In the last video, we saw how the Keynesian Cross
could help us visualize an increase in
government spending which was a shift in our
aggregate planned expenditure line right over here
and we saw how the actual change, the actual
increase in output if you take all the
assumptions that we took in this, the actual
change in output and aggregate income was larger
than the change in government spending.
You might say okay, Keynesian thinking, this
is very left wing, this is the
government's growing larger right here.
I'm more conservative. I'm not a believer in
Keynesian thinking.
The reality is you actually might be.
Whether you're on the right or the left,
although Keynesian economics tends to be
poo-pooed more by the right and embraced more
by the left, most of the mainstream right policies,
especially in the US, have actually been very
Keynesian.
They just haven't been by manipulating this
variable right over here.
For example, when people talk about expanding
the economy by lowering taxes, they are a
Keynesian when they say that because if we were
to rewind and we go back to our original
function so if we don't do this, if we go back to
just having our G here, we're now back on this
orange line, our original planned expenditure,
you could, based on this model right over here,
also shift it up by lowering taxes.
If you change your taxes to be taxes minus
some delta in taxes, the reason why this is going
to shift the whole curve up is because you're
multiplying this whole thing by a negative
number, by negative C1.
C1, your marginal propensity to consume, we're
assuming is positive.
There's a negative out here.
When you multiply it by a negative, when you
multiply a decrease by a negative, this is a
negative change in taxes, then this whole thing
is going to shift up again.
You would actually shift up.
You would actually shift up in this case and
depending on what the actual magnitude of the
change in taxes are, but you would actually
shift up and the amount that you would shift up -
I don't want to make my graph to messy so
this is our new aggregate planned expenditures -
but the amount you would move up is by this
coefficient down here, C1, -C1 x -delta T.
You're change, the amount that you would move up,
is -C1 x -delta T, if we assume delta T is
positive and so you actually have a C1, delta T.
The negatives cancel out so that's actually how
much it would actually move up.
It's also Keynesian when you say if we
increase taxes that will lower aggregate output
because if you increase taxes, now all of a
sudden this is a positive, this is a positive
and then you would shift the curve by that
much.
You would actually shift the curve down and
then you would get to a lower equilibrium GDP.
This really isn't a difference between
right leaning fiscal policy or left leaning
fiscal policy and everything I've talked about
so far at the end of the last video and this video
really has been fiscal policy.
This has been the spending lever of fiscal policy
and this right over here has been the taxing lever
of fiscal policy.
If you believe either of those can effect
aggregate output, then you are essentially
subscribing to the Keynesian model.
Now one thing that I did touch on a little bit
in the last video is whatever our change is,
however much we shift this aggregate planned
expenditure curve, the change in our output
actually was some multiple of that.
What I want to do now is show you mathematically
that it actually all works out that the multiple is
actually the multiplier.
If we go back to our original and this will just
get a little bit mathy right over here so I'm
just going to rewrite it all.
We have our planned expenditure, just to redig
our minds into the actual expression, the
planned expenditure is equal to the marginal
propensity to consume times aggregate income
and then you're going to have all of this
business right over here.
We're just going to go with the original one,
not what I changed.
All this business, let's just call this B.
That will just make it simple for us to manipulate
this so let's just call of this business right
over here B.
We could substitute that back in later.
We know that an economy is in equilibrium
when planned expenditures is equal to output.
That is an economy in equilibrium so let's set this.
Let's set planned expenditures equal to
aggregate output, which is the same thing as
aggregate expenditures, the same thing as
aggregate income.
We can just solve for our equilibrium income.
We can just solve for it.
You get Y=C1xY+B, this is going to look very
familiar to you in a second.
Subtract C1xY from both sides.
Y-C1Y, that's the left-hand side now.
On the right-hand side, obviously if we subtract
C1Y, it's going to go away and that is equal to B.
Then we can factor out the aggregate income from
this, so Yx1-C1=B and then we divide both sides
by 1-C1 and we get, that cancels out.
I'll write it right over here.
We get, a little bit of a drum roll, aggregate
income, our equilibrium, aggregate income,
aggregate output.
GDP is going to be equal to 1/1-C1xB.
Remember B was all this business up here.
Now what is this?
You might remember this or if you haven't seen
the video, you might want to watch the video
on the multiplier.
This C1 right over here is our marginal
propensity to consume.
1 minus our marginal propensity to consume
is actually - And I don't think I've actually
referred to it before which let me rewrite it here
just so that you know the term - so C1 is equal to
our marginal propensity to consume.
For example, if this is 30% or 0.3, that means
for every incremental dollar of disposable
income I get, I want to spend $.30 of it.
Now 1-C1, you could view this as your marginal
propensity to save.
If I'm going to spend 30%, that means I'm going
to save 70%.
This is just saying I'm going to save 1-C1.
If I'm spending 30% of that incremental
disposable dollar, then I'm going to save 70% of it.
This whole thing, this is the marginal
propensity to consume.
This entire denominator is the marginal propensity
to save and then one over that, so 1/1-C1 which
is the the same thing as 1/marginal propensity
to save, that is the multiplier.
We saw that a few videos ago.
If you take this infinite geometric series,
if we just think through how money spends, if I
spend some money on some good or service, the
person who has that money as income is going
to spend some fraction of it based on their
marginal propensity to consume and we're assuming
that it's constant throughout the economy at all
income levels for this model right over here.
Then they'll spend some of it and then the person
that they spend it on, they're going to spend
some fraction.
When you keep adding all that infinite series up,
you actually get this multiplier right over here.
This is equal to our multiplier.
For example, if B gets shifted up by any amount,
let's say B gets shifted up and it could get
shifted up by changes in any of this stuff
right over here.
Net exports can change, planned investments
can change, could be shifted up or down.
The impact on GDP is going to be whatever that
shift is times the multiplier.
We saw it before.
If, for example, if C1=0.6, that means for
every incremental disposable dollar, people will
spend 60% of it.
That means that the marginal propensity to save
is equal to 40%.
They're going to save 40% of any incremental
disposable dollar and then the multiplier is
going to be one over that, is going to be 1/0.4
which is the same thing as one over two-fifths,
which is the same thing as five-halves, which
is the same thing as 2.5.
For example, in this situation, we just saw that
Y, the equilibrium Y is going to be 2.5 times
whatever all of this other business is.
If we change B by, let's say, $1 billion and
maybe if we increase B by $1 billion.
We might increase B by $1 billion by increasing
government spending by $1 billion or maybe having
this whole term including this negative right
over here become less negative by $1 billion.
Maybe we have planned investment increase by
$1 billion and that could actually be done a little
bit with tax policy too by letting companies
maybe depreciate their assets faster.
If we could increase net exports by $1 billion.
Essentially any way that we increase B by $1 billion,
that'll increase GDP by $2.5 billion, 2.5 times
our change in B.
We can write this down this way.
Our change in Y is going to be 2.5 times our
change in B.
Another way to think about it when you write
the expression like this, if you said Y is a
function of B, then you would say look the slope
is 2.5, so change in Y over change in B is
equal to 2.5, but I just wanted to right this
to show you that this isn't some magical
voodoo that we're doing.
This is what we looked at visually when we looked
at the Keynesian Cross.
This is really just describing the same
multiplier effect that we saw in previous videos
and where we actually derived the actual multiplier.