Dynamic pricing with service unbundling

Abstract

In this study, we investigate unbundling when a firm dynamically prices a basic service, while separating the sale of a fixed-price add-on. We characterize the optimal dynamic unbundling pricing policy and investigate its structural properties. We find that the value function with unbundling increases in the degree of dependence between consumers’ reservation prices for basic service and add-on. However, there are no similar monotonicity properties for the optimal price of the basic service. For several families of commonly used joint distributions, we show that the influence of the dependence parameter on the optimal price of the basic service depends on a threshold, which is a function of the dependence parameter. Moreover, the price of the bundled service is higher under unbundling when the add-on price is high, and vice versa. Our model is then compared with the bundling model through a numerical experiment. Among most cases where unbundling outperforms, the degree of dependence is non-negative. It is further revealed that given the non-negativity of dependence, unbundling is worth practicing under the following situations: (i) the variance of the reservation price for the basic service (add-on) is low (high); (ii) the mean of the reservation price for the basic service (add-on) is high (low); (iii) the demand intensity is low; (iv) the capacity of the basic service is high; and (v) the incremental cost of the basic service (add-on) is low (high). Finally, unbundling can improve the firm's expected profit and the consumers’ surplus at the same time.