Question

Suppose the current money stock in the economy is $1 billion, and the Fed sets 10% reserve requirements. a)If people hold all the money as currency, what is the money multiplier and what is the quantity of money in the economy? b) If people hold all the money as demand deposits and banks maintain 10% reserve ratio, what is the money multiplier and what is the quantity of money in the economy? c)If people hold half of their money as currency and another half as demand deposits, and banks maintain 10% reserve ratio, what is the money multiplier and what is the quantity of money in the economy? d)Under the same condition as (c), if Fed sells $1 million of government bonds, what is the money multiplier and what is the quantity of money in the economy? e)Under the same condition as (c), if the Fed raises reserve requirements to 20% of deposits, what is the money multiplier and what is the quantity of money in the economy?

Answer 1

Money Multiplier (MM) = (1 + cr) / (cr + er + rr), where

cr: Currency-deposit ratio

er: Excess reserves ratio (maintained by commercial banks)

rr: Required reserves ratio (set by Fed)

Quantity of money = Money stock x MM = $1 billion x MM

(a) rr = 10% = 0.1 and cr = 100% = 1

MM = (1 + 1) / (1 + 0.1) = 2 / 1.1 = 1.82

Quantity of money = $1 billion x 1.82 = $1.82 billion

(b) rr = 0.1, cr = 0 and er = 10% = 0.1

MM = 1 / (0.1 + 0.1) = 1 / 0.2 = 5

Quantity of money = $1 billion x 5 = $5 billion

(c) rr = 0.1, cr = 50% = 0.5 and er = 10% = 0.1

MM = (1 + 0.5) / (0.5 + 0.1 + 0.1) = 1.5 / 0.7 = 2.14

Quantity of money = $1 billion x 2.14 = $2.14 billion

(d) rr = 0.1, cr = 50% = 0.5 and er = 10% = 0.1

MM = (1 + 0.5) / (0.5 + 0.1 + 0.1) = 1.5 / 0.7 = 2.14

When Fed sells $1 million of government bonds, quantity of money decreases by ($1 million x 2.14) = $2.14 million.

New quantity of money = $(1,000 - 2.14) million = $997.86 million

(e) rr = 20% = 0.2, cr = 50% = 0.5 and er = 10% = 0.1

MM = (1 + 0.5) / (0.5 + 0.1 + 0.2) = 1.5 / 0.8 = 1.875

Quantity of money = $1 billion x 1.875 = $1.875 billion