,l$ . These optimal advertisement levels exhibit clear patterns. First of all, the provider always includes maximum advertisements for free users once advertisements are introduced, which is consistent with both the theoretical result in Proposition 2(iii) and the numerical observation in Figure 3 of the Spotify model without customized advertisements. Furthermore, when customizing advertisements, the maximum advertisements and the timing of their introductions differ among different user types. One can see that the maximum advertisements ${\alpha }_{ij}=\varphi u_i/d_j$ for each type $ij$ are determined by ${\mathrm{\Pi }}_F^{ij}=\varphi u_i-{\alpha }_{ij}{d}_j=0$ . In terms of timing, advertisements are introduced simultaneously for users of the same disutility from advertisements $d_j$ even if they have different utility from the service $u_i$ , whereas they are introduced later for users of higher disutility $d_h$ than $d_l$ . Note that the timing of introducing advertisements is a trade-off between the user base growth (proportional to utility $u_i$ ) and advertising revenue (proportional to ${\alpha }_{ij}$ ), and that the maximum advertisements ${\alpha }_{ij}=\varphi u_i/d_j$ are proportional to $u_i$ for the same $d_j$ and decreasing in $d_j$ . Therefore, the aforementioned trade-off is identical for users with the same $d_j$ but different $u_i$ , whereas it leans away from advertisements for users with higher $d_j$ and the same $u_i$ . In short, advertisements are introduced at the same time for users with the same $d_j$ but different $u_i$ , whereas they are introduced later for users with larger $d_j$ and the same $u_i$ , to more efficiently manage growth and monetization.

To summarize, although our Spotify model (3) assumed perfectly correlated user utility from the service and disutility from advertisements which removed the need for customized advertisements, its key findings that the provider always offers full free service and always includes maximum advertisements are found robust in the alternative Spotify model (6) with potentially independent user dis/utility and customized advertisements. The study of the latter model further informs the timing and maximum levels of advertisements for heterogenous users and demonstrates the value of customized advertisements in managing growth and monetization in the freemium business model.

5. General Freemium Model

In Sections 3 and 4, we analyzed two models inspired by two representative freemium services—Dropbox and Spotify. Specifically, the cloud-storage service provided by Dropbox is incompatible with advertisements and depends significantly on the network effect to enhance user utility, whereas the music-streaming service of Spotify naturally accommodates advertisements and does not exhibit a significant network effect. Our analysis yielded contrasting insights for these freemium variants. For the Dropbox model, we found that the limiting-feature-based freemium model is only sustainable with a sufficiently important network effect (otherwise, a regular subscription model should be adopted), and the optimal freemium configuration (free service and subscription price) may be non-monotonic over time. For the Spotify model, we found that, with third-party advertising, the service provider should always offer full free service while including maximum advertisements for free users, which suggests that advertising is a more effective monetization strategy than limiting features for Spotify-like services. In both models, the service provider prioritizes growth in early stages and gradually shifts the focus to monetization in later stages, with the freemium model demonstrating versatility in meeting different needs of the service in different stages.

Although the Dropbox and Spotify models well capture their respective inspirations, it is of interest to also investigate a general freemium model encompassing features of the Dropbox and the Spotify models, namely the network effect and advertisements. In fact, whereas Spotify’s core music-streaming service fits our Spotify model well, the company has recently been advocating its networking functions such as playlist sharing and collaboration and “shaping up to be a social network” (Perez, 2024). Therefore, the general freemium model may be a better fit for the future Spotify, and its analysis may answer questions such as whether advertising is generally a more effective monetization strategy than limiting features in the presence of the network effect. By combining Problems (2) and (3), we arrive at the proportion of premium users and the formulation of the general problem:

Lemma 4 (General model premium subscription)

The proportion of premium users in the general freemium model is $1-F(u^{*})$ , where

(i)

$u^{*}=p/[(1+a-\varphi )(1-\theta +\theta w(\varphi ,n))]$ , if $p<(1+a-\varphi )(1-\theta +\theta w(\varphi ,n))$ ;

(ii)

$u^{*}=1$ , otherwise.

