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.

Consumption function, where’s your junction?

I love these videos. I never had economics in school and it's all very interesting. One thing I don't like though is the use of c0 and c1. They look like they should be part of a series c0, c1, c2, etc, while actually c0 is a dollar amount and c1 is a scalar. It's just an aesthetic thing I guess, but I'd be happier if c0 was written as a capital, like all the other dollar amounts: C0.

this has really helped me a lot, I'm doing my 1st year economics in university and the course is totally new to me, things appear to be strange in the lectures but your short tutorials have given me a very broad understanding of the topic and I feel I've learnt better than all the others who depend on the lecturer, please post more tutorials and thank you very much for the initiative of creating these videos 🙂

Why doesnt AE line start from 0?

only if you stopped repeating yourself. man its gets confusing when you keep saying it over and over again.

it's help me to understanding the basic of the planned spending for my final exam. thank a lot

very useful, thank u so much!

Y is output. Why is (Y-T) disposable income?

The video is nonsense. From about 10:00 to 11:43, Khan Academy says:

(delta Y) = (delta G) x (a multiplier)

PEMDAS says that's illegal addition: delta G

before multiplication

Illegal math means the video is nonsense.

It is really useful , as a beginner I can understand this stuff suddenly . Became your follower and support you !

can expected expenditure be equal to real expenditure?

what is the 45 degree line concept..

Jesus man, thank you!

very helpful

there is no difference comparing this video and the previous one

its good but khan academy is not for searching sample question

i appreciate you mr khan

Lol pop that G Khan

I should've never signed up for this class