This paper studies the business practice of offering discounts to new customers in markets with switching costs. In a two-period homogeneous-good duopoly model, it is shown that the equilibrium amount of discounts increases continuously in the expected switching costs of a typical consumer. In equilibrium, firms offer the same prices and discounts in a mature market even if they have different market shares, and the demands faced by these firms in a new market become more elastic. Firms are worse off engaging in the discriminatory pricing, while consumers need not necessarily benefit from it. There is costly equilibrium switching of consumers, which creates a dead-weight loss to the society.