Despite the mixed empirical evidence, many economists stillhold to the view that Internet will promote competition betweenfirms,thereby lowering prices and increasing economic welfare. This paperpresents a search model that provides a different view. We analyzethemarket for a homogeneous good where some consumers are fully informedwhile others are not. Depending on the parameter values, there may bethree types of equilibria and the comparative statics results aredifferent for each of these equilibria. For example, a reduction insearch cost may raise equilibrium prices when consumers' searchintensity is low, but reduce prices when consumers search intensityis high. These different comparative statics results may explain themixed empirical evidence found so far.