Two types of stores compete by choosing prices for a homogeneous good with constant marginal costs. The first type is in charge of two prices, while the second type is a regular firm that chooses one price. Consumers search sequentially with perfect recall. Some consumers have zero search costs, and some of them get first price quotation for free then incur positive search costs for each next price drawn. We examine whether the firrm of the first type can exploit its additional market power and compete for both types of consumers simultaneously by setting different prices and creating a price dispersion in equilibrium. Three types of equilibria are considered, which fully exhaust the parameter space. In all types of equilibria, the presence of the firm of the first type leads to uniformly higher profits for both firm types of firms when compared with the Stahl(1989) model in which all firms are identical. Furthermore, being a regular firm is beneficial for some parameter values in terms of higher profits.