I study the implications of learning by doing in production for optimal monetary policy using a basic New Keynesian model. Learning-by-doing is modeled as a stock of skills that accumulates based on past employment. The presence of this learning-by-doing externality breaks the ’divine coincidence’ result, that by stabilising inflation the output gap will automatically be closed, for a variety of shocks that are important in explaining the buseiness cycle. In this context, the policy maker must consider the impact on future productivity of any trade-off between output and inflation today. The appropriate inflation-output trade off is between inflation today and the present value of deviations in the output gap. The approach to optimal monetary policy follows Woodford (2010) permitting a study of variations in key parameters and steady states which is uncommon in the literature that relies on a quadratic approximation to the utility function. Exploiting this variation I find that learning induces a small increase in the importance of the output gap under a cost-push shock for the (more realistic case) of a distorted steady state. The welfare costs of business cycles are shown to be significantly larger even under the optimal policy.