Question

4. Consider the following questions about the money supply.
a) The monetary base is equal to $0.5 trillion, the non-banking public holds 25 cents in currency for each dollar of demand deposit they hold, and banks hold 5 cents in reserve for each dollar of demand deposits they create. Calculate the money supply.
b) The monetary base is equal to $1.0 trillion, the non-banking public holds 40 cents in currency for each dollar of demand deposit they hold, and banks hold 30 cents in reserve for each dollar of demand deposits they create. Calculate the money supply.
c) By how much does the central have to increase the monetary base in part (b) to keep the money supply at the level shown in (a)? Show your work.

Answer 1

Money multiplier (MM) = (1 + c) / (c + r) where c: Currency-deposit ratio and r: Reserve-deposit ratio

Money supply (MS) = Monetary base x MM

(a)

c = $0.25 / $1 = 0.25

r = $0.05 / $1 = 0.05

MM = (1 + 0.25) / (0.25 + 0.05) = 1.25 / 0.3 = 4.17

MS ($ trillion) = 0.5 x 4.17 = 2.085

(b)

c = $0.40 / $1 = 0.4

r = $0.30 / $1 = 0.3

MM = (1 + 0.4) / (0.4 + 0.3) = 1.4 / 0.7 = 2

MS ($ trillion) = 1 x 2 = 2

(c)

MS needs to increase by $(2.085 - 2) = $0.085 trillion = $85 billion.

Increase in MB = Increase in MS / MM

(i) If MM = 4.17 (as in part a),

Increase in MB ($ billion) = 85 / 4.17 = 20.38

(ii) If MM = 2 (as in part b),

Increase in MB ($ billion) = 85 / 2 = 42.5

NOTE: part (c) does not mention whether we need to consider the MM for part (a) or part (b), so I've considered both cases.