I want to now build on what we did in the last
video on the Keynesian Cross and planned
aggregate expenditures and fill in a little bit more
on the details and think about how this could be
of useful conceptual tool for Keynesian thinking.
Let's just review a little bit.
I'll rebuild our planned aggregate expenditure
function, but I'll fill in little bit of the details.
Let's say this is planned, planned aggregate
expenditures and this is going to be equal to
consumption.
You'll often see it in a book written like this:
Consumption as a function of aggregate income
minus taxes and I want to be very clear here.
They're not saying that this term should be
aggregate income times aggregate income
minus taxes.
They're saying that consumption is a function of
this right over here; the same way we would say
that F is a function of X, but if you give me a
Y-T or essentially if you give me a disposable
income right over here, I will give you a consumption.
If you actually want to deal with this directly
mathematically, analytically, you'd have to define
what this function is, but I'll write it like this
now and in the next step I'll actually define what
our consumption function is.
This is just saying an arbitrary consumption function
and it is a function of disposable income.
It's going to be your consumption function plus
your planned investment, which we're going to
assume is constant, plus government expenditures
plus net exports.
Plus net exports.
A couple of videos ago we built some simple models
for consumption function so let's put one of those in.
Let's say that our consumption function,
so aggregate consumption is a function of
disposable income, as a function of income
minus taxes.
Let's say that's going to be equal to some
autonomous expenditure
plus the marginal propensity to consume.
(Maybe I don't have to keep switching colors because
we've seen this before.)
Plus the marginal propensity to consume
times disposable income. Times disposable income.
Now you see that consumption, aggregate
consumption is being defined.
It's being defined as a function of
disposable income.
That's what that notation right over there means.
We could substitute this function expression
with this stuff in green right over here.
We can say aggregate planned expenditure,
is equal to, this is our consumption function,
so it's equal to (Oh, I'll do it in that same
yellow.) it's equal to autonomous consumption
plus the marginal propensity to consume times
disposable income which is aggregate income
minus taxes and then of course we have the
other terms plus planned investment plus
government spending plus net exports.
Plus net exports.
Then we can simplify this a little bit just so
it makes clear what parts of this are constant
and what parts aren't, what parts are a function
of income.
For the sake of this little lesson right over here,
you might remember a few videos ago,
we can have a debate whether taxes should be
a function of income or not.
In the real world, taxes really are a function
of income, but for the sake of this analysis
we'll just assume that like investment,
planned investment, government spending and
net exports, we'll assume for the sake of
this presentation we're going to assume this is
constant. Assume that this is constant.
This is constant.
If we assume that that's a constant, we can
multiply (And actually even if we didn't
assume it's a constant we could still multiply,
but then we'd want to redefine this in terms of Y)
but we can distribute the C1 and so we get
- We get; I don't have to keep writing that
- this part right over here, we have our
autonomous expenditures,
(C1xY)+(C1 x aggregate income) - the marginal
propensity to consume times taxes + all of this
other stuff.
Actually I could just copy and paste that,
plus all of this other stuff.
Let me copy it and then let me paste it.
Plus all of this other stuff and that is equal to
our planned expenditures; planned expenditures.
Now we can think about well this part right over here,
this is the function, this is how aggregate
income is really driving it.
Everything else is really a constant here.
Let's write it in those terms.
We have aggregate planned expenditure is equal
to the marginal propensity to consume times
our aggregate income; times our aggregate income.
That's this term right over here.
I'll box it off.
Everything else is a constant, so plus the C sub 0
which was our autonomous expenditures,
minus (C sub 1 X T)
so the marginal propensity to consume times T
and these are both constants for the sake of
our analysis so this whole thing is a constant
and then plus all that other stuff.
Then plus all of that other stuff there.
This might look like a really fancy, complicated
formula, but it's actually pretty straight forward
because we're assuming for the sake of our analysis
that all of this, all of this right over here,
all of this is constant.
If you were to plot this right over here,
it would look something like this.
Let us plot it.
Really this is almost exactly what we did in the
last video, but we're now filling in some details.
Our independent variable is going to be
aggregate income or GDP, however you want to
view it, and then our vertical axis is expenditures.
Expenditures.
