In this scenario with two authorities following one objective each, none of the authorities would be subject to a policy trade-off, as the number of instruments matches the number of objectives. Nevertheless this reasoning cannot be used to exclude all conflict situations. In practice central banks’ responsibilities concerning financial stability vary a lot.
For example, no general financial stability objective can be derived from the Treaty or the Statute of the ECB. Nevertheless the ECB has the task to contribute to policies pursued by the competent authorities relating to the stability of the financial system [art. 105(5) of the Treaty, art. 3.3 and 25.1 of the Statute].