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This paper quantifies the costs of mitigating exchange rate volatility within the context of a flexible inflation targeting central bank. Within a standard linear-quadratic formulation of inflation targeting, we append a term that penalises deviations in the exchange rate to the central bank's loss function. For a simple forward-looking new-Keynesian model, we show that the central bank can reduce volatility in the exchange rate relatively costlessly by aggressively responding to the real exchange rate. However, when we append correlated shocks to better match summary statistics of the Australian data, we find that the costs associated with reducing exchange rate volatility are larger: output volatility increases substantially. Finally, we apply our method to a variant of a small backward-looking new-Keynesian model of the Australian economy. Under this model, large increases in inflation and output volatility accrue if the central bank attempts to mitigate exchange rate volatility. [ABSTRACT FROM AUTHOR]