# The Money Multiplier

The increase in the money supply combined with lower interest rates as outlined above should help jump-start an ailing economy, but there’s even another benefit to this: the amount that this new injection of money will eventually grow into. This is determined by the money multiplier. Let’s take a look at an example.

· Assume the Fed purchases a \$1000 bond from Commercial Bank. Commercial now has added \$1000 cash to its account.

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· Assume that the reserve requirement is 10%.

· Commercial banks may now loan or invest \$900 of that \$1000 (10% of \$1000 or \$100 must be kept in reserves.

· Assume it loans \$900 to John Smith. John Smith then deposits that \$900 into his bank.

· His bank now has an extra \$900 and can loan or invest \$810 (it must keep 10% x \$900 or \$90 in reserves.

· The initial \$1000 injection into the economy has now grown to \$1810.

· We can calculate the total amount of money that the original \$1000 increase will grow into by using the following formula (I’ve simplified the formula in your text to make sure you understand the concept):

· Potential Money Multiplier = 1 ÷ required reserve ratio.

· In this case, 1 ÷ 10% =10 or an initial injection of money into the spending stream will grow by 10x.

· In the above case, the \$1000 injection will grow into a \$10,000 injection (10 x \$1000).

Let’s look at the first few rounds of the money multiplier:

 Money Pultiplier Round Total Reserves Deposits Desired reserves Loans Total increase in the quantity of money 1 \$1,000 \$1,000 \$100 \$900 \$1,000 2 \$900 \$900 \$90 \$810 \$1,810 3 \$810 \$810 \$81 \$729 \$2,539

If we followed this through to the finish we’d find an increase in the money supply of \$10,000. We used \$1000 to simplify things, but in reality, the Fed has been purchasing billions of dollars of bonds in the attempt to revive the US economy from the 2008 recession.

In theory, all of the above definitely shows a way in which an economy can bounce back from a recession or depression. The one thing it doesn’t take into consideration, however, is the cooperation of the financial institutions involved. After the 2008 crash banks tended to lean toward the  DESIRED reserve ratio, actually keeping more money on hand in reserves because of the high level of risk. This, of course, put the brakes on the money multiplier. Let’s look at what occurred:

Banks pre-2008 desired reserve ratio was about 1.2%

After the crash, banks increased their desired reserve ratio to upwards of 12% even though the Fed’s required reserve ratios were between 0% and 3% and up to 10% on deposits exceeding a certain level.

This had the effect of limiting the multiplier from a normal value of 9 (a deposit would grow into 9x that amount) to a value of 5 (see pg. 503).

The Fed now has to wait until DESIRED reserve ratios decrease enough to allow injections of money (purchasing bonds) can take full advantage of the multiplier effect.

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