This article examines a two-period differentiated-products duopoly in which consumers are partially "locked in" by switching costs that they face in the second period. While these switching costs naturally make demand more inelastic in the second period, they also do so in the first period, because consumers recognize that a firm with a higher market share charges a higher price in the second period and hence is a less attractive supplier to which to be attached. Prices are lower in the first period than subsequently, because firms compete for market share that is valuable later. But prices may be higher in both periods than they would be in a market without switching costs.