Optimal per-use rentals and sales of durable products and their distinct roles in price discrimination

We consider a setting in which consumers experience distinct instances of need for a durable product at random intervals. Each instance of need is associated with a random utility and the consumers are differentiated according to the frequency with which they experience such instances of need. We use our model of consumer utility to characterize the firm's optimal strategy of whether to sell, rent, or do a combination of both in terms of the transaction costs and consumers' usage characteristics. We find that the two modes of operation serve different roles in allowing the firm to price discriminate. While sales allow the firm to discriminate among consumers of different usage frequencies, rentals allow it to discriminate according to consumers' realized valuations. Consequently, even when transaction costs are negligible, it is often optimal for the firm to simultaneously rent and sell its product. In addition, we find that although sales and rentals are substitutes and that the offering of sales weakly increases rental prices, it is possible that the introduction of rentals to a pure selling operation can either increase or decrease the optimal sales prices.