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# Money multiplier

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Assume the banking system is in reserve equilibrium. The Fed conducts an open market purchase of Treasury securities in the amount of \$1 billion. The reserve requirement against deposits is 10%. Identify the potential amount of the money supply increase as a consequence of the Fed's action and describe fully how money is created by the banking system subsequent to the Fed's open market purchase of Treasury securities in the amount of \$1 billion.

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#### Solution Preview

Money multiplier represents the ability of a fractional-reserve banking system to create money within the economy, that is, for each dollar of reserves; the money supply is some multiple of that value.

The Money Multiplier

The money multiplier tells us the maximum amount of new demand-deposit money that can be created by a single initial dollar of excess reserves. This multiplier, m, is the inverse of the reserve requirement, R: m = 1/R. This note will demonstrate that fact.

Suppose some initial amount, d1, is deposited into the banking system. With a reserve requirement of R, this deposit creates initial excess reserves equal to E1 = (1 - R) x d1. Assuming all of this amount is lent out and redeposited within the system, these excess reserves become new money: D M1 = E1 = (1 - R) x d1. This second deposit creates its own excess reserves equal to E2 = (1 - R) x D M1 = (1 - R) x E1. Again, this is redeposited as new money, so that D M2 = (1 - R) x E1. Continuing on like this ...

#### Solution Summary

Money multiplier is summarized.

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