Suppose the banking system has vault cash of \($1,000,\) deposits at the Fed of \($2,000,\) and demand deposits of \($10,000\).

a. If the reserve requirement is 20 percent, what is the maximum potential increase in the money supply, given the banks’ reserve position?

b. If the Fed now purchases \($100\) worth of government bonds from private bond dealers, what are the excess reserves of the banking system?

(Assume that the bond dealers deposit the \($100\) in demand deposits.) How much can the banking system increase the money supply, given the new reserve position?