The long-run output-inflation trade-off in the presence of menu costs

We examine the long-run output-inflation trade-off under the assumption that firms face menu costs and set prices in a state dependent fashion. We argue that these characteristics capture the idea that the long-run output-inflation trade-off is driven by (predictable) trend inflation, and the degree of price rigidity should be chosen optimally by firms in the long run, at least on average. We find that state dependent pricing implies a non-trivial departure from long-run monetary neutrality in terms of output, and a larger one in terms of utility. This is because trend inflation substantially influences average mark-ups, relative price distortions, and resources required for changing prices. The optimal level of long-run inflation is zero.