Question

# 4. Money Supply (a) Express the money multiplier (m) as a function of the currency-deposit ratio...

4.

Money Supply

(a) Express the money multiplier (m) as a function of the currency-deposit ratio and reserve to deposit ratio. Say, the reserve-deposit ratio is 20% and the currency-deposit ratio is 40%. If the monetary base is \$18million, what is the total money supply in the economy?

(b) What fraction of money supply is held as deposits?

(c) If several new ATMs are erected all throughout a country so that it is now much easier for people to withdraw money from their bank accounts, what will be the impact on the components of m and m (how will they change, increase, decrease or remain same)?

#### Homework Answers

Answer #1

(a)

Currency deposit ratio (cr) = 40% = 0.4

Reserve deposit ratio (rr) = 20% = 0.2

m = (1 + cr) / (cr + rr) = (1 + 0.4) / (0.4 + 0.2) = 1.4 / 0.6 = 2.33

Money supply (MS) (\$ million) = Monetary base (MB) x m = 18 x 2.33 = 42

(b)

MS = Currency (C) + Deposits (D)

18 = (D x cr) + D [Since cr = (C/D), we have C = D x cr]

18 = (D x 0.4) + D

18 = 1.4D

D = 12.86

Fraction of money supply held as deposit = D / M = 12.86 / 18 = 0.7143 (= 71.43%)

(c)

Easy withdrawal of money will reduce demand for keeping currency, which will decreasing currency-deposit ratio. Therefore, (1 + cr) will decrease and (cr + rr) will decrease, and since rr < 1,

(1 + cr) > (cr + rr), or

-(1 + cr) < -(cr + rr)

Therefore money multiplier will increase.

A decrease in money multiplier will decrease money supply.

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