How Freemium Gets Consumers to Pay a Premium: The Role of Loss-Aversion

Abstract

We consider the optimal pricing of a freemium product offered by a firm to consumers who are loss-averse with stochastic and endogenous reference points, and the role of the consumers' surprise on their purchase decision about the premium version, after experiencing the free version. We formulate the problem as a multistage Stackelberg game and investigate its equilibrium by determining the consumers' optimal purchase plan, the firm's optimal price to charge for the premium version, and the optimal quality level that the firm sets for the premium version. We show that a consumer becomes more willing to buy the premium version if he becomes somewhat dissatisfied to realize that the free version's value is lower than his expectation. This result goes against the common advice by practitioners that the firms must under-promise and over-deliver to ensure higher profitability. We show that the somewhat-dissatisfied consumer is not only more willing to buy the premium version, but he also could pay a price higher than its realized value. This is a result that does not occur when the consumer is satisfied or entirely dissatisfied with the free version. It also explains the real phenomenon in which many consumers run up massive bills in using freemium products. We show that, increasing the premium version's quality could cause the firm to optimally reduce its price, which is in contrast to our common quality-price intuition: a higher quality product should be sold more expensively. When the quality, price and the consumer's purchase plan are jointly optimized, we show that, the optimal price can increase in the order quantity. This behavior counters the common expectation that when the firm has more available units it should sell them cheaper to avoid the risk of unsold inventory.

Keywords: Stackelberg Game; Freemium; Loss aversion; Pricing; Personal Equilibrium; Gain-Loss Utility