Some Different Views
The feedback
loop that is central in the multiplier model is illustrated
below. Consumption, investment, and government spending
determine actual income. Actual income and taxes determine
expected disposable income, and finally expected disposable
income determines what consumption will be.
The feedback loop is the reason that investment and
government spending have multiplier effects. A drop in
investment, for example, begins by reducing actual income by
the amount of the drop. Then the lower level of actual
income changes expected income, and consumption also
declines. Hence a $1.00 decline in investment will,
according to the logic of this model, cause a decline in
income of more than $1.00.
We argued that
the equilibrium condition for this model is that expected
income equal actual income. There is another way to look at
this equilibrium condition that is often useful. Expected
income can be divided into three parts. First some is
removed as taxes, and then what is left is divided between
consumption and expected savings, or:
(4) Yexp = T + C + Sexp
We have also argued that actual income is made up of
three types of spending: consumption, investment, and
government spending, or:
(5) Yact = C + I + G
In equilibrium these two equation are equal, or:
(6) T + C + Sexp = C + I + G
Subtracting C from both sides gives us the equilibrium
condition in this form:
(7) Sexp + T = I + G
In words, this equation says that equilibrium exists at
that level of income for which the amount people intend to
withdraw from the flow of spending either as taxes or
savings just equals the amount they intend to add to the
flow of spending as investment or government spending.
This way of explaining equilibrium can be illustrated
with an analogy to a leaky bucket. In the leaky bucket
higher levels of water create more pressure and thus faster
leakage. An equilibrium level of water occurs when the
leakage just equals the inflow of water. In the multiplier
model, investment and government spending are inflows and
taxes and expected saving are leakages. As income increases,
so does leakage in the form of expected savings. Just as
there will be only one level of water in the bucket for
which leakages will equal inflows, so there will be only one
level of income in the model for which leakages will equal
inflows.
This alternative way of presenting the equilibrium
condition can also be shown with graphs. In the top part of
the illustration below, the difference between the C and the
C+I+G lines is investment plus government spending, which
the bottom part graphs separately as the I+G line. Because
the distance between the C line and the C+I+G line is
constant in the top part, the I+G line is flat in the bottom
part. The difference between the 45-degree line and the C
line is the difference between expected income and
consumption, or taxes plus planned savings, which is graphed
as the S+T line in bottom part. Because the C line begins
above the 45-degree line, the S+T line in bottom part begins
with a negative value. It rises to zero when the C line
crosses the 45-degree line, and then continues to rise as
the gap between the 45-degree line and the C line
widens.
Equilibrium exists when the C+I+G line crosses the
45-degree line. At this level of expected income, the
distance between the C and the C+I+G lines (which is
investment plus government spending) just equals the
distance between the C line and the 45-degree line (which is
savings plus taxes). Thus equilibrium exists when investment
plus government spending equals expected savings plus
taxes.
Next we look at real-world implications
of this model.
Copyright
Robert Schenk
|