$$\begin{array}{rl}\underset{\rho (t),p(t),\varphi (t),a(t)}{max}& {\int }_0^{\mathrm{\infty }}[n(t)[(1-F(u^{*}))p(t)+F(u^{*})a(t)q]\\ & -C(\rho (t))]e^{-rt}\mathrm{d}t\end{array}$$

(5)

$$\begin{array}{rl}\text{s.t.}& \mathrm{d}n(t)/\mathrm{d}t=[\rho (t)+\mathrm{\Pi }(p(t),\varphi (t),a(t),n(t))n(t)]\\ & \times [1-n(t)],\\ & \mathrm{\Pi }(p(t),\varphi (t),a(t),n(t))\\ & ={\int }_0^{u^{*}(t)}{\mathrm{\Pi }}_F(u,\varphi (t),a(t),n(t))\mathrm{d}F(u)\\ & +{\int }_{u^{*}(t)}^1{\mathrm{\Pi }}_P(u,p(t),n(t))\mathrm{d}F(u),\\ & {\mathrm{\Pi }}_F(u,\varphi (t),a(t),n(t))=u[1-\theta +\theta w(\varphi (t),n(t))]\\ & \times [\varphi (t)-a(t)],\\ & {\mathrm{\Pi }}_P(u,p(t),n(t))=u[1-\theta +\theta w(\varphi (t),n(t))]-p(t),\\ & {\mathrm{\Pi }}_F(u^{*},\varphi (t),a(t),n(t))={\mathrm{\Pi }}_P(u^{*},p(t),n(t)),\\ & n(0)=0,\rho (t)\ge 0,0\le \varphi (t)\le 1,0\le a(t)\le \varphi (t),\\ & 0\le p(t)\le p^U=[1+a(t)-\varphi (t)]\\ & \times [1-\theta +\theta w(\varphi (t),n(t))].\end{array}$$

Problem (5) can be analyzed similarly to Problems (2) and (3). We omit Pontryagin’s maximum principle for the general problem for brevity, and summarize the properties that structurally describe the provider’s optimal policies in the following proposition.

Proposition 3 (General model optimal policies)

The optimal dynamic operating policies of the general model satisfy the following:

(i)

The promotion effort ${\rho }^{*}(t)$ decreases over time and converges to 0 as $t\to \mathrm{\infty }$ .

(ii)

The provider does not include advertisements or offer premium subscription until some finite threshold times (which can be 0 and different for advertisements and premium subscription).

(iii)

The provider always offers full free service ${\varphi }^{*}(t)\equiv 1$ and always includes maximum advertisements $a^{*}(t)\equiv 1$ for free users after introducing advertisements.

(iv)

The premium subscription price $p^{*}(t)$ may be non-monotonic over time and converges to $p^{*}(\mathrm{\infty })=(1+q)/2$ as $t\to \mathrm{\infty }$ .

One can immediately see that Proposition 3 is a hybrid of Propositions 1 and 2. This is unsurprising given that Problem (5) is a hybrid of Problems (2) and (3). The most important observation is that the general model behaves like the Spotify model where the provider always offers full free service and maximum advertisements and exclusively adopts the advertising monetization strategy. We formalize this finding in the following corollary.

Corollary 2 (Comparison of monetization strategies)

Advertising is a more effective monetization strategy than limiting features in the general model.

The same intuition from the Spotify model applies: advertising generates revenue from both free and premium users, whereas limiting features only generates revenue from premium users. Therefore, wherever third-party advertising is viable, the providers should fully embrace the advertising monetization strategy without limiting features for free users. On the other hand, for services where third-party advertising is unsuitable, limiting free service features with premium upgrades offers an alternative monetization strategy.

On the other hand, the potentially non-monotonic freemium configuration of the Dropbox model is inherited by the general model. In our discussion following Figure 1, we identified this behavior as a result of the high network effect importance. In Figure 5 which illustrates the optimal operating policies of the general freemium model, one can see that the non-monotonic freemium configuration also occurs with high network effect importance, reaffirming our earlier explanation.

Figure 5.

