1 Money Multiplier Suppose the reserve requirement, R¯, is 0.1. a. If the Federa

Question

1 Money Multiplier

Suppose the reserve requirement, R¯, is 0.1.
a. If the Federal reserve prints $323 million worth of paper currency and mails a dollar bill to every resident of the United States, how much will they ultimately increase the money supply?

b. Describe the mechanism by which this increase in the money supply comes about.

c. Suppose half of the banks in the country have a reserve requirement of 0.2 and half have the requirement of 0.1, Then how much will be created, assuming that money alternates between the two types and starts at a R¯ = 0.1 bank.

Please answer b) & c)

PS: Please be specific and include all of the work. Thanks

Explanation / Answer

Ans.

part a.)R=0.1 and let H be the new money printed by the Federal Reserve.

Money Multiplier=1/R=1/.1=10.

Hence the solution to part a. is that Money Supply will increase by $3230 million which 10 times the money printed.

part b.) The Mechanism is as follows.

For example, when the central bank prints H dollars of bills and transfer them to the banks, it increases the money supply directly by H in the first period. Then banks under the reserve requirement keep R*H with the central bank and lend (1-R)*H away to their customers who make new (1-R)*H deposits in the bank, this increases the money supply further by the new deposits created. This process goes on for n times with ((1-R)n)*H new deposits created in every step. The money supply increase by the sum of all the new deposits created in the process discussed above which is:

H + (1-R)*H +(1-R)2*H +(1-R)3*H +(1-R)4*H ...........=H/R.

part c.) H +0.9*H +0.9*0.8*H+(0.9)2*(0.8)*H +(0.9)2*(0.8)2*H.................=1.9*H/(1-0.8*0.9)=6.785714*H=$2191.786 million.

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