Rejoinder to Shin and Sudhir and to Cabral

We begin by thanking our discussants, Jiwoong Shin and K. Sudhir (2009) and Luís Cabral (2009), for their thoughtful comments on our research (Dubé, Hitsch, and Rossi 2009). Both commentaries focus on the stylized (“simple”) model in our article, which we used to motivate our more general empirical model. Shin and Sudhir solve a two-period Hotelling model. They find a U-shaped relationship between switching costs and the average (expected) price across both periods. Though noteworthy in their own right, the results Shin and Sudhir obtain for the two-period model are not comparable to those we obtained in our infinite-horizon model. Shin and Sudhir acknowledge this point in their discussion. In our model, the relationship between equilibrium prices and switching costs is influenced by both harvesting and investment motives. In Period 2 of Shin and Sudhir’s model, there is no investment motive, because the firm ceases to exist in the next period. In Period 1 of the model, there are no existing loyal customers, so the harvesting motive is absent. Averaging the first and second period prices cannot be viewed as an approximation to the infinitehorizon steady-state price. We also argue that our infinite-horizon model provides a good approximation to the actual marketing environment in which firms are not expecting to terminate products in the near future. In our empirical application, we consider longstanding products for which there is no known terminal period. Cabral’s discussion summarizes the results of a model he analyzed in Cabral (2008), which includes our simple, motivating model as a special case. In an infinite-horizon game, two symmetric firms compete for one buyer, who is loyal either to Firm 1 or to Firm 2 (alternatively, there are many buyers, but the firms can discriminate between loyal and nonloyal customers). Cabral (2008) shows that as long as the cost of switching is sufficiently small, average (expected) prices decrease. In his commentary herein, Cabral provides the following intuition for why this result occurs. The harvesting motive works in opposite directions for both firms: The firm that “owns” the loyal customer increases its price, while its competitor decreases price. For a sufficiently small switching cost, the average price stays approximately constant. The investment motive works in the same direction for both firms: If a firm lowers its price, the chance of keeping or gaining a loyal customer increases, and therefore the continuation value of the firm increases. Thus, the investment motive has a first-order