We study a novel class of noisy rational expectations equilibria in markets with large number of agents. We show that, as long as noise (liquidity traders, endowment shocks) increases with the number of agents in the economy, the limiting competitive equilibrium is well-defined and leads to non-trivial information acquisition, and partially revealing prices, even if per-capita noise tends to zero. We find that in such equilibrium risk sharing and price revelation play different roles than in the standard limiting economy in which per-capita noise is not negligible. We apply our model to study information sales by a monopolist, information acquisition in multi-asset markets, and derivatives trading, and show that our model leads to qualitatively different results with respect to those in the existing literature. Our notion of large noise is shown to be necessary and sufficient to have limiting economies with perfectly competitive behavior.