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Nothing? For it to increase the price it assume a demand that's higher than the supply that's still there. Also that people are willing to pay more due to an artificial restraint on supply. This may work with oil, but a speculative token?

And thus you understand why I wrote some of the articles I have written. A token must have a function to stake it's value on. Even crude oil would be worthless, if no one had given it a function.

But we're still left with, does staking have a positive effect on price? Is there any evidence that staking more tokens leads to price appreciation or stability? Even if we assumes some function, doesn't capital move toward liquidity?

To answer that question, consider how the real action of mining more of a commodity, such as copper or lithium, affect the long-term price of that commodity. What affect does mining (staking) more of this commodity have on its price?

Staking is actually more about liquidity and price stability than it is about price increase. Rarity creates a price increase, but also increases the volatility of it. Having enough to meet exchange needs is the real reason for staking.

But staking pulls tokens off the market and decreases liquidity. And mining happens at the same rate regardless of how much is staked. Am I misunderstanding you?

Yes it pulls coins off, but that's not the liquidity part. Liquidity is a measure of availability vs demand. Staking increases liquidity by adding new coins. Demand lowers it.