Optimal Monetary Policy with Imperfect Common Knowledge

We study optimal nominal demand policy in an economy with monopolistic competition and flexible prices when firms have imperfect common knowledge about the shocks hitting the economy. Information imperfections emerge endogenously because firms are assumed to have finite (Shannon) capacity to process information. We then ask how policy that minimizes a quadratic objective in output and prices depends on firms' processing capacity. When price setting decisions are strategic complements, for a large range of capacity values optimal policy nominally accommodates mark-up shocks in the short-run. This holds even if the policy maker observes shocks imperfectly or is uncertain about firms' capacity parameter. With persistent mark-up shocks accommodation may increase in the medium term, but decreases in the long-run thereby generating a hump-shaped price response and a slow reduction in output