Question

Suppose total deposits of the commercial banking sector were $4,000 billion, the reserve requirement were 10%, excess reserves were $600 billion, and currency holdings were $1,000 billion.

a. Calculate the ratio of excess reserves to deposits (%) and currency holdings to deposits (%). What is the value of the monetary base?

b. Calculate the money multiplier for each of these three changes. For each case, what would be the impact on the money supply (deposits + currency) of a $200 billion increase in the monetary base?

i. The reserve requirement was reduced to 5% (everything else remains the same as in part ‘a’).

ii. The ratio of excess reserves rose to 25% (everything else remains the same as in part ‘a’).

iii. The ratio of currency holdings to deposits fell to 15% (everything else remains the same as in part ‘a’)

Answer 1

(a)

(1) Excess reserves-Deposit ratio (er) = $600 billion / $4,000 billion = 0.15 = 15%

(2) Currency deposit ratio (cr) = $1,000 billion / $4,000 billion = 0.25 = 25%

(3) Monetary base (MB) = Currency + Reserves

Required reserves = Deposits x Required reserves ratio (rr) = $4,000 billion x 10% = $400 billion

Total reserves = Required reserves + Excess reserves = $(400 + 600) billion = $1,000 billion

Therefore,

MB = $(1,000 + 1,000) billion = $2,000 billion

(b) Money multiplier (MM) = (1 + cr) / (cr + er + rr), and Increase in money supply (MS) = Increase in MB x MM

(i) MM = (1 + 0.25) / (0.25 + 0.15 + 0.05) = 1.25 / 0.45 = 2.78

Increase in MS = $200 billion x 2.78 = $556 billion

(ii) MM = (1 + 0.25) / (0.25 + 0.25 + 0.10) = 1.25 / 0.6 = 2.08

Increase in MS = $200 billion x 2.08 = $416 billion

(iii) MM = (1 + 0.15) / (0.15 + 0.15 + 0.1) = 1.15 / 0.4 = 2.875

Increase in MS = $200 billion x 2.875 = $575 billion