>You can already buy shares in a nations economy - it is called owning currency.

An interesting point! Yes, that is definitely one way that currency could be looked at...

>The big difference from stocks is that most countries issue new shares (dollars, etc) to keep the price stable (indirectly via careful control of interest rates).

Agreed -- but if we were really to analyze things, scrutinize the way things really work at the highest degree of resolution, then we would have to observe that:

a) There are multiple countries/currencies in the world.

b) That each country's/currency's inflation rate is different than all of the other countries/currencies.

c) If each country's/currency's inflation rate is different, this means that each countries's issuance of new shares (and control of interest rates) -- their financial policies, are, by comparison, either more effective, on par, or less effective than those of other countries used for comparison...

Phrased another way:

All countries do not control the rate of inflation of their currencies equally.

Phrased another way:

Some nations are better at controlling their currency's rate of inflation than other nations.

True or not true?

>I am simplifying terribly

As am I! :-)

>but just as shares represent a fraction of a company, cash represents a share of a nation’s economy.

Again, an interesting point!

And yes, I could agree with that!