Money, Banking, and International FinanceSmall business contracts with a construction company to renovate his business.
Construction company receives a check for $8,100 and deposits this check in its bank. We
record the transaction below:
Construction Company’s Bank
Assets Liabilities
Required Reserves $810
Excess Reserves 7,290
Loans 0
Deposits $8,100Construction company’s bank must hold 10% of this deposit, equaling $810. Remaining
reserves, $7,290, earn no interest, and consequently, this bank grants a loan. Did you notice the
change in the money supply? Money supply has expanded by $27,100, which includes the
$10,000 in your account, $9,000 in the car dealer’s account, and $8,100 in the construction
company’s account. When the construction company’s bank grants a loan, then the money
supply would increase again, and multiple deposit expansion occurs infinitely.
We can derive the maximum change in the money supply when the monetary base changes.
First, we start with the formula for total reserves in Equation 1.
Total Reserves = Required Reserves + Excess Reserves ( 1 )In this case, excess reserves equal zero because banks earn no interest. Banks grant loans
using their excess reserves. Second equation calculates required reserves. When a bank accepts a
new checking account, the bank must hold a percentage of the deposit, which is Equation 2.
Required Reserves = Deposits × Required Reserve Ratio (rr) ( 2 )We substitute Equation 2 into Equation 1 and set the excess reserves equal to zero, which
yields Equation 3.
Total Reserves = Deposits × rr ( 3 )Did you notice the money supply changes when the Federal Reserve changes the bank
reserves? We show reserve changes in Equation 4 and deposit changes in Equation 5. The Δ
symbol means change, and we take the difference between two adjacent time periods. First time
period is t, while the future time period is t+1.
∆Reserves = Total Reservest+1 – Total Reservest ( 4 )∆Deposits = Depositst+1 – Depositst ( 5 )