PROBLEM SET #08: THE CREATION OF MONEY
===========================================================
When you have completed this Problem Set, you should have a
better understanding of the following ECONOMIC CONCEPTS:
**Open Market Operations
**Reserve Requirements
**The (Simple) Money Multiplier
===========================================================
I.
INTRODUCTION
Welcome back to Excel!
In this problem set you will
analyze how the central bank of a country can use two of
its major monetary policy tools -- open market operations
and reserve requirements -- to change the volume of money
in the economy. You will trace the effects of changes in
monetary policy through the first ten banks in the
imaginary land of Tenbank. (Tenbank probably has hundreds
of banks, but you will be able to learn a great deal by
examining just ten of them!)
We will assume that all banks in the country are members of
the central banking system (known as the Federal Reserve
System, or the Fed, in the United States), and that
checkable deposits are the only form of "money"; that is,
there are no coins or paper money in this economy. This
assumption will allow us to calculate the money supply in
the country by adding up all the checkable deposits in the
banks. Students who have studied the components of the
money supply may recognize that we are focusing here on a
very liquid definition of money. In particular, we have
also made the simplifying assumption that the only
component of M1 is checkable deposits. This model is very
simple, but we can use it to understand how a larger system
would work.
Furthermore, we assume that the banks in Tenbank hold no
excess reserves. Since the only way the banks in Tenbank
can make profits is by loaning out the money deposited with
them, and since the central bank does not pay any interest
on the reserves held by the banks, bankers will hold
minimum reserves as long as the outlook for the future
economic health of Tenbank is optimistic.
08-1
Let's get started!
===========================================================
II.
INSTRUCTIONS
STEP 1 -- RETRIEVING THE WORKSHEET
A worksheet for this problem set has been prepared for you.
Retrieve it from the website, it is named PS-08. The
worksheet titled PROBLEM SET #08 -- THE CREATION OF MONEY
should appear on your computer monitor.
As mentioned above, the two types of monetary policy
actions you will be investigating are changes in the
reserve requirement and open market operations. Reserve
requirements, which are set by the central bank, establish
a minimum level of deposits that banks must hold back,
either in their own vaults or on deposit with the central
bank. These moneys cannot be loaned out or invested, but
instead are used to guarantee that the bank has (as least
some) funds available for customers who wish to make
withdrawals. If the Fed increases the reserve requirement,
banks will have less money to lend and hence the money
supply in the economy will shrink. Alternatively, if the
Fed decreases the reserve requirement, banks will have more
money to lend and the money supply will grow.
Open market operations refer to the central bank's purchase
or sale of government securities, or bonds. When the
central bank purchases securities from private holders of
bonds, or from the Treasury, the Fed takes the bonds in
exchange for money payments. In this case, the Fed will be
injecting reserves and hence money into the economy.
Alternatively, when the central bank sells bonds it will
exchange some of its bonds for money and the money supply
in Tenbank will decrease. (When the Fed receives money, it
is removed from the economy.) We will see that the
resulting change in the money supply will be much greater
than the amount of the central bank's initial purchase or
sale! This is what we mean when we say that the banking
system can "create" money.
Take a minute to look around the worksheet. Note that each
bank in Tenbank begins with a balance of 200 (million
dollars) in demand deposits. (Information on all ten banks
08-2
will probably not fit onto your computer screen at once;
you can use the arrow keys to move around the worksheet.)
Our assumption of equal size banks is in no way necessary
or restrictive. It will, however, be easier to see the
changes in the money supply that result from changes in
monetary policy when we have banks that are all exactly
alike.
Note further that this worksheet has been designed so that
you can see how each change in Fed policy "trickles"
through the banking system. At the top of the worksheet,
you have space for Fed policy parameters, such as the
reserve requirement and open market purchases or sales.
The lower portion of the worksheet contains balance sheet
information for the ten banks in this simple banking
system.
STEP 2A -- COMPLETING THE BANK BALANCES
Assume that the initial reserve requirement is 10% and that
the central bank of Tenbank, which we will now refer to as
the Fed, decides to increase the quantity of money in the
economy. Pursuant to that objective, the Fed performs an
open market operation and purchases 50 (million) dollars
worth of bonds.
Enter the reserve requirement, .10, in cell B4.
Change the format of the cell to percent.
Enter the value of the Fed's open market purchase, 50, in cell E4.
When the Fed buys the bonds, it purchases them from a bond
dealer. Assume that the bond dealer will take 50 (million)
dollars in bonds from her company's private securities
portfolio and sell them to the Fed. The bond dealer, in
return, will receive a check from the Fed which she will
then deposit in her account at Bank 1.
Bank 1 experiences two important changes. First, its
demand (or checkable) deposits increase by 50. Second, its
loan office can loan out 90% of the 50 (million) dollars to
new borrowers. (Why only 90%?)
