Investment and real interest rates

WEBVTT
Kind: captions
Language: en

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In our planned expenditure
remodel we've been

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assuming that planned investment is fixed.

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What I want to do in
this video is think about

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how real interest rates
drive planned investment.

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Think about the function investment as a

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function of real interest
rates. Planned investment as

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a function of real interest rates.

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Talking about real
interest rates, I'm really

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just talking about nominal interest rates

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factoring out or
discounting what's going on

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with inflation. There's
other videos where we

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go into more depth about
that. Another thing

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if there were no
inflation real and nominal

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rates would be the same thing.

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I want to tackle it with
a very tangible example.

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Let's say this up coming
year there's a bunch

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of potential planned projects.

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Let's call this projects.
Theses are potential

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investments. You have
projects, and then you have

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some level of expected return.

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Each of the people who are thinking about

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these projects, they all
have their spreadsheets

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out, and they've taken
in risk and probabilities

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and all of the rest. They've come up with

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their expected return numbers.

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Let's say project A has
an expected return of

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20%, B 18%, C 16%. I'll do a couple more.

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D is 10% , E is 5% and F is 2%.
Let's say initially in one state

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of affairs interest rates
are relatively high.

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Let's R1 is equal to 19% interest rates.

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We have 19% real interest
rates. These are the

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real expected returns.
Which of these projects

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will actually be invested in?

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Which of the ones will people actually do?

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If someone has the cash, they say well,

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I could either lend my money out for 19%,

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or I could do this project and get 20%.

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If they have the cash
they would definitely

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do this. If they don't
have the cash, they could

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say, well, I could
borrow the money for 19%,

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and I could invest it at 20%.
I'll make money off of that.

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Project A will definitely be done.

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What about project B?

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Project B, if the person
actually has the cash

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on hand to do project
B, they say I could do

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project B and get an 18% real return,

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or I could lend that
money out and get a 19%

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in real return. Actually, I would not do

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project B. I'll just say
I would not do anything

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that has a even a lower real return.

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If I could potentially
do project B, but I had

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to borrow the money,
if I have to borrow the

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money at 19% real interest, and I'm only

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getting 18% on it, that's a
money loosing proposition.

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I wouldn't do B, and I
definitely wouldn't do

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all these things that get a lower return.

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When I have high interest
rates right over here

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the only thing I would do is project A.

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Let's think about what
would happen if interest

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rates went down.

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If real interest rates went down.

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Let's say real interest
... let's call that R2.

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Real interest rates go
down to ... let's say

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they go down to 3%. Once
again, project A you

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are definitely going
to do. If you have the

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money on hand, you get
20% doing project A.

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You definitely don't want
to lend it out at 3%.

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If you don't have the
money on hand, you can

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borrow at 3% and invest at 20%.

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By the same logic, people
would do project B.

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You could borrow at 3% and make 18%.

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If you have the money,
you get 18% verses 3% on

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your money, so you definitely do this.

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You do all of these up to project E.

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If you have the money,
you would rather put that

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money and get 5% then lend
it out and only get 3%.

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You'll even do project
E if you need to borrow

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it and still makes sense.
Borrow money at 3%,

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invest it at 5%, your
making some real return.

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The only one that you would not
do is project F right over here.

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Here you aren't actually
covering your cost of

00:03:59.810 --> 00:04:01.996
borrowing. If you have to borrow at 3% and

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invest at 2%, doesn't make sense.

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If you have the money,
you would rather lend

00:04:06.334 --> 00:04:08.553
your money at 3% then
do project F. So, your

00:04:08.553 --> 00:04:13.404
definitely not going to
do F in this scenario.

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Obviously do it in neither scenario.

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Right over here, you'd
do all of the above.

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You would do A, B, C,
D, not all of the above.

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All of the above except
for F. A, B, C, D, and E.

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Let's just think about the
rough level of investments.

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If we were to plot on
this axis right over here,

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if we were to plot the
investments as a function

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of real interest rate,
and over here we actually

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have the ... independent
variables are real

00:04:51.478 --> 00:04:54.314
interest rate. At a high
real interest we had

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a low level investment.
We only did project A.

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That's right over there. That's A only.

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This is when we were at R1.

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When we lowered interest
rates to R2, we had a

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much higher level of investment.

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We did all of these
projects right over here.

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You had a much higher level of investment.

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This is A, B, C, D, and
E. You see that you have

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an inverse relationship.
The lower the real

00:05:23.070 --> 00:05:25.565
interest rate, the more
investment that's going

00:05:25.565 --> 00:05:27.598
to go on. The higher the
interest rate, the less

00:05:27.598 --> 00:05:29.405
investment that goes on.

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You can debate whether
it's a curve or a line,

00:05:31.600 --> 00:05:34.074
bur for the sake of
simplicity, we'll assume

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that it looks something
like ... I'll draw a

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dotted line it's easier for me do that.

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It might look something like that.

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Now, we can use this
insight to start thinking

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about how a change in
real interest rate might

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shift our plan expenditures on our

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[unintelligible 05:50]
and from that we can

00:05:52.128 --> 00:05:54.128
start to think about the IS curve.

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The famous IS curve and the ISLM model.


Keynesian cross and the multiplier

WEBVTT
Kind: captions
Language: en

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In the last video, we saw
how the Keynesian Cross

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could help us visualize an increase in

00:00:05.670 --> 00:00:07.691
government spending
which was a shift in our

00:00:07.691 --> 00:00:10.940
aggregate planned expenditure
line right over here

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and we saw how the
actual change, the actual

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increase in output if you take all the

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assumptions that we
took in this, the actual

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change in output and
aggregate income was larger

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than the change in government spending.

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You might say okay,
Keynesian thinking, this

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is very left wing, this is the

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government's growing larger right here.

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I'm more conservative.
I'm not a believer in

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Keynesian thinking.

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The reality is you actually might be.

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Whether you're on the right or the left,

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although Keynesian economics tends to be

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poo-pooed more by the
right and embraced more

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by the left, most of the
mainstream right policies,

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especially in the US,
have actually been very

00:00:51.692 --> 00:00:52.691
Keynesian.

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They just haven't been
by manipulating this

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variable right over here.

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For example, when people
talk about expanding

00:00:58.140 --> 00:01:01.400
the economy by lowering taxes, they are a

00:01:01.400 --> 00:01:03.869
Keynesian when they say
that because if we were

00:01:03.869 --> 00:01:06.077
to rewind and we go back to our original

00:01:06.077 --> 00:01:08.943
function so if we don't
do this, if we go back to

00:01:08.943 --> 00:01:15.560
just having our G here,
we're now back on this

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orange line, our original
planned expenditure,

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you could, based on this
model right over here,

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also shift it up by lowering taxes.

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If you change your taxes to be taxes minus

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some delta in taxes, the
reason why this is going

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to shift the whole curve
up is because you're

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multiplying this whole thing by a negative

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number, by negative C1.

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C1, your marginal
propensity to consume, we're

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assuming is positive.

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There's a negative out here.

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When you multiply it
by a negative, when you

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multiply a decrease by
a negative, this is a

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negative change in taxes,
then this whole thing

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is going to shift up again.

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You would actually shift up.

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You would actually shift
up in this case and

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depending on what the
actual magnitude of the

00:02:05.139 --> 00:02:08.144
change in taxes are,
but you would actually

00:02:08.144 --> 00:02:10.664
shift up and the amount
that you would shift up -

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I don't want to make my graph to messy so

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this is our new aggregate
planned expenditures -

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but the amount you
would move up is by this

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coefficient down here, C1, -C1 x -delta T.

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You're change, the amount
that you would move up,

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is -C1 x -delta T, if we assume delta T is

00:02:32.737 --> 00:02:37.873
positive and so you
actually have a C1, delta T.

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The negatives cancel out
so that's actually how

00:02:39.733 --> 00:02:42.073
much it would actually move up.

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It's also Keynesian when you say if we

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increase taxes that will
lower aggregate output

00:02:46.473 --> 00:02:51.267
because if you increase
taxes, now all of a

00:02:51.267 --> 00:02:54.751
sudden this is a positive,
this is a positive

00:02:54.751 --> 00:02:56.471
and then you would shift the curve by that

00:02:56.471 --> 00:02:57.475
much.

00:02:57.475 --> 00:02:59.875
You would actually
shift the curve down and

00:02:59.875 --> 00:03:06.139
then you would get to a
lower equilibrium GDP.

00:03:06.139 --> 00:03:09.011
This really isn't a difference between

00:03:09.011 --> 00:03:12.902
right leaning fiscal
policy or left leaning

00:03:12.902 --> 00:03:14.713
fiscal policy and
everything I've talked about

00:03:14.713 --> 00:03:16.819
so far at the end of the
last video and this video

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really has been fiscal policy.

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This has been the spending
lever of fiscal policy

00:03:21.011 --> 00:03:23.822
and this right over here
has been the taxing lever

00:03:23.822 --> 00:03:25.136
of fiscal policy.

00:03:25.136 --> 00:03:27.135
If you believe either of those can effect

00:03:27.135 --> 00:03:30.070
aggregate output, then you are essentially

00:03:30.070 --> 00:03:33.206
subscribing to the Keynesian model.

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Now one thing that I did
touch on a little bit

00:03:35.802 --> 00:03:38.791
in the last video is
whatever our change is,

00:03:38.791 --> 00:03:41.294
however much we shift
this aggregate planned

00:03:41.294 --> 00:03:44.958
expenditure curve, the
change in our output

00:03:44.958 --> 00:03:47.368
actually was some multiple of that.

00:03:47.368 --> 00:03:49.668
What I want to do now is
show you mathematically

00:03:49.668 --> 00:03:52.044
that it actually all works
out that the multiple is

00:03:52.044 --> 00:03:54.372
actually the multiplier.

00:03:54.372 --> 00:03:56.293
If we go back to our
original and this will just

00:03:56.293 --> 00:03:58.743
get a little bit mathy
right over here so I'm

00:03:58.743 --> 00:04:00.204
just going to rewrite it all.

00:04:00.204 --> 00:04:04.196
We have our planned
expenditure, just to redig

00:04:04.196 --> 00:04:07.289
our minds into the actual expression, the

00:04:07.289 --> 00:04:08.619
planned expenditure is
equal to the marginal

00:04:08.619 --> 00:04:12.941
propensity to consume
times aggregate income

00:04:12.941 --> 00:04:14.205
and then you're going to have all of this

00:04:14.205 --> 00:04:15.676
business right over here.

00:04:15.676 --> 00:04:16.872
We're just going to go
with the original one,

00:04:16.872 --> 00:04:18.000
not what I changed.

00:04:18.000 --> 00:04:20.210
All this business, let's just call this B.

00:04:20.210 --> 00:04:22.621
That will just make it
simple for us to manipulate

00:04:22.621 --> 00:04:25.624
this so let's just call
of this business right

00:04:25.624 --> 00:04:26.624
over here B.

00:04:26.624 --> 00:04:28.933
We could substitute that back in later.

00:04:28.933 --> 00:04:33.161
We know that an economy is in equilibrium

00:04:33.161 --> 00:04:36.291
when planned expenditures
is equal to output.

00:04:36.291 --> 00:04:39.473
That is an economy in
equilibrium so let's set this.

00:04:39.473 --> 00:04:43.439
Let's set planned expenditures equal to

00:04:43.439 --> 00:04:45.471
aggregate output, which
is the same thing as

00:04:45.471 --> 00:04:46.957
aggregate expenditures, the same thing as

00:04:46.957 --> 00:04:49.211
aggregate income.

00:04:49.211 --> 00:04:52.705
We can just solve for
our equilibrium income.

00:04:52.705 --> 00:04:53.791
We can just solve for it.

