A Bayesian supply function equilibrium is characterized in a market where firms have private information about their uncertain costs. It is found that with supply function competition, and in contrast to Bayesian Cournot competition, competitiveness is affected by the parameters of the information structure: supply functions are steeper with more noise in the private signals or more correlation among the costs parameters. In fact, for large values of noise or correlation supply functions are downward sloping, margins are larger than the Cournot ones, and as we approach the common value case they tend to the collusive level. Furthermore, competition in supply functions aggregates the dispersed information of firms (the equilibrium is privately revealing) while Cournot competition does not. The implication is that with the former the only source of deadweight loss is market power while with the latter we have to add private information. As the market grows large the equilibrium becomes competitive and we obtain an approximation to how many competitors are needed to have a certain degree of competitiveness.