In this paper, we introduce private information into a market with search frictions and evaluate the relative efficiency of two pricing mechanisms, price posting and bargaining. Each seller chooses investment that determines the quality of the good. This quality is the seller's private information before matching and it will be observed in a match. Sellers enter a search market competitively and can choose either to post prices or to bargain. In this environment, a pricing mechanism affects efficiency through the choice of quality and the number of trades. Bargaining induces the efficient choice of quality but an inefficient number of trades because the division of the match surplus is generically inefficient. By directing buyers' search, posted prices internalize search externalities and induce the constrained efficient outcome in the case of public information. However, when the quality is private information, this role of posted prices in directing search can conflict with their role in signaling quality. Focusing on this conflict, we find that bargaining could yield higher efficiency than price posting. We characterize the parameter regions in which each of the two mechanisms dominates in efficiency.
