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Do congestion externalities offer a reason to depart from complete price stability as the only goal of monetary policy in a New Keynesian model featuring search frictions, and under what conditions is the welfare cost of labor-market distortions sizable? This paper tries to answer these questions by deriving a linear quadratic framework for optimal monetary policy analysis – ala Benigno and Woodford (2005) – that is consistent with a Pareto inefficient labor market allocation, where the Hosios (1990) condition is not satisfied, and as a consequence, the flexible-price steady state of the model is distorted. The results indicate that maximization of expected utility of the representative household is equivalent to minimizing a quadratic loss function that consists of inflation, and two appropriately defined gaps involving unemployment and labor market tightness; and that search externalities give rise to an endogenous cost-push term in the New Keynesian Phillips Curve. Hence, full stabilization of both inflation and the welfare relevant unemployment gap is not feasible and deviation from complete price stability is welfare improving (because it allows to contain inefficient unemployment fluctuations). The inflation-unemployment trade-off and the welfare cost of search externalities are shown to be quantitatively sizable in response to shocks when steady state distortions are large and thereby the cost-push term is more volatile over the business cycle. Finally, a monetary policy rule that responds to unemployment growth rate is presented to be more efficient than a rule responding to unemployment gap.