Tax Multiplier - The investment function, Macroeconomics Video Lecture | Macro Economics - B Com

[Music]
this is a continuation of our lesson on
the different multiplier effects of
fiscal policy in our two previous
lessons on fiscal policy we talked about
the different types of policies a
government may use in order to either
stimulate or contract aggregate demand
in the economy with the aim of achieving
certain macroeconomic objectives in our
previous lesson we talked about what is
known as the government spending
multiplier or the Keynesian spending
multiplier in that lesson we explained
the difference between marginal
propensity to consume and marginal
propensity to save and showed how we
could determine the Keynesian spending
multiplier which could also be found by
dividing one by the marginal rate of
leakage or one divided by the marginal
propensity to save now for IB economic
students the marginal rate of leakage as
we explained includes the marginal
propensity to save the marginal
propensity to import and the marginal
rate of Taxation if you're an AP
economics student you are expected to
know the simple Keynesian spending
multiplier which is 1 divided by the
marginal propensity to save now today
we're going to be talking about how a
change in the tax rate in a nation can
affect aggregate demand by calculating
what's known as the tax multiplier the
tax multiplier is defined as the
expected increase in aggregate demand
which will result from a particular
decrease in taxes for example if a
government were to lower taxes by 1
billion dollars how much will this
ultimately increase aggregate demand to
determine exactly how much aggregate
demand will increase by following a
particular decrease in taxes we must
consider the multiplier effect of a cut
in taxes now I should point out that the
multiplier effect works in both
directions
so another question we could answer is
how much would a great demand decrease
by following a 1
dollar increase in taxes when taxes are
cut aggregate demand will increase by a
multiple of the amount that the tax cut
equaled on the other hand if taxes are
raised aggregate demand will fall by a
particular multiple of the tax increase
so how do we determine what the tax
multiplier is let's assume that in a
particular country the marginal
propensity to consume is 0.4 this gives
us a marginal propensity to save of 0.6
with this information we can determine
how large the tax multiplier will be in
a nation let's start with an example
let's say that a government lowers taxes
on households by 1 billion dollars how
will this affect household disposable
income and how will it affect the level
of consumption and therefore aggregate
demand in the economy a tax cut unlike
an increase in government spending does
not provide direct stimulus to aggregate
demand rather it counts on households to
increase consumption based on their
marginal propensity to consume so what
does happen though
is that a tax cut leads to an increase
in disposable income which I'll use di
is the abbreviation of 1 billion dollars
so now households have an additional
billion dollars of disposable income not
all of this will be used to consume
however since households tend to save 60
percent of every additional dollar they
earn in disposable income how much will
consumption actually increase by as we
see based on the marginal propensity to
consume consumption will increase by 0.4
billion dollars while savings increases
by zero point six billion dollars so as
we see a decrease in taxes increases
disposable income however aggregate
demand will not increase by the full
amount of this tax cut
since households have the opportunity to
save and consume in fact what happens is
the 1 billion dollar tax cut leads to
only 400 million dollars of new spending
so aggregate demand will only increase
by 400 million dollars now this differs
from an increase in government spending
by the same amount because as we saw in
our previous video lesson an increase in
government spending
will do
correctly stimulate aggregate demand
increase household incomes by 1 billion
dollars which will then lead to further
increases in consumption in this case
however the 1 billion dollar tax cut
only leads to 400 million dollars of new
aggregate demand which turns into new
incomes of 400 million which again will
be multiplied by the marginal propensity
to consume so there will be further
increases in consumption and aggregate
demand however the ultimate increase in
aggregate demand of a 1 billion dollar
cut in taxes will be considerably less
than the ultimate increase in aggregate
demand resulting from a 1 billion dollar
increase in government spending now to
actually find the size of the tax
multiplier there's a very simple formula
we can use to determine how much
aggregate demand will increase following
a particular change in taxes we can find
the tax multiplier which is negative MPC
divided by the marginal propensity to
save so why is there a negative sign
here the negative sign indicates that
the change in aggregate demand will
always be inversely proportional to the
change in taxes so if taxes fall there
will be a negative multiplier therefore
aggregate demand will increase if Texas
rise there will be a negative multiplier
therefore aggregate demand will decrease
let's find out exactly how much our good
demand would rise by following our 1
billion dollar tax cut so the 1 billion
dollar tax cut will lead to a change in
aggregate demand of negative 0.4 divided
by 0.6 which gives us a multiplier of
negative 0.67 what does this mean for
the increase in aggregate demand
resulting from a 1 billion dollar tax
cut if taxes fall by 1 billion in other
words taxes changed by negative 1
billion dollars we can multiply this by
negative 0.67 to find that the ultimate
increase in aggregate demand will only
be 670 million dollars a 1 billion
dollar tax cut when multiplied by the
tax multiplier of negative 0.67 will
lead to an increase in aggregate demand
of 0.67 billion dollars which is equal
to 670 million dollar
how would this compare to the effect of
a 1 billion dollar increase in
government spending well let's find out
what our government spending multiplier
would be given a marginal propensity
consume of 0.4 and a marginal propensity
