Kenneth R. Szulczyk
If we write Equation 3 for two adjacent time periods: t and t+1. Equations become Total
Reservest+1 = Depositst+1 × rr and Total Reservest = Depositst × rr. Then we subtract the equation
for the time period t+1 from the equation for the time period t, yielding Equation 6.
∆Reserves = ∆Deposits × rr ( 6 )We solve Equation 6 for change in deposits, yielding the money supply equation in
Equation 7.
rrΔ = Δ
1
Deposits Reserves^ (^7 )^If the Federal Reserve increases the monetary base by buying $10,000 of T-bills,
subsequently, the bank reserves increase by $10,000. If the required reserve ratio equals 10%,
then we substitute this into Equation 7. Consequently, checkable deposits would rise by
$100,000. We call this formula the simple deposit multiplier, which equals ( 1 ÷ rr ). Simple
deposit multiplier shows the maximum increase of the money supply for a change in bank
reserves.
Simple deposit multiplier assumes the banks lend all their excess reserves. Banks continue
to lend until the Fed’s entire increase in reserves becomes required reserves held by the banking
system. If the required reserve ratio equaled zero, then a one-dollar increase in reserves would
expand the money supply infinitely because the banks do not hold any reserves.
Leakages cause the money multiplier to be smaller in the real world. Some people withdraw
cash, when they deposit checks at the bank while some banks do not lend all their excess
reserves. For example, banks refused to grant loans during financial panics, such as the 2008
Financial Crisis. Instead, banks invested in safe investments, like U.S. government securities.
Some economists argue the Federal Reserve could inject trillions of dollars into the banking
system without creating inflation by purchasing bad loans and government debt. However, these
economists are wrong. If banks held onto the entire excess reserves, the money multiplier would
equal one. Thus, if the Fed increased the monetary base by $1 trillion, then it expands the money
supply by $1 trillion as it buys assets from the public. A rapid, expanding money supply creates
inflation. If the banks lent their excess reserves, then the money supply would increase more
than $1 trillion, creating greater inflation.
The Fed decreased the monetary base by selling its assets, contracting both bank reserves
and the money supply. We call the Fed selling securities the multiple deposit contraction.
Transaction is similar to multiple deposit expansion, except the numbers become negative.
Consequently, the Fed can control the monetary base easily but has less control over the
money supply. For instance, people can change their behavior that largely impacts bank
reserves. For example, you went to your bank to withdraw $200. We record the transaction in
the T-account on the next page: