Journal article: New-Keynesian macroeconomics usually provides recommendations for monetary policy in an economy where a subsidy eliminates the mark-up at the steady state: the natural output is then optimal. In this paper, we propose to study the fluctuations around an inefficient natural output. We show that the cost of business cycles is usually underestimated. As monopolists, firms seek to preserve their expected mark-up: the interplay between the price setting by each firm and aggregate fluctuations leads to lower consumption and employment than their counterparts in an economy with flexible prices. The cost of fluctuations increases with the degree of the distortions at the steady state. However, when the utility function is iso-elastic, the optimal monetary policy is not changed: targeting zero inflation is still desirable and leads to replicate the flexible-price allocation.