You have 2 banks, and for simplicity, an equal amount of gold is deposited in each.
- The “Rothbard Bank” issuing notes only backed up by 100% gold. You deposit 1oz of gold, and you get a note (claim) that says on it
“Rothbard Bank Note, 1oz Gold, backed by 100% gold”
- The “Kaz Bank” issuing notes backed up by only fractional reserves, say typically 10% (just an example). You “deposit” 1oz of gold, and you get a note that says on it:
“Kaz Bank Note, 1 oz Gold, not backed by 100% gold. Should more customers show up then our available reserves, we become illiquid” , so that it is clear that the entire process is voluntary and that no fraud is committed.
We have in circulation two types of notes: Kaz notes with supply of M1, Rothbard notes with supply of M2.
M1>M2 by the very definition of the problem.
Here is the million dollar question:
What is the exchange rate between M1 and M2?
The answer to this question reveals everything we need to know about this idea behind voluntary fractional reserve banking.