It is well known that the Internet has significantly reduced consumers' search costs online. But relatively little is known about how search costs affect consumer demand structure in online markets. In this paper, we identify the impact of search costs on firm competition and market structure by exploring a unique theoretical insight that search costs create a kink in aggregate demand when firms change prices. The significance of the kink reflects the magnitude of online search costs and the kinked demand function provides information on how search costs affect competition in the online market. Using a dataset collected from Amazon and Barnes & Noble, we find that search costs vary significantly across online retailers. Consumers face low search costs for price information from Amazon.com. It leads to a higher price elasticity when the firm reduces prices than when it increases prices, increasing Amazon's incentive to engage in price competition. On the other hand, consumers face relatively higher search costs for price information from Barnes & Noble. This leads to a lower price elasticity when Barnes & Noble reduces prices than when it increases prices, reducing Barnes & Noble's incentive to engage in price competition. We also find that search costs decrease with the passage of time as the information about price changes dissipates among consumers, leading to increased price elasticity over time. Finally, we highlight that search costs are lower for popular books compared to rare and unpopular books. These findings have implications for the impact of the Internet on the Long Tail phenomenon.