The paper shows that the introduction a Eurobond together with fiscal capacity at the centre would produce macro-stabilisation benefits both for the core and periphery of the Eurozone and would also achieve a rebalancing of the policy mix away from monetary towards fiscal stimulus. To demonstrate these benefits, we trace the shock-responses in a stylised model of the economy of the Eurozone with a core and a peripher to see how it would behave under alternative conditions. Alongside standard demand and supply shocks, we include financial risk-premium shocks by explicitly modelling bond yields, bank lending and public debt dynamics. We replace national bonds with Eurobonds on banks and ECB s balance sheets, and we introduce fiscal capacit at the centre with the power to adjust the aggregate fiscal stance. We conclude that had a Eurobond/fiscal capacity existed at the onset of the Great Financial Crisis, the recession would have been much more muted, and with much less need for unconventional monetary policy. Comments on an earlier version of this paper received at a seminar organised by ACES on 21 st January 2020 are gratefully acknowledged. The authors take full responsibility for all remaining errors and omissions.