In the scenario I described above each country could spend all their wealth if they do desired. Nations constantly create money and handle deposits so even if they wanted it all in cash that they never spend (which no one does) they could do that in both the $100 and $200 scenario because as nations they can create currency. If the currency is backed by wealth of nations then inflation is less (ie, a country printing $100 with $1 in wealth is in trouble, but a country printing $100 with $100 in wealth is less in trouble).
Fortunately, while these concepts are a little non-intuitive, it’s possible to study, learn, and use them to influence our decision. Or to help me decrease confusion on the relationship of purchasing power and wealth.