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> supply (or probably more correct, holdings) of gold determine the money supply when a gold standard is in place

It does not when the money is not convertible to gold. Such is a fictitious gold standard.

The bank runs in the Depression were caused by inflation devaluing the value of a dollar by about half since 1914, yet was still convertible to gold. People suddenly realized they could DOUBLE THEIR MONEY by converting their paper money to gold. So they ran to the banks to do this. Of course, there wasn't enough gold to support that, and the banks collapsed. The runs did not stop until FDR made it illegal to exchange dollars for gold.

> The inflation of the US currency happened much later

Check the historical inflation figures. The dollar lost half its value 1914-29.



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