"bad money drives out good"
attributed to Sir Thomas Gresham(1519–1579), financial agent of Queen Elizabeth I.
In this simple form, many argue that the statement is actually false, and that actually "good money drives out bad".
The corrected version of the "Law" should be:
"Bad money drives out good if they exchange for the same price."
What the "Law" refers to is that if there are two types of coins with the same face value but different "intrinsic values" (for example one group of coins have been debased by addition of cheaper metals) then holders of the coins will choose to spend the debased coins (keeping them in circulation) while holding onto the more "precious" ones (removing them from circulation). As a result, the majority of the coins in circulation will be the "bad" debased coins which will have driven out the "good" coins.
Even though coins no longer have significant values due to their metal contents, we can still observe a version of this law in practice everyday. Ask yourself this: when you are at the cashier about to pay for your purchase, you look into your wallet and and see that you have two banknotes that you can use... One of the banknotes is brand new (you just got it from the ATM) while the other is crumpled and dirty. Which one do you spend?
The "Law" can be adopted successfully to many other areas as well (law, politics, morals, etc.)
For example, waiting in line for the bus. If some people respectfully wait in line (good) while others cut-in (bad). If there aren't sufficient social forces at work to discourage cutting-in (good and bad have the same value) then even though initially there may be some people continuing to wait in line, eventually they will get fed up with having their rights violated and will also stop waiting in line. As a result Bus Stops will become increasingly chaotic and dangerous.
Another example would be a country where some people evade taxes (bad) while others pay their full taxes (good). I will not get into a discussion of whether it is good or bad for the government to be doing this or how large the government should be. However, most people would agree that it is good and even necessarry for the government to be be providing at least Public goods like roads, lighting, public-national security. In this case the tax-evaders will be free riders and will have to be carried by the others. This may lead to providing an insufficient amount of public goods or budget deficits (which may in turn lead to printing of excess money and inflation).
One of the solutions that the government may choose could be to increase taxes. This would be most unfortunate as its main effect would be to harm the tax-payers while not affecting tax-evaders. At its extreme tax-payers would go bankrupt leaving the market to tax-evaders (bad drives out the good). A much better solution would be to catch and punish the tax-evaders! In fact you don't need to catch every single tax-evader, you just need to make it optimal to pay taxes.This can be done by increasing the expected benefits of paying taxes or reducing the expected benefits of evading taxes. To reduce the incentive to evade taxes you should either increase the likelihood of getting caught or increase the punishment when you are caught. Both of these will make it less worthwhile to evade taxes. However, a word of caution: this will only work if you are also able to prevent the bribery of the officials!
Links to information about Gresham's Law:
Gresham's Law by Edna Carew in The Language of Money
Why pay dear when you can pay cheap ?
Uses and Abuses of Gresham's Law in the History of Money by Robert Mundell at Columbia University
Put together by ATJ