Deposit Creation

The amount of deposits the banks can create depends upon (i) the amount of cash with bank, i.e., the amount of high powered money (H) and (ii) the ratio of bank’s cash reserve against deposits (b) and ratio of cash to bank deposits held by the public (x). Let cash with the banks be equal to R and cash with public (non bank) be C, then the volume of high powered money H equals to total cash held in the economy, i.e.,

H = C + R (i)
If banks keep cash reserve ratio denoted by x against their deposits D, then
R = xD (ii)
And if public keep as cash a ratio of deposits denoted by b, then
C = bD
Now, substituting the value of C(equation (iii))and R (equation(ii)) in equation (i), we get,
H = bD + xD
or D( b+ x)= H
or D = H/(b+x)

This equation shows that if people do not want to keep any portion of bank deposits as cash, i.e., ratio of cash held by public (b) is zero, then total deposits would be equal to H X 1/x, i.e., cash with banks multiplied by the reciprocal of cash reserve ratio but when public wants to hold some portion of deposits as cash, i.e., b is positive, to that extent, deposit creation will become lower.