Optimal operating policies of general freemium model. (a) $\theta =0.25$ and (b) $\theta =0.75$ . Notes: This example is generated with $q=0.5$ , $C(\rho )=2{\rho }^2$ , $r=0.05$ .

Figure 5(a) with low network effect importance ( $\theta$ ) is similar to Figure 3 without a network effect as expected. Consistent with Proposition 3, even Figure 5(b) with high network effect importance still resemble Figure 3 without a network effect more than Figure 1 with a network effect but no advertisements; in particular, in Figure 5(b), it is optimal to offer full service to free users ( ${\varphi }^{*}(t)=1$ ), as opposed to offering limited free service as shown in Figure 1. The optimal premium subscription price initially decreases then increases similarly to shown in Figure 1(c), and the cause is once again the network effect as for the latter. In early stages, the network effect and thus the overall user experience is limited by the small user base, and stimulating growth through word-of-mouth is inefficient. Therefore, the provider focuses on monetization through advertising ( $a(t)=1$ ) and its removal (high $p^{*}$ ) in the earliest stages while depending on promotion to stimulate growth. As the user base grows, the increasing network effect improves user experiences and word-of-mouth quickly becomes an important driver of growth, and the provider accordingly eases off monetization through premium subscription (causing decreasing $p^{*}$ ) to assist the word-of-mouth-driven growth until a critical mass is reached and the overall focus is shifted back to monetization (causing increasing $p^{*}$ ).

To summarize, we analyze the general freemium model with both a network effect and advertisements, and find that the general model’s optimal policies are a hybrid of those for the Dropbox and Spotify models. Overall, the general optimal policies resemble those for the Spotify model and depend exclusively on advertising for monetization. This finding confirms that advertising is a generally more effective monetization strategy than limiting features. On the other hand, similar to the Dropbox model, the presence of the network effect may cause non-monotonic optimal freemium configurations.

6. Additional Analyses

In this section, we perform additional analyses on the freemium models and derive further insights.

6.1. Sensitivities

Having investigated the optimal operational policies for three variants of the freemium model, in this section, we perform sensitivity analyses of the optimal total discounted operating profit and time to introduce premium subscription in these model variants. In particular, we present them in contour graphs for varying parameters and derive insights for managing these business models.

6.1.1. Dropbox Freemium Model

For this model, the most crucial parameters are the importance of network effect $\theta$ and the promotion cost $C$ . Figure 6 plots the optimal total discounted operating profit and time to introduce premium subscription for varying $\theta$ and $c$ (with promotion cost function $C(\rho )=c{\rho }^2$ ). The impact of $c$ on the total profit is straightforward: costlier promotion leads to reduced profit. On the other hand, with costlier promotion, the provider has to depend more on word-of-mouth to stimulate user base growth by postponing introducing premium subscription to improve early stage user experience. A similar explanation applies to the impact of $\theta$ : a stronger network effect lends more importance to early stage growth, which necessitates postponing the introduction of premium subscription and leads to reduced total profit. Overall, the sensitivity analysis suggests that service providers heavily depending on word-of-mouth and the network effect should postpone the introduction of premium subscription.

Figure 6.

Sensitivities to $\theta$ and $c$ of the Dropbox model. (a) Total discounted operating profit and (b) time to introduce premium subscription. Notes: This example is generated with $C(\rho )=c{\rho }^2$ and $r=0.05$ .

6.1.2. Spotify Freemium Model

For this model, the most crucial parameters are the unit advertising revenue $q$ and the promotion cost $C$ . Figure 7 plots the optimal total discounted operating profit and time to introduce premium subscription for varying $q$ and $c$ (with promotion cost function $C(\rho )=c{\rho }^2$ ). The impact of $c$ is similar to that in Figure 6. As for the unit advertising revenue $q$ , it is intuitive that higher $q$ improves the service provider’s total profit. On the other hand, more lucrative advertising lends more importance to early stage growth, which necessitates postponing the introduction of premium subscription. Overall, the sensitivity analysis suggests that service providers with lucrative advertising opportunities should postpone the introduction of premium subscription.

Figure 7.

