idea

Fractional reserve banking is a money creation system based on debt, in which banks are only required to keep a fraction of the money deposited, and can loan the remaining portion.

This is a currency creation scheme. For example, with a 10% fraction system, banks can re-emit 90% as debt in the form of a loan. These 90% are re-injected in the system, change hands, and can be re-deposited into a bank account with the same rule.

This means that a system based on fractional reserve banking effectively can create in the economic system $\frac{1}{F}$ times the amount of currency introduced by the central reserve. For example, with 10% reserve, banks can create 10x the amount they receive. $100 introduced can generate $1000 created.

The american system sets the reserve ratio between 8% and 10%... and was reduced to 0% in 2020.

While it allows for economic flexibility by letting banks create money, FRB lacks resiliency. It transforms capital into debt, and the money created is effectively backed only by the trust that this debt will be repayed, i.e. the trust in the system altogether. A loss of trust from people with capital in the bank can entirely collapse the entire system if they reach the amount actually in reserves. Creditors would lose access to their capital altogether, and the currency would become greatly devaluated, to the point where it might become worthless.

The lower the number, the more fragile the system.

references

calculation for limit of created currency

Using $E_i$ as the amount of currency introduced by the central reserve, $F$ the fraction banks are required to keep in reserve, $e_n$ the amount emitted for a particular deposit, we are trying to solve for the total amount of currency emitted $E_t$.

$$ E_t = \sum_{n=0}^{\infty}{e_n} $$

Let's introduce $R = 1 - F$, the fraction of money re-emitted by the bank in the form of a loan.

$$ e_0 = E_i ; \space e_n = e_{n-1} \times R $$ $$ e_1 = e_0 \times R = E_i \times R $$ $$ e_2 = e_1 \times R = E_i \times R^2 $$ $$ ... $$ $$ e_n = E_i \times R^n $$

Since $0 < R < 1$ we recognize a geometric sum, and so:

$$ E_t = \sum_{n=0}^{\infty}{e_n} = \sum_{n=0}^{\infty}{E_i \times R^n} = \sum_{n=0}^{\infty}{E_i \times R^n} $$

$$ \Rightarrow E_t = \frac{E_i}{1 - R} \Rightarrow E_t = E_i \times \frac{1}{F} $$

example of collapse

Crypto in general, and FTX in particular.

Zimbabwe.