00:04:53.791 --> 00:04:59.740
You get Y=C1xY+B, this
is going to look very

00:04:59.740 --> 00:05:01.203
familiar to you in a second.

00:05:01.203 --> 00:05:04.495
Subtract C1xY from both sides.

00:05:04.495 --> 00:05:08.044
Y-C1Y, that's the left-hand side now.

00:05:08.044 --> 00:05:10.070
On the right-hand side,
obviously if we subtract

00:05:10.070 --> 00:05:14.806
C1Y, it's going to go away
and that is equal to B.

00:05:14.806 --> 00:05:20.139
Then we can factor out
the aggregate income from

00:05:20.139 --> 00:05:28.089
this, so Yx1-C1=B and
then we divide both sides

00:05:28.089 --> 00:05:34.945
by 1-C1 and we get, that cancels out.

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I'll write it right over here.

00:05:37.289 --> 00:05:41.794
We get, a little bit of
a drum roll, aggregate

00:05:41.794 --> 00:05:45.603
income, our equilibrium, aggregate income,

00:05:45.603 --> 00:05:47.775
aggregate output.

00:05:47.775 --> 00:05:57.072
GDP is going to be equal to 1/1-C1xB.

00:05:57.072 --> 00:05:59.729
Remember B was all this business up here.

00:05:59.729 --> 00:06:01.873
Now what is this?

00:06:01.873 --> 00:06:03.287
You might remember this
or if you haven't seen

00:06:03.287 --> 00:06:04.737
the video, you might
want to watch the video

00:06:04.737 --> 00:06:06.012
on the multiplier.

00:06:06.012 --> 00:06:08.496
This C1 right over here is our marginal

00:06:08.496 --> 00:06:12.090
propensity to consume.

00:06:12.090 --> 00:06:14.620
1 minus our marginal propensity to consume

00:06:14.620 --> 00:06:15.806
is actually - And I
don't think I've actually

00:06:15.806 --> 00:06:18.041
referred to it before which
let me rewrite it here

00:06:18.041 --> 00:06:21.292
just so that you know the
term - so C1 is equal to

00:06:21.292 --> 00:06:25.855
our marginal propensity to consume.

00:06:25.855 --> 00:06:29.994
For example, if this is
30% or 0.3, that means

00:06:29.994 --> 00:06:31.873
for every incremental dollar of disposable

00:06:31.873 --> 00:06:34.954
income I get, I want to spend $.30 of it.

00:06:34.954 --> 00:06:38.958
Now 1-C1, you could view
this as your marginal

00:06:38.958 --> 00:06:41.678
propensity to save.

00:06:41.678 --> 00:06:44.292
If I'm going to spend
30%, that means I'm going

00:06:44.292 --> 00:06:46.333
to save 70%.

00:06:46.333 --> 00:06:48.600
This is just saying
I'm going to save 1-C1.

00:06:48.600 --> 00:06:50.739
If I'm spending 30% of that incremental

00:06:50.739 --> 00:06:54.802
disposable dollar, then I'm
going to save 70% of it.

00:06:54.802 --> 00:06:56.470
This whole thing, this is the marginal

00:06:56.470 --> 00:06:57.536
propensity to consume.

00:06:57.536 --> 00:07:00.545
This entire denominator
is the marginal propensity

00:07:00.545 --> 00:07:06.138
to save and then one over
that, so 1/1-C1 which

00:07:06.138 --> 00:07:08.544
is the the same thing
as 1/marginal propensity

00:07:08.544 --> 00:07:11.136
to save, that is the multiplier.

00:07:11.136 --> 00:07:12.475
We saw that a few videos ago.

00:07:12.475 --> 00:07:14.207
If you take this infinite
geometric series,

00:07:14.207 --> 00:07:16.203
if we just think through
how money spends, if I

00:07:16.203 --> 00:07:19.287
spend some money on some
good or service, the

00:07:19.287 --> 00:07:21.291
person who has that
money as income is going

00:07:21.291 --> 00:07:23.536
to spend some fraction
of it based on their

00:07:23.536 --> 00:07:25.739
marginal propensity to
consume and we're assuming

00:07:25.739 --> 00:07:27.802
that it's constant
throughout the economy at all

00:07:27.802 --> 00:07:30.909
income levels for this
model right over here.

00:07:30.909 --> 00:07:33.612
Then they'll spend some
of it and then the person

00:07:33.612 --> 00:07:35.000
that they spend it on,
they're going to spend

00:07:35.000 --> 00:07:35.803
some fraction.

00:07:35.803 --> 00:07:38.288
When you keep adding all
that infinite series up,

00:07:38.288 --> 00:07:41.749
you actually get this
multiplier right over here.

00:07:41.749 --> 00:07:48.738
This is equal to our multiplier.

00:07:48.738 --> 00:07:54.408
For example, if B gets
shifted up by any amount,

00:07:54.408 --> 00:07:57.316
let's say B gets shifted
up and it could get

00:07:57.316 --> 00:07:59.138
shifted up by changes in any of this stuff

00:07:59.138 --> 00:08:00.076
right over here.

00:08:00.076 --> 00:08:01.789
Net exports can change,
planned investments

00:08:01.789 --> 00:08:04.397
can change, could be shifted up or down.

00:08:04.397 --> 00:08:08.627
The impact on GDP is
going to be whatever that

00:08:08.627 --> 00:08:12.425
shift is times the multiplier.

00:08:12.425 --> 00:08:13.733
We saw it before.

00:08:13.733 --> 00:08:23.190
If, for example, if C1=0.6, that means for

00:08:23.190 --> 00:08:25.806
every incremental disposable
dollar, people will

00:08:25.806 --> 00:08:27.209
spend 60% of it.

00:08:27.209 --> 00:08:31.773
That means that the
marginal propensity to save

00:08:31.773 --> 00:08:33.871
is equal to 40%.

00:08:33.871 --> 00:08:36.137
They're going to save
40% of any incremental

00:08:36.137 --> 00:08:42.233
disposable dollar and
then the multiplier is

00:08:42.233 --> 00:08:45.806
going to be one over
that, is going to be 1/0.4

00:08:45.806 --> 00:08:48.192
which is the same thing
as one over two-fifths,

00:08:48.192 --> 00:08:51.292
which is the same thing
as five-halves, which

00:08:51.292 --> 00:08:53.959
is the same thing as 2.5.

00:08:53.959 --> 00:08:58.190
For example, in this
situation, we just saw that

00:08:58.190 --> 00:09:01.876
Y, the equilibrium Y is
going to be 2.5 times

00:09:01.876 --> 00:09:04.407
whatever all of this other business is.

00:09:04.407 --> 00:09:08.043
If we change B by, let's
say, $1 billion and

00:09:08.043 --> 00:09:12.211
maybe if we increase B by $1 billion.

00:09:12.211 --> 00:09:14.536
We might increase B by
$1 billion by increasing

00:09:14.536 --> 00:09:17.314
government spending by $1
billion or maybe having

00:09:17.314 --> 00:09:20.294
this whole term including
this negative right

00:09:20.294 --> 00:09:24.470
over here become less
negative by $1 billion.

00:09:24.470 --> 00:09:26.204
Maybe we have planned
investment increase by

00:09:26.204 --> 00:09:29.010
$1 billion and that could
actually be done a little

00:09:29.010 --> 00:09:31.036
bit with tax policy too
by letting companies

00:09:31.036 --> 00:09:33.074
maybe depreciate their assets faster.

00:09:33.074 --> 00:09:35.743
If we could increase net
exports by $1 billion.

00:09:35.743 --> 00:09:38.804
Essentially any way that we
increase B by $1 billion,

00:09:38.804 --> 00:09:44.181
that'll increase GDP by
$2.5 billion, 2.5 times

00:09:44.181 --> 00:09:45.375
our change in B.

00:09:45.375 --> 00:09:48.003
We can write this down this way.

00:09:48.003 --> 00:09:54.140
Our change in Y is going
to be 2.5 times our

00:09:54.140 --> 00:09:55.471
change in B.

00:09:55.471 --> 00:09:56.873
Another way to think
about it when you write

00:09:56.873 --> 00:09:59.733
the expression like
this, if you said Y is a

00:09:59.733 --> 00:10:02.073
function of B, then you
would say look the slope

00:10:02.073 --> 00:10:08.027
is 2.5, so change in Y over change in B is

00:10:08.027 --> 00:10:11.110
equal to 2.5, but I just
wanted to right this

00:10:11.110 --> 00:10:12.339
to show you that this isn't some magical

00:10:12.339 --> 00:10:13.804
voodoo that we're doing.

00:10:13.804 --> 00:10:15.958
This is what we looked at
visually when we looked

00:10:15.958 --> 00:10:17.043
at the Keynesian Cross.

00:10:17.043 --> 00:10:19.628
This is really just describing the same

00:10:19.628 --> 00:10:22.803
multiplier effect that
we saw in previous videos

00:10:22.803 --> 00:10:26.803
and where we actually derived
the actual multiplier.


Details on shifting aggregate planned expenditures

WEBVTT
Kind: captions
Language: en

00:00:00.547 --> 00:00:02.805
I want to now build on
what we did in the last

00:00:02.805 --> 00:00:05.975
video on the Keynesian Cross and planned

00:00:05.975 --> 00:00:08.549
aggregate expenditures and
fill in a little bit more

00:00:08.549 --> 00:00:12.068
on the details and think
about how this could be

00:00:12.068 --> 00:00:15.607
of useful conceptual tool
for Keynesian thinking.

00:00:15.607 --> 00:00:17.676
Let's just review a little bit.

00:00:17.676 --> 00:00:21.539
I'll rebuild our planned
aggregate expenditure

00:00:21.539 --> 00:00:24.396
function, but I'll fill in
little bit of the details.

00:00:24.396 --> 00:00:28.069
Let's say this is
planned, planned aggregate

00:00:28.069 --> 00:00:30.622
expenditures and this
is going to be equal to

00:00:30.622 --> 00:00:32.720
consumption.

00:00:32.720 --> 00:00:33.871
You'll often see it in a
book written like this:

00:00:33.871 --> 00:00:37.473
Consumption as a function
of aggregate income

00:00:37.473 --> 00:00:40.287
minus taxes and I want
to be very clear here.

00:00:40.287 --> 00:00:43.739
They're not saying that
this term should be

00:00:43.739 --> 00:00:47.022
aggregate income times aggregate income

00:00:47.022 --> 00:00:48.011
minus taxes.

00:00:48.011 --> 00:00:50.210
They're saying that
consumption is a function of

00:00:50.210 --> 00:00:53.373
this right over here;
the same way we would say

00:00:53.373 --> 00:00:57.670
that F is a function of
X, but if you give me a

00:00:57.670 --> 00:01:00.535
Y-T or essentially if
you give me a disposable

00:01:00.535 --> 00:01:06.139
income right over here, I
will give you a consumption.

00:01:06.139 --> 00:01:08.290
If you actually want to
deal with this directly

00:01:08.290 --> 00:01:10.872
mathematically, analytically,
you'd have to define

00:01:10.872 --> 00:01:13.136
what this function is, but
I'll write it like this

00:01:13.136 --> 00:01:15.873
now and in the next step
I'll actually define what

00:01:15.873 --> 00:01:17.269
our consumption function is.

00:01:17.269 --> 00:01:20.603
This is just saying an
arbitrary consumption function

00:01:20.603 --> 00:01:24.689
and it is a function of disposable income.

00:01:24.689 --> 00:01:28.534
It's going to be your
consumption function plus

00:01:28.534 --> 00:01:31.459
your planned investment,
which we're going to

00:01:31.459 --> 00:01:36.091
assume is constant, plus
government expenditures

00:01:36.091 --> 00:01:38.340
plus net exports.

00:01:38.340 --> 00:01:40.471
Plus net exports.