Sensitivities to $q$ and $c$ of the Spotify model. (a) Total discounted operating profit and (b) time to introduce premium subscription. Notes: This example is generated with $C(\rho )=c{\rho }^2$ and $r=0.05$ .

6.1.3. General Freemium Model

For the general freemium model with both a network effect and advertisements, we focus on the importance of the network effect $\theta$ and the advertising revenue $q$ . Figure 8(a) shows that, whereas more lucrative advertising (higher $q$ ) significantly improves the service provider’s total profit, the network effect’s impact is minimally positive. The impact of $q$ is unsurprising given that advertising is the dominant monetization strategy in the general model (recall Section 5). By contrast, the network effect has an ambiguous effect: on the one hand, it accelerates the user base growth and thus indirectly improves revenue; on the other hand, it necessitates postponing the introduction of premium subscription which hurts revenue. These effects largely cancel each other, leading to a minimally positive overall impact. This however does not mean that the service provider can ignore the network effect. On the contrary, Figure 8(b) shows that the service provider should significantly postpone the introduction of premium subscription with a stronger network effect (and more lucrative advertising); failure to do so may stifle early stage user base growth and affect the total profit.

Figure 8.

Sensitivities to $q$ and $\theta$ of the general model. (a) Total discounted operating profit and (b) time to introduce premium subscription. Notes: This example is generated with $C(\rho )={\rho }^2$ and $r=0.05$ .

6.2. Liquidity Constraint

A recurring phenomenon in our analysis thus far is that the provider may hold back introducing premium subscription while heavily promoting the service in its early stages to stimulate initial user base growth (Propositions 1–3). Such a strategy imposes pressure on the provider’s early stage cash flow and may not be viable for providers with limited cash reserves or lines of credit. In this section, we use the general model as an example to investigate the impact of liquidity constraints. Specifically, we assume that the provider has an initial cash reserve $L_0>0$ and denote its cash level at any time $t$ by $L(t)$ . We model the provider’s cash level dynamics and require $L(t)\ge 0$ for all $t$ by adding the following three constraints to Problem (5):

$$\begin{array}{rl}\mathrm{d}L(t)/\mathrm{d}t& =n(t)[(1-F(u^{*}))p(t)\\ & +F(u^{*})a(t)q]-C(\rho (t)),\\ L(0)& =L_0>0,L(t)\ge 0.\end{array}$$

The constraint $L(t)\ge 0$ is a pure-state constraint known to significantly complicate the optimal control problem (Sethi, 2019). Therefore, we numerically evaluate the general model with liquidity constraints and illustrate the results in Figure 9 using the same parameters as shown in Figure 5.

Figure 9.

Optimal operating policies of general model with liquidity constraints. (a) $\theta =0.25$ and (b) $\theta =0.75$ . Notes: This example is generated with $q=0.5$ , $C(\rho )=2{\rho }^2$ , $r=0.05$ , and $L_0=2$ (scaled down by a factor of 20 to fit in the figure).

Comparing Figure 9 with Figure 5 reveals the impact of liquidity constraints. With a limited initial cash reserve, the provider is more frugal in early promotion and more aggressive in premium subscription introduction and pricing to reduce cash draining. When the cash reserve is depleted, the provider then balances cost and revenue and sustains the cash level at depletion for some time. Interestingly, the period of depleted cash reserve is marked by increased promotion and free service and reduced premium subscription price. This observation may seem counterintuitive because one’s knee-jerk reaction to a cash shortage may be to increase revenue and reduce cost. However, in a service’s early stages, user base growth is more important than profit. Although the provider can use the revenue generated from premium subscription to promote user base growth, if the promotion effect does not offset the negative impact of premium subscription on user base growth, the provider should instead curb premium subscription, allocate all available resources to promotion and offer free service to stimulate user base growth. Finally, after a critical mass is established, the provider is no longer cash-constrained and switches back to similar policies as shown in Figure 5.

In summary, whereas freemium service providers operating under tight budget constraints may intuitively prioritize revenue generation and cost saving, our finding instead suggests that, even with limited cash reserves in early stages, service providers should still drive user base growth with promotion and free service, and fund the growth with premium subscription if needed.

