Question

Assume that bank deposits (D) are $3,200 million, the required reserve ratio (rr) is 10%, and currency outstanding (C) is $400 million. By how much should the FED change the monetary base (?B) and in which direction in order to decrease the money supply by $100 million? Hint: Start by deriving the more complex money multiplier and also assume that banks choose not to hold any excess reserves (ER = 0, which therefore means ER/D = 0).

Answer 1

Consider the given problem here the required reserve ratio (rr) is “10%=0.1” and excess reserve is “0”, => the “required reserve ratio” is same as “desire reserve ratio” that is “0.1”.

Now, “C=400” and “D=3200”, => the “currency drain ratio” is “cd” is “400/3200 = 1/8 = 0.125”.

So, the money multiplier is given by, “m = (1 + cd)/(cd + rr) = (1 + 0.125)/(0.125 + 0.1).

=> m = 1.125/0.225 = 5, => m = 5.

So, the change in the money supply is given by, dM = m*dB, here “B” the monetary base.

=> if “dM = (-$100)”, => dB = dM/m = (-$100/5) = (-$20).

So, in order to decrease the money supply by “$100 million” the FED should decrease the “B” by “$20” million.