00:01:40.471 --> 00:01:43.967
A couple of videos ago we
built some simple models

00:01:43.967 --> 00:01:46.475
for consumption function so
let's put one of those in.

00:01:46.475 --> 00:01:50.207
Let's say that our consumption function,

00:01:50.207 --> 00:01:53.943
so aggregate consumption is a function of

00:01:53.943 --> 00:01:56.337
disposable income, as a function of income

00:01:56.337 --> 00:01:58.078
minus taxes.

00:01:58.078 --> 00:02:00.821
Let's say that's going to be equal to some

00:02:00.821 --> 00:02:03.388
autonomous expenditure

00:02:03.388 --> 00:02:07.299
plus the marginal propensity to consume.

00:02:07.299 --> 00:02:08.881
(Maybe I don't have to keep
switching colors because

00:02:08.881 --> 00:02:10.407
we've seen this before.)

00:02:10.407 --> 00:02:12.382
Plus the marginal propensity to consume

00:02:12.382 --> 00:02:17.050
times disposable income.
Times disposable income.

00:02:17.050 --> 00:02:19.379
Now you see that consumption, aggregate

00:02:19.379 --> 00:02:21.545
consumption is being defined.

00:02:21.545 --> 00:02:24.139
It's being defined as a function of

00:02:24.139 --> 00:02:25.933
disposable income.

00:02:25.933 --> 00:02:28.076
That's what that notation
right over there means.

00:02:28.076 --> 00:02:31.073
We could substitute
this function expression

00:02:31.073 --> 00:02:33.293
with this stuff in green right over here.

00:02:33.293 --> 00:02:38.440
We can say aggregate planned expenditure,

00:02:38.440 --> 00:02:41.466
is equal to, this is our
consumption function,

00:02:41.466 --> 00:02:44.407
so it's equal to (Oh,
I'll do it in that same

00:02:44.407 --> 00:02:49.944
yellow.) it's equal to
autonomous consumption

00:02:49.944 --> 00:02:52.538
plus the marginal
propensity to consume times

00:02:52.538 --> 00:02:55.042
disposable income which
is aggregate income

00:02:55.042 --> 00:02:57.669
minus taxes and then of course we have the

00:02:57.669 --> 00:03:01.403
other terms plus planned investment plus

00:03:01.403 --> 00:03:05.133
government spending plus net exports.

00:03:05.133 --> 00:03:09.139
Plus net exports.

00:03:09.139 --> 00:03:10.997
Then we can simplify
this a little bit just so

00:03:10.997 --> 00:03:13.469
it makes clear what parts
of this are constant

00:03:13.469 --> 00:03:15.801
and what parts aren't,
what parts are a function

00:03:15.801 --> 00:03:18.037
of income.

00:03:18.037 --> 00:03:20.672
For the sake of this little
lesson right over here,

00:03:20.672 --> 00:03:22.416
you might remember a few videos ago,

00:03:22.416 --> 00:03:24.594
we can have a debate
whether taxes should be

00:03:24.594 --> 00:03:26.142
a function of income or not.

00:03:26.142 --> 00:03:28.183
In the real world, taxes
really are a function

00:03:28.183 --> 00:03:30.343
of income, but for the
sake of this analysis

00:03:30.343 --> 00:03:33.144
we'll just assume that like investment,

00:03:33.144 --> 00:03:34.858
planned investment,
government spending and

00:03:34.858 --> 00:03:38.483
net exports, we'll assume for the sake of

00:03:38.483 --> 00:03:40.112
this presentation we're
going to assume this is

00:03:40.112 --> 00:03:45.533
constant. Assume that this is constant.

00:03:45.533 --> 00:03:46.870
This is constant.

00:03:46.870 --> 00:03:48.669
If we assume that that's
a constant, we can

00:03:48.669 --> 00:03:50.689
multiply (And actually even if we didn't

00:03:50.689 --> 00:03:52.405
assume it's a constant
we could still multiply,

00:03:52.405 --> 00:03:55.267
but then we'd want to
redefine this in terms of Y)

00:03:55.267 --> 00:03:59.760
but we can distribute the C1 and so we get

00:03:59.760 --> 00:04:01.675
- We get; I don't have
to keep writing that

00:04:01.675 --> 00:04:03.669
- this part right over here, we have our

00:04:03.669 --> 00:04:05.019
autonomous expenditures,

00:04:05.019 --> 00:04:11.873
(C1xY)+(C1 x aggregate
income) - the marginal

00:04:11.873 --> 00:04:16.407
propensity to consume
times taxes + all of this

00:04:16.407 --> 00:04:17.878
other stuff.

00:04:17.878 --> 00:04:20.229
Actually I could just copy and paste that,

00:04:20.229 --> 00:04:21.630
plus all of this other stuff.

00:04:21.630 --> 00:04:24.669
Let me copy it and then let me paste it.

00:04:24.669 --> 00:04:28.549
Plus all of this other
stuff and that is equal to

00:04:28.549 --> 00:04:32.469
our planned expenditures;
planned expenditures.

00:04:32.469 --> 00:04:35.207
Now we can think about well
this part right over here,

00:04:35.207 --> 00:04:40.337
this is the function,
this is how aggregate

00:04:40.337 --> 00:04:41.818
income is really driving it.

00:04:41.818 --> 00:04:43.669
Everything else is really a constant here.

00:04:43.669 --> 00:04:45.602
Let's write it in those terms.

00:04:45.602 --> 00:04:46.879
Let's write it in those terms.

00:04:46.879 --> 00:04:50.406
We have aggregate planned
expenditure is equal

00:04:50.406 --> 00:04:54.533
to the marginal propensity
to consume times

00:04:54.533 --> 00:04:57.659
our aggregate income;
times our aggregate income.

00:04:57.659 --> 00:04:59.208
That's this term right over here.

00:04:59.208 --> 00:05:00.470
I'll box it off.

00:05:00.470 --> 00:05:05.422
Everything else is a
constant, so plus the C sub 0

00:05:05.422 --> 00:05:07.728
which was our autonomous expenditures,

00:05:07.728 --> 00:05:10.034
minus (C sub 1 X T)

00:05:10.034 --> 00:05:12.341
so the marginal propensity
to consume times T

00:05:12.341 --> 00:05:14.603
and these are both
constants for the sake of

00:05:14.603 --> 00:05:16.540
our analysis so this
whole thing is a constant

00:05:16.540 --> 00:05:18.736
and then plus all that other stuff.

00:05:18.736 --> 00:05:21.673
Then plus all of that other stuff there.

00:05:21.673 --> 00:05:24.272
This might look like a
really fancy, complicated

00:05:24.272 --> 00:05:26.677
formula, but it's actually
pretty straight forward

00:05:26.677 --> 00:05:29.736
because we're assuming for
the sake of our analysis

00:05:29.736 --> 00:05:33.481
that all of this, all
of this right over here,

00:05:33.481 --> 00:05:35.936
all of this is constant.

00:05:35.936 --> 00:05:38.412
If you were to plot this right over here,

00:05:38.412 --> 00:05:41.088
it would look something like this.

00:05:41.088 --> 00:05:44.272
Let us plot it.

00:05:44.272 --> 00:05:46.012
Really this is almost
exactly what we did in the

00:05:46.012 --> 00:05:49.003
last video, but we're now
filling in some details.

00:05:49.003 --> 00:05:51.177
Our independent variable is going to be

00:05:51.177 --> 00:05:54.096
aggregate income or
GDP, however you want to

00:05:54.096 --> 00:06:00.810
view it, and then our
vertical axis is expenditures.

00:06:00.810 --> 00:06:03.869
Expenditures.

00:06:03.869 --> 00:06:06.905
Expenditures and so if
we wanted to plot this,

00:06:06.905 --> 00:06:09.603
the constant part, this
thing right over here,

00:06:09.603 --> 00:06:14.406
if I were to redefine
this whole thing as B,

00:06:14.406 --> 00:06:16.206
that would be where we intersect the

00:06:16.206 --> 00:06:18.422
vertical axis, that B right over there.

00:06:18.422 --> 00:06:20.206
I could rewrite this whole
thing, but that would

00:06:20.206 --> 00:06:21.874
just be a pain so I'll
just call this B, but

00:06:21.874 --> 00:06:24.246
this whole thing is B and then we'd have

00:06:24.246 --> 00:06:27.753
an upward sloping line
assuming that C1 is positive.

00:06:27.753 --> 00:06:29.361
It's going to have a slope less than one.

00:06:29.361 --> 00:06:31.207
We're assuming that people
won't be able to spend

00:06:31.207 --> 00:06:33.371
more than their aggregate income.

00:06:33.371 --> 00:06:34.669
They're only going to
spend a fraction of their

00:06:34.669 --> 00:06:35.492
aggregate income.

00:06:35.492 --> 00:06:39.045
This is going to be between zero and 1.

00:06:39.045 --> 00:06:42.654
We will have our aggregate
planned expenditures

00:06:42.654 --> 00:06:45.736
would be line that might
look something like this.

00:06:45.736 --> 00:06:49.483
Aggregate planned expenditures.

00:06:49.483 --> 00:06:51.537
To think about our
Kenyesian Cross, you can't

00:06:51.537 --> 00:06:55.470
have an economy in equilibrium
if aggregate output

00:06:55.470 --> 00:06:59.936
is not equal to aggregate expenditures.

00:06:59.936 --> 00:07:01.603
To think about all of
the different scenarios

00:07:01.603 --> 00:07:04.930
where the economy is in
equilibrium, we draw a line

00:07:04.930 --> 00:07:07.237
at a 45 degree angle because
at every point on this

00:07:07.237 --> 00:07:11.336
line, output is equal to expenditures.

00:07:11.336 --> 00:07:14.339
Output is equal to
expenditures so we get our

00:07:14.339 --> 00:07:18.663
45 degree line looks something like this.

00:07:18.663 --> 00:07:20.984
Just as a little bit of
review, what this is really

00:07:20.984 --> 00:07:24.553
saying is look out of
this, if we have this

00:07:24.553 --> 00:07:26.736
aggregate planned
expenditures, this is going

00:07:26.736 --> 00:07:28.467
to be the equilibrium point.

00:07:28.467 --> 00:07:32.272
This is the point where expenditures is

00:07:32.272 --> 00:07:34.339
equal to output.

00:07:34.339 --> 00:07:38.206
If for whatever reason
the economy is performing,

00:07:38.206 --> 00:07:41.339
is outputting above
that equilibrium point,

00:07:41.339 --> 00:07:44.004
then output which is this line.

00:07:44.004 --> 00:07:46.404
This line could be used
as output or expenditures

00:07:46.404 --> 00:07:48.017
because it's the line where they're equal

00:07:48.017 --> 00:07:49.268
to each other.

00:07:49.268 --> 00:07:51.795
This is where actual
output is outperforming

00:07:51.795 --> 00:07:56.382
planned expenditures I
should say and you have

00:07:56.382 --> 00:07:58.213
all this inventory building up.

00:07:58.213 --> 00:08:00.210
You have all this inventory
building up and so the

00:08:00.210 --> 00:08:02.208
actual investment would be larger than the

00:08:02.208 --> 00:08:03.631
planned investment
because you have all that

00:08:03.631 --> 00:08:06.608
inventory built up.

00:08:06.608 --> 00:08:09.282
If output is below equilibrium,

00:08:09.282 --> 00:08:11.291
then the planned
expenditures are higher than

00:08:11.291 --> 00:08:13.296
output and so people are essentially;

00:08:13.296 --> 00:08:15.336
the economies are going
to have to actually

00:08:15.336 --> 00:08:17.290
dig in to inventory.

00:08:17.290 --> 00:08:19.799
The actual investment is
going to be lower than

00:08:19.799 --> 00:08:21.137
the planned investment.

