Pricing Optimization And Operations Research Of The Freemium Information Product Based On Consumer Learning

Freemium has increasingly been recognized as a promising business model for the information product.Since the marginal production cost of the information product is considered negligible,providing free version of the information product is feasible for the firm.And the free version can attract a lot of users to install the information product.The increase of user base will lead to higher consumers’ valuations of the information product because of positive network externality.Meanwhile,the information product is usually based on innovative information and communication technologies.Consumers need a process to learn those new technologies.On the one hand,using and learning the information product incurs adoption cost.On the other hand,consumers can learn the information related to the information product which has an impact on the consumption behavior of the consumers.Considering the influence of the consumer learning on the firm decision,we introduce two research problems.Considering the method adopted by the firm to reinforce the intensity of consumer learning,we also introduce two research problems.We first develop models to solve the above optimization problems.And then the corresponding numerical examples are analyzed according to the optimization results.First,because learning the premium version which contains more features will incur higher cost,we study an optimization problem of the price when the premium version is higher than the adoption cost of the free version.The benchmark model with only releasing the premium version and the model with simultaneously providing the free and premium versions to the market are first built.Given all external parameters fixed,the optimal price of the premium version and the corresponding optimal revenue are then obtained analytically under two cases.Next,conditions that guarantee the firm to acquire a higher revenue by simultaneously providing the two versions by comparing to the optimal revenues under two cases are derived.Product quality designing towards several different objectives is discussed as well by numerical analysis.The results show that the firm will realize more profit by adopting freemium and be given more freedom in pricing and quality designing if the network externality intensity is strong.Second,considering the firm takes advantage of consumer learning to reduce the adoption cost of the information product,we study an optimization problem of the price considering a sequential release strategy.The firm sequentially offers the free version and the premium one to the market.The lifetime of information product is divided into two stages by the releasing time of the premium version.We develop a two-stage model to solve the optimal pricing problem for the firm.Given all external parameters fixed,the optimal price of the premium version and the corresponding optimal profit are first obtained analytically.Conditions to guarantee a higher profit for the firm releasing the information product in two stages compared to simultaneously releasing free and premium versions are then constructed.Following numerical analysis conducts sensitivity analysis on the optimal profit against the rate of the reduced adoption cost,and the problem of expanding the feasible area of releasing the information product in two stages by optimizing the rate of the reduced adoption cost.The results show that the firm has no intention to release the information product in two stages if the cost of reinforcing the consumer learning is too high;otherwise,the firm will realize more profit by releasing the information product in two stages when the network externality intensity is strong.Third,we study a decision optimization problem with nudging.we assume the firm offers the free version prior to the premium version in the hope of reducing adoption cost of the information product.The firm can choose whether to nudge to reinforce consumer learning in the free stage.We develop a two-stage model to jointly optimize the nudge effort to reinforce consumer learning and the price of the premium version.Comparing the adoption cost of the free version with the intensity of network externality and finds the market has two scenarios:high adoption cost market and low adoption cost market.In each scenario,the optimal price of the premium version when the firm does not nudge is first obtained analytically;a threshold on unit cost is then found for the firm to decide whether to nudge to reinforce consumer learning;closed-form solutions to the joint optimization problem are obtained as well regarding different conditions.Three important conclusions are obtained.In addition,several numerical examples are given to examine the impact of the quality of premium version on optimal profit,and check sensitivities towards external parameters.The results show that: 1)the firm favor to reduce adoption cost of the information product through reinforcing consumer learning more than to improve the quality of the premium version.2)When the firm provides high-quality premium version,builds strong network externality,or control the adoption cost of information product at a moderate level,she is more likely to reinforce consumer learning by nudging.3)In some cases,the firm only obtains a sub-optimal outcome.Last,we study a decision optimization problem with delaying to release the premium version.we assume the firm takes advantage of consumer learning to increase the consumer’s preference or taste of product quality.The firm can choose whether to delay releasing the premium version to reinforce consumer learning in the free stage.We develop a two-stage model to optimize the release time and price of the premium version.A threshold on discount rate to guarantee that such a delayed release is desirable is first found.Given all external parameters fixed,the optimal release time and corresponding price of the premium version are then obtained under different conditions.Finally,the learning function in the two-stage model is changed,and the robustness of the model is tested and the influence of external parameters on the optimal release time of premium version and the optimal profit under different learning functions are discussed through numerical analysis.The results show that the adoption cost and the network externality have a significant impact on the firm’s decision.Concretely,if the adoption cost and the network externality are too low,the firm should delay the premium version as long as possible;otherwise,the firm should offer the free version and premium version to the market sequentially.In this paper,the consumer learning is considered in the freemium model,which is valuable in theory and practice.This paper researches the scenario that the adoption cost of the premium version is higher and introduces a sequential release strategy to take advantage of consumer learning in freemium model,which contributes new insights that are more practical in theory.In addition,conclusions provide the condition of sequential release strategy in freemium model and the optimal operation decisions of the firm under this strategy,which provide decision support regarding operational strategy for firms using the freemium model.