6.3. Multiple Premium Tiers

Thus far, we have considered a service provider offering a single premium tier; one may wonder if offering more premium tiers can improve the provider’s profit. In this section, we extend the general model of Section 5 to allow for two premium tiers on top of the free tier: Tier 0 offers ${\varphi }_0\in [0,1]$ unit of service with relative advertising level $a_0\in [0,1]$ free of charge, Tier 1 offers ${\varphi }_1\in [{\varphi }_0,1]$ unit of service with relative advertising level $a_1\in [0,a_0]$ at price $p_1$ (a partial premium tier), and Tier 2 offers full service with no included advertisements at price $p_2\ge p_1$ (a full premium tier). The Tier 0, 1, and 2 users’ net utilities per unit time are, respectively:

$$\begin{array}{rl}{\mathrm{\Pi }}_0(u)=& u[1-\theta +\theta w({\varphi }_0,n)]({\varphi }_0-a_0),\\ {\mathrm{\Pi }}_1(u)=& u[1-\theta +\theta w({\varphi }_0,n)]({\varphi }_1-a_1)-p_1,\\ {\mathrm{\Pi }}_2(u)=& u[1-\theta +\theta w({\varphi }_0,n)]-p_2.\end{array}$$

By comparing the net utilities, we derive the base utility thresholds of users choosing each tier.

Lemma 5 (Multiple-tier premium subscription)

Given $p_1$ , $p_2$ , ${\varphi }_0$ , ${\varphi }_1$ , $a_0$ , and $a_1$ , the proportions of Tier 1 and Tier 2 users are, respectively, $F(u_2^{*})-F(u_1^{*})$ and $1-F(u_2^{*})$ , where $u_1^{*}=p_1/[(a_0-a_1-{\varphi }_0+{\varphi }_1)(1-\theta +\theta w({\varphi }_0,n))]$ and $u_2^{*}=(p_2-p_1)/[(1+a_1-{\varphi }_1)(1-\theta +\theta w({\varphi }_0,n))]$ .

Despite the ability to offer a partial premium tier, we show that the service provider never does so:

Proposition 4 (No partial premium tier)

Assuming uniform base utility distribution $F(x)=x$ , under the provider’s optimal operating policies $p_1^{*}(t)$ , $p_2^{*}(t)$ , ${\varphi }_0^{*}(t)$ , ${\varphi }_1^{*}(t)$ , $a_0^{*}(t)$ , and $a_1^{*}(t)$ , no partial premium tier will be offered: $u_1^{*}(p_1^{*}(t),p_2^{*}(t),{\varphi }_0^{*}(t),{\varphi }_1^{*}(t),a_0^{*}(t),a_1^{*}(t),n^{*}(t))=u_2^{*}(p_1^{*}(t),p_2^{*}(t),{\varphi }_0^{*}(t),{\varphi }_1^{*}(t),a_0^{*}(t),a_1^{*}(t),n^{*}(t))$ for all $t$ .

Proposition 4 shows that, in this model, the provider may only offer a full premium tier and never a partial premium tier. Incidentally, Spotify only offers one full individual premium subscription (with another student premium subscription and two more family premium subscriptions ² ). On the other hand, Dropbox does offer two individual and two team premium subscriptions. ³ We note that, in practice, multiple premium tiers may be offered for reasons not captured by this model, such as catering to customers of different budgets.

6.4. Ad-Supported Free Model and Value of “mium”

Another popular online service business model is the ad-supported free model, as adopted for example by Facebook, X (formerly Twitter) and TikTok, where the service is free for all and revenue generation is exclusively through advertisements (without paid advertisement removal). Such a model is a special case of the general freemium model (5) without limiting features or premium subscription, namely

$$\begin{array}{rl}\underset{\rho (t),a(t)}{max}& {\int }_0^{\mathrm{\infty }}[n(t)a(t)q-C(\rho (t))]e^{-rt}\mathrm{d}t\end{array}$$

