In order to maintain stable prices, the size of the money supply should grow or shrink at the same rate that the economy itself grows or shrinks. Historically, capital and technology improvements have caused a 2-3% increase in productivity, ever since the industrial revolution.
Moneys based upon industrial processes, most notably mining of metals and coin minting, would then naturally increase the money supply at about the right rate, assuming improvements in the relevant disciplines occurred at about the same rate as everything else.
Obviously, Moore's Law pushes certain specific disciplines a lot faster than the rest of the economy. Computing hardware tech advances about 40% every year, over the last 50 years. Kryder's Law and Butters's Law, for hard disks and network bandwidth, goes even faster. Those, in turn, make automation and computerization of other industries cheaper, and they continue to improve in productivity.
When the increase in money supply is tied to increases in productivity, naturally, the people providing the innovations and advances reap the benefits by getting the new money first.
This does not imply that the controller of a fiat currency should set a target inflation rate. That new money is going to the wrong people. It goes to the bankers who happen to be robbing the economy at exactly the same rate that inventors and innovators are adding to it. They are now treading water to stay right where they were before, and everyone else loses ground.
If you have no mechanism to ensure that the growth in the money supply goes directly to the people growing the economy, you are better off establishing a completely fixed money supply. That allows innovators to gain as they should, but with steadily falling prices rather than stable prices. That complicates the business math somewhat, but if everyone just assumes the same 2.5% annual growth in the economy over the same fixed money supply, it isn't that hard to work out.
If people can use Quickbooks to run their business, they can handle a fixed-quantity money supply. What no one likes is a steadily inflating money supply where only the people running like mad on the treadmill can stay in the same place, while fat cats in motorized carts throw pennies at them.
Bitcoin has a bit of a compromise, in that the people reaping the inflation windfall are the ones covering the actual operating costs of the system. But it is unfortunately not tied to the value of goods and services in the Bitcoin economy. Fixing the money supply increase in advance requires that you predict how quickly suppliers and consumers will adopt the medium of exchange. I think the guesser guessed wrong. But even so, the proof of concept is pretty darned good, for the first iteration. The only real danger is that it is good enough that people will never migrate to anything better.