to save of 0.6 the spending multiplier
which is K will equal 1 over 1 minus 0.4
which is 1 over 0.6 which is 1 point 6 7
now an increase in government spending
of 1 billion will lead to 1 point 6 7
times 1 billion which is 1 point 6 7
billion dollar increase in aggregate
demand a tax cut of 1 billion dollars
led to only 670 million dollars of new
aggregate demand whereas a government
spending increase of the same amount
leads to 1 point 6 7 billion dollars of
new aggregate demand as we can see
government spending is more effective at
stimulating aggregate demand due to the
fact that G is a direct component of
aggregate demand whereas a tax cut does
not have a direct effect on aggregate
demand rather it is indirect it
increases household disposable income
but some of that increase in income will
go towards savings and a smaller
proportion will go towards consumption
leading to more aggregate demand next
we're going to look at an actual
question from an AP economics exam which
asks us to apply both the government
spending multiplier and the tax
multiplier to a particular situation so
here's an actual Advanced Placement
economics question relating to both the
spending and the tax multiplier let's
read the question and then illustrate
the problem that it describes on a graph
on the right and then see if we can
figure out exactly what the correct
answer would be the question is assume
that current real gross domestic product
falls short of full employment output by
500 billion dollars and the marginal
propensity to consume is 0.8 let's look
at a graph on the right first and
illustrate what the question describes
which is a 500 billion dollar
recessionary gap now assuming a marginal
propensity to consume of 0.8 we can
determine what the government spending
multiplier would be this will help us
answer C Part I which asks calculate the
minimum increase in government spending
that could bring about full employment
so our spending multiplier
is 1 divided by 1 minus 0.8 which is the
marginal propensity to consume which
gives us 1 divided by 0.2 which gives us
a spending multiplier of 5 now how much
would government spending have to
increase by in order to achieve a 500
billion dollar increase in aggregate
demand in order to return this economy
to its full employment level as we
learned in our previous lesson the
required change in government spending
equals the desired change in aggregate
demand divided by the Keynesian spending
multiplier in this case we know that the
desired change in aggregate demand is
500 billion and the multiplier is 5
giving us an increase in government
spending of 100 billion dollars now
looking at our graph on the right we can
illustrate how a 100 billion dollar
increase in government spending will be
multiplied and result in a 500 billion
dollar increase in aggregate demand so a
government stimulus of only one hundred
billion dollars will shift ad out to ad
one and as we can see the immediate
effect will be a relatively small
increase in national output however
following the multiplier effect of this
government spending aggregate demand
will shift up by a full 500 billion
dollars and this economy should return
to a level of output equal to its full
employment level so here we see that the
increase in government spending leads to
an increase in ad but then due to the
multiplier effect we get a much larger
increase in aggregate demand in the end
now there's still a second part to this
question
so look at part two of this question
assume that instead of increasing
government spending the government
decides to reduce personal income taxes
will the reduction in personal income
taxes required to achieve full
employment be larger than or smaller
than the government spending change you
calculated in Part C I explained why to
help us answer this question it might
help to actually determine what the tax
multiplier is now we can solve for the
tax multiplier using the equation we
learned previously which is negative MPC
over the marginal propensity to save now
we know that this
households will spend 80% of any change
in income so we assumed that they will
save the other 20% so- MPC over mps
equals negative 0.8 / 0.2 which is
negative 4 in order to find the needed
change in taxes all we have to do is
divide the desired change in aggregate
demand by the tax multiplier in this
case once again our desired change in
aggregate demand is 500 billion and now
our tax multiplier is negative for 500
billion divided by negative 4 gives us
the result of negative 125 what does
this tell us this tells us that taxes
must fall by 125 billion dollars notice
that the 100 billion dollar increase in
government spending could bring about a
five hundred billion dollar increase in
aggregate demand however if we decide to
cut taxes a 125 billion dollar tax cut
will be needed this will increase
households disposable income which will
lead to an increase in consumption
however the tax cut needed is quite a
bit larger than the government spending
increase that would bring about the same
change in aggregate demand this is
because a tax cut is an indirect
injection into the nation's economy and
in fact due to the marginal propensity
to consume of 0.8 a 125 billion dollar
tax cut will actually only lead to an
increase in consumption of 100 billion
dollars since 20% of that tax cut will
go towards savings let's wrap up our
lesson now by reviewing what we've
talked about the marginal propensity to
consume and marginal propensity to save
or if you're an IB student the marginal
rate of leakage helps us determine what
does government spending multipliers and
the tax multipliers will be by
understanding how aggregate demand will
change following a change in government
spending or change in taxes we can help
determine an appropriate fiscal policy
response to a particular recessionary
gap or in the case of demand pull
inflation and inflationary gap if an
economy is experiencing demand pull
inflation the multiplier effect works in
the opposite direction as well so a
particular increase in taxes
will reduce aggregate demand by more
than the initial increase in taxes or a
particular decrease in government
spending will decrease aggregate demand
by more than the initial decrease in
spending