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.
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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.
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MB
MB’
i
i
100
110
Ms
Ms’
400
440
MB
M
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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
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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).
A COUPLE MONEY SUPPLY PROBLEMS FOLLOW - Money Supply Problem 1
You are hired by Ben Bernanke to run the trading desk at the New York Fed and Ben tells
you that he wants you to increase the money supply (M1) by 33 percent. He warns you to
be careful because in these uncertain times, the money multiplier tends to become very
unstable. He suggests that you stay ‘closely connected’ with the banking sector and he gives
you a list of phone numbers to do so. Note that in this problem, we are not targeting the
federal funds rate, we are targeting the growth rate of M1, as in quantitative easing.
Reserve Market
Initial Conditions
rr/D= .10
C = 400 b
D = 2000 b
ER = 00 (not a typo)
M=C+D
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a) (6 points)
i) Calculate the MB.
ii) Calculate the money multiplier.
iii) What is the money supply (use mm x MB to calculate this)?
Show work
MB = C + RR + ER = 400 + 200 + 0 = 600 = MB
MM = [(C/D + 1) / (C/D + RR/D + ER/D)] = [(.20 + 1) / (.20 + .10 ] = 4 = MM
M = 4 x 600 = 2400 = M = C + D
So you decide to inject $100 billion in reserves via open market purchases with phone in hand. Recall, Ben
said to watch that multiplier and so you start making some calls. Just as you suspected, the banks aren’t
making any loans, that is, they are sitting on all $100 billion in excess reserves.
b) (6 points) Given these new conditions, redo part a).
MB = C + RR + ER = 400 + 200 + 100 = 700 = MB
MM = [(C/D + 1) / (C/D + RR/D + ER/D)] = [(.20 + 1) / (.20 + .10 + .05 ] = 3.42857 = MM
M = 3.42857 x 700 = 2400 = M = C + D
c) (4 points) Now Ben calls and asks you how things are going and you tell him that you injected $100
billion in the system but it didn’t work. In the space below, write down what you would say to Ben (i.e.,
explain why the injection did not work).
BANKS ARE HOLDING ON TO THE ER – THEY NEVER GET A CHANCE TO BE INVOLVED IN
THE MULTIPLE CREATION OF DEPOSIT SINCE THEY NEVER ENTER THE SYSTEM (THEY
NEVER GOT LOANED OUT – BANKS ARE HOARDING THEM)
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Now you get some calls from bankers and you learn that there has been some ‘internal substitution’ within
the M1 money supply. In particular, households prefer to hold more currency relative to deposits, i.e., the
currency to deposit ratio rises. The numbers are as follows:
rr/D= .10
C = 800 b
D = 1600 b
ER =100 b
d) (6 points) redo part a)
MB = C + RR + ER = 800 + 160 + 100 = 1060 = MB
MM = [(C/D + 1) / (C/D + RR/D + ER/D)] = [(.50 + 1) / (.50 + .10 +.0625 ] = 2.264 = MM
M = 2.264 x 1060 = 2400 = M = C + D
e) (4 points) Now Ben is not pleased with your work, and calls again. Assuming that the money multiplier
is now stable (i.e., the value in part d), what must you do, in terms of open market
operations, to hit the 33 percent money growth rate desired by Ben and the FOMC?
Please show all work!
WE FIRST IDENTIFY THE TARGET MONEY SUPPLY, CALL IT M* = (1 + .333) x 2400 = 3200 = M*
WE KNOW THE MONEY MULTIPLIER IS STABLE AT 2.264 = MM
THE ONLY UNKNOWN IS THE APPROPRIATE MONETARY BASE (CALL IT MB*) AND THAT IS
CONVENIENT SINCE YOU CAN INFLUENCE THE MB THROUGH OPEN MARKET OPERATIONS
3200 = 2.264 X MB*
MB* = 1413
SINCE THE ‘OLD’ MB = 1060, THEN YOU NEED TO CONDUCT SOME MAJOR OPEN MARKET
__________ TO RAISE MB FROM 1060 – TO 1413, OPEN MARKET ______ = 353
f) (8 points) Calculate the total percent change in the monetary base, the money multiplier, and the money
supply (from part a) to part e)) and compare to the actual real world percent changes since this crisis began
in August of 2007 to the present. Please use the following links and click “view data” on the upper left to
obtain the actual real world values. For the monetary base start in August 2007 (this is monthly data), for
the money multiplier start 8/15/07 (bi-weekly data) and for M1 start at 8/13/2007 (also weekly data)).
From a) to e)
MB went from 600 to 1413, an increase of 135.5%
MM went from 4 to 2.264, a decrease of 43.4%
M went from 2400 to 3200, an increase of 33%
Real world
MB went from 853 to 2009, an increase of 135.5%
MM went from 1.579 to .898, a decrease of 43.1%
M went from 1360 to 1853, an increase of 36.25%
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g) (10 points) List the three ‘policy alternatives’ in terms of dealing with the zero bound from Bernanke,
Reinhart, and Sack , Monetary Policy Alternatives at the Zero Bound: An Empirical Assessment (2004):.
For your convenience, you can use the info from the second paragraph from this link (click Here). After
stating these three policy alternatives, provide proof that the Fed is currently pursuing all three of these
policy alternatives. Make sure you provide sources!
