Economics 102
Homework #5
Due: March 24th at the beginning of class
Complete all of the problems. Please do not write your answers on this sheet. Show all
of your work.
1. Suppose that the economy initially has $700 in reserves.
To solve all of the parts to this problem we only need the following two
equations:
Money Supply(MS) = Reserves * Money Multiplier(mm)
mm = 1/required reserve ratio(rr), or rr = 1/mm
a. If the required reserve ratio is 20%, what is the total money supply, assuming
there is no cash being held? What is the money multiplier? What is the amount
of loans outstanding in the banking system?
To find the money supply, we need to use the first equation above:
MS = reserves($700) * mm
But to solve this we need to know the money multiplier,
mm = 1/rr, mm = 1/.20 = 5
We can now use the mm to solve for the money supply:
MS = 700 * 5 = 3,500.
To find the amount of loans outstanding recreate a balance sheet for the economy
assuming there is only one bank: Remember that bank reserves do not count in
the money supply, and since there is no cash being held, MS = deposits.
Assets
Reserves $700
Loans
2800
Liabilities
Deposits $3500
In order to get the balance sheet to balance, there are $2,800 in loans outstanding
in the banking system
b. How much does the money supply increase when the Fed adds $100 in new
reserves?
New money supply = new reserves * mm,
new MS = $100 * 5 = 500
c. If the Fed wants to make the money multiplier 10, what do they need to set the
required reserve ratio to? If they make this change what happens to the money
supply (keep in mind there are now $800 in reserves)?
From the second formula above, rr = 1/mm, rr = 1/10 = 0.1 = 10%.
MS = reserves ($800) * mm(10) = 8,000
So the money supply doubles from $4,000 to $8,000.
d. If a bank in this economy has $200 of reserves, $250 of loans and $450 of
deposits, how much excess reserves are they holding (use the required reserve
ratio from part c.)? How much could the bank make in additional loans?
The first thing we need to find is how much the bank is required to hold in
reserve. From part c, we know that the reserve requirement is 10%. Since the
bank has 450 in deposits there required reserves = 450(10%) = 45. They are
holding $200 in reserves, but they only need to be holding $45, so the bank has
$155 in excess reserves. The bank could loan out this additional money making
$155 in additional loans right away. Then this $155 would go through the money
creation process and become (155*10) or $1550 of additional loans. When you
add the $1,550 to the $250 of loans the bank had already made, the total loan
amount is $1,800.
e. If the Fed wants to double the money supply, specify precisely two ways in which
they could accomplish this. (Your answers should include numbers.)
If we want to cut the money supply in half the easiest way to do this is by
multiplying both sides of the money supply equation by two:
2 * MS = (Reserves * mm) * 2
This means the Fed either needs to double the money multiplier, or double the
amount of reserves. The Fed has three tools at their disposal to help accomplish
this.
1. Change the required reserve ratio: This would be the easiest, in order
to double the mm the Fed should simply cut the reserve requirement in
half. To check this cut the rr from 10% to 5%. If the following two
equations are true(they are) then this is one way to cut the money
supply in half:
Initial MS ($8,000) = Initial reserves($800) * (1/.10)
Double old money supply ($16,000) = ($800) * (1/.05)
2. Perform Open Market Operations: The Fed could purchase
government bonds in the open market, this would increase the amount
of reserves outstanding in the economy. In order for the Fed to
increase the money supply from $8,000 to $16,000, they would have to
sell $800 worth of loans. The reason this number is so small is that the
money multiplier works when money is added to the economy.
3. Lower the discount rate: When the Fed lowers the discount rate it
makes it less expensive for banks to borrow reserves. This has the
effect of increasing the amount of reserves in the economy. It is
unclear how much the discount rate would have to be lowered in order
to get the amount of reserve to be twice what it was before. This may
be a small of large decrease in the discount rate. The key is that the
Fed would have to lower the discount rate until there were $1,600 in
reserves in the economy.
2. For the following questions, assume there is a 10% required reserve ratio:
a. A bank has $300 of reserves, $300 of loans and $600 of deposits, how much
excess reserves are they holding? How much could the bank make in additional
loans right now? How much will the money supply increase after the money
creation process is finished?
The first thing we need to find is how much the bank is required to hold in
reserve. We know that the reserve requirement is 10%. Since the bank has 600 in
deposits their required reserves = 600(10%) = 60. They are holding $300 in
reserves, but they only need to be holding $60, so the bank has $240 in excess
reserves. The bank could loan out this additional money making $240 in
additional loans, this $240 would go through the money creation process and
become (240*10) or $2400 of additional loans, so the money supply increases by
$2,400 after the money creation process is finished.
b. A bank has total reserves of $450 and excess reserves of $150. What is the banks
current deposit balance? What is the banks current loan balance? What is the
maximum amount of deposits this bank can have?
To figure out the current deposit balance we need to know how much the bank is
holding in required reserves. Total reserves = required reserves + excess reserves,
450 = 300 + excess reserves, excess reserves = $300. We can then use the money
multiplier to figure out the current deposit balance, 300*mm(10) = $3,000.
To find the current loans balance, recreate a balance sheet for the bank:
Remember that bank reserves do not count in the money supply, and since there is
no cash being held, MS = deposits.
Assets
Reserves $450
Loans
2,550
Liabilities
Deposits $3,000
The maximum amount of deposits the bank can have is equal to:
Total reserves*mm = 450*10 = $4,500.