This article attempts to assess to what extent the central bank or the government should respond to developments that can cause financial instability, such as housing or asset bubbles, overextended budgetary policies or excessive public and household debt. To analyse this question, we set up a simple reduced-form model in which monetary and fiscal policy interact, and imbalances (bubbles) can occur in the medium-run. Considering several scenarios with both benevolent and idiosyncratic policy-makers, the analysis shows that the answer depends on a number of characteristics of the economy, as well as on the monetary and fiscal policy preferences with respect to inflation and output stabilisation. We show that socially optimal financial instability prevention should be carried out by: (i) both monetary and fiscal policy (sharing region) under some circumstances; and (ii) fiscal policy only (specialisation region) under others. There is, however, a moral hazard problem: both policy-makers have an incentive to be insufficiently pro-active in safeguarding financial stability and shift the responsibility to the other policy. Specifically, under a range of circumstances, we obtain a situation in which neither policy mitigates instability threats (indifference region). These results can be related to the build-up of the current global financial crisis, and have strong implications for the optimal design of the delegation process.