Expenditures and so if we wanted to plot this,
the constant part, this thing right over here,
if I were to redefine this whole thing as B,
that would be where we intersect the
vertical axis, that B right over there.
I could rewrite this whole thing, but that would
just be a pain so I'll just call this B, but
this whole thing is B and then we'd have
an upward sloping line assuming that C1 is positive.
It's going to have a slope less than one.
We're assuming that people won't be able to spend
more than their aggregate income.
They're only going to spend a fraction of their
aggregate income.
This is going to be between zero and 1.
We will have our aggregate planned expenditures
would be line that might look something like this.
Aggregate planned expenditures.
To think about our Kenyesian Cross, you can't
have an economy in equilibrium if aggregate output
is not equal to aggregate expenditures.
To think about all of the different scenarios
where the economy is in equilibrium, we draw a line
at a 45 degree angle because at every point on this
line, output is equal to expenditures.
Output is equal to expenditures so we get our
45 degree line looks something like this.
Just as a little bit of review, what this is really
saying is look out of this, if we have this
aggregate planned expenditures, this is going
to be the equilibrium point.
This is the point where expenditures is
equal to output.
If for whatever reason the economy is performing,
is outputting above that equilibrium point,
then output which is this line.
This line could be used as output or expenditures
because it's the line where they're equal
to each other.
This is where actual output is outperforming
planned expenditures I should say and you have
all this inventory building up.
You have all this inventory building up and so the
actual investment would be larger than the
planned investment because you have all that
inventory built up.
If output is below equilibrium,
then the planned expenditures are higher than
output and so people are essentially;
the economies are going to have to actually
dig in to inventory.
The actual investment is going to be lower than
the planned investment.
It will be dug into a little bit because that
eating into the inventory, it would be considered
to be negative investment.
Now the whole reason that I set up this whole thing,
this was all review maybe with a little bit
more detail than we did in the last video,
is beyond using the Keynesian Cross for this
kind of equilibrium analysis, is to use it to
go into the Keynesian mindset of how can we
actually change the equilibrium then because
if we just change the output, it's natural if
output is too high, inventories build up.
People will say oh my inventories are building up.
I'm going to produce less, output will go down.
If inventories are being eaten into,
they'll produce more and we'll go back to the
equilibrium.
But what if the equilibrium is not where,
in our opinion, the economy should be?
What if it's well below full employment?
What if it's well below our potential?
For example, what if the economy's potential at
full employment is an output that is something
over here.
You could debate what that point is, but how do you
get it to there because you can't just increase the
supply; you can't just increase the output; that will
just make our inventories build up.
From a Keynesian point of view, we could say
well you want to just shift this actual curve
and there's a bunch of ways in which you can
shift the curve.
In general, you can change any of these variables
right over here, all the things that we assumed
are constant, and that would shift the curve.
For example, the government could say hey, I'm
going to take; the G was at some level.
What if I pop that G up?
What if I turn that into whatever our existing
G is and then we add some change in G?
They add some incremental.
Well now this is going to be bigger by this
increment right over here.
Maybe we'll call it this right over here.
What will happen to the curve?
It will shift up by that increment.
Let's see what happens when we shift the curve up
by that increment and I'll do that in that
magenta color.
If we shift this curve up by delta G,
if we shift it up by delta G, it's going to look
something like this.
You're not changing the slope of the curve.
That's this right over here.
You're just changing its intercept, so we just
added delta G up here.
This would be B, the original B plus delta G.
I guess you could say it that way.
Our new planned expenditures might look
something like this.
Our new planned expenditures might look something
like that and that's pretty interesting because
now our equilibrium point is at a significantly
higher point.
Our equilibrium point, our change in our equilibrium,
so our delta in output actually went up by more.
Our delta in output was larger than our change
in spending so it seems like it was well worth it
if you believe this analysis right here.
Visually the reason why it happened was because
this line right here had a lower slope.
The new intersection point between it and essentially
a slope of 1, it had to be pushed out more.
What we'll see in the last video is that this
actually works out mathematically as well.
It's consistent with what we learned about the
multiplier effect and that's actually the reason
algebraically why this is happening, why you're
getting a bigger change in output than the
incremental shift in demand.
That's because of the multiplier effect and we'll
see it in the next video.