5.10: The Money Supply II

The money multiplier model explains how the money supply is linked to the monetary base. The money supply, denoted by M, consists of the currency, C, held by the public and the deposits, D, held in banks. The monetary base, denoted by B, is the sum of the currency held by the public and the reserves, R, kept by banks. Therefore, M equals C plus D, while B equals C plus R.

The relationship between these variables highlights how the supply of money depends not only on the monetary base but also on two important ratios: the currency–deposit ratio (cr) and the reserve–deposit ratio (rr). The currency–deposit ratio reflects how much currency the public prefers to hold compared to bank deposits. The reserve–deposit ratio shows the reserves that banks maintain relative to deposits. Together, these ratios influence the total money supply, which can be expressed as the monetary base multiplied by the money multiplier.

The money multiplier is given by the sum of the currency–deposit ratio and one, divided by the sum of the currency–deposit ratio and the reserve–deposit ratio. This formula shows how much money supply can be generated from each unit of the monetary base.

In the money multiplier model, the money supply, shown as M, includes the currency, shown as C, held by the public on hand, and the deposits, shown as D, held by the public in banks.

Recall that the monetary base, B, is the sum of currency held by the public and reserves, R, held by banks.

So, M equals C plus D, and B equals C plus R.

To see how the money supply relates to the monetary base, divide the first equation by the second.

Next, divide the numerator and the denominator on the right-hand side by D.

Here, the quotient of C and D represents the currency-deposit ratio, or cr.

The quotient of R and D represents the reserve-deposit ratio or rr.

Now, solve for M by bringing B to the right side of the equation.

It follows that the money supply, M, is related to the monetary base, the currency–deposit ratio, and the reserve–deposit ratio.

This fraction—the sum of the currency–deposit ratio and one, divided by the sum of the currency–deposit ratio and the reserve–deposit ratio–is called the money multiplier.

It shows how much money supply can be created from each dollar of the monetary base.