Question

1) Suppose the Fed's required reserve ratio (REQ) is 20%. Further suppose that the Fed buys $100 million of U.S. Treasury securities from a dealer, Mary Jones, who deposits the check, which is drawn on the Fed, in her bank. This deposit increases her bank's reserve account (∆R) with the Fed by $100 million as well as its demand deposits, its total reserves, and the overall level of M1. What is the money multiplier?1) Suppose the Fed's required reserve ratio (REQ) is 20%. Further suppose that the Fed buys $100 million of U.S. Treasury securities from a dealer, Mary Jones, who deposits the check, which is drawn on the Fed, in her bank. This deposit increases her bank's reserve account (∆R) with the Fed by $100 million as well as its demand deposits, its total reserves, and the overall level of M1. What is the money multiplier?

2)Assume REQ is 0.15 and the behavior of banks and depositors responds to interest rates such that banks do not make all the loans they can but rather want to hold 1% of their deposits (TDD) in excess reserves (ER), with the result that the ratio, ER/TDD , equals 0.01. Also assume that the interest rate is at the level where the public will hold only 75% in checkable deposits (rather than a 100% maximum) and thus 25% in cash or currency (C) such that the ratio C/TDD = 0.33. With these assumptions, what is the money multiplier?

Answer 1

1. We know that money multiplier is given by

Money multiplier=1/required reserve ratio

in our case

money multiplier= 1/.2=5

Since 100 million was deposited

money multiplier in amount (money supply)= 100*5=500 million.

2. The required ratio itself is .15. On top of that, the banks keep .01 in ER. And the public also keeps .25 of what it gets in currency. This is called money drainage. Where there is drainage, the formua for money multiplier is

(1+drainage ratio)/(required reserve ratio+drainage ratio).

Putting values in

1+.25/(.16+.25)

1.25/.41

=3.049.