00:08:21.137 --> 00:08:24.059
It will be dug into a
little bit because that

00:08:24.059 --> 00:08:26.588
eating into the inventory,
it would be considered

00:08:26.588 --> 00:08:28.839
to be negative investment.

00:08:28.839 --> 00:08:31.273
Now the whole reason that
I set up this whole thing,

00:08:31.273 --> 00:08:32.937
this was all review
maybe with a little bit

00:08:32.937 --> 00:08:35.172
more detail than we did in the last video,

00:08:35.172 --> 00:08:38.252
is beyond using the
Keynesian Cross for this

00:08:38.252 --> 00:08:41.287
kind of equilibrium
analysis, is to use it to

00:08:41.287 --> 00:08:43.940
go into the Keynesian
mindset of how can we

00:08:43.940 --> 00:08:46.005
actually change the
equilibrium then because

00:08:46.005 --> 00:08:48.334
if we just change the
output, it's natural if

00:08:48.334 --> 00:08:50.940
output is too high, inventories build up.

00:08:50.940 --> 00:08:52.755
People will say oh my
inventories are building up.

00:08:52.755 --> 00:08:55.188
I'm going to produce
less, output will go down.

00:08:55.188 --> 00:08:56.739
If inventories are being eaten into,

00:08:56.739 --> 00:08:58.133
they'll produce more
and we'll go back to the

00:08:58.133 --> 00:08:59.301
equilibrium.

00:08:59.301 --> 00:09:01.404
But what if the equilibrium is not where,

00:09:01.404 --> 00:09:03.933
in our opinion, the economy should be?

00:09:03.933 --> 00:09:07.162
What if it's well below full employment?

00:09:07.162 --> 00:09:10.706
What if it's well below our potential?

00:09:10.706 --> 00:09:14.000
For example, what if the
economy's potential at

00:09:14.000 --> 00:09:18.240
full employment is an
output that is something

00:09:18.240 --> 00:09:18.910
over here.

00:09:18.910 --> 00:09:20.616
You could debate what that
point is, but how do you

00:09:20.616 --> 00:09:23.263
get it to there because
you can't just increase the

00:09:23.263 --> 00:09:25.435
supply; you can't just
increase the output; that will

00:09:25.435 --> 00:09:28.272
just make our inventories build up.

00:09:28.272 --> 00:09:29.490
From a Keynesian point
of view, we could say

00:09:29.490 --> 00:09:32.742
well you want to just
shift this actual curve

00:09:32.742 --> 00:09:34.516
and there's a bunch of
ways in which you can

00:09:34.516 --> 00:09:35.671
shift the curve.

00:09:35.671 --> 00:09:37.606
In general, you can change
any of these variables

00:09:37.606 --> 00:09:40.067
right over here, all the
things that we assumed

00:09:40.067 --> 00:09:42.479
are constant, and that
would shift the curve.

00:09:42.479 --> 00:09:45.812
For example, the government
could say hey, I'm

00:09:45.812 --> 00:09:48.269
going to take; the G was at some level.

00:09:48.269 --> 00:09:50.072
What if I pop that G up?

00:09:50.072 --> 00:09:53.813
What if I turn that into
whatever our existing

00:09:53.813 --> 00:09:57.817
G is and then we add some change in G?

00:09:57.817 --> 00:10:00.066
They add some incremental.

00:10:00.066 --> 00:10:02.227
Well now this is going
to be bigger by this

00:10:02.227 --> 00:10:04.073
increment right over here.

00:10:04.073 --> 00:10:07.006
Maybe we'll call it this right over here.

00:10:07.006 --> 00:10:08.144
What will happen to the curve?

00:10:08.144 --> 00:10:10.658
It will shift up by that increment.

00:10:10.658 --> 00:10:13.007
Let's see what happens
when we shift the curve up

00:10:13.007 --> 00:10:14.814
by that increment and I'll do that in that

00:10:14.814 --> 00:10:15.723
magenta color.

00:10:15.723 --> 00:10:18.602
If we shift this curve up by delta G,

00:10:18.602 --> 00:10:21.391
if we shift it up by delta
G, it's going to look

00:10:21.391 --> 00:10:24.004
something like this.

00:10:24.004 --> 00:10:25.729
You're not changing
the slope of the curve.

00:10:25.729 --> 00:10:27.315
That's this right over here.

00:10:27.315 --> 00:10:29.225
You're just changing its
intercept, so we just

00:10:29.225 --> 00:10:30.648
added delta G up here.

00:10:30.648 --> 00:10:33.267
This would be B, the
original B plus delta G.

00:10:33.267 --> 00:10:35.736
I guess you could say it that way.

00:10:35.736 --> 00:10:39.006
Our new planned expenditures might look

00:10:39.006 --> 00:10:40.816
something like this.

00:10:40.816 --> 00:10:42.739
Our new planned expenditures
might look something

00:10:42.739 --> 00:10:44.939
like that and that's
pretty interesting because

00:10:44.939 --> 00:10:50.720
now our equilibrium point
is at a significantly

00:10:50.720 --> 00:10:53.005
higher point.

00:10:53.005 --> 00:10:56.403
Our equilibrium point, our
change in our equilibrium,

00:10:56.403 --> 00:11:00.340
so our delta in output
actually went up by more.

00:11:00.340 --> 00:11:06.007
Our delta in output was
larger than our change

00:11:06.007 --> 00:11:09.640
in spending so it seems
like it was well worth it

00:11:09.640 --> 00:11:11.561
if you believe this analysis right here.

00:11:11.561 --> 00:11:13.671
Visually the reason why
it happened was because

00:11:13.671 --> 00:11:16.462
this line right here had a lower slope.

00:11:16.462 --> 00:11:20.210
The new intersection point
between it and essentially

00:11:20.210 --> 00:11:23.337
a slope of 1, it had
to be pushed out more.

00:11:23.337 --> 00:11:24.779
What we'll see in the
last video is that this

00:11:24.779 --> 00:11:26.872
actually works out mathematically as well.

00:11:26.872 --> 00:11:28.939
It's consistent with
what we learned about the

00:11:28.939 --> 00:11:31.006
multiplier effect and
that's actually the reason

00:11:31.006 --> 00:11:33.803
algebraically why this
is happening, why you're

00:11:33.803 --> 00:11:37.882
getting a bigger change in output than the

00:11:37.882 --> 00:11:39.862
incremental shift in demand.

00:11:39.862 --> 00:11:41.604
That's because of the
multiplier effect and we'll

00:11:41.604 --> 00:11:45.000
see it in the next video.


Keynesian Cross

WEBVTT
Kind: captions
Language: en

00:00:00.425 --> 00:00:02.426
What I want to introduce
you to in this video

00:00:02.426 --> 00:00:06.429
is the idea of a Keynesian Cross.

00:00:06.429 --> 00:00:09.349
This is one of the tools of
analysis of Keynesian thinking

00:00:09.349 --> 00:00:12.131
which is really the idea
that maybe every now and then

00:00:12.131 --> 00:00:13.933
the GDP, when it's at equilibrium,

00:00:13.933 --> 00:00:15.374
isn't at an optimal state.

00:00:15.374 --> 00:00:17.736
It's operating well below potential

00:00:17.736 --> 00:00:19.667
and the way that we might be able to get.

00:00:19.667 --> 00:00:21.736
If you are a follower
of Keynesian thinking,

00:00:21.736 --> 00:00:23.007
the way that we can get it closer to,

00:00:23.007 --> 00:00:24.869
potential closer to full employment

00:00:24.869 --> 00:00:28.459
is by somehow affecting
aggregate demand in some way.

00:00:28.459 --> 00:00:29.262
What we'll see is,

00:00:29.262 --> 00:00:31.668
we're going to build up our
Keynesian Cross analysis

00:00:31.668 --> 00:00:34.996
based on what we understand
from the consumption function.

00:00:34.996 --> 00:00:36.834
We're going to first start thinking about

00:00:36.834 --> 00:00:38.932
planned expenditures.

00:00:38.932 --> 00:00:40.329
We're going to think about what happens

00:00:40.329 --> 00:00:44.062
when planned expenditures
deviates from actual output,

00:00:44.062 --> 00:00:46.928
from actual expenditures, right over here.

00:00:46.928 --> 00:00:48.600
This is very similar to
what we're done before

00:00:48.600 --> 00:00:50.401
but we're actually thinking
of it in terms of planning.

00:00:50.401 --> 00:00:52.529
Let's say we have planned expenditures,

00:00:52.529 --> 00:00:54.746
expenditures planned

00:00:54.746 --> 00:00:57.535
and we could just write the components

00:00:57.535 --> 00:00:59.063
of aggregate expenditure here.

00:00:59.063 --> 00:01:01.759
Well, you're going to
have consumer spending,

00:01:01.759 --> 00:01:04.196
you're going to have investment.

00:01:04.196 --> 00:01:05.600
I'm going to be careful here,

00:01:05.600 --> 00:01:07.201
I'm going to call it planned investment.

00:01:07.201 --> 00:01:10.858
This is exactly what firms
are looking to produce.

00:01:10.858 --> 00:01:12.729
The reason why I differentiate this here

00:01:12.729 --> 00:01:14.928
is because, if for whatever reason,

00:01:14.928 --> 00:01:17.755
aggregate expenditure
is less than they expect

00:01:17.755 --> 00:01:20.082
then they might build up inventories

00:01:20.082 --> 00:01:22.262
and those inventories get
counted as investments.

00:01:22.262 --> 00:01:24.596
Those would be excess
inventories above and beyond

00:01:24.596 --> 00:01:25.793
the planned inventories.

00:01:25.793 --> 00:01:28.793
If actual demand is higher than expended

00:01:28.793 --> 00:01:30.834
then it might eat in to inventories

00:01:30.834 --> 00:01:32.502
and when inventories are eaten into

00:01:32.502 --> 00:01:34.498
it actually takes away
from planned investments

00:01:34.498 --> 00:01:36.004
there would actually be kind of a,

00:01:36.004 --> 00:01:38.335
you would be eating into
the total investment

00:01:38.335 --> 00:01:39.129
in that situation.

00:01:39.129 --> 00:01:40.533
That's why I'm going to differentiate

00:01:40.533 --> 00:01:43.996
between planned investment
and actual investment.

00:01:43.996 --> 00:01:47.672
Then of course, you
have government spending

00:01:47.672 --> 00:01:50.392
and then finally you have net exports.

00:01:50.392 --> 00:01:54.086
For the sake of the analysis
of the Keynesian Cross,

00:01:54.086 --> 00:01:56.595
once again, this is a
super over simplification,

00:01:56.595 --> 00:02:00.382
we're going to assume that
at any given level of GDP

00:02:00.382 --> 00:02:03.382
or aggregate output that
these are all constant.

00:02:03.382 --> 00:02:05.123
That these are not really dependent

00:02:05.123 --> 00:02:07.259
on aggregate output or GDP

00:02:07.259 --> 00:02:09.592
which is of course a
huge over simplification.

00:02:09.592 --> 00:02:11.004
If we were to plot any of these

00:02:11.004 --> 00:02:15.595
versus aggregate income

00:02:15.595 --> 00:02:18.058
we'd say that they are really a flat line.

00:02:18.058 --> 00:02:23.860
Maybe planned investment might
look something like that.

00:02:23.860 --> 00:02:26.592
Maybe government spending
would look something like that.

00:02:26.592 --> 00:02:28.831
No ways at some level that's preplanned,

00:02:28.831 --> 00:02:31.596
it's exogenous to our model.

00:02:31.596 --> 00:02:33.079
It's not dependant in any way.

00:02:33.079 --> 00:02:34.525
It's an external factor.

