Common monetary policy with asymmetric shocks

What policy objective should a common central bank in a heterogeneous monetary union pursue? Should it base its decisions on the EU-wide average of inflation and growth or should it instead focus on (appropriately weighted) national welfare losses based on national rates of inflation and growth? We find that a central bank that minimises the sum of national welfare losses reacts less to common shocks. This can lead to higher average union-wide expected welfare if the variability of common shocks is large relative to the inflation bias and if idiosyncratic demand shocks in the non-tradables sector are not too high.