Problem 20 What is the formula for the mone... [FREE SOLUTION]

Chapter 27: Problem 20

What is the formula for the money multiplier?

Short Answer

Expert verified

The formula for the money multiplier is: \[mm = \frac{1}{rr} + 1\], where "rr" represents the reserve ratio.

Step by step solution

Define the Reserve Ratio

First, we need to define the reserve ratio. The reserve ratio (rr) is the portion of depositors' balances that banks must hold in reserve. The reserve ratio is usually expressed as a percentage, so a reserve ratio of 0.20 or 20% means that banks must retain 20% of their deposits and can lend out the remaining 80%.

Initial Deposit Multiplier

Now, let's define the initial deposit multiplier. The initial deposit multiplier (idm) is the amount by which the banking system can multiply an initial deposit by lending it out repeatedly. The formula for the initial deposit multiplier is: \[idm = \frac{1}{rr}\] For example, if the reserve ratio is 20%, the initial deposit multiplier would be: \[idm = \frac{1}{0.20} = 5\]

Calculate the Money Multiplier

Finally, let's derive the formula for the money multiplier (mm). The money multiplier is the total amount of money that the banking system can create through lending, based on an initial deposit. The formula for the money multiplier is: \[mm = idm + 1\] Where "idm" is the initial deposit multiplier, and the "+1" accounts for the funds that the banks do not lend out (i.e., the reserves). Using the example of an initial deposit multiplier of 5: \[mm = 5 + 1 = 6\] So the formula for the money multiplier is: \[mm = \frac{1}{rr} + 1\] In conclusion, the formula for the money multiplier is: \[mm = \frac{1}{rr} + 1\] Where "rr" is the reserve ratio.