(6)

$$\begin{array}{rl}\text{s.t.}& \mathrm{d}n(t)/\mathrm{d}t=[\rho (t)+\mathrm{\Pi }(a(t),n(t))n(t)][1-n(t)],\\ & \mathrm{\Pi }(a(t),n(t))={\int }_0^1{\mathrm{\Pi }}_F(u,a(t),n(t))\mathrm{d}F(u),\\ & {\mathrm{\Pi }}_F(u,a(t),n(t))=u[1-\theta +\theta w(1,n(t))][1-a(t)],\\ & n(0)=0,\rho (t)\ge 0,0\le a(t)\le 1.\end{array}$$

As a special case of the general freemium model, the free model generates less profit than the former. In fact, because the threshold in Proposition 3(ii) for offering a premium subscription is finite, the free model’s profit must be strictly less. The more interesting question is by how much the general freemium model outperforms the free model, namely the value of “mium.” To address this question, we perform extensive numerical experiments comparing the free and the general freemium models’ profits for varying importance of the network effect $\theta$ and advertising revenue $q$ . The general freemium model’s percentage profit improvements upon the free model are presented in Table 1.

Table 1.

General model’s percentage profit improvements upon free model for varying $\theta$ and $q$ with $C(\rho )=2{\rho }^2$ .

$\theta \mathrm{\setminus }q$	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9
0.1	315.3%	121.1%	61.9%	34.5%	19.5%	10.6%	5.2%	2.1%	0.4%
0.2	315.8%	120.6%	61.3%	34.0%	19.1%	10.3%	5.0%	1.9%	0.3%
0.3	316.5%	120.1%	60.8%	33.6%	18.7%	10.0%	4.7%	1.7%	0.3%
0.4	317.3%	119.6%	60.2%	33.1%	18.3%	9.6%	4.4%	1.5%	0.2%
0.5	318.5%	119.2%	59.7%	32.5%	17.8%	9.2%	4.1%	1.4%	0.2%
0.6	319.8%	118.7%	59.1%	32.0%	17.3%	8.7%	3.8%	1.2%	0.2%
0.7	332.4%	118.3%	58.5%	31.3%	16.6%	8.3%	3.6%	1.1%	0.2%
0.8	323.3%	117.8%	57.8%	30.4%	15.9%	7.9%	3.4%	1.1%	0.1%
0.9	325.4%	117.2%	56.8%	29.4%	15.3%	7.5%	3.2%	1.0%	0.1%

Table 1 exhibits strong patterns. First, the value of “mium” can be highly significant for low advertising revenue, but diminishes when the advertising revenue increases. To understand this observation, note that the freemium model provides two advertisement-related incomes: direct advertising revenues, and advertisement-removal revenue (through premium subscription); the former is also available for the ad-supported free model whereas the latter is the value of “mium.” When the former is lucrative, the latter is relatively less important; whereas when advertising revenues diminish, the value of “mium” becomes increasingly significant. Second, the value of “mium” is relatively insensitive to the importance of the network effect. This is because advertisements and premium subscription both depend on the user base which is similarly impacted by the network effect. Third, the value of “mium” increases in the importance of the network effect $\theta$ when the advertising revenue is small ( $q=0.1$ ) but decreases in $\theta$ otherwise. This observation suggests that advertisements and premium subscription both benefit from higher importance of the network effect, but the former benefits more than the latter. Therefore, when advertisements are not lucrative, the value of “mium” increases in the importance of the network effect; but when advertisements are lucrative and themselves benefit significantly from higher importance of the network effect, the freemium model which partly replaces advertising revenue with premium subscription revenue benefits less from higher importance of the network effect than the ad-support free model.

In summary, we find that the general freemium model’s profit improvement upon the free model (the value of “mium”) can be significant when advertisements are not lucrative; otherwise, it is minimal. This suggests that the ad-support free model could perform well in booming economies with strong advertising demands, but when advertising demands diminish during economic downturns, the freemium model with revenue from advertisement removal can substantially outperform the former.

