Question

Assume that the currency-deposit ratio is 0.5, the required reserve ratio is 0.1, and the excess reserves to deposit ratio is 0.15. If the monetary base is $2 trillion, find (a) the amount of currency in circulation in billions of dollars; (b) required reserves in billions of dollars; and (c) excess reserves in billions of dollars. (d) simple deposit multiplier which ignores leakages. The amount of currency in circulation in billions of dollars: Required reserves in billions of dollars: Excess reserves in billions of dollars: Simple deposit multiplier is:

Answer 1

(a)

Currency to deposit ratio = 0.5 => C/D = 0.5 => D = 2C where C = currency in circulation and D = deposit

Money supply(M) = ((cr + 1)/(cr + rr + er))*MB where MB = monetary base = 2 trillion

where cr = currency to deposit ratio = 0.5, rr = required reserve ratio = 0.10 and excess reserve ratio = 0.15.

=> M = ((0.5 + 1)/(0.5 + 0.15 + 0.10))*2 trillion = 4 trillion = 4000 billion

M = C + D => M = C + 2C => M = 3C => 3C = M = 4000 billion

=> C = 1333.33 billion -----------------Currency

(b)

rr = RR/D where RR = Required reserves

=> 0.1 = RR/D => RR = 0.1D = 0.1*2C = 0.1*2*4000/3 = 266.67 billion

Hence, Required reserves = 266.67 billion

(c)

Formula : er = ER/D where ER = Excess reserves

=> 0.15 = ER/D => ER = 0.15D = 0.15*2C = 0.15*2*4000/3 = 400 billion

Hence, Excess reserves = 400 billion.

(d)

Simple deposit multiplier = 1/rr = 1/0.1 = 10(Simple deposit multiplier is the multiplier when C and ER both are 0 => cr = 0 and er = 0. So, multiplier = (cr + 1)/(cr + rr + er) = (0 + 1)/(0 + 0+ rr) = 1/rr)

Hence, Simple deposit multiplier = 10