When Should Software Firms Commercialize New Products ... - MISRC

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αb + 1 ≤ 2 γ αa ¡ 0 αa γ αb + δb = 0 γ + 1 αa αb = − 2γ γ δ b 1 1 αb + δb = + 2 2γ αb Figure 2: Firm’s Optimal Strategies 0 + 1 > 2 γ αa ¢¡ αb + δb = 0 αa γ 1 1 αb + δb = + 2 2γ always dominated. Such an outcome may occur in a number of scenarios, including when adjustment factor δb is small or negative, when the true value added through model B is relatively small (i.e., small γ), or when the consumer prior on the value of the basic module is high (i.e., high αa). Note that, in the FLF case, the freemium-generated change (increase or decrease) in the consumer valuation of module B is δbb. Thus, if offering A for free does not increase the valuation of B by at least the consumer prior on the value of module A (i.e. αaa), then the firm does not find it optimal to offer A for free in both periods. Furthermore, whenever αa ≤ γ+1 2 and αb ≤ γ+1 αa 2γ − γ δ b 1 (or, equivalently, α ≤ 2 ), model CE is dominated. In such cases, because the overall prior on the full product is too low, it is optimal to offer a freemium strategy, thus allowing customers to adjust their priors on each module at the beginning of period 1. The choice between TLF and FLF depends on the value of αb+δb. If δb is high enough, by offering module A for free the firm will elevate consumers’ expectation of module B value sufficiently high to ensure optimality of FLF. Otherwise, the firm will offer the entire product for free in the first period since selling A and B together during second period under perfect information is better than selling only B for two periods under adjusted priors (imperfect information). On the other hand, when (i) αa ≤ γ+1 2 and αb > γ+1 αa 2γ − γ , or (ii) αa > γ+1 2 (or, equivalently, α > 1 2 ), we see that TLF is a dominated strategy. In this region, in particular, thefirmwouldalways preferCE over TLF sinceforegoing period1sales issuboptimalwhen consumers have high willingness to pay from the very beginning for the full product. This 22
comparison follows directly from Propositions 1 and 3 since 13−4 √ 10 < 1 2 . Furthermore, in this high α region, if δb is sufficiently large, CE will, in turn, be dominated by FLF. Now that we established that, in certain scenarios, freemium models can yield a higher profit compared to the baseline model, a question of high managerial relevance is how much more a firm could gain by switching to a freemium model. Changes in product marketing strategy are usually a costly undertaking since they involve new advertising approaches, business process redesigning, employee re-training, etc. Therefore, such transitions make more sense when the profit improvements are of significant magnitudes. For example, when αb +δb ≥ 13−4 √ 10 and α ≥ 13−4 √ 10, it immediately follows that: π ∗ FLF −π∗ CE π ∗ CE = γδb −αa γαb +αa and π ∗ FLF −π∗ TLF π ∗ TLF = γ(2αb +2δb −1)−1 . γ +1 In such a case, a large δb value makes the FLF approach extremely desirable to the firm. Furthermore, when αa is very small or γ is very large, the magnitude of the relative profit gain from switching from CE to FLF depends on the ratio δb. We can also explore other αb regions of the feasible parameter space for similar insights. The following corollary to Propositions 1, 2, and 3 provides insights into the asymptotic potential profit gains from switching between models: Corollary 3. The following hold true: π (a) lim δb→∞ ∗ FLF −π∗ CE π∗ CE π (b) lim αa,αb,δb→0 ∗ TLF −π∗ CE π∗ CE π (c) lim αa,αb→0 ∗ FLF −π∗ CE π∗ CE π = lim δb→∞ ∗ FLF −π∗ TLF π∗ TLF π = lim αb,δb→0 ∗ TLF −π∗ FLF π∗ FLF π = lim αa,αb→0 ∗ TLF −π∗ CE π∗ CE = ∞, ∀ αa,αb > 0, = ∞, = ∞, ∀ δb > 0. <strong>When</strong>consumerpriorsonthesoftwaremodulesareverysmall(lowαa, αb), thereisalot to gain by switching to a freemium model, as illustrated in parts (b) and (c) of Corollary 3. ThesameistruewhenofferingAforfreeleadstoabigupwardsadjustmentoftheconsumers’ valuation of B (high δb). Moreover, we note that even switching between two freemium models can greatly increase profitability depending on αa, αb, and δb. While Corollary 3 describes extreme cases, profit gains can be significant by switching between models even for moderate parameter values. For example, consider a case where α ∈ [0.4,0.5], γ = 4, 23
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When Should Software Firms Commercialize New Products ... - MISRC

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