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I have heard the saying, "Bad money drives good money out of circulation," (Gresham's Law) many times.

I'm wondering if it's true, what it really means. What's good money? What's bad money?

And if this is true, what evidence do we have and do we know why this happens?

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Gresham's law has to do with commodity money. When several types of commodity money are available (e.g., both gold and silver coins), the one with the lowest quality will drive the rest out of circulation. The underlying idea is that everyone will try to hoard the "good money" while using the "bad money" for payments.

You have a full description of this issue in wikipedia.

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It happens when two commodities are perceived of having unequal values, but being subject to externalities that enforce the equality of their prices.

For instance, if I draw a smiley face on a dollar bill, that dollar bill might be rejected by certain machines or clerks, and thus have a value less than an ordinary dollar. But since the bill is legal tender, its price is not up for negotiation. People will be thus incentivized against "buying" the dollar bill for a commodity worth one dollar, and this will cause it to fall out of circulation.

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Money is a store of value and whilst today we have paper money and digital money originally it was thought money itself should be represented by something valuable: hence bronze, silver and gold coinage.

Good money is money whose commodity value is roughly equal to its face value.

Bad money is money whose commodity value is much less than its face value. One reason for the term bad money is that the coinage has been debased. For example, a gold coin which is in fact mostly bronze.

Now obviously, as the good coinage is intrinsically worth more we can exchange it for a much larger amount of bad coinage which is intrinsically worth a lot less. Hence bad money drives out good money.

It's not a term that makes much sense in the modern money system where money is represented both by paper and digitally, in other words, by law.

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Gresham's law is old, predating the modern widespread use of fiat currency by centuries. So the first thing to know for Gresham's law is that it's talking about coinage with significant commodity value (the coins themselves are valuable because they are made of valuable material.) The next thing to know about is "debasement". It's an ancient approach to try and cover shortages of valuable metals. Basically, use less gold/silver/whatever when you make coins and you can now pay off your debts and obligations with something that's technically the same but has less intrinsic/commodity value.

Gresham's law most obviously applies when a government first debases a currency - you've now got a large number of coins on the street that are legally the same but which possess a differences in intrinsic value. People move as quickly as they can to use the newer, debased currency to pay for things while hoarding every single one of the older, better coins they can. This quickly makes it so that the majority of coins in circulation are the newer, debased type. In this case, the "bad" currency is the new, debased currency with less intrinsic value. The "good" currency is the old, purer currency with more intrinsic value.

If you want evidence, I can show you a modern example. The United States does, in fact, mint a silver dollar (comprised of 99+% silver) which has a nominal value of one dollar. As in, if you really wanted to, you could use it to buy a soda at McDonald's or something. You could use them to pay traffic fines... but you'd be an absolute fool to pay for anything with a silver dollar, and nobody is ever going to pay you with one except as a joke/gift. They're worth over 15 dollars just in terms of raw silver, so using a silver dollar to buy something is like throwing away 14 dollars. Instead, anybody with sense uses dollar bills to pay for stuff if they're not just paying electronically.

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