Managing presales with two payments and return policy when consumers are time-inconsistent

We consider a firm using presales with two payments—including an upfront deposit and a postponed arrear—to sell a product to time-inconsistent consumers under various return policies. With the passage of time, consumers decide whether to preorder the product by paying the deposit, whether to settle the balance by paying the arrear by the due date, and, when returns are allowed, whether to return a fully paid product for a refund after its fitness is revealed. Canceling a preorder before settling the balance or failing to settle the balance on time causes a deposit payer to lose deposit. Consumers use quasi-hyperbolic discounting to weigh intertemporal utilities and exhibit time inconsistency when making purchase decisions. Our results indicate that, as consumers' time inconsistency weakens, the firm manages the deposit and the arrear to induce no, some, and all deposit payers, in that sequence, to settle the balance. It has mixed effects on the profit of the firm and consumer surplus but always causes social welfare to improve since actual sales increase. Regarding the choice of return policy, the firm prefers full returns while consumers prefer no returns when consumers are time-inconsistent; they share similar preferences when consumers are time-consistent. Moreover, we find that consumers' imbalance (caused by time-inconsistent preference) is less likely to occur as consumers are more sophisticated, as the presales period shortens, as the product value increases, or as the product is more likely to be a good fit. In addition, allowing a quick refund for fully paid but not yet delivered products can completely deter imbalance, while this option harms the firm and may or may not benefit consumers. All this yields novel insights into managing presales with two payments and returns when consumers are time-inconsistent.