00:02:34.525 --> 00:02:35.605
Assuming it's fixed,

00:02:35.605 --> 00:02:37.666
it's not dependent on aggregate income.

00:02:37.666 --> 00:02:40.004
So government spending
looks something like that

00:02:40.004 --> 00:02:42.797
and net exports, maybe it
looks something like that.

00:02:42.797 --> 00:02:45.690
The one factor that you can imagine

00:02:45.690 --> 00:02:46.433
because I said we're going to build

00:02:46.433 --> 00:02:47.758
on top of the consumption function

00:02:47.758 --> 00:02:51.465
that we're going to assume
is driven by aggregate income

00:02:51.465 --> 00:02:53.764
is consumption right over here.

00:02:53.764 --> 00:02:56.535
The way that this thing will look,

00:02:56.535 --> 00:02:58.401
the way that this thing will look

00:02:58.401 --> 00:02:59.518
is you have ...

00:02:59.518 --> 00:03:04.055
So let me draw another
plot right over here,

00:03:04.055 --> 00:03:05.583
draw another plot.

00:03:05.583 --> 00:03:07.920
We have aggregate income,

00:03:07.920 --> 00:03:09.980
that is going to be our
independent variable

00:03:09.980 --> 00:03:16.290
and then over here we can
just view this as expenditure.

00:03:16.290 --> 00:03:19.186
If we were just to plot consumer spending,

00:03:19.186 --> 00:03:20.389
we've seen that before

00:03:20.389 --> 00:03:22.510
especially if we assume a
linear consumption function.

00:03:22.510 --> 00:03:24.762
What we've studied in the last few videos

00:03:24.762 --> 00:03:27.257
is all linear consumption functions

00:03:27.257 --> 00:03:29.193
and depending on how you write it,

00:03:29.193 --> 00:03:30.590
but they all look something like this.

00:03:30.590 --> 00:03:34.526
They have a positive
vertical axis intercept

00:03:34.526 --> 00:03:37.193
and they have upward
slope that is less than 1.

00:03:37.193 --> 00:03:39.927
Consumption by itself would
look something like this,

00:03:39.927 --> 00:03:41.459
this would be consumer spending

00:03:41.459 --> 00:03:45.928
as a function of aggregate income.

00:03:45.928 --> 00:03:47.675
Then if you all all of
these constants to it

00:03:47.675 --> 00:03:54.529
then your graph for aggregate
planned expenditures

00:03:54.529 --> 00:03:55.758
would look something like this.

00:03:55.758 --> 00:03:57.862
if you added just in net exports

00:03:57.862 --> 00:03:59.033
it would get a little bit higher

00:03:59.033 --> 00:04:00.004
because these are constant.

00:04:00.004 --> 00:04:01.284
Any point you would add this much,

00:04:01.284 --> 00:04:03.036
if you add government a
little higher than that

00:04:03.036 --> 00:04:05.037
and if you add all of them
including planned investments

00:04:05.037 --> 00:04:06.535
you might get something that looks,

00:04:06.535 --> 00:04:08.134
and I'll do it in this
color right over here,

00:04:08.134 --> 00:04:13.665
you might get something
that looks like this.

00:04:13.665 --> 00:04:16.954
I'm just starting off
with consumer spending.

00:04:16.954 --> 00:04:20.328
I'm using a linear consumption function,

00:04:20.328 --> 00:04:21.363
you don't have to,

00:04:21.363 --> 00:04:22.732
but it makes the Keynesian Cross analysis

00:04:22.732 --> 00:04:25.465
a lot more cross like
and easier to analyse.

00:04:25.465 --> 00:04:28.069
If you add all what we
assumed to be constant things

00:04:28.069 --> 00:04:31.613
and aggregate expenditures
is going to be up here.

00:04:31.613 --> 00:04:33.037
This right over here

00:04:33.037 --> 00:04:36.006
is aggregate planned
expenditures I should say.

00:04:36.006 --> 00:04:40.132
Now, we know from the
circular flow in the economy

00:04:40.132 --> 00:04:44.205
that when an economy is at equilibrium,

00:04:44.205 --> 00:04:48.200
your aggregate output is equal
to your aggregate expenditures

00:04:48.200 --> 00:04:49.402
or your aggregate expenditures

00:04:49.402 --> 00:04:51.465
is equal to your aggregate income.

00:04:51.465 --> 00:04:53.871
Really, at an equilibrium,

00:04:53.871 --> 00:04:56.039
these two things are going to be equal.

00:04:56.039 --> 00:04:58.203
We can actually plot a line
that shows all the points

00:04:58.203 --> 00:04:59.468
that those are equal.

00:04:59.468 --> 00:05:02.930
That would be a line that
has essentially a slope of 1

00:05:02.930 --> 00:05:05.599
where Y is always equal to expenditures.

00:05:05.599 --> 00:05:10.537
It might look something like this.

00:05:10.537 --> 00:05:13.036
This is where the name
Keynesian cross comes from

00:05:13.036 --> 00:05:14.948
because essentially you
have planned expenditures

00:05:14.948 --> 00:05:18.069
and then right over here you
have the equilibrium line

00:05:18.069 --> 00:05:19.622
or what I call the equilibrium line

00:05:19.622 --> 00:05:21.931
because these are all points where income

00:05:21.931 --> 00:05:23.802
is equal to expenditure.

00:05:23.802 --> 00:05:25.676
Right over here, income
is equal to expenditure.

00:05:25.676 --> 00:05:27.121
Income is equal to expenditure.

00:05:27.121 --> 00:05:29.949
When you look at aggregate
planned expenditures

00:05:29.949 --> 00:05:32.136
or you can even view
this as aggregate demand

00:05:32.136 --> 00:05:34.864
as a function of aggregate income.

00:05:34.864 --> 00:05:36.198
This is actual point

00:05:36.198 --> 00:05:39.801
where the actual economy is at equilibrium

00:05:39.801 --> 00:05:44.081
where expenditures are actually equal to,

00:05:44.081 --> 00:05:46.726
where expenditures are
actually equal to output.

00:05:46.726 --> 00:05:48.864
Actually, it's a little bit
skewed the way I drew it

00:05:48.864 --> 00:05:51.195
but these actually
should be like a square.

00:05:51.195 --> 00:05:53.083
Actually, let me see if
I can draw a little bit

00:05:53.083 --> 00:05:55.078
clearer than that.

00:05:55.078 --> 00:05:57.462
Just so it will actually
looks like a 45 degree line.

00:05:57.462 --> 00:06:02.926
It should really be a 45
degree line like that.

00:06:02.926 --> 00:06:04.866
That seems a little bit better.

00:06:04.866 --> 00:06:08.258
That's the point at which
we are at equilibrium.

00:06:08.258 --> 00:06:09.419
Actually, I don't like that

00:06:09.419 --> 00:06:11.196
because it makes it a little
bit harder to analyse.

00:06:11.196 --> 00:06:12.799
But hopefully you get the idea.

00:06:12.799 --> 00:06:14.401
This should be a line
that's where expenditures

00:06:14.401 --> 00:06:16.597
is equal to aggregate income.

00:06:17.443 --> 00:06:19.733
Like this so it intersects at a point

00:06:19.733 --> 00:06:21.938
that's a little bit
easier for me to analyse.

00:06:21.938 --> 00:06:25.664
Now, this is where the Keynesian Cross

00:06:25.664 --> 00:06:27.112
becomes a kind of interesting tool

00:06:27.112 --> 00:06:28.852
because we could start to think about

00:06:28.852 --> 00:06:30.653
what happens in situations.

00:06:30.653 --> 00:06:35.487
This is an equilibrium level of GDP.

00:06:35.487 --> 00:06:37.314
What happens if for whatever reason

00:06:37.314 --> 00:06:39.587
that aggregate income

00:06:39.587 --> 00:06:41.650
is higher than that equilibrium level?

00:06:41.650 --> 00:06:43.181
Let's think about scenario.

00:06:43.181 --> 00:06:44.919
Let's say we're over here.

00:06:44.919 --> 00:06:46.522
Let me do that in magenta.

00:06:46.522 --> 00:06:48.250
Let's say we're over here.

00:06:48.250 --> 00:06:50.451
Let's call that Y1.

00:06:50.451 --> 00:06:51.586
What is going on?

00:06:51.586 --> 00:06:54.323
What is going on right over here at Y1?

00:06:54.323 --> 00:06:56.582
Over here, the aggregate output

00:06:56.582 --> 00:06:58.317
which is the same thing
as aggregate income

00:06:58.317 --> 00:06:59.983
is right over here.

00:06:59.983 --> 00:07:02.121
Well, this is the actually
planned expenditures,

00:07:02.121 --> 00:07:03.659
is right over here.

00:07:03.659 --> 00:07:06.919
All of these excess. All of these excess

00:07:06.919 --> 00:07:09.711
above the planned demand,

00:07:09.711 --> 00:07:12.253
these are essentially going
to be inventories building up.

00:07:12.253 --> 00:07:15.582
The economy is producing
more than it actually needs,

00:07:15.582 --> 00:07:17.913
inventories are going to build up.

00:07:17.913 --> 00:07:20.335
Firms are not selling
all of their products

00:07:20.335 --> 00:07:22.332
and that excess built up inventory

00:07:22.332 --> 00:07:24.256
is going to be reflected in investment.

00:07:24.256 --> 00:07:27.372
In this case, this delta.

00:07:27.372 --> 00:07:29.918
This delta is going to be added
to your planned investment

00:07:29.918 --> 00:07:32.314
to get what the actual
investment might be.

00:07:32.314 --> 00:07:35.320
When an economy is at that state

00:07:35.320 --> 00:07:37.147
then firms would say, "Oh my god!

00:07:37.147 --> 00:07:39.117
"We're building inventory
more than we expected.

00:07:39.117 --> 00:07:40.507
"We're not selling our products.

00:07:40.507 --> 00:07:41.919
"We're going to lower output

00:07:41.919 --> 00:07:46.265
"so there's a natural
feedback mechanism for the GDP

00:07:46.265 --> 00:07:47.812
"to go back to equilibrium."

00:07:47.812 --> 00:07:49.234
Let's think about what happens

00:07:49.234 --> 00:07:51.384
if it's below that equilibrium point.

00:07:51.384 --> 00:07:53.920
Let's say that GDP is,

00:07:53.920 --> 00:07:56.067
let's call that right over here.

00:07:56.067 --> 00:07:57.588
This is Y2.

00:07:57.588 --> 00:07:59.064
Actually, I could write it as a subscript.

00:07:59.064 --> 00:08:00.383
I don't know, I wrote a superscript there.

00:08:00.383 --> 00:08:03.649
We could call this Y2.

00:08:03.649 --> 00:08:08.911
Over here, aggregate demand
at this level of output

00:08:08.911 --> 00:08:11.662
is more than what's actually being output.

00:08:11.662 --> 00:08:13.265
People want more goods and services.

00:08:13.265 --> 00:08:14.526
Right over here,

00:08:14.526 --> 00:08:16.264
this is a deficit of output

00:08:16.264 --> 00:08:17.795
and so this shows that people

00:08:17.795 --> 00:08:19.597
will be digging into inventory.

00:08:19.597 --> 00:08:21.062
That the existing inventories

00:08:21.062 --> 00:08:22.928
or the existing investment was not enough.

00:08:22.928 --> 00:08:25.265
Or, I guess another way to think it,

00:08:25.265 --> 00:08:27.661
essentially, inventories
will be contracting.

00:08:27.661 --> 00:08:30.062
Let's say business was constant.

00:08:30.062 --> 00:08:33.080
I had a lemonade stand,
I just keep an inventory

00:08:33.080 --> 00:08:35.161
of 5 cups of lemonade on hand

00:08:35.161 --> 00:08:37.126
and I sell a cup every hour.

