Question

1. Suppose that households wished to maintain $1.00 in pocket money (currency and coin) and $10.00 in liquid savings assets (small CDs, money funds, and savings accounts) for every $1.00 in their checking accounts (transaction deposits). If banks choose their desired reserves to be ten cents for every dollar of transaction deposits, what are the reserve multiplier and the money (M2) multiplier if the Federal Reserve’s reserve requirement ratio is:

Answers/Explanation

2. If households’ currency-deposit ratio is 1.25, and they desire to maintain $9.25 in liquid savings assets for each dollar in their checking accounts, what must the banks’ excess reserves ratio be if the money multiplier is 10? If the banks changed their excess reserves ratio to one dollar for every $1,000 of transaction deposits, compute the effect this would have on the money multiplier.

Answers/Explanation

Answer 1

1)

$10 is kept as liquid assets and $1 is kept as pocket money and $1 is kept in checking.

M2 includes both $1 in pocket and $1 in checking, and $10 is not in M2 because it's a liquid asset.

Therefore: $2/$12 = 12%

We divide by $12 because the total amount is $12; the amount in M2 is $2. We can do this because the reserve requirement = 1/money multiplier. The two are intimately linked.

2)

e want x/(9.25+x) = 0.0125

x = 0.0125(9.25) + 0.0125x

0.9875x = 0.115625

x = 0.117088

If the money multiplier is 10, the reserve ratio is 1/10 or 10%

So the excess reserves ratio must be:

11.7% - 10% = 1.7%

If the banks changed their excess reserves ratio to one dollar for every $1,000 of transaction deposits, compute the effect this would have on the money multiplier.

$1/$1,000 = 0.1%

The real reserve ratio would then be 10% + 0.1% = 10.1%

So the money multiplier = 1/0.101 = 9.9

Which is lower than the original money multiplier.