Typical people like to keep a fraction (c) of their money in currency, and the r

Question

Typical people like to keep a fraction (c) of their money in currency, and the remainder in checkable deposit accounts. Suppose private banks are not required to and indeed do not keep any reserves at all, and the money multiplier is 4. A typical person with $1, 000 worth of money would:

A. Keep $500 in currency and $500 in checkable deposits

B. $1000 in in currencey/$0 in checkable deposits

c.$250 in currency/$750 in checkable deposits

D. $0 in currencey/ $1,000 in checkable deposits

E. $750 in currencney/ $250 in checkable deposits.

I really do not understand how to properly apply the money multiplier, especially in this case.

Explanation / Answer

monetary base = currency C + reserve R

here since banks donot hold any R = 0.

cr = C/D-----cr- currency deposit ratio.

D - deposits..

monetary base B = C + R.

money multiplier m.

M = C + D.

m = M / B.

m = [ C+ D ] / [ C+ R ]

m = [ C+ D] / C.

C + D = 1000-----given.

m = 4 given.

4*C = 1000.

C = 250.

D = 750.

SO OPTION -(C).

250 IN CURRENCY AND 750 IN DEPOSITS.

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