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Money multiplier. How does it work?

Banks must have on reserve a certain percentage (the legal reserve requirement) of its total deposits. Banks keep these amounts (required reserves) on deposit at a Federal Reserve Bank.
If a bank's actual reserves exceed the required reserves, the difference is the excess reserves with which bank can extend loans. Therefore, the single bank creates money supple equal to its excess reserves.
The interesting fact is that money creation for the banking system as a whole (D) is a product of excess reserves by the Money Multiplier. D = E*m
So, the Money Multiplier is the maximum amount of money that the banking system generates with each dollar of excess reserves. The formula for money multiplier is

m = 1/r,

where r is the legal reserve requirement.

The answer is simple.

Assuming a required reserve ratio r=20%. The old woman deposited d=100$ in First bank. With a 20% requirement, the First bank has d*r = 20$ reserve requirement. The amount of excess reserves is

E1 = d*(1-r)
E1 = 100*(1-0.2)=80 $

The First Bank lends out this amount to the Second Bank. So, the Second Bank’s excess reserves is
E2 = E1*(1-r)
E2 = 80*(1-0.2) = 64$

Redeposited E2 creates excess reserves in the Third Bank E3:

E3 = E2*(1-r) = E1*(1-r)2
E3 = 80*(1-0.2) 2 = 51.2$

and so on.

The total increase in the money supply D is:

D = E1*(1 + (1-r) + (1-r)2 + (1-r)3 +… +(1-r)n+ ...)

Let's multiply D by the term (1 - r) and subtract this from D:

D - D*(1-r) =
     E1*(1 + (1-r) + (1-r)2 + ... +*(1-r)n+ ...)
        – E1*((1-r) + (1-r)2 +...+*(1-r)n+ ...) = E1

D * r= E1

D= E1/r
D= E1*m

in our case

m = 1/r = 5

D = 80*5 = 400 - the increase in the money supply for the banking system as a whole.

And the old woman don't suspect that her 100$ deposit has 400$ macroeconomic effect :-)

Posted by mazoo at April 19, 2005 9:24 PM

Related posts:

The Multiplier Effect Feb 27, 2005

Comments

hmm is there any way this can look simpler ?

I guess im pretty dumb

Posted by: Ken at March 21, 2006 10:45 AM

I was thinkin the same thing dam econ 211 is killing me

Posted by: lol at April 11, 2006 3:59 AM

very easy to understand ,thanks

Posted by: marina at March 18, 2008 6:31 AM