Optimal Temporal Customer Purchasing Decisions Under Trade-In Programs with Up-Front Fees

To entice customers to purchase both current and new generation products over time, many firms offer different trade-in programs including programs that require customers to pay an up-front fee. To examine the effectiveness of the trade-in programs, we develop a two-period model in which a firm sells the first generation product in the first period and the second generation product in the second period; however, the firm offers a trade-in program that customers can participate in when purchasing the first generation product in the first period. To participate, each customer has to pay a nonrefundable fee in the first period so that she has the option to trade-in her first generation product and receive a prespecified trade-in value to be used for the purchase of the second generation product in the second period. To capture market heterogeneity and market uncertainty, we examine the case when the valuation of the first generation product varies among customers and the valuation of the second generation product is uncertain a priori. By analyzing a two-period game, we determine the optimal purchasing behavior of each rational customer, and we show that the firm is always better off by offering its own trade-in programs. Also, our numerical analysis reveals that trade-in programs can benefit the firm significantly especially when (i) the residual value of the first generation product is high; (ii) the expected incremental value of the second generation product is high; or (iii) the valuation of the second generation product is highly uncertain.