Why does paper money have value?
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Because we say so. That’s it.
So long as we all agree it carries value, then it is an effective currency. If we decided one day that it had more value, then it would. If we decided it had less, than it would.
That being said, there is effectively an agreement in place that its value be fixed to the value of digital currency, and likewise that both values be matched to the overall economy.
The former is true because banks say so; a bank will exchange paper money for digital money at a 1:1 rate, so their values are fixed.
The latter is true because the dollar (or whatever your country’s currency is) is pretty much the only currency used, and bartering is almost unheard of. Digital or physical, your local currency is the only thing that people use to spend on goods and services, so it is necessarily true that the total value of all goods and services be equal to the total value of all money spent.
This is why inflation happens. As more money is in circulation, more money is spent, but no additional goods or services are rendered, so the value of all the money is spread out over more individual dollars, and each dollar must therefore have less value.
If some other currency was introduced, without a fixed exchange rate to the regular currency, then it would have a destabilizing effect on this whole system; it would cast doubt on the value of the dollar.
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