We study optimal advertising and entry timing decisions for a new product being sold in two-segment markets in which followers are positively influenced by elites, whereas elites are either unaffected or repulsed by product popularity among followers. Key decisions in such markets are not only how much to advertise in each segment over time but also when to enter the follower segment. We develop a continuous-time optimal control model to examine these issues. Analysis yields two sets of two-point boundary value problems where one set has an unknown boundary value condition that satisfies an algebraic equation. A fast solution methodology is proposed. Two main insights emerge. First, the optimal advertising strategy can be U-shaped, that is, decreasing at first to free-ride peer influence but increasing later on to thwart the repulsion influence of overpopularity causing disadoption. Second, in markets where cross-segment repulsion triggers disadoption, advertising is only moderately effective, and entry costs are high, managing both advertising and entry timing can result in significantly higher profits than managing only one of these levers. In markets without disadoption, with high advertising effectiveness or with low entry costs, in contrast, delaying entry may add little value if one already manages advertising optimally. This implies that purveyors of prestige or cool products need not deny followers access to their products in order to protect their profits, and can use advertising to speed up the democratization of consumption profitably.This paper was accepted by Juanjuan Zhang, marketing.

The evolution of quality expectations over time is an important driver of customer satisfaction and retention. This study investigated the dynamic properties of customers’ quality expectation updating from an analytical perspective and provides new evidence on the psychological correlates of the discrepancies between expectations and experiences in the realm of consumer decision making. In doing so, we focus on the dynamics of expectation formation by adopting a nonlinear complex systems approach based on well-established behavioral theories. Using stability analysis, we find analytical results which are supported empirically by an experiment that there is considerable heterogeneity in how consumers calibrate their quality expectations. Specifically, we demonstrate analytically that in some cases individuals will converge to a specific quality expectation (reach a stable fixed point), while in other cases their expectations will oscillate between a small number of points periodically. This is remarkable because the existence of the latter is not due to changes in quality performance but merely accrue endogenously and depend on individuals’ disconfirmation functions. To our knowledge, this is the first time in the marketing literature that the corresponding gaps between quality expectations and quality provided are analyzed in the long run. Our analytical and empirical findings also suggest that being more responsive to a person’s expectations can increase the portion of those individuals that are able to better calibrate. Finally, we also demonstrate that calibration ability is associated with how thoughtful or impulsive information is used to update one’s expectation. A more deliberative processing style, which includes using a wider range of information, seems to be related to fewer unrealistic expectations and better calibrations, while a more impulsive processing style is related to more unrealistic expectations. In addition to providing a better understanding of dynamic expectation formation, these results can pave the way for interventions that foster more accurate quality expectations. From a managerial perspective, our findings imply that communicating quality perceptions are only to a certain extent under managerial control. To recognize this, firms are advised to segment customers based on their information processing style and to customize their marketing actions accordingly.

Production emissions in the industrial sector are a major source of environmental pollution. In this paper, we explore how emission considerations are integrated with production decisions. We develop a dynamic model consisting of two firms located in the same industrial park, which satisfies exogenously given demands in separate markets. The two firms can build up or rundown stocks (full backlogging), both of which are costly. The emission cost depends on the total output of the two firms. We develop Nash equilibrium feedback strategies, where each firm decides on its output based on its inventory or the inventories of both. We also develop a social planning solution where decisions are centralized. We present the analytic results for the total profits in these settings. The results show the benefits of a decentralized approach over a centralized one, provided there is a mechanism for coordination. Finally, emission costs are compared for the various solution concepts.