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Money Multiplier: Target Money Supply

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Assume an economy in which the reserve ratio is 15 percent, people hold 10 percent of their deposits in the form of cash, and there are no other leakages.

a. Compute the value of the money multiplier.
b. If the current level of high-powered money is $1,500 billion, what is the money supply in this economy?
c. How much does the money supply change if the Federal Reserve buys $30 billion of US government treasury bills from a government bond dealer? How about if banks borrowing reserves from the Federal department decline by $6 billion?
d. If the Federal Reserve sets a target money supply of $6,424 billion, what would it have to do to achieve that target?

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Solution Preview

It is given that the reserve ratio is 15% and people hold 10% of their deposits as cash. People's holding of cash is a currency drain and it is equal to 10% or 0.1. There are no other leakages.

a. In the presence of currency drain (people holding deposits as cash), the money multiplier is given as
Multiplier = (1 + Currency Drain Ratio) / (Currency Drain Ratio + Required Reserve Ratio).
Using the values given above we get:
Multiplier = (1 + 0.1) / (0.1 + ...