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.

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.