Click Here for latest FOMC Statement
Click Here for the Fed’s Balance Sheet
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Money Supply Problem 2 – Econ 304 - THIS PROBLEM DEALS WITH
THE SO-CALLED EXIT STRATEGY - THE FEAR OF COURSE IS
THAT WHEN THE BANKS START TO GET RID OF ALL THESE
EXCESS RESERVES, THE MONEY MULTIPLIER WILL 'BLOW UP'
AND SO WILL THE MONEY SUPPLY AND SO WILL INFLATION???
(AT LEAST THE HAWKS THINKS SO). THIS IS WHERE THE
NEWLY ACQUIRED (10/2008) ' PAYING INTEREST ON EXCESS
RESERVES TOOL' COMES INTO PLAY
You are the director of monetary affairs at the fed and you are in charge of keeping track
of the money supply, making sure it does not fall, as it did in the Great Depression, but
also making sure it does not ‘blow up’ as we know it might, knowing that the banks are
sitting on piles and piles of excess reserves (see pic below). Click Here and Here for the
reasons why banks are holding so much excess reserves (remember, the Fed is paying 25
basis points or .25% (=.0025 in decimal form) You have the following initial conditions:
RR/D= .10
C = 200 b
D = 1000 b
ER = 900 b
a) (6 points)
i) Calculate the MB.
ii) Calculate the money multiplier.
iii) What is the money supply (use mm x MB to calculate this)?
Show work
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MB = C + RR + ER = 200 + (.10 x 1000) + 900 = 1200 = MB
MM = [(C/D + 1) / (C/D + RR/D + ER/D)] = [(.20 + 1) / (.20 + .10 + .90)] = 1 = MM (CLICK HERE!)
M = 1 x 1200 = 1200 = M
Now you know that if these banks get rid of their excess reserves all at once, the amount of open market
sales that you need to conduct (to keep a handle on the money supply) will be massive and raise more than
one eyebrow in Washington (from the politicians) as the infamous ‘exit strategy’ will be full speed ahead..
Suppose that you had major influence and convinced the banks that it would be much more stabilizing for
all parties if they gradually lent out their excess reserves rather than lending them out all at once. As
such, you convince the banks to cut (lower) their excess reserve to deposit ratio in half (note: the ER/D
ratio is cut in half not ER itself). Assuming importantly that:
 The C/D and RR/D remain the same as in the initial conditions (they are stable)
 The monetary base does not change
b) (4 points) Repeat part a) part ii) and iii)
MM = [(C/D + 1) / (C/D + RR/D + ER/D)] = [(.20 + 1) / (.20 + .10 + .45)] = 1.6 = MM
M = 1.6 x 1200 = 1920 = M
NOTE – THE NEW M IS 60% HIGHER GIVEN THAT THEY ARE LENDING OUT THEIR
EXCESS RESERVES – THIS IS A BIG CONCERN (MAINLY AN INFLATION CONCERN) –
THE FED GOES OUT OF THEIR WAY TO CONVINCE EVERYONE THAT THEY HAVE AN
EXIT STRATEGY – AND WHAT IS THAT? MAKE IT MORE COSTLY TO LEND OUT THESE
EXCESS RESERVES BY ___________________________.
c) (5 points) Given these new conditions, calculate the amount of currency (C) and deposits (D) (i.e.,
separate the ‘new’ money supply into its two components).
WE NEED TO USE THE INFORMATION THAT WE HAVE:
START WITH:
1) M = C + D DIVIDE BOTH SIDES BY D AND WE HAVE
2) M/D = C/D + D/D WE KNOW M = 1920, C/D = .2, D/D = 1 PLUGGING ALL THIS IN
3) 1920/D = .2 + 1……D = 1600, C = .20 x 1600 = 320 = C
d) (10 points) We also know that the monetary base did not change but its make up has. Calculate the new
make up of the monetary base (make sure you separate total reserves into its required and excess
components).
WE KNOW 2 OF THE 3 COMPONENTS OF THE MONETARY BASE
C= 320 AND RR = .10 x 1600 = 160 = RR WE ALSO KNOW THAT THE MB DID NOT CHANGE
(BY CONSTRUCTION AND EQUALS 1200 = MB) PUTTING ALL THIS TOGETHER
1200 = 320 + 160 + ER SOLVE FOR ER
ER = 720 - CHECK WORK – IS 720/1600 = 0.45?? YES!
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e) (5 points) Given that 10% is the optimal growth rate of the money supply (from its initial value in part
a), what type and how many open market operations do you need to conduct to achieve this target,
given what happened to the money supply in part b)? Assume importantly that the money multiplier is
stable at its new level (after the banks cut E/D in half).
WE FIRST IDENTIFY THE TARGET MONEY SUPPLY, CALL IT M* = (1 + .1)x 1200 = 1320
WE KNOW THE MONEY MULTIPLIER IS STABLE AT 1.6 = MM
THE ONLY UNKNOWN IS THE APPROPRIATE MONETARY BASE (CALL IT MB*) AND THAT IS
CONVENIENT SINCE YOU CAN INFLUENCE THE MB THROUGH OPEN MARKET OPERATIONS
1320 = 1.6 X MB*
MB* = 825
SINCE THE ‘OLD’ MB = 1200, THEN YOU NEED TO CONDUCT SOME MAJOR OPEN MARKET
__________ TO LOWER MB FROM 1200 – TO 825, OPEN MARKET ______ = 375
f) Doing what you need to do in part e) may be politically unpopular since it is a massive contractionary
move and given the unemployment rate well above NAIRU, is there another way to keep the money supply
from ‘blowing up” other than OMO? Click Here for a Huge Hint!
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