Optimal pricing and delayed incentives in a heterogeneous consumer market

Delayed incentives in the form of cash mail-in rebates have become very popular. We develop and solve a model for jointly determining optimal price and rebate value for a heterogeneous consumer market. Consumers are divided into three segments: rebate independent, fully rebate dependent and partially rebate dependent, Partially rebate-dependent consumers' redemption probability depends on the value of the rebate relative to a reference value. Data show that the probability of redemption increases linearly in rebate value for small rebate values and at a decreasing rate as the rebate value becomes large. The model shows that two consumer attributes are critical in determining the effectiveness of rebates. The first is the reference value. The larger the reference value, the larger the optimal rebate value and the higher the profit. The second is the distribution of consumers among the three segments. Profit decreases as the proportion of consumers in the probabilistic redeemers segment decreases. There is, however, a threshold value where profit increases as the proportion of consumers in the partially rebate-dependent segment decreases, This occurs because as the rebate-independent and fully rebate-dependent consumers are priced out of the market a seller can increase both price and rebate value substantially without having to be burdened by the heavy cost of rebates for the fully rebate-dependent segment. If the reference value for the partially rebate-dependent segment is high, such a strategy may prove profitable.