00:08:37.126 --> 00:08:39.326
If all of a sudden people
start buying 2 cups an hour

00:08:39.326 --> 00:08:41.862
my inventory is going to
start getting depleted

00:08:41.862 --> 00:08:43.266
and so this is what's reflected.

00:08:43.266 --> 00:08:47.537
Actual output is below what's demanded.

00:08:47.537 --> 00:08:49.158
When firms start seeing

00:08:49.158 --> 00:08:50.742
that their inventories
get depleted, they say,

00:08:50.742 --> 00:08:51.478
"Oh my god!

00:08:51.478 --> 00:08:53.199
"I don't want to run out
of my goods and services.

00:08:53.199 --> 00:08:55.131
"Let me start producing more."

00:08:55.131 --> 00:08:56.129
Then when we're talking about inventories

00:08:56.129 --> 00:08:57.800
we're really talking about goods.

00:08:57.800 --> 00:08:59.463
So let me produce more.

00:08:59.463 --> 00:09:01.546
So output will once again

00:09:01.546 --> 00:09:04.638
want to naturally go
to that feedback point.

00:09:04.638 --> 00:09:06.221
Hopefully that makes
a little bit of sense.

00:09:06.221 --> 00:09:08.608
In the next few videos we'll
be using the Keynesian Cross

00:09:08.608 --> 00:09:12.200
to think about the
Keynesian line of reasoning.

00:09:12.200 --> 00:09:14.220
If you change one of these,

00:09:14.220 --> 00:09:18.220
how that might affect the
new equilibrium level of GDP.


Consumption function with income dependent taxes

WEBVTT
Kind: captions
Language: en

00:00:00.266 --> 00:00:02.350
In the last video where we generalized

00:00:02.350 --> 00:00:04.940
the linear consumption function.

00:00:04.940 --> 00:00:08.605
I said that the tax, the
total amount of taxes,

00:00:08.605 --> 00:00:11.017
the aggregate taxes are constant,

00:00:11.017 --> 00:00:12.600
all of these were constants right here.

00:00:12.600 --> 00:00:13.940
You can merge them into a constant

00:00:13.940 --> 00:00:17.736
that ended up being our
independent variable intercept

00:00:17.736 --> 00:00:18.803
right over here.

00:00:18.803 --> 00:00:23.351
YouTube user nilsor1337
asks a very interesting

00:00:23.351 --> 00:00:24.519
and good question.

00:00:24.519 --> 00:00:29.069
"Aren't taxes in some way a
function of aggregate income?

00:00:29.069 --> 00:00:30.609
"In most modern economies

00:00:30.609 --> 00:00:32.273
"people pay a percentage of their income.

00:00:32.273 --> 00:00:36.401
"In general, the tax base
grows as aggregate income

00:00:36.401 --> 00:00:38.518
"or as GDP grows.

00:00:38.518 --> 00:00:41.187
"Is it appropriate to make this constant?"

00:00:41.187 --> 00:00:43.118
The simple answer is it
depends on how carefully

00:00:43.118 --> 00:00:44.682
you want to model it.

00:00:44.682 --> 00:00:46.680
In some cases you might just say,

00:00:46.680 --> 00:00:48.451
"Well, let's just assume
that this is a bulk tax.

00:00:48.451 --> 00:00:50.269
"We're just trying to
understand one aspect of it."

00:00:50.269 --> 00:00:52.722
You will see that in
some economics courses

00:00:52.722 --> 00:00:54.179
or some economics textbooks.

00:00:54.179 --> 00:00:56.600
The other way is you
could actually model it

00:00:56.600 --> 00:00:57.715
a little bit more realistic.

00:00:57.715 --> 00:00:59.516
You could say, "Hey, taxes really are

00:00:59.516 --> 00:01:01.448
"a function of aggregate income."

00:01:01.448 --> 00:01:05.315
We could say that T really
is going to be equal

00:01:05.315 --> 00:01:06.718
to some tax rate.

00:01:06.718 --> 00:01:12.585
I'll write that as a lower
case t times aggregate income.

00:01:12.585 --> 00:01:15.387
In a place like the U.S.,
this might be close to

00:01:15.387 --> 00:01:18.650
the 30% of aggregate income or 20%.

00:01:18.650 --> 00:01:20.248
Whatever it might be or aggregate income

00:01:20.248 --> 00:01:22.782
is what is going to go for taxes.

00:01:22.782 --> 00:01:23.969
If you do it this way,

00:01:23.969 --> 00:01:25.315
and you substitute back to this

00:01:25.315 --> 00:01:28.586
you could actually get an
expression for consumption

00:01:28.586 --> 00:01:29.804
in terms of aggregate income

00:01:29.804 --> 00:01:34.922
that takes into consideration
the idea that taxes

00:01:34.922 --> 00:01:36.651
are function of aggregate income.

00:01:36.651 --> 00:01:38.048
Just to do that algebraically,

00:01:38.048 --> 00:01:39.789
we can rewrite this expression up here.

00:01:39.789 --> 00:01:47.648
You have aggregate consumption =
my marginal propensity to consume

00:01:47.648 --> 00:01:55.556
times aggregate income +
autonomous consumption,

00:01:55.556 --> 00:01:57.941
the amount that would be
consumed no matter what.

00:01:57.941 --> 00:02:01.861
Minus the marginal propensity to consume,

00:02:01.861 --> 00:02:02.997
shows up again.

00:02:02.997 --> 00:02:07.024
Instead of writing T right over here,

00:02:07.024 --> 00:02:10.799
I'm going to write lower case t x Y,

00:02:10.799 --> 00:02:14.440
tax rate times aggregate income.

00:02:14.440 --> 00:02:19.132
Times the tax rate times aggregate income.

00:02:19.132 --> 00:02:22.361
I just took this, instead
of writing upper case T,

00:02:22.361 --> 00:02:25.463
I wrote lower case t
times aggregate income

00:02:25.463 --> 00:02:27.272
and they should be the same thing.

00:02:27.272 --> 00:02:30.671
But now we've expressed t as a
function of aggregate income.

00:02:30.671 --> 00:02:32.529
Now we can merge both of these,

00:02:32.529 --> 00:02:34.339
these are something
times aggregate income.

00:02:34.339 --> 00:02:36.196
We can combine those 2 terms.

00:02:36.196 --> 00:02:40.737
This one and this one write over here.

00:02:40.737 --> 00:02:46.599
If we factor our a
common factor of c1 x Y,

00:02:46.599 --> 00:02:48.535
we get, let me write it this way.

00:02:48.535 --> 00:02:50.241
Actually, let me just combine them first

00:02:50.241 --> 00:02:52.165
so that the algebra doesn't confuse you.

00:02:52.165 --> 00:03:00.401
We get C = c1 x Y.

00:03:00.401 --> 00:03:02.834
Marginal propensity to
consume times aggregate income

00:03:02.834 --> 00:03:04.209
and I'm going to write this one.

00:03:04.209 --> 00:03:08.906
Minus the marginal propensity
to consume times ...

00:03:08.906 --> 00:03:10.160
I'll switch the order here.

00:03:10.160 --> 00:03:11.415
Well, let me not switch the order,

00:03:11.415 --> 00:03:13.338
times the tax rate,

00:03:13.338 --> 00:03:15.669
not just the aggregate total tax value

00:03:15.669 --> 00:03:22.295
but the actual tax rate
times aggregate income.

00:03:22.295 --> 00:03:23.734
That's those 2 terms there

00:03:23.734 --> 00:03:26.400
and then we're just left with
the autonomous consumption.

00:03:26.400 --> 00:03:29.150
So, plus the autonomous consumption.

00:03:29.150 --> 00:03:31.265
Over here, we have a common factor.

00:03:31.265 --> 00:03:34.471
We can factor out the c1 and the Y,

00:03:34.471 --> 00:03:36.338
or essentially the marginal
propensity to consume

00:03:36.338 --> 00:03:38.149
and the aggregate income.

00:03:38.149 --> 00:03:40.648
This is just algebraic
manipulation right over here.

00:03:40.648 --> 00:03:45.525
We get aggregate consumption is equal to,

00:03:45.525 --> 00:03:56.609
let's see, we could write this c1(1 - t)Y.

00:03:56.609 --> 00:03:58.070
You can multiply this out to verify.

00:03:58.070 --> 00:03:59.397
If you multiply it all out

00:03:59.397 --> 00:04:04.296
then the 1st term is c1(1)Y
is this right over here

00:04:04.296 --> 00:04:08.291
and c1(-t)Y is this term right over here.

00:04:08.291 --> 00:04:13.397
Then you're left with your
autonomous consumption.

00:04:13.397 --> 00:04:14.707
This actually makes a lot of sense

00:04:14.707 --> 00:04:15.962
because when you write it like this,

00:04:15.962 --> 00:04:17.289
when you write it like this

00:04:17.289 --> 00:04:19.044
you could look at this
term right over here.

00:04:19.044 --> 00:04:20.998
What is this term right over here?

00:04:20.998 --> 00:04:26.002
Well, (1 - t)Y, if the tax rate is 30%

00:04:26.002 --> 00:04:28.964
then this 1 - 30% is going to be 70%.

00:04:28.964 --> 00:04:31.064
70% x aggregate income,

00:04:31.064 --> 00:04:33.068
that's essentially what
people get in their pockets.

00:04:33.068 --> 00:04:34.797
This whole term right over here

00:04:34.797 --> 00:04:36.868
is essentially disposable income.

00:04:36.868 --> 00:04:42.400
Disposable income right over here.

00:04:42.400 --> 00:04:43.464
We could actually,

00:04:43.464 --> 00:04:44.963
if we wanted to write this
as some other variable

00:04:44.963 --> 00:04:46.207
we could just put that
variable right over there

00:04:46.207 --> 00:04:47.465
and say it's disposable income

00:04:47.465 --> 00:04:49.297
and then it actually becomes a very simple

00:04:49.297 --> 00:04:50.398
thing to graph.

00:04:50.398 --> 00:04:51.998
We could graph this 2 different ways.

00:04:51.998 --> 00:04:56.722
If we wanted to write a
function of aggregate income

00:04:56.722 --> 00:04:59.292
we would graph it like this.

00:04:59.292 --> 00:05:01.374
Now, when we express it this way,

00:05:01.374 --> 00:05:03.796
taxes as a function of aggregate income

00:05:03.796 --> 00:05:06.208
now our vertical intercept.

00:05:06.208 --> 00:05:07.671
This is aggregate consumption.

00:05:07.671 --> 00:05:10.796
Our vertical intercept is
this term right over here.

00:05:10.796 --> 00:05:12.928
That is C [not]

00:05:12.928 --> 00:05:15.131
and our slope is all of this business.

00:05:15.131 --> 00:05:25.357
The slope of our line
is going to be C1(1 - t)

00:05:25.357 --> 00:05:27.118
and this right over here,

00:05:27.118 --> 00:05:29.397
the independent variable
is aggregate income.

00:05:29.397 --> 00:05:32.791
Another option, we could
set some other variable

00:05:32.791 --> 00:05:36.057
to what we could say disposable income.

00:05:36.057 --> 00:05:43.996
Let me call it Y disposable = (1 - t)Y

00:05:43.996 --> 00:05:45.260
then we could write this.

00:05:45.260 --> 00:05:47.621
It's essentially equal to this
business right over there.

00:05:47.621 --> 00:05:50.131
Then we could rewrite the
consumption function as

00:05:50.131 --> 00:05:56.203
aggregate consumption =
marginal propensity to consume

00:05:56.203 --> 00:06:01.449
times disposable income + sum
level of autonomous consumption.

00:06:01.449 --> 00:06:09.193
plus sum level of autonomous consumption.

00:06:09.193 --> 00:06:10.540
This actually takes us back to the basics.

