This paper provides a sensitivity analysis of the relative performance of inflation targeting, price level targeting, and hybrid targeting, the combination of these two. A simple, three-period, steady state to steady state economy is presented, where monetary policy is facing various sets of forward and backward looking expectations, social preferences on inflation and output gap stabilization, and degrees of cost push shock persistence. we derive optimal policy mix under the whole spectrum of these economic conditions, reporting also the criteria of the replicability of the theoretically optimal solution. The main intention of the examination is to reveal the nature of each interrelation between economic and policy parameters. The results show that (i) the relative strength of regimes depends heavily on the preconditions, and that (ii) the relationships of parameters related to the performance are non-linear and occasionally non-monotonic as well. our model specification is somewhat restrictive, however, contrary to the related literature, the examination, even in the intermediate cases, can be conducted analytically.