My suspicion is before we get anywhere near 2 billion people using bitcoins that there will be factors at play that will dwarf the impact on price arising out of adoption and its use in day-to-day transactions.
My fear is as the realisation dawns on the bigger players that Bitcoin is 'the one' that it will be pumped by banks and central banks who can magic large sums of fiat into existence with which to buy bitcoin (and who may even dump gold temporarily), creating the ultimate bitcoin megabubble so that billions of latecomer ordinary people and businesses buying their first bitcoins will be shafted as the great bitcoin dump starts, into pms, into land, artwork etc. into a 'better' crypto - assets that had been neglected for the period bitcoin was so attractive, even back into fiat (they could use this point to launch more 'stable' 'new crypto-dollar or new crypto-pound etc.) until bitcoin finds a stable long-term pricepoint well below (even orders of magnitude below) the hyped price the masses bought at. Problem is of course nobody beforehand can know what this price will be. We would still be in a much better world than today because with bitcoin established fiats (old or new) will not be that attractive but if central banks are deliberately hyperinflating forcing people into crypto on their pump stage people could end up with 1000th of what they had before.
Btw, I'm only just exploring this idea so please point out if there's an obvious reason this is not how the future looks!
Unfortunately this scenario is almost a certainty if Bitcoin achieves mass adoption, such is the nature of financial bubbles. I don't see any effective way of preventing it. Caveat emptor.
it's in my opinion a very likely possibility and although it's completely evil to do that, anyone who invested before the banks (that means we all), would also get enormous wealth in the process, provided you use hold on your bitcoins for long enough and than use a fraction of your enormous wealth to buy hard assets, such as houses, land, stock, maybe even complete companies, and whatever you like. Maybe some precious metal as well although they may lose much of their value if bitcoin becomes gold 2.0
So even though this scenario will bring many people into poverty i'd still be happy if it happens. By now pretty much everyone in the world has at least heard of bitcoin and has probably heard some 'conspiricy theorists' about how corrupt banks are and how corrupt the financial system is. If they still want to hold on to their fiat, it's their own problem, let them keep their trash while it lasts.
Also, even though many people will at first become poorer for it (all the wealth for the first-movers has to come from somewhere) eventually the wealth will become more evenly distributed because unlike the current system there's no one who can just magically pop currency into existence. So once you spent a bitcoin, you spent it, and someone else has it. You'll have to earn more bitcoin before you can spend it again.