00:06:10.540 --> 00:06:14.533
This takes us back to our
very original situation here

00:06:14.533 --> 00:06:16.203
where we had some autonomous consumption

00:06:16.203 --> 00:06:18.783
plus our marginal propensity to consume

00:06:18.783 --> 00:06:20.791
times disposable income.

00:06:20.791 --> 00:06:22.617
If we wanted to plot it this way

00:06:22.617 --> 00:06:24.122
as a function of disposable income,

00:06:24.122 --> 00:06:25.365
not aggregate income

00:06:25.365 --> 00:06:28.766
then it would look like this.

00:06:28.766 --> 00:06:31.087
This is consumption, and now
this is an aggregate income,

00:06:31.087 --> 00:06:34.021
this is disposable income

00:06:34.021 --> 00:06:38.921
which is the same thing as (1 - t)Y.

00:06:38.921 --> 00:06:42.000
Now, still our vertical
intercept is C [not]

00:06:42.000 --> 00:06:46.665
and our line slope is the
marginal propensity to consume.

00:06:46.665 --> 00:06:49.330
This is C1 just like that.

00:06:49.330 --> 00:06:51.789
All of these are completely
valid consumption functions

00:06:51.789 --> 00:06:55.414
and I thank nilsor1337
for bringing up a topic

00:06:55.414 --> 00:06:57.161
that actually was a
cause of confusion for me

00:06:57.161 --> 00:06:58.590
because it really does depend.

00:06:58.590 --> 00:07:01.255
Because I thought the way, he or she,

00:07:01.255 --> 00:07:02.662
originally thought about the problem.

00:07:02.662 --> 00:07:04.082
Well, taxes are a function

00:07:04.082 --> 00:07:07.858
and a lot of econ books tend
to treat this as a constant.

00:07:07.858 --> 00:07:10.162
That is actually just
an assumption they make

00:07:10.162 --> 00:07:11.923
to often simplify the calculations.

00:07:11.923 --> 00:07:13.653
If they don't want to make that assumption

00:07:13.653 --> 00:07:17.524
you can still show that
it is a linear function,

00:07:17.524 --> 00:07:21.296
that aggregate consumption
is still a linear function

00:07:21.296 --> 00:07:25.000
of aggregate income.


Generalized linear consumption function

WEBVTT
Kind: captions
Language: en

00:00:00.220 --> 00:00:02.737
Male: In the last video,
we began our exploration

00:00:02.737 --> 00:00:04.736
of what a consumption function is.

00:00:04.736 --> 00:00:06.331
It's a fairly straightforward idea.

00:00:06.331 --> 00:00:08.234
It's a function that describes how

00:00:08.234 --> 00:00:12.138
aggregate income can drive
aggregate consumption.

00:00:12.138 --> 00:00:14.479
We started with a fairly
simple model of this,

00:00:14.479 --> 00:00:16.233
a fairly simple consumption function.

00:00:16.233 --> 00:00:17.536
It was a linear one.

00:00:17.536 --> 00:00:19.313
You had some base level of consumption,

00:00:19.313 --> 00:00:21.007
regardless of aggregate income,

00:00:21.007 --> 00:00:22.977
and then you had some level of consumption

00:00:22.977 --> 00:00:25.143
that was essentially induced by having

00:00:25.143 --> 00:00:27.276
some disposable income.

00:00:27.276 --> 00:00:30.149
When we plotted this linear
model, we got a line.

00:00:30.149 --> 00:00:32.005
We got a line right over here.

00:00:32.005 --> 00:00:33.400
I pointed out in the last video

00:00:33.400 --> 00:00:35.312
this does not have to be the only way

00:00:35.312 --> 00:00:37.413
that a consumption
function can be described.

00:00:37.413 --> 00:00:39.867
You might use some fancier
mathematical tools.

00:00:39.867 --> 00:00:42.137
Maybe you can construct
a consumption function.

00:00:42.137 --> 00:00:43.360
You have an argument.

00:00:43.360 --> 00:00:45.002
You would argue that
the marginal propensity

00:00:45.002 --> 00:00:47.532
to consume is higher at lower levels

00:00:47.532 --> 00:00:50.401
of disposable income and
that it kind of tapers out

00:00:50.401 --> 00:00:52.199
as disposable income, as aggregate

00:00:52.199 --> 00:00:54.004
disposable income goes up.

00:00:54.004 --> 00:00:55.822
You might think that maybe you should have

00:00:55.822 --> 00:00:57.741
a fancier consumption function

00:00:57.741 --> 00:00:59.902
that when you graph it
would look like this

00:00:59.902 --> 00:01:01.407
and then you would have to use things

00:01:01.407 --> 00:01:03.872
fancier than just what
we used right over here.

00:01:03.872 --> 00:01:05.400
What I want to do in this video

00:01:05.400 --> 00:01:08.153
is focus more on a linear model.

00:01:08.153 --> 00:01:10.074
The reason why I'm going to focus on

00:01:10.074 --> 00:01:12.817
a linear model is because,
one, it's simpler.

00:01:12.817 --> 00:01:14.486
It'll be easier to manipulate.

00:01:14.486 --> 00:01:16.933
It's also the model that tends to be used

00:01:16.933 --> 00:01:18.736
right when people are starting to digest

00:01:18.736 --> 00:01:20.668
things like consumption functions

00:01:20.668 --> 00:01:24.133
and building on them to learn about things

00:01:24.133 --> 00:01:25.600
like, and we'll do this in a few videos,

00:01:25.600 --> 00:01:27.129
the Keynesian Cross.

00:01:27.129 --> 00:01:29.160
What I'm going to do is,
I'm going to do two things.

00:01:29.160 --> 00:01:31.069
I'm going to generalize this linear

00:01:31.069 --> 00:01:32.935
consumption function,
and I'm going to make it

00:01:32.935 --> 00:01:35.334
a function not just of disposal income,

00:01:35.334 --> 00:01:38.067
not just of aggregate disposable income,

00:01:38.067 --> 00:01:39.493
which is what we did in the last video,

00:01:39.493 --> 00:01:43.131
but as a function of
income, of aggregate income.

00:01:43.131 --> 00:01:45.566
Then we will plot that generalized one

00:01:45.566 --> 00:01:46.820
based on the variables.

00:01:46.820 --> 00:01:48.075
It's really going to be the same thing.

00:01:48.075 --> 00:01:49.402
We're just not going to use these numbers.

00:01:49.402 --> 00:01:51.071
We're going to use
variables in their place.

00:01:51.071 --> 00:01:54.408
Let's give ourselves a
linear consumption function.

00:01:54.408 --> 00:01:58.707
We can say that aggregate consumption

00:01:58.707 --> 00:02:00.266
where we're going to have some base level

00:02:00.266 --> 00:02:02.390
of consumption no matter
what, even if people

00:02:02.390 --> 00:02:04.810
have no aggregate income,
they need to survive.

00:02:04.810 --> 00:02:06.063
They need food on the table.

00:02:06.063 --> 00:02:08.476
Maybe they'll have to dig
in savings somehow to do it.

00:02:08.476 --> 00:02:10.663
So, some base level of consumption.

00:02:10.663 --> 00:02:13.892
I'll call that lower case c sub zero.

00:02:13.892 --> 00:02:17.394
Or lowercase c with a subscript
of zero right over there.

00:02:17.394 --> 00:02:20.328
That's the base level
of aggregate consumption

00:02:20.328 --> 00:02:23.991
or it's sometimes referred
to as autonomous consumption.

00:02:23.991 --> 00:02:30.922
This is autonomous
consumption because people

00:02:30.922 --> 00:02:32.662
will do it on their own, or in aggregate

00:02:32.662 --> 00:02:34.265
they will do it on their
own, even if they have

00:02:34.265 --> 00:02:36.451
no aggregate income.

00:02:36.451 --> 00:02:39.591
Then we will have the part that is due,

00:02:39.591 --> 00:02:42.396
directly due, to having
some aggregate income.

00:02:42.396 --> 00:02:44.884
We call that the induced consumption,

00:02:44.884 --> 00:02:46.379
because you can view it as being induced

00:02:46.379 --> 00:02:48.258
by having some aggregate income.

00:02:48.258 --> 00:02:51.194
Above and beyond what the
base level of consumption,

00:02:51.194 --> 00:02:54.382
people are going to consume some fraction

00:02:54.382 --> 00:02:56.219
of their disposable income.

00:02:56.219 --> 00:03:04.217
So we'll say disposable income.

00:03:04.217 --> 00:03:05.733
They're not going to consume all

00:03:05.733 --> 00:03:06.639
of their disposable income.

00:03:06.639 --> 00:03:07.736
They might save some of it.

00:03:07.736 --> 00:03:09.468
So they're going to consume the fraction

00:03:09.468 --> 00:03:12.664
that's essentially their
marginal propensity to consume.

00:03:12.664 --> 00:03:17.051
This right over here, I'll
do that in this orange color.

00:03:17.051 --> 00:03:22.367
Marginal propensity to consume.

00:03:22.367 --> 00:03:23.753
Hopefully this makes intuitive sense.

00:03:23.753 --> 00:03:25.317
This says, look, if this was 100,

00:03:25.317 --> 00:03:27.646
people are going to
consume 100 no matter what,

00:03:27.646 --> 00:03:30.389
100 billion whatever
your unit of currency is.

00:03:30.389 --> 00:03:31.725
Now, if their marginal propensity

00:03:31.725 --> 00:03:34.651
to consume is, let's say, it is 1/3.

00:03:34.651 --> 00:03:37.313
You have now above and beyond this

00:03:37.313 --> 00:03:40.581
people have disposable
income of let's say 900,

00:03:40.581 --> 00:03:43.644
this is saying that
they want to consume 1/3

00:03:43.644 --> 00:03:46.481
of that disposable income they're getting.

00:03:46.481 --> 00:03:48.186
That is, if you give them 900 of extra

00:03:48.186 --> 00:03:50.050
disposable income, they're propensity

00:03:50.050 --> 00:03:52.730
to consume that incremental income,

00:03:52.730 --> 00:03:54.146
they're going to consume 1/3 of it.

00:03:54.146 --> 00:03:56.318
So this would be 1/3, so it would be 900.

00:03:56.318 --> 00:03:57.782
Let me give an example.

00:03:57.782 --> 00:04:00.587
If you had a situation,
you could have a situation,

00:04:00.587 --> 00:04:05.447
where c-nought is equal to 100.

00:04:05.447 --> 00:04:15.156
If you have disposable
income is equal to 900,

00:04:15.156 --> 00:04:18.315
and c1 is equal to 1/3, or we could say

00:04:18.315 --> 00:04:21.886
0.333 repeating forever, c1 is 1/3.

00:04:21.886 --> 00:04:23.584
Then this makes sense.

00:04:23.584 --> 00:04:25.721
On their own people
would consume this much,

00:04:25.721 --> 00:04:27.319
but now they have this disposable income.

00:04:27.319 --> 00:04:29.227
Their marginal propensity to consume

00:04:29.227 --> 00:04:30.914
if you give them 900 extra of income,

00:04:30.914 --> 00:04:33.178
they're going to consume 1/3 of that.

00:04:33.178 --> 00:04:35.473
So then you're going to
have, your consumption

00:04:35.473 --> 00:04:38.185
is going to be equal to, for
this case right over here,

00:04:38.185 --> 00:04:47.794
your consumption is going to
be 100 plus 1/3 times 900.

00:04:47.794 --> 00:04:49.766
So your consumption in this situation,

00:04:49.766 --> 00:04:53.542
your induced consumption, 1/3 times 900,

00:04:53.542 --> 00:04:56.931
would be 300, maybe it's
in billions of dollars,

00:04:56.931 --> 00:04:58.458
300 billion dollars.

