A finite number of sellers (n) compete in schedules to supply an elastic demand. The costs of the sellers have uncertain common and private value components and there is no exogenous noise in the system. A Bayesian supply function equilibrium is characterized; the equilibrium is privately revealing and the incentives to acquire information are preserved. Price-cost margins and bid shading are 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. Private information coupled with strategic behavior induces additional distortionary market power above full information levels and welfare losses which can be counteracted by subsidies. As the market grows large the equilibrium becomes price-taking, bid shading is of the order of 1/ n , and the order of magnitude of welfare losses is 1/ n2 . The results extend to demand schedule competition and a range of applications in product and financial markets are presented.