Design and pricing of extended warranty menus with reference effects

Abstract

Consumer durables increasingly come with extended warranty menus—beyond manufacturers’ base warranties—that offer multiple options with differentiated protection lengths and prices. When choosing from an extended warranty menu, consumers might not only evaluate the intrinsic utility of each option but also form a reference point against which the available options are compared. In this paper, we posit that consumers compare the price-length ratios of available options when determining their willingness to pay, and investigate the design and pricing of extended warranty menus under such reference effects. To this end, we adapt the standard multinomial logit choice model to incorporate two types of reference point that are generated endogenously and exogenously, respectively, with respect to the given menu. We show that if the warranty options are ordered in the protection length, then the optimal pricing policies prescribe the same adjusted markup and the same price-length ratio alternately. We further extend our analysis to price competition under reference effects, where multiple firms compete in the aftermarket, each offering a single extended warranty. We prove the existence of a unique Nash equilibrium and develop an efficient method to identify it. Numerical examples are presented to illustrate the analytical findings, and sensitivity analyses are conducted to examine the impact of reference-effect coefficients on the optimal pricing policies. Overall, this work highlights the importance of incorporating reference effects into the design and pricing of extended warranty menus.