00:04:58.458 --> 00:05:00.669
Then your autonomous
consumption would be 100.

00:05:00.669 --> 00:05:04.927
They would add up to 400.

00:05:04.927 --> 00:05:07.869
Once again, this is autonomous
and this is induced.

00:05:07.869 --> 00:05:16.091
Autonomous, this right over
here is induced consumption.

00:05:16.091 --> 00:05:17.915
Now, I did write it in general terms.

00:05:17.915 --> 00:05:21.208
I'm using variables here
instead of, or constants, really

00:05:21.208 --> 00:05:25.621
instead of using the numbers
we saw in the last example.

00:05:25.621 --> 00:05:27.578
But I also said that I would express

00:05:27.578 --> 00:05:30.950
aggregate consumption
as a function not just

00:05:30.950 --> 00:05:33.714
of disposable income
but of aggregate income;

00:05:33.714 --> 00:05:35.702
not just of aggregate disposable income

00:05:35.702 --> 00:05:37.214
but aggregate income.

00:05:37.214 --> 00:05:39.383
The relationship is fairly simple between

00:05:39.383 --> 00:05:42.131
disposable income and overall income.

00:05:42.131 --> 00:05:46.194
We saw over here, in
aggregate, you have income,

00:05:46.194 --> 00:05:47.979
but the government in
most modern economies

00:05:47.979 --> 00:05:50.382
takes some fraction of that out for taxes.

00:05:50.382 --> 00:05:53.195
What's left over is disposable income.

00:05:53.195 --> 00:05:57.004
Just a reminder, income in aggregate,

00:05:57.004 --> 00:05:58.540
aggregate income is the same thing as

00:05:58.540 --> 00:05:59.625
aggregate expenditures,

00:05:59.625 --> 00:06:01.052
which is the same thing
as aggregate output.

00:06:01.052 --> 00:06:04.382
This right over here is GDP.

00:06:04.382 --> 00:06:06.541
So this right over here is, let me do this

00:06:06.541 --> 00:06:08.867
in a color, I've used
almost all my colors.

00:06:08.867 --> 00:06:11.248
This is equal to GDP.

00:06:11.248 --> 00:06:14.649
Disposable income is essentially GDP,

00:06:14.649 --> 00:06:20.890
or you could say aggregate
income, minus taxes.

00:06:20.890 --> 00:06:22.947
I'm going to do the taxes
in a different color.

00:06:22.947 --> 00:06:26.594
Minus taxes.

00:06:26.594 --> 00:06:27.987
So we can express disposable income

00:06:27.987 --> 00:06:32.120
as aggregate income, this right over here

00:06:32.120 --> 00:06:36.873
is the same thing as
aggregate income minus taxes.

00:06:36.873 --> 00:06:38.992
We could rewrite our
whole thing over again.

00:06:38.992 --> 00:06:43.801
Aggregate consumption is equal
to autonomous consumption

00:06:43.801 --> 00:06:46.323
plus the marginal propensity to consume

00:06:46.323 --> 00:06:51.739
times aggregate income,
which is the same thing

00:06:51.739 --> 00:06:58.507
as GDP, times aggregate
income minus taxes.

00:06:58.507 --> 00:07:01.179
We fully generalized
our consumption function

00:07:01.179 --> 00:07:04.328
and now we've written it as a
function of aggregate income,

00:07:04.328 --> 00:07:06.999
not just aggregate disposable income.

00:07:06.999 --> 00:07:09.268
To make you comfortable
that this is still a line

00:07:09.268 --> 00:07:11.945
if we were to plot it as a function

00:07:11.945 --> 00:07:14.213
of aggregate income instead
of disposable income,

00:07:14.213 --> 00:07:16.419
let me manipulate this thing a little bit.

00:07:16.419 --> 00:07:19.342
We could distribute c1, which is our

00:07:19.342 --> 00:07:21.595
marginal propensity to consume, and we get

00:07:21.595 --> 00:07:27.198
aggregate consumption is equal
to autonomous consumption

00:07:27.198 --> 00:07:28.681
and then we're going to distribute this,

00:07:28.681 --> 00:07:31.196
plus c, so we're going to multiply it

00:07:31.196 --> 00:07:32.431
times both of these terms,

00:07:32.431 --> 00:07:34.599
plus our marginal propensity to consume

00:07:34.599 --> 00:07:38.640
times aggregate income,

00:07:38.640 --> 00:07:41.883
and then minus our marginal
propensity to consume

00:07:41.883 --> 00:07:46.799
times our taxes.

00:07:46.799 --> 00:07:50.142
Since we want it as a
function of aggregate income,

00:07:50.142 --> 00:07:52.059
everything else here is really a constant.

00:07:52.059 --> 00:07:54.059
We're assuming that those
aren't going to change.

00:07:54.059 --> 00:07:55.421
Those are constant variables.

00:07:55.421 --> 00:07:57.392
What we could do is we could rewrite this

00:07:57.392 --> 00:07:59.330
in a form that you're
probably familiar with.

00:07:59.330 --> 00:08:01.266
Back in algebra class
you probably remember

00:08:01.266 --> 00:08:07.403
you can write it in the form y=mx+b where

00:08:07.403 --> 00:08:09.594
x is the independent variable,

00:08:09.594 --> 00:08:11.191
y is the dependent variable.

00:08:11.191 --> 00:08:12.256
If you were to plot this,

00:08:12.256 --> 00:08:17.899
on the horizontal axis is your x axis,

00:08:17.899 --> 00:08:20.350
your vertical axis is your y axis.

00:08:20.350 --> 00:08:22.272
This right over here
would have a y intercept,

00:08:22.272 --> 00:08:26.664
or your vertical axis intercept
of b, right over there.

00:08:26.664 --> 00:08:29.009
Then it would be a line with slope m.

00:08:29.009 --> 00:08:32.730
If you were to take your
rise divided by your run,

00:08:32.730 --> 00:08:34.409
or how much you move up
when you move to the right

00:08:34.409 --> 00:08:38.330
a certain amount, that gives you your m.

00:08:38.330 --> 00:08:40.138
Slope is equal to m.

00:08:40.138 --> 00:08:41.662
The same analogy is here.

00:08:41.662 --> 00:08:43.880
We can rewrite this in that form,

00:08:43.880 --> 00:08:46.828
where our dependent
variable is no longer y.

00:08:46.828 --> 00:08:48.956
Our dependent variable
is aggregate consumption.

00:08:48.956 --> 00:08:53.161
Our independent variable is
not x, it is aggregate income.

00:08:53.161 --> 00:08:54.602
So let's write it in that form.

00:08:54.602 --> 00:08:57.868
We can write it as dependent variable, c,

00:08:57.868 --> 00:08:59.471
which we'll plot on the vertical axis,

00:08:59.471 --> 00:09:03.367
is equal to the marginal
propensity to consume

00:09:03.367 --> 00:09:07.354
times aggregate income,

00:09:07.354 --> 00:09:08.832
I'll do that purple color,

00:09:08.832 --> 00:09:09.933
times aggregate income,

00:09:09.933 --> 00:09:15.031
plus autonomous consumption,

00:09:15.031 --> 00:09:22.280
minus marginal propensity
to consume times taxes.

00:09:22.280 --> 00:09:23.838
It looks all complicated, but you just

00:09:23.838 --> 00:09:27.082
have to realize that this
part right over here,

00:09:27.082 --> 00:09:29.612
this is all a constant.

00:09:29.612 --> 00:09:34.937
It is analogous to the
b if you were to write

00:09:34.937 --> 00:09:37.457
things in kind of
traditional slope intercept

00:09:37.457 --> 00:09:38.934
form right over here.

00:09:38.934 --> 00:09:40.790
When we plot the line, if you have no

00:09:40.790 --> 00:09:44.437
aggregate income, this is what your

00:09:44.437 --> 00:09:45.870
consumption is going to be.

00:09:45.870 --> 00:09:48.037
Let me draw that.

00:09:48.037 --> 00:09:54.847
Once again, our dependent
variable is aggregate consumption.

00:09:54.847 --> 00:09:57.190
Our independent variable
in this is no longer

00:09:57.190 --> 00:09:59.255
disposable income like
we did in the last video.

00:09:59.255 --> 00:10:04.933
It is now aggregate income.

00:10:04.933 --> 00:10:06.734
If there's no aggregate income,

00:10:06.734 --> 00:10:08.455
this is the independent
variable right over here,

00:10:08.455 --> 00:10:09.750
if there's no aggregate income,

00:10:09.750 --> 00:10:11.188
then your consumption is just going to be

00:10:11.188 --> 00:10:12.926
this value right over here.

00:10:12.926 --> 00:10:14.394
So your consumption is just going to be

00:10:14.394 --> 00:10:17.147
that value right over
there, which is c-nought

00:10:17.147 --> 00:10:20.579
minus c1 times t.

00:10:20.579 --> 00:10:25.719
Then as you have larger values of

00:10:25.719 --> 00:10:28.678
aggregate income, c1, that fraction of it,

00:10:28.678 --> 00:10:32.130
is what's going to contribute
to the induced consumption.

00:10:32.130 --> 00:10:34.517
What you essentially
have is this is the slope

00:10:34.517 --> 00:10:36.667
of our line, this right
over here is our slope.

00:10:36.667 --> 00:10:38.503
Just to kind of draw the analogy,

00:10:38.503 --> 00:10:42.085
if you were to say y
is equal to mx plus b.

00:10:42.085 --> 00:10:43.872
Actually, maybe I'll write it like this.

00:10:43.872 --> 00:10:49.658
If you were to write c is equal to m ...

00:10:49.658 --> 00:10:51.888
and I don't want to
confuse you if this m and b

00:10:51.888 --> 00:10:53.183
seem completely foreign.

00:10:53.183 --> 00:10:55.625
It comes from kind of
a traditional algebra

00:10:55.625 --> 00:10:58.109
grounding in slope and y intercept.

00:10:58.109 --> 00:11:04.919
If I were to say c is equal to my plus b,

00:11:04.919 --> 00:11:05.975
this is the slope.

00:11:05.975 --> 00:11:10.300
This is our vertical or our
dependent variable intercept

00:11:10.300 --> 00:11:11.607
right over here.

00:11:11.607 --> 00:11:13.568
That's where we intercept the dependent

00:11:13.568 --> 00:11:14.805
variable axis.

00:11:14.805 --> 00:11:16.084
And this is our slope.

00:11:16.084 --> 00:11:18.195
It's our marginal propensity to consume.

00:11:18.195 --> 00:11:21.473
Our line will look something like this,

00:11:21.473 --> 00:11:25.436
where the slope is equal to the marginal

00:11:25.436 --> 00:11:28.672
propensity to consume,
which is equal to c1.

00:11:28.672 --> 00:11:30.233
If people all of a sudden are more likely

00:11:30.233 --> 00:11:32.733
to spend a larger
fraction of their income,

00:11:32.733 --> 00:11:36.777
then the marginal propensity to consume

00:11:36.777 --> 00:11:38.941
would be higher and our
slope would be higher.

00:11:38.941 --> 00:11:40.363
We would have a line that looks like that.

00:11:40.363 --> 00:11:41.934
We always assume that the marginal

00:11:41.934 --> 00:11:44.319
propensity to consume will be less than 1.

00:11:44.319 --> 00:11:45.942
So we'll never have a slope of 1.

00:11:45.942 --> 00:11:47.637
We'll also never have a negative slope

00:11:47.637 --> 00:11:49.410
because we assume that this is positive.

00:11:49.410 --> 00:11:51.780
If people are more likely
to save than consume

00:11:51.780 --> 00:11:54.612
when they have extra
income, then this line

00:11:54.612 --> 00:11:56.101
might look something like that.

00:11:56.101 --> 00:11:57.840
It might have a lower slope.