A firm might not have perfect information about its own productivity, because observing the true realization might be too costly in terms of op- portunity costs of attending to other sources of uncertainty. Building on Sims (1998, 2003), I use insights from information theory to study the be- havior of information constrained firms. The focus is on the informational friction on the firm side only. This allows analyzing the implications of imperfect information for individual firms. Additionally, a welfare analysis is conducted by solving a social planner's problem. Interestingly, a com- parison using approximations in log-deviations is not applicable, although such an approximation is often used in the literature. In the decentralized economy, output might not be maximized under full information. Further- more, the distortions due to monopolistic competition are increasing in the amount of information agents are allowed to process.