# The Money Multiplier and Multiple Deposit Expansion.

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The Money Multiplier and Multiple Deposit Expansion

Begin with the End in Mind Dollar value of Required Reserves = Amount of deposit X required reserve ratio Excess Reserves = Total Reserves – Required Reserves Maximum amount a single bank can loan = the change in excess reserves caused by a deposit The money multiplier = 1/required reserve ratio Total Change in Loans in the entire banking system= amount single bank can lend X money multiplier Total Change in the money supply = Total Change in Loans + \$ amount of Fed action Total Change in demand deposits = Total Change in Loans + any cash deposited

Calculating the Money Multiplier The money multiplier shows us the impact of a change in demand deposits on loans and eventually the money supply. To calculate the money multiplier, divide 1 by the required reserve ratio. Money multiplier = 1 / reserve ratio Ex. If the reserve ratio is 25%, then the multiplier = 1 /.25 = 4 Ex. If the reserve ratio is 10%, then the multiplier=1/.1=10

Happy Birthday to my wife Jarafreen! If the Federal Reserve buys bonds from a primary securities dealer he/she will deposit that money into a demand deposit account Therefore required reserves needs to be accounted for If the Federal Reserve buys bonds from “the public” no required reserve is automatically necessary

Types of Multiple Deposit Expansion Questions Type 1: Calculate the initial change in excess reserves - a.k.a. the amount a single bank can loan from the initial deposit (same answer for Fed with a PSD involved or individual deposit) Type 2: Calculate the change in loans in the banking system (same answer for Fed with PSD) or individual deposit) Type 3: Calculate the change in the money supply (DIFFERENT answer for Fed or individual deposit) Type 4: Calculate the change in demand deposits (same answer for Fed with PSD or individual deposit) Add on Fed or individual deposit at the end

Assume the federal reserve buys a \$1,000 bond from a bank. Calculate the maximum change in the money supply as a result of this bond purchase.

Initial Change in Excess Reserves Given a required reserve ratio of 20%, assume the Federal Reserve purchases \$100 million worth of US Treasury Securities on the open market from a primary security dealer. Determine the amount that a single bank can lend from this Federal Reserve purchase of bonds. (AKA figure out ER) The amount of new demand deposits – required reserve = The initial change in excess reserves \$100 million – (\$100 million * 20%) \$100 million – \$20 million = \$80 million in ER

Change in Loans in the Banking System Given a required reserve ratio of 20%, assume the Federal Reserve purchases \$100 million worth of US Treasury Securities on the open market from a primary security dealer. Determine the maximum change in loans in the banking system from this Federal Reserve purchase of bonds. The initial change in excess reserves * The money multiplier = max change in loans \$80 million * (1/20%) \$80 million * (5) = \$400 million max in new loans

Change in the Money Supply Given a required reserve ratio of 20%, assume the Federal Reserve purchases \$100 million worth of US Treasury Securities on the open market from a primary security dealer. Determine the maximum change in the money supply from this Federal Reserve purchase of bonds. The maximum change in loans + \$ amount of Federal Reserve action \$400 million + \$100 million = \$500 million max change in the money supply

Change in Demand Deposits Given a required reserve ratio of 20%, assume the Federal Reserve purchases \$100 million worth of US Treasury Securities on the open market from a primary security dealer. Determine the maximum change in demand deposits from this Federal Reserve purchase of bonds. The maximum change in loans + \$ amount of initial deposit ER*money multiplier+\$amount of initial deposit (\$500)=\$400+\$100 \$400 million + \$100 million = \$500 million max change in demand deposits

Can Jane change demand deposits?—YES, her own Given a required reserve ratio of 20%, assume Jane deposits \$100 of cash into her checking account. Determine the maximum change in demand deposits from this action. Bank loans out \$80, holds \$20 in required reserves 1/.2=5 So the money multiplier is 5 \$80*5=400 Do I add on the \$100 Jane deposited? Did she change a demand deposit? Yes and yes

Can Jane directly change the money supply? No So if the question is asking about changing the money supply go through it but do NOT add Jane’s \$100 deposit. Remember that if the Fed buys bonds directly from the bank’s balance sheet all of it goes into excess reserves. However don’t “tack on” the Fed action as additional money supply because: – No DD was created and it’s not new cash in the banking system