Money Supply Notes – Econ 304
Define money as above:
1) M = C + D where C = currency (cash) and D = demand deposits (checking accounts)
The Fed has pretty darn good control over what is referred to as the monetary base (MB) (also referred to as high powered money since changes in MB due to open market operations result in high powered effects, via the money multiplier, on the money supply). Define MB as follows with C = currency as before, R equals total reserves, a combination of required reserves (RR) and excess reserves (ER).
2) MB = C + R
Divide 1) by 2)
3) M/MB = (C + D)/(C + R)
Now a “trick” – divide the numerator and denominator of the RHS (right hand side) of 3) by D
4) M/MB = (C /D+ D/D)/(C/D + R/D)
Let’s do a few things to 4) – a) get MB on RHS, b) D/D = 1, and c) R = RR + ER
5) M = [(C /D+ 1)/(C/D + RR/D + ER/D)] MB
The term in brackets is referred to as the money multiplier, which is a little different than what you saw in principles. Equation 5) implies that the money multiplier is influenced by household behavior via C/D, which is determined by us. C/D is simply the currency to deposit ratio. For example, if you typically carry $100 in cash and you have $1000 in a demand deposit, then your C/D is 0.1. Think about what happened to C/D during Y2K.
Equation 5) also implies that bank behavior influences the money multiplier via ER/D. Even though banks tend to get rid of excess reserves (ER) since they earn zero interest, sometimes they hold on to them. What do you think banks were doing during Y2K? Probably holding a lot of ER to meet the liquidity needs of their customers (they anticipated significant withdrawals)!
The last player that has influence over the money multiplier is the Fed themselves via RR/D which is simply the reserve requirement ratio (this is what you were supposed to learn in principles). Note that if we let C/D and ER/D equal zero, the money multiplier collapses to 1/(RR/D) which is the ‘simple’ money multiplier that you may or may not have learned about in principles.
Specifics on the money multiplier: If C/D, ER/D, or RR/D go up, then the multiplier falls. This is important, because if MB remains constant, the money supply will fall along with the multiplier. We will now use an example that is a simplified version of what happened during the great depression.
Graphical Analysis, connecting the reserve market to the money market.
Initial Conditions
Let C/D = .2 , RR/D = .1 and ER/D = 0
Money Multiplier = (.2 +1)/ (.2 + .1 + 0) = 4
What does this mean?
A couple things: first, suppose the MB is $ 100 billion ; M = $ 400 billion
Second, a 10 billion dollar open market purchase will result in a $40 billion increase in the money supply (remember high powered money!) See the two graphs below.
The Great Depression – an Example
The Fed is blamed by some for causing the great depression or at the very least, failing to respond appropriately as in they should of conducted more open market purchases! Of course hindsight is 20/20.
What will a bank run do to C/D ratios?
So C/D rose dramatically as people were trying to get their cash – remember, there was no FDIC insurance back then.
ER/D also rose for two reasons – one, banks were keeping ER to meet the liquidity needs of their customers and two, had no one to lend to – banks are reluctant to make loans in such a dismal environment (i.e., the default risk of the borrower is naturally high in such a dismal environment).
Ironically, RR/D went up as well. The Fed was young, less than 20 years in existence and felt that raising the required reserve ratio would make banks more sound as well as giving the public more confidence so that they would not run on banks – in hindsight, raising the required reserve ratio was a mistake!
All three components of money multiplier rose during the great depression – impact on money multiplier?
Recall Money Multiplier equals:
[(C /D+ 1)/(C/D + RR/D + ER/D)]
Initially, let C/D = .2 , RR/D = .1 , and ER/D = 0
With numbers:
[(.2+ 1)/(.2 + .1 + 0)] = 4 = MONEY MULTIPLIER
Now account for changes in C/D, RR/D, ER/D
Let C/D up to .5, RR/D up to .2, ER/D up to .3 WHY WOULD WE EXPECT THIS TO HAPPEN DURING THE GREAT DEPRESSION???????
[(.5+ 1)/(.5 + .2 + .3] = 1.5
NEW Multiplier = 1.5
With numbers – before the great depression
M = ( 4 ) MB
If MB = $ 100 billion ; M = $ 400 billion
Now great depression hits and the multiplier falls to 1.5
MB still at $100 billion – M = 150 billion
NOTE - IN THIS "EXTREME EXAMPLE" THE ONLY REASON THE MONEY SUPPLY HAS CHANGED IS BECAUSE THE _____ AND THE _____ CHANGED!
Now the Fed isn’t blind – they buy $ 100 billion in Gov Securities, increasing MB by $100 billion – Money Supply up to $300 billion (1.5 times $200 billion) – still a 25% drop from where it was initially.
So the Fed pumped up the Monetary Base via open market purchases – but it was not enough to offset the dramatic fall in the money multiplier – they should have been easier!!
The lesson here is that the Fed has incomplete control over the money supply and in order to have better control, they better try to figure out what determines C/D and ER/D ratios. In normal times, these are pretty stable so that ‘normally,’ the Fed has pretty good control over the money supply (M1).
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