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Question

# Suppose that the Federal Reserve (the Fed) buys $100 million of government debt obligations from private owners. This creates$100 million of new money and sets off a chain reaction because of the "fractional reserve" banking system. When the $100 million is deposited into private bank accounts, the banks keep only 15% in reserve and may loan out the remaining 85%, creating more new money: (.85)(100) million dollars. The companies that borrow this money turn around and spend it, and the recipients deposit the money in their bank accounts. Assuming that all the (.85)(100) million is redeposited, the banks may again loan out 85% of this amount, creating$(.85)^2(100)$million additional dollars. This process may be repeated indefinitely. Compute the total amount of new money that can be created theoretically by this process, beyond the original$100 million. (In practice, only about an additional \$300 million is created, usually within a few weeks of the action of the Fed.)

Solution

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Step 1
1 of 5

To find the amount created, notice that the money generated by each tax cut gives geometric series and find its sum using the standard formula $S=\dfrac{a_0}{1-r}$.

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