Striking the balance: Optimizing pricing schemes for time-sensitive buyers

This study explores the fundamental trade-off between time and money in pricing strategies. Specifically, we investigate the optimization of pricing schemes tailored for identical items, catering to heterogeneous, time-sensitive buyers. Our analysis aims to determine the optimal pricing scheme, which is achieved through the development of an efficient algorithm within a Bayesian framework. Notably, our findings elucidate the relationship between the loss of buyers’ wasted time and the corresponding impact on the seller's revenue. Additionally, we conduct a comparative evaluation of two types of pricing schemes, namely the k-step function and fixed pricing, shedding light on their respective efficacy in revenue. Furthermore, we delve into the underlying mechanics of the optimal pricing scheme under a general setting, offering closed form expressions over the product distribution. Through illustrative examples, we highlight how the positive correlation between the valuation of the item and the cost per unit time could help increase revenue.