Optimal monetary policy is studied in a model with no contractual restrictions or physical costs of changing prices. Nevertheless, the price level is sticky in a range of markup indeterminacy, and inflation occurs only when employment presses against capacity. Under full information, the monetary authority can exploit price level stickiness to minimize the markup and keep employment at a constrained optimum without inflation. Under uncertainty, negative aggregate demand shocks produce real contractions and positive shocks raise the price level. The monetary authority can raise the likelihood that aggregate demand will maximize employment, but at the cost of higher expected inflation.