We explore the distortions in business cycle models arising from inefficiencies in price setting and in the search process matching firms to unemployed workers, and the implications of these distortions for monetary policy. To this end, we characterize the tax instruments that would implement the first best equilibrium allocations and then examine the trade-offs faced by monetary policy when these tax instruments are unavailable. Our findings are that the welfare cost of search inefficiency can be large, but the incentive for policy to deviate from the inefficient flexible-price allocation is in general small. Sizable welfare gains are available if the steady state of the economy is inefficient, and these gains do not depend on the existence of an inefficient dispersion of wages. Finally, the gains from deviating from price stability are larger in economies with more volatile labor flows, as in the U.S.