I investigate the optimal monetary policy in a New Keynesian macroeconomic framework with the sticky information model of price adjustment. The model is solved for optimal policy, and welfare implications of three alternative monetary policy regimes under this optimal policy are compared when there is a cost-push shock to the economy. These monetary policy regimes are the unconstrained policy, price-level targeting and inflation targeting regimes. The results illustrate that optimal policy depends on the degree of price stickiness and the persistence of the shock. Inflation targeting emerges as the optimal policy if prices are flexible enough or the shock is persistent enough. However, the unconstrained policy or price-level targeting might be preferable to inflation targeting if prices are not very flexible and the shock is not very persistent. The results also show that as prices become more flexible, the welfare loss usually gets bigger.