Problem: Given that the reserve requirement is 10%, if Bank A has excess reserves of $100, show how the banking system can produce a multiple expansion of bank deposits, although the individual Bank A cannot.

• Bank A obtains excess reserves of $100 due to an action (such as a purchase of a government bond on the open market) of the Fed. The Fed's role here is important because if 'the bank obtains excess reserves due to another reason, such as an ordinary situation of a paycheck being deposited by a customer of A, it is likely that the gain in reserves by A is offset by an equal loss of reserves in another bank.

• Bank A now has the ability to create new loans. They can lend $100.00, the amount of the excess reserves. At this point the money supply has increased by $100 (checking accounts, system-wide, have increased by that amount). The borrower spends the $100 and A loses the $100.00 in reserves when the check clears. Bank A is "loaned up."

• But bank B experiences two things: 1) they have a new checking account deposit by a customer in the amount of $100.00, and, when they send the deposited check for collection, 2) they have $100.00 more reserves. Bank B must hold some of those additional reserves (they must hold $10.00 as back-up for the new deposit). That means they have $90.00 in excess reserves. They can create new loans amounting to $90.00. This additional "new money" is an indirect result of the l''ed'.s action. The total of newly created checking accounts so far is $190.

• Bank C creates $81.00 in new loans. Bank D creates $72.90, etc.  In the end the total increase in the money supply which results from the $100.00 in excess reserves is $1000.00 (the calculation is $100.00 X l/.l =$1000.00).* Conclusion: Bank A can only create new loans on a one-for-onc basis with excess reserves, hut the existence of the original $100.00 in excess reserves leads to a total of $1000.00 in new loans, counting down-stream effects, assuming that all banks lend as much as they can.

   *the deposit multiplier is 1/.1, or 10  -- it is always found by dividing the reserrve requirement, as a decimal, into 1