Gresham's Law
What is Gresham's Law?
Gresham's law says that when law fixes the rate between two moneys, the one overvalued at that rate stays in circulation and the undervalued one is hoarded.
The law needs a legal or customary fixed rate between two moneys, such as a rule that a worn coin and a full-weight coin both settle a one-dollar debt. At that forced rate one money is worth more as metal, or as a foreign claim, than it is as a means of payment, so holders spend the cheaper money and keep the dearer one. Circulation fills with the money the law overvalues while the undervalued money is melted, exported or stored, which is what people mean by bad money driving out good. The mechanism reverses once the fixed rate is removed: if people may price the two moneys freely, they refuse the weaker one at par and the better money takes over, a pattern called Thiers' law. That is why households in a collapsing-currency economy end up transacting in dollars rather than hoarding them.
Gresham's Law: a worked example
A country's law says any coin stamped one dollar settles a one-dollar debt. Full-weight coins contain 0.04 ounces of gold, worn coins contain 0.03 ounces, and gold sells for 30 dollars an ounce. The metal in a full coin is worth 0.04 x 30 = 1.20 dollars; the metal in a worn coin is worth 0.03 x 30 = 0.90 dollars. Paying a 100-dollar debt with worn coins costs 100 x 0.90 = 90 dollars of gold, while paying with full coins costs 100 x 1.20 = 120 dollars of gold. Every debtor saves 30 dollars by handing over worn coins, so worn coins circulate and full coins get melted for the 1.20 dollars of metal inside them.
The mistake students make with gresham's law
Students quote 'bad money drives out good' as though it always holds and then apply it to any weak currency. The law works only while a fixed official rate forces people to accept both moneys at par; take the compulsion away and the opposite happens, because a free seller simply discounts the weaker money. A second slip is reading 'bad' as counterfeit. Bad here means overvalued at the official rate, which usually means less metal or a weaker claim, not fake.
Gresham's Law questions
Why does Gresham's law require a fixed rate between the two moneys?
Without a fixed rate, sellers just discount the weaker money, so nobody gains by spending it instead of the stronger one. A legal tender rule that forces both moneys to settle the same debt is what creates the arbitrage: the holder pockets the gap between a coin's legal face value and its higher market value by paying with the inferior coin. Remove the compulsion and the gap gets priced rather than exploited.
Does Gresham's law apply to modern fiat money?
It does not apply within a single fiat currency, because a ten-dollar note has no metal to melt and no cheaper twin trading at the same legal value. It still applies wherever an official rate is imposed between two moneys, such as a country whose central bank fixes an overvalued official rate for its currency while a parallel market rate exists. Residents settle domestic obligations in the officially overvalued currency and hold the dollars they can only obtain at the parallel rate.
What is Thiers' law?
Thiers' law is the mirror image of Gresham's law: when people are free to choose which money to accept, good money drives out bad. It describes very high inflation, when shops and households start quoting and settling in a stable foreign currency and refuse the local one at face value. The two laws are consistent because each assumes a different rule about whether the rate between the moneys is forced or free.
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