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Unformatted text preview: Homework #3 Key
1. Consider the following balance sheet. All figures are millions of dollars.
Net worth 1000
100 Suppose the Federal Reserve buys $100 worth of bonds from this bank. Assume the required
reserve ratio is 5%.
a. Illustrate the initial change in the balance sheet.
Bonds decline by 100 and reserves increase by 100.
b. Can this bank make any new loans? How much?
Yes, 150. Note the bank started with excess reserves of 50.
c. If banks make as many loans as possible and the public does not change their currency
holding, by how much will the money supply increase as a result of this open market
operation? Identify the final balance sheet values. Hint: use the formula.
The money multiplier is 20. The change in reserves is 150 (the amount of excess
reserves the bank started with after the bond sale). The money supply will increase by
3,000. Deposits and loans will both increase by 3,000.
d. How does your answer to part c change if the currency-deposit ratio is 50%?
The money multiplier is now 2.73. The money supply will only increase by 409.10.
e. Why would the Fed want to buy the bonds from the bank?
To reduce interest rates.
2. In the bank, deposits are 5,000, reserves are 1,000, bonds are 1,000, and loans are 3,000. The
required reserve ratio is 10%.
a. Set up the balance sheet for the banking system.
Assets are reserves, bonds, and loans. Deposits are liabilities.
b. Excess reserves are __500_____. Note that required reserves must be 20% of deposits.
Anything above this is excess.
c. The bank can make a new loan of _500_____.
d. When the new loan is made and the funds are removed from the bank, how does this
affect the balance sheet? Set up a new one.
Loans rise by 500 and reserves fall by 500.
e. When the new loan is made, spent, and redeposited in the bank, a new loan of _450____
can be made.
f. You have looked at round 1 and round 2 of this process. Fill in the table to show the next
few rounds of the loan process.
Round 5 New Loan
328.05 Total New Deposits
2,047.55 g. If this process continues, the bank holds no excess reserves, and the public does not
change their currency holdings, how much new money can be created in total? $5,000
h. Illustrate the final bank balance sheet.
Reserves stay at 1,000, bonds stay at 1,000, loans rise to 8,000, and deposits rise to
3. State whether each of the following examples would cause the money supply to increase or
decrease. Explain briefly.
a. The Fed increases the required reserve ratio.
Decrease because fewer loans can be made.
b. Banks decide to hold more excess reserves.
Decrease because fewer loans will be made.
c. The Fed decides to pay interest on the reserves that banks hold at their district Federal
Decrease because banks will hold more reserves. It is true that if banks earn interest
then they will ultimately have more reserves to lend but I would expect this to be a
4. How would each of the following affect M1 and M2?
a. Individuals can now write checks against their saving or money market accounts.
Decrease in M1. M2 will not change. Hold more in saving and less in checking.
b. The stock market crashes and individuals are worried about further declines in the stock
Increase in M2. No change in M1. People move out of stock and into saving.
c. All checking accounts now pay some interest.
Increase M1 and no change M2. Hold more in checking and less in saving. 5. Money demand in an economy where no interest is paid on money is Md
= 500 + 0.2Y − 1000i.
P € a. Suppose that P=100, Y=1000, and i=0.10. Find real money demand, nominal money
demand, and velocity.
Nominal money demand = 60,000
Real money demand = 600
Velocity = 1.67
b. The price level doubles from 100 to 200. Find real money demand, nominal money
demand, and velocity.
Nominal = 120,000
Real = 600
Velocity = 1.67
c. Starting from the values of the variables given in part (a), and assuming that the money
demand function as written holds, determine how velocity is affected by an increase in
real income, and by an increase in the nominal interest rate.
Start with the quantity theory and then substitute in nominal money demand which is
equal to money supply:
MV = PY
P (500 + 0.2Y − 1000i ) 500 + 0.2Y − 1000i An increase in real income will increase velocity
€ An increase in the interest rate will increase velocity
6. Assume that the quantity theory of money holds and that velocity is constant at 4. Output is
fixed at its full-employment value of 12,000, and the price level is 2.
a. Determine the real demand for money and the nominal demand for money.
Nominal money demand equals nominal money supply. Real money demand equals
nominal money demand divided by price level.
Nominal money demand = 6,000
Real money demand= 3,000
b. In this same economy the government fixes the nominal money supply at 4,500. With
output fixed at its full-employment level and with the assumption that prices are flexible,
what will be the new price level?
P = 1 .5
c. Return to the values you found for part a. If over time full employment output increases
by 25%, what has to happen to the nominal money supply in order to keep the price level
7. The money supply is $6,000,000, currency held by the public is $2,000,000, and the reservedeposit ratio is 0.25. Find deposits, bank reserves, the monetary base, and the money
Deposits = 4 million
Reserves = 1 million
Monetary base = 3 million
Money multiplier = 2
8. In a different economy, bank reserves are $5,000,000, the monetary base is $10,000,000, and
bank deposits are $20,000,000. Find the money supply and the money multiplier.
Money supply = 25 million
Money multiplier = 2.5
9. Explain why people in today’s economy are worried that inflation will increase in the future.
Banks are holding large amounts of excess reserves. If these reserves are lent there
could be a large increase in the money supply.
10. Think about how the different markets we have discussed are linked together in the long run.
Suppose there is a decline in consumer confidence in a large country like the United States.
Please answer the following three questions assuming no change in monetary or fiscal policy.
a. How is the real interest rate affected? Explain.
More saving, r decreases.
b. How is potential output affected? Explain.
In the long run, lower r stimulates I so K and hence Y increase.
c. How is the price level affected? Explain.
It falls. The decrease in r and increase in Y both increase money demand. ...
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This note was uploaded on 11/08/2011 for the course ECO 3203 taught by Professor Yang during the Fall '10 term at University of Central Florida.
- Fall '10