Signaling Quality via Long Lines and Uninformative Prices

Abstract

Problem definition: We study the following puzzle: why do firms sometimes nurture long wait lines, rather than raising prices (to eliminate these lines)? Academic/practical relevance: In economic theory, prices are studied as a signal of quality, in absence of congestion (wait lines). We study price signaling when customers not only infer quality information from the price, but also from wait lines. Methodology: We developed a stylized model based on queuing and price signaling theory. The firm, privately informed about its quality (high or low), first determines its price. Next, customers arrive according to a Poisson process, observe the price and the wait line upon arrival, and decide whether to purchase. Results: When the proportion of informed consumers is low, to separate on price a high-quality firm must raise its price above the monopoly price. We show that there exist pooling equilibria in which firms instead charge a price lower than the monopoly price. We characterize two pooling equilibria. In both equilibria, a high-quality firm on average has a longer queue than a low-quality one, and long lines signal high quality. In the first one, the price is sufficiently low that short lines in turn signal low quality, so that the queue length almost perfectly reveals the type of the firm. In the second one, the price is in an intermediate range (but remains lower than the monopoly price), and short lines are an imperfect signal of quality. In each of the pooling equilibria, the high-quality firm earns a higher profit than in the separating equilibrium, despite the longer lines. Managerial implications: An empirical implication of our model is that, over time, when more customers become informed about the quality, the price of a new high-quality good should increase and the expected waiting lines should decrease. Our model integrates elements of price signaling in economics and equilibrium queueing in operations research. We hope that our research stimulates further interest in signaling games in service operations environments.