THE ECONOMICS OF MONEY,BANKING, AND FINANCIAL MARKETS 456

424 PA R T V Central Banking and the Conduct of Monetary Policy An important characteristic of the money multiplier is that it is less than the simple deposit multiplier of 10 found earlier in the chapter The key to understanding this result is to realize that although there is multiple expansion of deposits, there is no such expansion for currency Thus, if some portion of the increase in high-powered money finds its way into currency, this portion does not undergo multiple deposit expansion In our simple model earlier in the chapter, we did not allow for this possibility, and so the increase in reserves led to the maximum amount of multiple deposit creation However, in our current model of the money multiplier, the level of currency does increase when the monetary base MB and chequable deposits D increase because c is greater than zero As previously stated, any increase in MB that goes into an increase in currency is not multiplied, so only part of the increase in MB is available to support chequable deposits that undergo multiple expansion The overall level of multiple deposit expansion must be lower, meaning that the increase in M, given an increase in MB, is smaller than the simple model earlier in the chapter indicated Money Supply By recognizing that the monetary base MB = MBn + BR, we can rewrite Equation as: Response to Changes in the (6) M m (MBn BR) Factors Now we can show algebraically all the results in Table 16-2, which shows the money supply response to the changes in the factors As you can see from Equation 6, a rise in MBn or BR raises the money supply M by a multiple amount because the money multiplier m is greater than one We can see that a rise in the desired reserve ratio lowers the money supply by calculating what happens to the value of the money multiplier using Equation in our numerical example when r increases from 5% to 10% (leaving all other variables unchanged) The money multiplier then falls from 4.2 to m 0.25 0.25 0.10 1.25 0.35 3.6 which, as we would expect, is less than 4.2.10 Similarly, we can see in our numerical example that a rise in currency lowers the money supply by calculating what happens to the money multiplier when c is raised from 0.25 to 0.30 The money multiplier becomes m 10 0.30 0.30 0.05 1.30 0.35 3.7 All the above results can be derived more generally from Equation as follows When r increases, the denominator of the money multiplier increases, and therefore the money multiplier must decrease As long as r is less than (as is the case using the realistic numbers we have used), an increase in c raises the denominator of the money multiplier proportionally by more than it raises the numerator The increase in c causes the multiplier to fall Recall that the money multiplier in Equation is for the M1+ definition of money A second appendix to this chapter on the book s MyEconLab at www pearsoned.ca/myeconlab discusses how the multiplier for M2+ is determined