We investigate the importance of the behaviour of the monetary authority for the dynamics of a currency union where cross-country asymmetries are not necessarily reflected in differences in economic size. We construct a stylised two-country general equilibrium model with sticky-prices to serve as laboratory for studying the operating characteristics of Taylor-type interest rate rules. We consider that the two countries in the union are different in terms of the price-setting practices of firms, and inspect the implications of alternative policy rules for the dynamics of the economy. The experiments carried out show, in general, that the way shocks propagate in the monetary union is linked to the systematic behaviour of the monetary authority. The reaction of the central bank to economic developments is important both at the union level and at the country level, namely to explain cross-country differences in economic behaviour. On the other hand, in our model the policy that stabilizes inflation is not necessarily the same that makes the output in the union less volatile. Also, the policy that reduces aggregate volatility does not necessarily imply the same for each country individually.