# Money Supply and Monetary Base

Money supply is the quantity of money available in an economy for immediate use. It equals the currency held by public plus demand deposits at banks and monetary base is the sum of total currency in circulation and the amount held by banks as reserves.

The difference between money supply and monetary base arises because a \$1 injected into the economy by the central bank results in a much larger increase in overall money through the process of credit creation.

Imagine that in a parallel universe, you are the Master of Coin in Westeros. You issue gold dragon coins which are backed 100% by gold. You observed that most people keep their coins at home. Let’s call this money C. You decide to create a separate office of Master of Vault where people can deposit their coins and receive certificates. Over time, the certificates became a popular medium of exchange due to their convenience. Let’s call these deposits of coins D. Money supply equals the sum of C and D.

$$Money\ Supply\ =\ C\ +\ D$$

Let the coins kept in the vault (i.e. bank reserves) equal R. Monetary base, in this case, is the sum of C and R.

$$Monetary\ Base\ =\ C\ +\ R$$

Because all the coins deposited are kept in reserve, D = R and money supply equals monetary base.

The Master of Vault notices that the daily inflows of coins are roughly equal to daily withdrawals and that most of the coins are sitting idle in the vault. He comes up with a wonderful idea: why not keep a reserve of 20% and lend the remaining 80% of the coins to people and earn interest for the Treasury. He tells you that there are 1 million coins in the vault and that if you lend 800,000 coins at 10% per annum, the Treasury can earn 80,000 coins. You gladly agree.

After three months, the Master of Vault comes to you with an interesting observation: all of the money that you lent out has turned up in the vault again because when the borrowers spent the money those who earned decided to deposit it back with the vault. This resulted in an increase in deposits by D1 i.e. 800,000 gold dragons. You decide to lend 80% of the new deposits D1 (which amount to 640,000 gold dragons) in another round of money creation. This results in increase in deposits by D2 (i.e. 640,000). In the third round of money creation, you lend 80% of the 640,000 gold dragons which in turn increase deposits by D3 (i.e. 512,000 gold dragons). This process continues until the total money which westerosi have in the deposit accounts equals 5,000,000 gold dragons.

## Money Multiplier

You can see that the increase in money supply M (i.e. C + D) is far larger than monetary base B (i.e. C + R).

The ratio of money supply to monetary base is called the money multiplier.

$$\frac{M}{B}=\frac{C+D}{C\ +\ R}$$

Let’s divide the numerator and denominator of the right-hand side by D i.e. the sum of total account balances that people hold.

$$\frac{M}{B}=\frac{\frac{C+D}{D}}{\frac{C\ +\ R}{D}}=\frac{\frac{C}{D}+1}{\frac{C}{D}+\frac{R}{D}}=\frac{cr\ +\ 1}{cr\ +\ rr}$$

The ratio of currency to deposits is the currency-deposit ratio (cr) which shows the percentage of money people keep in the form of cash (instead of in banks). The proportion of deposits which banks do not lend out and keep in their vaults in the form of cash (to meet immediate demand by deposit-holders) is called the reserve-deposit ratio (also called the reserve requirement).

In case of Westeros, money multiplier is 5:

$$MM=\frac{1+0}{0+0.2}=5$$

CR is zero because we assume that people keep all their money in banks.

The money multiplier establishes the relationship between money supply and monetary base:

$$Money\ Supply\ =\ MM\times Money\ Base=5\times1,000,000\ GD=5,000,000\ GD$$