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Hopefully I can clear up some confusion and offer some possibilities as to how the two ideas are consistent.
Gresham's Law only really applies when there are rules and regulations governing the exchange rate of currencies. When that happens, the currency that is undervalued relative to the market will go out of circulation. For example, if based on market supply and demand, a gold coin should be worth 2 silver coins, but the government says that they're worth the same whenever you buy or sell anything, no one would be willing to trade using the gold coins.
Now let's investigate the "convergence" idea. Imagine their are two currencies issued by different governments: shitcoin and hardcoin. Shitcoin is fiat money and hardcoin is commodity based money. Moreover, the government that runs shitcoin is known to print it endlessly.
If you misunderstood Gresham's Law, you might think that shitcoin will drive out hardcoin because people will want to hoard hardcoin and they'll only want to spend shitcoin.
But that's wrong because you're forgetting that in every transaction there's both a buyer and a seller. Buyers may prefer to use up their shitcoin, but sellers won't want to accept the shitcoin. The exchange rate between shitcoin and hardcoin will go up in hardcoin's favor until an equilibrium is reached. If shitcoin devalues in this way, the government of shitcoin may have to print more shitcoin, leading to even more devaluation. If shitcoin enters into a hyperinflationary spiral, it could get to the point where it becomes almost worthless, and most economic transactions are just done in hardcoin.
So, to recap, Gresham's Law only applies when there are artificial rules governing the exchange rate between two currencies. In other cases, you should simply expect the exchange rate between the two currencies to adjust in favor of the harder money, which is what we're seeing with Bitcoin. Whether or not the market "converges" to the better currency probably depends on other factors than simply this exchange rate story.
Great answer. To add to your scenario a little, you could imagine also that if there are merchants who accept both shitcoin and hardcoin, consumers might dump their shitcoin there. The tendency to do so would be stronger the more fixed the merchant holds the shitcoin/hardcoin exchange rate. That's where Gresham's Law plays out on the micro scale.
As to whether a better money does drive out the worse money, how would we know it's the better money if it didn't?
In a subjective value framework, the only standard by which something is better money is that people prefer using it to other monies for money stuff, right?
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30 sats \ 0 replies \ @Fabs 12 Aug
Damn dude, that's a solid explainer.
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If shitcoin devalues in this way, the government of shitcoin may have to print more shitcoin, leading to even more devaluation. If shitcoin enters into a hyperinflationary spiral, it could get to the point where it becomes almost worthless, and most economic transactions are just done in hardcoin.
Or, more realistically (which happened in our world), the shitcoin country will use the shitcoin-printing-power to quickly finance the army that takes over the hardcoin country, 'solving' the problem via force.
My hope is that bitcoin is different - it's a bottom up revolution. It's individuals that adopt it. Central power cannot possibly coerce each individual (With gold that was doable because of banks that held gold instead of individuals).
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