A Micro-Founded Model of Repeat Buying Based on Information Tracking

A consumer decides whether to incur a constant flow cost to keep track of information on a firm's new product, which updates her expected valuation according to a Brownian motion. The consumer's purchase need follows a Poisson arrival over time, and upon an arrival, she decides whether to make a purchase or not. We characterize the consumer's utility-maximizing tracking and purchasing decisions in closed form. Our model naturally generates three segments of consumers: buyers, trackers and deflectors, who differ in their expected valuations. We find that consumers who are about to drop out tend to purchase less frequently, and who are currently alive are more likely to stay alive and continue to make purchases in the future. This endogenous customer loyalty is captured by a one-parameter survivor function that features an initial steep drop and an asymptotic slow decay at the rate of inverse square root of time. Moreover, we prove sub-exponential distribution of purchase instances and provide closed-form formula for the firm's expected revenue. We show that consumers may benefit from a higher information tracking cost due to a lower price set by the firm. We estimate the model numerically by two methods: random walk simulation and numerically solving a heat diffusion equation. A comprehensive study shows that after incorporating consumer heterogeneity in the need arrival rate, our model provides a similar level of fit and prediction accuracy compared with popular existing models such as Pareto/NBD and BG/NBD. For the study, consumers' information tracking cost is estimated to be about $4.5 per annum. Based on the estimates, our model allows a marketing manager to infer the likelihood of which segment a consumer belongs to based on her past purchase history