Keynesian Cross

Analyzing planned expenditures versus actual output using the Keynesian Cross
More free lessons at: http://www.khanacademy.org/video?v=sTw0e-hwYAQ

What I want to introduce
you to in this video

is the idea of a Keynesian Cross.

This is one of the tools of
analysis of Keynesian thinking

which is really the idea
that maybe every now and then

the GDP, when it's at equilibrium,

isn't at an optimal state.

It's operating well below potential

and the way that we might be able to get.

If you are a follower
of Keynesian thinking,

the way that we can get it closer to,

potential closer to full employment

is by somehow affecting
aggregate demand in some way.

What we'll see is,

we're going to build up our
Keynesian Cross analysis

based on what we understand
from the consumption function.

We're going to first start thinking about

planned expenditures.

We're going to think about what happens

when planned expenditures
deviates from actual output,

from actual expenditures, right over here.

This is very similar to
what we're done before

but we're actually thinking
of it in terms of planning.

Let's say we have planned expenditures,

expenditures planned

and we could just write the components

of aggregate expenditure here.

Well, you're going to
have consumer spending,

you're going to have investment.

I'm going to be careful here,

I'm going to call it planned investment.

This is exactly what firms
are looking to produce.

The reason why I differentiate this here

is because, if for whatever reason,

aggregate expenditure
is less than they expect

then they might build up inventories

and those inventories get
counted as investments.

Those would be excess
inventories above and beyond

the planned inventories.

If actual demand is higher than expended

then it might eat in to inventories

and when inventories are eaten into

it actually takes away
from planned investments

there would actually be kind of a,

you would be eating into
the total investment

in that situation.

That's why I'm going to differentiate

between planned investment
and actual investment.

Then of course, you
have government spending

and then finally you have net exports.

For the sake of the analysis
of the Keynesian Cross,

once again, this is a
super over simplification,

we're going to assume that
at any given level of GDP

or aggregate output that
these are all constant.

That these are not really dependent

on aggregate output or GDP

which is of course a
huge over simplification.

If we were to plot any of these

versus aggregate income

we'd say that they are really a flat line.

Maybe planned investment might
look something like that.

Maybe government spending
would look something like that.

No ways at some level that's preplanned,

it's exogenous to our model.

It's not dependant in any way.

It's an external factor.

Assuming it's fixed,

it's not dependent on aggregate income.

So government spending
looks something like that

and net exports, maybe it
looks something like that.

The one factor that you can imagine

because I said we're going to build

on top of the consumption function

that we're going to assume
is driven by aggregate income

is consumption right over here.

The way that this thing will look,

the way that this thing will look

is you have ...

So let me draw another
plot right over here,

draw another plot.

We have aggregate income,

that is going to be our
independent variable

and then over here we can
just view this as expenditure.

If we were just to plot consumer spending,

we've seen that before

especially if we assume a
linear consumption function.

What we've studied in the last few videos

is all linear consumption functions

and depending on how you write it,

but they all look something like this.

They have a positive
vertical axis intercept

and they have upward
slope that is less than 1.

Consumption by itself would
look something like this,

this would be consumer spending

as a function of aggregate income.

Then if you all all of
these constants to it

then your graph for aggregate
planned expenditures

would look something like this.

if you added just in net exports

it would get a little bit higher

because these are constant.

Any point you would add this much,

if you add government a
little higher than that

and if you add all of them
including planned investments

you might get something that looks,

and I'll do it in this
color right over here,

you might get something
that looks like this.

I'm just starting off
with consumer spending.

I'm using a linear consumption function,

you don't have to,

but it makes the Keynesian Cross analysis

a lot more cross like
and easier to analyse.

If you add all what we
assumed to be constant things

and aggregate expenditures
is going to be up here.

This right over here

is aggregate planned
expenditures I should say.

Now, we know from the
circular flow in the economy

that when an economy is at equilibrium,

your aggregate output is equal
to your aggregate expenditures

or your aggregate expenditures

is equal to your aggregate income.

Really, at an equilibrium,

these two things are going to be equal.

We can actually plot a line
that shows all the points

that those are equal.

That would be a line that
has essentially a slope of 1

where Y is always equal to expenditures.

It might look something like this.

This is where the name
Keynesian cross comes from

because essentially you
have planned expenditures

and then right over here you
have the equilibrium line

or what I call the equilibrium line

because these are all points where income

is equal to expenditure.

Right over here, income
is equal to expenditure.

Income is equal to expenditure.

When you look at aggregate
planned expenditures

or you can even view
this as aggregate demand

as a function of aggregate income.

This is actual point

where the actual economy is at equilibrium

where expenditures are actually equal to,

where expenditures are
actually equal to output.

Actually, it's a little bit
skewed the way I drew it

but these actually
should be like a square.

Actually, let me see if
I can draw a little bit

clearer than that.

Just so it will actually
looks like a 45 degree line.

It should really be a 45
degree line like that.

That seems a little bit better.

That's the point at which
we are at equilibrium.

Actually, I don't like that

because it makes it a little
bit harder to analyse.

But hopefully you get the idea.

This should be a line
that's where expenditures

is equal to aggregate income.

Like this so it intersects at a point

that's a little bit
easier for me to analyse.

Now, this is where the Keynesian Cross

becomes a kind of interesting tool

because we could start to think about

what happens in situations.

This is an equilibrium level of GDP.

What happens if for whatever reason

that aggregate income

is higher than that equilibrium level?

Let's think about scenario.

Let's say we're over here.

Let me do that in magenta.

Let's say we're over here.

Let's call that Y1.

What is going on?

What is going on right over here at Y1?

Over here, the aggregate output

which is the same thing
as aggregate income

is right over here.

Well, this is the actually
planned expenditures,

is right over here.

All of these excess. All of these excess

above the planned demand,

these are essentially going
to be inventories building up.

The economy is producing
more than it actually needs,

inventories are going to build up.

Firms are not selling
all of their products

and that excess built up inventory

is going to be reflected in investment.

In this case, this delta.

This delta is going to be added
to your planned investment

to get what the actual
investment might be.

When an economy is at that state

then firms would say, "Oh my god!

"We're building inventory
more than we expected.

"We're not selling our products.

"We're going to lower output

"so there's a natural
feedback mechanism for the GDP

"to go back to equilibrium."

Let's think about what happens

if it's below that equilibrium point.

Let's say that GDP is,

let's call that right over here.

This is Y2.

Actually, I could write it as a subscript.

I don't know, I wrote a superscript there.

We could call this Y2.

Over here, aggregate demand
at this level of output

is more than what's actually being output.

People want more goods and services.

Right over here,

this is a deficit of output

and so this shows that people

will be digging into inventory.

That the existing inventories

or the existing investment was not enough.

Or, I guess another way to think it,

essentially, inventories
will be contracting.

Let's say business was constant.

I had a lemonade stand,
I just keep an inventory

of 5 cups of lemonade on hand

and I sell a cup every hour.

If all of a sudden people
start buying 2 cups an hour

my inventory is going to
start getting depleted

and so this is what's reflected.

Actual output is below what's demanded.

When firms start seeing

that their inventories
get depleted, they say,

"Oh my god!

"I don't want to run out
of my goods and services.

"Let me start producing more."

Then when we're talking about inventories

we're really talking about goods.

So let me produce more.

So output will once again

want to naturally go
to that feedback point.

Hopefully that makes
a little bit of sense.

In the next few videos we'll
be using the Keynesian Cross

to think about the
Keynesian line of reasoning.

If you change one of these,

how that might affect the
new equilibrium level of GDP.