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If there is a difference between the supply curves of bitcoin, gold, and fiat, I'd say it's that fiat has no connection to the real world, while gold and bitcoin do. So I'd expect the supply curves of gold and bitcoin to be similar, while the supply curve for fiat should be insane.
From the Alex Salter article:
All else equal, a higher relative price of gold means a larger quantity supplied of monetary gold.
This is the kind of thing that I find very confusing. When we talk about stock of gold, we might say there are ~290k tonnes of gold that are accessible to humans. Barring alchemy or some golden asteroid, this is the total stock of gold (I've heard there is a lot of other gold, such as gold dissolved in the oceans or in the Earth's core, but supposedly it's unlikely it will ever be worth reclaiming).
Now, as the price of gold goes up, we might see gold deposits that couldn't be mined profitably get turned into meaningful sources of gold on the market. Additionally, we might see gold that was being used for other things get (jewelry, industrial uses) get sold for monetary uses. These kind of transformations seem like they are of the same kind to me: it's just somebody owning gold who wasn't previously willing to sell it, but now is.
Okay, so higher prices can't really increase the stock (that 290k tonne number from above) but they certainly can increase the supply of gold for sale in the market.
This seems like it would be more or less the same for Bitcoin: there are only ever going to be 21 million bitcoins.
But as the price of bitcoin goes up, we might begin to see new sellers (for instance among long term holders who had some number in their head at which they would trade some of their holdings for a nicer house or a fancy boat or whatever other thing they want).
So, no matter how much the price of bitcoin increases, we aren't changing the 21 million cap, but there certainly are sellers who weren't willing to trade their coins earlier, but are now. In my mind this seems very similar to the way you described gold's supply curve.
I have a really hard time with where economists draw the distinction between stock and supply.
For instance, you say above:
Bitcoin has a vertical supply curve, as its supply responds in no way to changes in its price.
More bitcoin will not be mined whether the price is $10 per coin or $100k per coin, but more gold might be mined if the price is $10k an ounce. This makes me think that you are right and that there is a difference between the supply curves of bitcoin and gold.
Okay, but I think maybe my problem is that I'm thinking about it backwards. Who cares how much of a thing there is? What matters is how badly people want it. If people want gold so badly that they are willing to pay $10k an ounce for it, there will certainly be people who raid their jewelry drawers (do people keep jewelry in drawers?) and if bitcoin hits $150k per coin, there will be people who are willing to sell who weren't willing to sell now.
Is there any relationship that can be determined from this? In the case of bitcoin it seems like people wanting it more would lead to higher price. In the case of gold, it seems like the same is true. The only thing that would change this is if gold that is sitting on the sidelines (in the ground or in drawers) comes into play. But then, if we have to count gold that sits on the sidelines, we have to count bitcoin that sits on the sidelines. So, I'm back to the only thing we can conclude is that people wanting it more means a higher price.
Now, fiat. People wanting more dollars should mean that dollars have a higher price. But...there actually is a way for dollars that didn't exist before to suddenly appear and get into people's hands. It's not just a matter of dollars that were sitting on the sidelines (stuffed in mattresses, or stashed away in safe deposit boxes), but actually new, magically created fresh dollars. And these new fresh dollars can be created ad infinitem. They aren't even made from paper, there is no real limit to how many can exist.
But honestly, I'm probably too ignorant of economics. I always feel like these concepts are kinda broken ways to talk about what we actually want to talk about and I just end up going in circles with myself.
This is the kind of thing that I find very confusing. When we talk about stock of gold, we might say there are ~290k tonnes of gold that are accessible to humans. Barring alchemy or some golden asteroid, this is the total stock of gold (I've heard there is a lot of other gold, such as gold dissolved in the oceans or in the Earth's core, but supposedly it's unlikely it will ever be worth reclaiming)
No, you're confusing what's physically available with what's economically available and/or in above-ground vaults
These kind of transformations seem like they are of the same kind to me: it's just somebody owning gold who wasn't previously willing to sell it, but now is.
No, this expands the supply of (monetary) gold, since the nonmonetary uses aren't impacting the money market. Larry White has some nice graphs to work this through in Better Money and Theory of Monetary Institutions. (You can probs find some presentations by him online as well.)

I think this is meaningfully different than gold's nonmonetary uses but I'll give it a think
So, no matter how much the price of bitcoin increases, we aren't changing the 21 million cap, but there certainly are sellers who weren't willing to trade their coins earlier, but are now. In my mind this seems very similar to the way you described gold's supply curve.
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Right, the stock of monetary gold is the current quantity of gold coins and bars.
The supply of monetary gold is people's willingness to transform gold in the ground or jewelry into monetary gold at each hypothetical gold price.
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I agree with you that bitcoin supply is not perfectly vertical, when we're discussing fiat prices, which is what I thought Den was doing. In that case, it should be the curve of how much bitcoin is available for purchase at each fiat price.
That's not how we usually talk about money supply, though, since the money we're usually talking about is also the unit of account and one of the uses of money is savings (so there's really no such thing as money on the sidelines). So, if we're talking about the bitcoin money supply, we have to include all of the bitcoin being used as money.
You could argue that the lost coins and dust are not currently being used as money. They might be a mechanism for bitcoin supply to be related to purchasing power.
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