Problem 5 -- Money multiplier
- The money multiplier is the reciprocal of the reserve ratio
It will be greater than one if the reserve ratio is less than one.
Since banks would not be able to make any loans if they kept 100 percent reserves, we can expect that the reserve ratio will be less than one.
- If the desired reserve-deposit ratio is 0.2, the reserve ratio will be 0.2 in the absence of any legal requirement that it be more(not mentioned in the problem). Hence the money multiplier will be 1/0.2 = 5, and an increase in bank reserves of $ 10 will lead to an increase in deposits of $50.
The problem takes it for granted that "deposits" are checkable deposits (which are money) rather than savings deposits, which are not.
The authors fail to tell the reader that reserves are only held (in the U.S. at any rate) against checkable deposits, so banks will in fact expand their checkable deposits by the maximum allowed by the "reserve-deposit ratio".
- The general rule for calculating the money multiplier is 1 / RR.
It gets more complicated if we take factors such as the public desire to hold currency as well as checking accounts, but we ignore those complications here.
- If the Fed wants to reduce the money multiplier, and hence the money supply, it can simply raise the reserve ratio.
In practice, it rarely does this, as it would demand drastic adjustment by banks.
Problem 6 -- The Fed and the Great Depression
See Table 10.7 to fill in the blanks, which you should do by calculating the money multiplier.
The data is from Milton Friedman and Anna J. Schwartz, A Monetary History of the United States , which places primary blame for the depression on the Fed's failure to prevent the contraction of the money supply.
Not everyone agrees with Friedman and Schwartz that the contraction of the money supply was the major problem (we will treat John Maynard Keynes' analysis of the depression later), but everyone agrees that it was a problem.
Play the Fed chairman of the day and try to keep the money supply stable at 44.1 billion dollars. Do not print money; do not change the reserve-deposit ratio, but buy or sell treasury bills.
How much in the way of Treasury bills will you have to buy or sell?
Date | Currency | Reserves/Deposits | Bank Reserves | Money Supply |
Dec. 1929 | 3.85 | 0.075 | 3.15 | ?? |
Dec. 1930 | 3.79 | 0.082 | 3.31 | ?? |
Dec. 1931 | 4.59 | 0.095 | 3.11 | ?? |
Dec. 1932 | 4.82 | 0.109 | 3.18 | ?? |
Dec. 1933 | 4.85 | 0.133 | 3.45 | ?? |
Answer:
Date | Actual Money Supply | Money multiplier | Target for Deposits | Needed Reserves | Fed purchase of T-Bills |
Dec. 1929 | 45.9 | 13.3 | 40.25 | 3.02 | -0.13 |
Dec. 1930 | 44.1 | 12.2 | 40.31 | 3.31 | 0 |
Dec. 1931 | 37.3 | 10.5 | 39.51 | 3.75 | 0.64 |
Dec. 1932 | 34.0 | 9.2 | 39.28 | 4.28 | 1.10 |
Dec. 1933 | 30.8 | 7.5 | 39.25 | 5.22 | 1.77 |
Note that we calculate:
- Target for deposits = 44.1 - currency
- Needed reserves = reserve ratio times target for deposits
- Fed purchase of T-Bills = Actual reserves minus needed reserves.
Problem 7 -- Quantity Equation
Given that:
- Real GDP = $ 8 trillion
- Nominal GDP = $ 10 trillion
- M1 money = $ 2 trillion
- M2 money = $ 5 trillion
Find the velocity of M1 and M2 by using the quantity equation.
The quantity equation is:
Money x Velocity = Nominal GDP
M V = P Y
So it follows that:
V = P Y divided by M
And the velocity of M1 is:
V of M1 = 10 trillion divided by 2 trillion = 5.0
And the velocity of M2 is:
V of M2 = 10 trillion divided by 5 trillion = 2.0
Problem 8 -- Money, Prices and Inflation
Year | Money supply | Velocity | Real GDP | Nominal GDP | Price Level |
2004 1000 | 8.0 | 12000 | 8000 | .67 |
2005 1050 | 8.0 | 12000 | 8400 | .70 |
Note that:
- Nominal GDP = Money supply times velocity
- Price level = Nominal GDP / Real GDP
- Inflation rate = (.70 - .67) / .67 = 5 percent
- Percent change in money supply = (8400 - 8000) / 8000 = 5 percent.
Given that real GDP and the velocity of money remained constant, a five percent increase in the money supply will mean a five percent increase in the price level.