Let's assume that when Bank 1 increases its lending
operations, the individual (or company) that borrows the
money deposits it into a bank, which happens to be Bank 2.
08-3
(Remember that demand deposits are the only form of
"money", checks must be deposited and written in order for
spending to occur.)
This process will continue through the entire banking
system of Tenbank. Your next step is to develop a general
formula that can be used to complete the Change in Balances
for the first ten banks in Tenbank. Before you begin
working on the Excel formula, let's try to get a better
understanding of the mechanics of the process in this
simplified economy. Please answer the following questions:
1. As a result of the Fed's purchase, how much money will the bond
dealer deposit into her account in Bank 1? _______________
2. Assuming that Bank 1 holds no excess reserves, how much money
will Bank 1 now be able to lend? ________________
3. Assuming that the money that is lent is deposited into Bank 2,
what will be Bank 2's change in balances? _________________
4. Assuming that Bank 2 holds no excess reserves, how much money
will Bank 2 now be able to lend? _________________
5. Assuming that the money that Bank 2 lends is deposited into Bank
3, what will be Bank 3's change in balances?
___________________
6. Assuming that Bank 3 holds no excess reserves, how much money
will Bank 3 now be able to lend? __________________
The answers are as follows: 1. $50.00, 2. $45.00, 3.
$45.00, 4. $40.50, 5. $40.50, 6. $36.45. If you do not
understand the answers to the questions above, you should
review the money creation process in your textbook and
notes, and/or see your instructor for help before
continuing.
The money creation process does not end with Bank 3, or for
that matter with Bank 10. A portion of the new deposit
continues to trickle throughout the banking system,
dampening with each move to a new bank as a portion of the
deposit is held as reserves and the rest is "loaned out".
08-4
You need to enter a formula in cell C13, that can be copied
through cell L13, that completes the Change in Balances for
the banks in Tenbank. Here's how to do it:
Bank 1's deposits increase by 50
= 50 x 0.90
Bank 2's deposits increase by 50 x 0.9
= 50 x 0.91
Bank 3's deposits increase by 50 x 0.9 x 0.9 = 50 x 0.92
And so on…
The Excel formula that you need to use has three
parts: the initial Purchase or Sale, one minus the
Reserve Requirement, and the exponent. You can use
Absolute Cell References (see PS-#06A, Step 3) to lock
in both the initial Purchase or Sale (in cell E4) and
one minus the Reserve Requirement (in cell B4).
The exponent, however, needs to increase by one as you
move from cell to cell (or bank to bank). Look at row
11 in your worksheet. The bank numbers there
conveniently increase by one as you move from bank to
bank! Therefore, the initial exponent in your formula
should be the number located in cell C11 minus one.
(If you need help using Excel's exponent key, please
see PS-#02B, Step 4.)
Hopefully you are ready to proceed.
Move the cursor to cell C13 and enter a formula for the Change in
Balances in Bank 1. (Hint: You should get 50.)
Copy your formula through cell L13. (Hint: The number in cell L13
should be 19.37102.)
Go to cell C15 and calculate the Ending Balance for Bank 1.
Copy this formula through cell L15. (Hint: The number in cell L15
should be 219.37102.)
STEP 2B -- CALCULATING THE MONEY SUPPLY IN TENBANK
Now you can complete the entries in row 7 of your
worksheet. The initial value of M1, to be entered in cell
B7, is the sum of all the Beginning Balances of the banks.
Use the SUM function to calculate this.
08-5
(See PS-#06A, Step 5, if you need help using the SUM
function.)
Use the SUM command again to find the new value of M1 in cell E7
after the Fed's bond purchase has worked its way through the banks
in Tenbank.
Then calculate the change in the money supply in cell H7.
Finally, (at least as far as this portion of the worksheet
is concerned), you can compare your answer for the change
in M1 in cell H7 with that obtained when you use the
(simple) money multiplier. As you may recall, the (simple)
money multiplier is equal to one over the reserve
requirement. So, the change in the money supply resulting
from the Fed's purchase of bonds can be found by
multiplying the amount of the purchase by the simple money
multiplier.
Move the cursor to cell E18 and perform this calculation.
(Hint: Do not use absolute cell reference here - this will
be helpful when you copy your worksheet in Steps 4 and 5.
Your answer should be 500. What is your money multiplier
here?)
STEP 3 -- DIAGRAM
Create a Column chart comparing the Beginning and Ending
balances for each of the ten banks. Use the numbers in
rows 12 and 15 respectively for your data. Specifically,
here is what you need to do:
Highlight cell A12. Then press the Ctrl key and highlight cell C12:L12.
Continue to press the Ctrl key and highlight cell A15, then cells
C15:L15.
Click on the Chart Wizard and Column graph option.
