Targeted vs. universal: Optimal strategies for multi-unit purchase coupons

Multi-unit purchase coupons offer discounts to consumers who purchase a specified quantity of a product. This paper examines a seller's choice between two strategies for multi-unit purchase coupons: the universal coupon strategy (U-Coupon), which offers coupons to all consumers, and the targeted coupon strategy (T-Coupon), which specifically targets consumers who have not made prior purchases. We find that the coupon discount offered under the T-Coupon strategy is higher than that under the U-Coupon strategy, suggesting that the T-Coupon strategy leads to greater price discrimination. Contrary to common wisdom, the T-Coupon strategy, despite its precise consumer targeting, is not always the optimal choice. Indeed, the U-Coupon strategy outperforms the T-Coupon strategy when there are substantial cost reductions from multi-unit sales or when product quality is well-maintained over time. In contrast, the T-Coupon strategy proves more effective when cost reductions are modest and quality retention is moderate. We verify that these findings remain robust, regardless of whether the retail price is determined endogenously or exogenously. Finally, we show that low consumer retention incentivizes the seller to adopt coupon strategies that maximize consumer surplus. Moreover, both coupon strategies enhance the seller's profit and consumer surplus in exogenous price scenarios, whereas the T-Coupon strategy may increase the seller's profit at the expense of consumer surplus in endogenous price scenarios.