On European macro algebra

This post by Paul Krugman seems a little confusing to me:

UNILATERAL FISCAL EXPANSION

Multiplier = 0.73
Bang per euro = 1.03

COORDINATED EXPANSION

Multiplier = 1.18
Bang per euro = 2.23

The bang per euro is what matters: the tradeoff between increased debt and effective stimulus is MUCH better for the EU as a whole than it is for any one country.

I would think that the bang per euro is 1.03 for any single country (with the rest going to the other EU countries), but 2.23 for the eurozone, regardless of who does a fiscal stimulus: any one country, or the whole of Europe. The difference then is only due to the frame of reference: the EU is a bigger area than one of its members, so the absolute effect of fiscal policy has to be bigger since less leakages occur via imports.

So, as a counterfactual, let’s say that Germany comes up with a fiscal stimulus of G bn euros and everybody else sits tight, it would imply a multiplicator of 1.03 for Germany and of 2.23 for the whole EU. So, Germany’s GDP increases by 1.03 times G and the EU’s GDP by 2.23 times G. (Other EU countries GDP increases by somewhere between 1.03 and 0.) If, on the other hand, all EU countries save for Germany come up with a coordinated fiscal policy, the multiplicators would not change, only G has increased. However, the bang for the buck would be still the same.

Nevertheless, I agree that Germany should join a coordinated fiscal stimulus by the European Union. Tomorrow I will explain why. (Tomorrow became Saturday.)