Chapter 18 continued

Fed, Depository institutions, and the Money Supply

Money Multiplier

Easy version of money multiplier is

1/Reserve Requirements.

However , this probably overstates the true money multiplier.

In reality, all banks do not lend out all they can (that is Excess Reserves do not equal zero) and further people hold some cash (whereas we assumed it all was deposited in the first version of the money multiplier).

 

 

TR= Total Reserves

RR= Required Reserves

ER= Excess Reserves

TR=RR + ER

ER=e(D) where e is the excess reserve ratio)

RR=rdD (reserve requirement * Deposits)

Substituting in and solving for D

D= 1/[(rd +e)*TR]

And

Change in D= 1/[(rd +e)*change in TR]

 

 

Overall Money supply equals

Demand deposits + Currency

D + C

D + cD

(1+c)D

Note that this assumes currency held is a ratio to Deposits.

MB = Monetary Base

= Total Reserves + currency

= TR + C

= (rd + e)D + cD

= (rd + e + c) D

thus D= [1/[(rd + e + c)] * MB

 

 

combining the relationships we have

M = D + C

= [1/[(rd + e + c)] * MB + cD

= [1/[(rd + e + c)] * MB +c[[1/[(rd + e + c)] * MB]

= [(1+ c)/(rd + e + c)]MB

Thus, the new relationship for the multiplier is found. It takes into account currency drain and the fact that banks will not lend out to their fullest.

Suppose c = .3, rd = .1, and e=.02

Then multiplier is

1.3/(.42) = 3.1 rather than the 8.33 when only e was considered or 10 when merely the reserve requirement was considered.

This suggests that the Fed’s power, is more limited than previously considered, but still substantial.

Let’s see what happens when these numbers change….

Increase in reserve requirements shrinks money supply

Increase in C shrinks money supply

Increase in e shrinks money supply.

Now look at the depression…all of these went up. Hence Money supply shrunk dramatically.

 

Chapter 19

M! at the end of 1998 was $1,093 Billion. Split about 50-50% between currency and checkable deposits. Thus average M1 is over $10,000 per household and each household has $5,056 in cash.

GDP is $8,680 so this gives a velocity of 7.9.

The $10,000 and $5,000 numbers are probably biased high as some of the money is held overseas, business dealings (both legal and illegal) etc.

Morever