Use the first option in the Chart sub-type window.
08-6
Title your chart: OPEN MARKET OPERATIONS IN TENBANK:
THE PURCHASE OF SECURITIES
Save your worksheet as PS 08.
STEP 4 -- AN OPEN MARKET SALE OF SECURITIES
In this step, you will be analyzing the effects of an open
market SALE of securities by the Fed. You will use the
same initial conditions that you used above; however, this
time the Fed will SELL bonds to the public. So, you will
begin this work by replicating the worksheet so that you
can make the necessary changes. (See PS-#04A, Step 3A if
you need help.)
Copy all of the information from cells A3:L18 to cells A22:L37.
Go to cell C32.
Look at the Excel formula in the formula bar near the top
of your worksheet. Notice that the Absolute Cell
references for the bond purchase and the reserve
requirement still refer to cells E4 and B4 respectively.
Note too, that the exponent portion of your formula that
was not locked-in with an absolute cell reference has been
automatically changed.
Use F2, the Edit key, (see PS 04B, Step 1B) to change the absolute
cell references to E23 and B23.
Copy your updated formula through cell L32.
This will not change anything for the moment, but now you
can make changes in the bottom portion of your worksheet
that will not alter any of your earlier results.
Suppose the Fed decides to sell (instead of purchase) 50
(million) dollars from its bond portfolio. Make the
appropriate change in cell E23 and note all the automatic
changes in the rest of your worksheet! Excel automatically
recalculates all of these cells for you, given the new data
that you have placed in cell E23.
08-7
Create a new Column chart comparing the Beginning and Ending
balances for each of the ten banks.
Use the Beginning and Ending balances in rows 31 and 34 respectively
Label your chart: OPEN MARKET OPERATIONS IN TENBANK:
THE SALE OF SECURITIES
Notice the change in M1 caused by this open market sale.
Carefully consider the differences between open market
purchases and sales by the Fed.
STEP 5 -- CHANGES IN RESERVE REQUIREMENTS
Copy the information from cells A22:L37 to cells A41:L56.
As before, use the Edit key to update the formula in cell
C51. (Don't forget to copy through cell L51.)
Adjust your worksheet so that row 41 is at the top of your monitor.
Move to cell B42 and change the reserve requirements to 99%.
Click on cell C51 and update the calculations in cells D51:L51.
SLOWLY change the reserve requirement from 99% to 50% to 20%
to 10% to 1%.
In each case note what happens to the Ending Balances for
each bank, and the change in M1. Note too, the
relationship between the change in M1 (in cell H45), and
the change in M1 via the money multiplier (in cell E56).
You will have to answer questions about these changes at
the end of the Problem Set, you may want to turn to
question 4 and complete it now.
STEP 6 -- FINISHING UP
Don't forget to Save your worksheet to your data disk.
Print your worksheet and graphs and move on to the
questions.
08-8
Before you turn off your computer, remember to properly
exit Excel.
Good work!
08-9
Questions for PROBLEM SET #08
Name: _______________________________
Section: ________
Use your worksheet and graphs to answer the following
questions as carefully and complete as you can.
1. a) According to the calculations in your worksheet, by
how much does the money supply in Tenbank change when the
reserve requirement is 10% and the Fed purchases 50
(million dollars) in securities?
b) What is the change in the money supply when you apply
the (simple) money multiplier equation instead? What
is your money multiplier under these conditions?
c) What accounts for the difference between your answers
to (a) and (b) above?
d) Under what economic circumstances might the Fed choose
to buy bonds?
2. a) Using the information in your worksheet, what happens
to the money supply in Tenbank when the central bank
sells 50 (million dollars) in bonds?
08-10
b) Under what economic circumstances might the Fed choose
to sell bonds?
3. In reality, the Fed doesn't deal with just one bond
dealer, but with a whole group of securities companies
who agree to assist the Fed in making open market
purchases and sales. Look again at your two bar graphs
and see if you can come up with a logical reason for this
policy. (Hint: Do some banks in Tenbank experience
greater changes than others? Is this desirable?)
4. a) In Step 5 of this Problem Set, you considered the
effects of various changes in reserve requirements. Use
your worksheet to complete the table below.
Reserve requirement
.01
.10
.20
.99
Change in M1
_____
_____
_____
_____
Change in M1 via
money multiplier
_____
_____
_____
_____
b) As the reserve requirement gets larger, what happens
to the relationship between the change in M1 (via
the banks in Tenbank) and the change in M1 via the
money multiplier? What is the explanation for the
change in the relationship?
08-11
5.
Go to the Fed website at http://www.federalreserve.gov.
After reviewing the contents of this site, write a
paragraph describing the Fed's current policy direction.
Carefully explain why this set of policies is appropriate
for the economy at this point in time.
08-12