Optimal Monetary Policy with Imperfect Common Knowledge

We study optimal nominal demand policy in a flexible price economy with monopolistic competition where 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 of firms are strategic complements, we find that policy should nominally accommodate white noise mark-up shocks for a large range of capacity values. This finding is robust to the policy maker observing shocks imperfectly or being uncertain about firms’ processing capacity. When mark-up shocks are persistent, accommodation may even have to increase in the medium term but has to decrease in the long-run, thereby generating a hump-shaped price response and a slow reduction in output. Instead, when prices are strategic substitutes, policy tends to react with nominal demand contractions to mark-up shocks. In addition, there might exist discontinuities between common knowledge equilibria and equilibria with small amounts of imperfect common knowledge.