Threshold discounts comparison: All-unit or incremental?

An increasingly ubiquitous discount format in retailing that is taking over traditional price cuts is threshold discount, under which a price reduction is awarded to a purchase that meets a minimum quantity or minimum spending requirement. One of the most frequently used forms of threshold discounts is the all‐unit discount, where a discount applies to all units of the promoted item that the customer purchases as long as the total basket size reaches the predetermined minimum requirement. On the other hand, under another type of threshold discounts known as incremental discount, the reduced price is granted for only the units purchased beyond the threshold; the customer still pays the full price for the first units up to the threshold. In this paper, we are interested in comparing the effectiveness of using all‐unit discounts and incremental discounts in a retail setting. We consider a retailer selling to a market of heterogenous consumers, whose purchase decisions are modeled and analyzed at the individual customer level. The optimal discount terms and the seller’s profits when using the all‐unit and incremental discounts are investigated under different market scenarios. We show that when the discount terms can be fully optimized, the incremental discount is always more profitable to the retailer than the all‐unit discount. Furthermore, in many cases, the resulting consumer utility as well as the social welfare is also greater under the incremental discount than under other discount schemes. Our study suggests that the incremental discount, while not currently popular in retailing, is in fact a very profitable and efficient retail pricing mechanism that deserves more attention.