Question

Money Multiplier (Based on Mankiw Ch.4 #5). Consider an economy with a monetary base of $1,000. People hold a third of their money in the form of currency (and thus two-thirds as bank deposits). Banks hold a third of their deposits in reserves. a.) What is the reserve-deposit ratio, the currency-deposit ratio, the money multiplier, and the money supply? b.) Say a financial crisis takes place which strikes fear in the population about the safety of banks. As a result, people now hold half their money in the form of currency. What is the new money multiplier? Did it rise or fall as a result of people holding more currency? What is the new money supply? c.) If, in the face of this panic, the central bank wants to conduct an open market operation to keep the money supply at its original level, does it buy or sell government bonds? Calculate, in dollars, how much the central bank needs to transact. d.) Say the financial crisis lowered banks' confidence in the public's ability to repay their debts, and as a result they cut back on lending and now hold half of their deposits in reserve. Taking the developments in this part and part b.) into account, what is the new money multiplier? Did it rise or fall as a result of banks holding more reserves? What is the new money supply? e.) Now how much does the central bank need to transact in order to keep the money supply at its original level? Is this more or less than in part d.)? Why?

Answer 1

a)

reserve ratio (r) the ratio of total deposits that the banks hold as reserves= 1/3

currency deposit ratio is the money that people want to hold as currency = 1/3

money multiplier = (k + 1)/(k + r) = (1/3 +1)/(1/3+ 1/3) = (4/3)/(2/3) = 2

Money supply(M) = m *Monetary Base(MB) = 2*1000 = $2000.

b) k’ = ½

new money multiplier (m’) = (k’+1)/(k’+r) = (½+1)/(1/2+1/3) = (3/2)/(5/6) = 1.8

new money spply(M’) = m’*MB = 1.8*1000 = $1800

c) Because the money supply has reduced in the face of panic, the central bank will have to increase money supply This will involve buying of government bonds in exchange of money.

M = m*MB

2000 = 1.8*(MB(=1000)+ dMB)

1000 +dMB = 2000/1.8

dMB = 2000/1.8 – 1000

dMB = 1111.11 – 1000 = 111.11

So the central bank need to transact $111.11

d) r’ = ½

k’ = ½

m’’ = (1/2+1)/(1/2+1/2) = 3/2 = 1.5

The money multiplier falls because when more money is kept as reserves the money multiplier strength weakens.

New money Supply (M’’) = m’’*$1000 = 1.5*1000 = $1500

Hi Please post sub-parts in lot of four. Thank you!