In macroland there is $12,000,000 in currency. the public holds half of the currency and banks hold the rest as reserves. if banks' desired reserve/deposit ratio is 12.5%, deposits in macroland equal and the money supply equals
a.$48,000,000; $75,000,000
b.$54,000,000; $54,000,000
c.$48,000,000; $54,000,000
d.$96,000,000; $96,000,000

C.$48,000,000; $54,000,000

Explanation:

First we lay out the data

Currency (C) = $6,000,000

Reserves (R) = $6,000,000

Reserve-Deposit Ratio (rr) = 12.5%

To find deposits we simply solve a rule of three. Reserves are 12.5% of what deposits are:

X                 100%

6,000,000 12.5%

6,000,000 x 100/12.5 = 48,000,000

So Deposits (D) are $ 48,000,000

Now, to find the money supply, we must solve this equation

M = m x B

Where M = Money supply, m = money multiplier and B = monetary base

Monetary base is equal to currency in hands of the public + reserves, so:

B = C + R

B = $6,000,000 + $6,000,000

B = $12,000,000

The money multiplier equals to

m = (cr + 1)/(cr + rr)

cr is currency - deposit ratio

In this case currency is $6,000,000 and deposits are $48,000,000, so the currency-deposit ratio (cr) is the same as the reserve-deposit ratio (rr) = 12.5%

Now we plug the amounts into the formula, remember that we must convert percentages into decimals when solving an equation:

m = (0.125 + 1) / (0.125 + 0.125)

m = 4.5

Finally, we can solve for the money supply. Money supply is equal to the monetary multiplier times the monetary base:

M = m x B

M = 4.5 x $12,000,000

M = $54,000,000

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