Learning and Forgetting: Modeling Optimal Product Sampling Over Time

Abstract

Firms use samples to increase the sales of almost all consumable goods, including food, health, and cleaning products. Despite its importance, sampling remains one of the most under-researched areas. There are no theoretical quantitative models of sampling behavior other than the pioneering work of Jain et al. (1995), who modeled sampling as an important factor in the diffusion of new products. In this paper we characterize sampling as having two effects. The first is the change in the probability of a consumer purchasing a product immediately after having sampled the product. The second is an increase in the consumer's cumulative goodwill formation, which results from sampling the product. This distinction differentiates our model from other models of goodwill, in which firm sales are only a function of the existing goodwill level. We determine the optimal dynamic sampling effort of a firm and examine the factors that affect the sampling decision. We find that although the sampling effort will decline over a product's life cycle, it may continue in mature products. Another finding is that when we have a positive change in the factors that increase sampling productivity, steady-state goodwill stock and sales will increase, but equilibrium sampling can either increase or decrease. The change in the sampling level is indeterminate because, while increased sampling productivity means that firms have incentives to increase sampling, the increase in the equilibrium goodwill level indirectly reduces the marginal productivity of sampling, thus reducing the incentives to sample. We discuss managerial implications, and how the model can be used to address various circumstances.