De geldhoeveelheid II

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.