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"The value of currencies (including most popular cryptocurrencies) is set by a market. Price rises or falls until the supply and demand of the currency are equalized"

Why exchange rates of national currency are usually stable, where as cryptocurrency like bitcoin and ethereum is highly volatile?

But how does the market calculate the price based on supply and demand that is visible in the cryptocurrency exchange? Can someone give some kind of simple math to understand? For example, I mint some utility coins or cryptocurrency on ethereum from thin air, decide an incentive system. How will the cryptocurrency gain value through trading?

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Prices are set the same way as in any other market, which is to say that there is a (continuous, ongoing) process of tâtonnement where (say) buyers find that they cannot purchase at the maximum price they are willing to pay, or sellers find that they cannot sell at the minimum price they are willing to accept, creating pressure to adjust those prices. In some markets, this will eventually lead to relatively stable prices (say, street food), while in others, prices are more volatile, depending on how elastic supply and demand are.

Conceptually speaking, the classic notion of price-setting is that of the Walrasian auctioneer who receives, from each participant in the market, the amount said participant is willing to buy / sell at any given price, and who then proceeds to calculate the equilibrium price, only after which trade will actually take place. Needless to say, like the "invisible hand", this is merely an aid to understanding.

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