## Money and the Federal Reserve -- Problems

Problem 1 -- See the link to Radford's article on the Assignments and Notes page

Problem 2 -- Data on M1, M2 and components
See the power point slides for this chapter.

Problem 3 -- Gorgonzola multiple deposit expansion
The problem requires reworking the text example.
Note below that the Gorgonzolan accountants follow the Dutch convention of abbreviating "guilders" as "fl." -- florins (the currency of Renaissance Florence -- were the unit of account in the Netherlands, even though they were not a means of exchange.
Hint: the inital stage is that the Gorgonzolan central bank puts 5,000,000 fl. into circulation;
imagine that the typical bank gets a new deposit of 5,000 fl.
The typical bank will also have reserves increasing by 5,000 fl. -- by much more than needed to meet the required reserve ratio.

It will therefore keep the 1,000 fl. needed to meet its target
reserve-deposit ratio of 0.20 ( 1000 fl / 5000 fl = 0.20)
and lend out the other 4,000 fl.

The process does not stop there -- the person who borrowed the 4,000 fl. will spend it, say on a new car.
The automobile dealer will not keep the 4,000 fl. in her purse, but will put it in a bank.
The second bank will thus have received a new deposit of 4,000 fl., and that immediately goes to reserves as well.
The second bank needs only 800 fl. as additional reserves against the new deposit, so it will
lend out the other 3,200 fl., and that will be redeposited in yet another bank.

The total money supply has already increased to 5,000 + 4,000 + 3,200 = 12,200 fl., and we can trace the process still further.

The process will continue until Deposits = (1 / RR) Reserves = 5 x 5, 000, 000 = 25, 000, 000

Problem 4 -- Bank reserves and the money supply
All the following require you to keep in mind the formula:

Deposits = ( 1 / RR) Reserves

and to remember that Money = Currency in circulation + Demand Deposits .
Note that only currency in circulation counts; vault cash or currency banks hold as reserves is not directly part of the money supply.

1. Given:
Bank reserves (vault cash) = 100;
Reserve-deposit ratio = 0.25
Currency in circulation = 200

Money = Currency in circulation + ( 1 / RR) Reserves

Money = 200 + ( 1 / 0.25 ) 100 = 600

2. Given:
Money supply = 500;
Reserve ratio = 0.25;
Currency in circulation = bank reserves = X (unknown)

Money = Currency in circulation + ( 1 / RR) Reserves

500 = X + ( 1 / 0.25 ) X = X + 4 X

500 = 5 X, so X = 100

Both the public and banks hold 100 in currency.

3. Given:
Money supply = 1,250
Bank reserves (vault cash) = 100;
Reserve-deposit ratio = X (unknown)
Currency in circulation = 250

Money = Currency in circulation + ( 1 / RR) Reserves

1,250 = 250 + MM (100) (MM = the money multiplier)

1,000 = MM (100)
.

Hence the money multiplier is 10, and the desired reserve-deposit ratio is 1/10.

Problems 5 and 6 omitted (currency-deposit ratio not covered)
For the curious, answers are available here.

Problem 7 -- Quantity Equation
Given that M1 = \$ 2 trillion and M2 = \$ 5 trillion, with
Nominal GDP = \$ 10 trillion and real GDP = \$ 8 trillion

We know that:

1. M1 velocity is 10 / 2 = 5.
2. M2 velocity is 10 / 5 = 2.
3. Price index is Nominal GDP / Real GDP = 10 / 8 = 1.25
4. M1 * V = P * Y = 5 * 2 = 1.25 * 8

Problem 8 -- Quantity Equation
Given that the money supply increased from 1,000 to 1050 (by 5 percent)
while the velocity stayed constant at 8 and real GDP stayed constant at 12,000, we must have an increase in the price level.

It is simple to calculate the inflation rate by treating the quantity equation in percent change format:

PC in M + PC in V = PC in Price + PC in real GDP

5 + 0 = Inflation rate + 0

It is a bit less simple to find the price level. Note in the first year, the money supply was 1,000 and its velocity was 8, so the total amount spent (= nominal GDP) was 8,000.

The price index is nominal GDP divided by real GDP = 8,000 / 12,000 = 0.667

The next year, the total amount spent was 1,050 X 8 = 8,400, so
the price index was 8,400 / 12,000 = 0.70.

The inflation rate calculated as percent change in the price indexes is 4.9948 percent (remember that the percent change quantity equation is approximate).