Genuine Question: How does an economy grow with a finite money supply?


In our economy today we have a money supply that is expanded through the process of fractional reserve banking. Which is to say banks lend out much more than they have on deposit. One of the benefits of this system is that the money supply naturally increases to meet the needs of a growing economy.

If we transitioned to a world that was entirely using something like Bitcoin, where there is a finite limit on the number of coins, how would the money supply be increased to support a growing economy?

I suppose one option would be to say you could run fractional reserve banking but with Bitcoin rather than with dollars - but then the currency in circulation is not Bitcoin but rather promises to payback Bitcoins. And there would be more of these IOUs than there are Bitcoins.

I see lots of posts about how transitioning an economy to Bitcoin and away from fiat currency solves inflation. This may be true, but wouldn't it also limit economic growth? What am I missing here.