constant, , and see that this multiplies the whole value of GDP
by :
- This is easily proved. The banking system wants sufficient
deposits (D) to establish the target ratio (v) of deposits to reserves
(R). This gives. Any change in D of size has to be
accompanied by a change in R of of sufficient size to restore
v. Thus, so and. This
can be shown also in terms of the deposits created by the
sequence in Table 26-7. Let v be the reserve ratio and
be the excess reserves per dollar of new deposits. If X dollars are
initially deposited in the system, the successive rounds of new
deposits will be The series
has a limit of
This is the total new deposits created by an injection of of
new reserves into the banking system. For example, when
, an injection of $100 into the system will lead to an
overall increase in deposits of $500.
θ
θ
z(θL⋅θK)^1 /^2 =z(θ^2 ⋅LK)^1 /^2 =θz(LK)^1 /^2 =θ⋅GDP
R/D=v ΔD
ΔR
ΔR/ΔD=v ΔD=ΔR/v ΔD/ΔR= 1 /v
e= 1 −
X,eX,e^2 X,e^3 X,...
X+eX+e^2 X+e^3 X+...
=X⋅[ 1 +e+e^2 +e^3 +...]
X⋅ 1 −^1 e
=X⋅ 1 −(^11 −v) = Xv
$X
v=0.20
