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In this paper we introduce the cost channel of monetary policy (e.g., Ravenna and Walsh, 2006) into an otherwise standard New Keynesian model of a two-country monetary union, which is being hit by aggregate, asymmetric and idiosyncratic shocks. The single central bank implements the optimal discretionary monetary policy by setting the union interest rate.The cost channel makes monetary policy less effective in combatting inflation, but it is shown that the optimal response to the decline in effectiveness is a stronger use of the instrument. Moreover, we show how the sign of the spillover effects of idiosyncratic shocks depends on the strength of the cost channel. If the cost channel exceeds a well-defined threshold, then the interest rate turns into a supply-side instrument.