7. Conclusion

In this article, we study the optimal dynamic operating policies of a freemium service provider throughout its lifetime with a focus on two monetization strategies—limiting features and advertising (and its removal). We adopt a hybrid of the Bass diffusion model and the replicator equation from evolutionary game theory to capture the user base growth, and model the provider’s dynamic decisions as an optimal control problem. We first analyze two variants of the freemium model inspired by two prominent examples, Dropbox and Spotify, which, respectively, adopt the monetization strategies of limiting features and advertising (and its removal). We establish the optimal dynamic operating policies for both variants. In both cases, we find that the service provider prioritizes growth in early stages and may not immediately introduce premium subscription, and shifts the focus to monetization in later stages after amassing a critical user base.

We also identify their distinctive operational characteristics. In the Dropbox-inspired ad-free freemium model with a network effect, the provider limits free service in order to drive premium subscription. We find that the Dropbox model is sustainable only when the network effect is sufficiently strong; otherwise, it will degenerate to a regular subscription model (with no free service) in the long run. Moreover, the optimal premium subscription price and free service critically depend on the network effect. Interestingly, with a strong network effect, the optimal free service and premium subscription price may be non-monotonic: the optimal free service (premium subscription price) may first increase (decrease) to foster word-of-mouth driven growth in early stages of the service and then decrease (increase) as the provider shifts its focus from growth to profitability in later stages. We also confirm that these results are robust with a generalized network effect.

In the Spotify-inspired ad-supported freemium model without a network effect, once premium subscription is introduced, the provider should offer full free service and include maximum advertisements, forgoing the limiting-features monetization strategy. This finding is consistent with practical anecdotes and suggests that advertising (and its removal) is a more effective monetization strategy than limiting features; the reason is that, with the advertising strategy, the freemium service provider can monetize both free users (through advertising) and premium users (through advertising removal). We also confirm that these results are robust with customized advertisements.

We then evaluate a general freemium model encompassing the Dropbox and the Spotify models, and confirm key results such as that the optimal operating policies exhibit a threshold structure, that advertising (and its removal) is a more effective monetization strategy than limiting features, and that with a strong network effect, the optimal free service and premium subscription price may be non-monotonic. Overall, we find all freemium model variants to be quite versatile in suiting distinct needs of a service in different stages from growth to monetization.

We then perform additional analyses and derive further insights. We show that a stronger network effect and more lucrative advertisements both require further postponing the introduction of premium subscription, which may exacerbate the provider’s early stage financial pressure; for which we then show that cash-constrained service providers should still curb premium subscription, allocate all available resources to promotion and offer free service to stimulate user base growth, rather than instinctively cut cost and attempt to generate more revenue. We also show that offering multiple tiers of premium subscription is unnecessary. Finally, we show that the general freemium model’s profit improvements upon the ad-supported free model (the value of “mium”) can be significant when advertisements are not lucrative but is otherwise minimal, suggesting that while the free model could perform well in booming economies with strong advertising demands, the freemium model can be uniquely suitable for service providers during economic downturns. A limitation of our model is that the user utility scales linearly in the amount of offered service. We have numerically observed that all structural results remain unchanged with quadratic utility functions, but leave the rigorous analysis to future work.

To summarize this article’s managerial implications for service providers adopting the freemium business model, they should be aware of the growth and monetization trade-off and appropriately postpone the introduction of premium subscription, and also be mindful of the key features of their services, as the optimal operating policies may drastically differ based on whether the service exhibits a strong network effect or whether including third-party advertisements is feasible. The providers should prioritize the advertising monetization strategy if possible, whereas limiting features offers an alternative monetization strategy when advertising is unavailable or unsuitable. Overall, the freemium model excels in the versatility to suit different needs of a service in different stages of its lifetime: it is highly effective in fostering growth in early stages as well as monetizing the user base in later stages. Additionally, the freemium model may prove especially valuable during economic downturns when direct advertising revenues diminish. These insights justify the adoption of the freemium business model and provide guidelines for its adopters.

Supplemental Material

sj-pdf-1-pao-10.1177_10591478251353052 - Supplemental material for From Growth to Monetization: Managing Freemium Services

Supplemental material, sj-pdf-1-pao-10.1177_10591478251353052 for From Growth to Monetization: Managing Freemium Services by Yunke Mai and Bin Hu in Production and Operations Management