0:00:00.566,0:00:02.900
In the last video we[br]hopefully got the intuition

0:00:02.900,0:00:05.816
between how real interest rates

0:00:05.816,0:00:08.002
might impact planned investment.

0:00:08.002,0:00:11.233
We saw that if real[br]interest rates went up,

0:00:11.233,0:00:15.484
then planned investment went down.

0:00:15.484,0:00:17.204
If real interest rates went down,

0:00:17.204,0:00:21.149
then planned investment went up.

0:00:21.149,0:00:22.937
What we want to do in this video is

0:00:22.937,0:00:25.067
take this conclusion right over here,

0:00:25.067,0:00:28.150
this hopefully fairly intuitive[br]conclusion right over here

0:00:28.150,0:00:30.150
and apply it to our Keynesian Cross

0:00:30.150,0:00:31.734
and think about how real interest rates

0:00:31.734,0:00:34.270
would effect overall planned expenditure

0:00:34.270,0:00:35.783
and what that would do in a model

0:00:35.783,0:00:37.982
like the Keynesian Cross,

0:00:37.982,0:00:42.934
what that would do to our[br]equilibrium real GDPs.

0:00:42.934,0:00:44.600
Just as a reminder,

0:00:44.600,0:00:46.849
let's just draw our Keynesian Cross first,

0:00:46.849,0:00:48.433
or parts of it.

0:00:48.433,0:00:49.933
On this axis right over here,

0:00:49.933,0:00:52.116
we have expenditures.

0:00:52.116,0:00:55.267
This axis right over here,

0:00:55.267,0:00:57.383
we have income.

0:00:57.383,0:00:59.515
We know, from many videos now,

0:00:59.515,0:01:01.515
that an economy is a equilibrium

0:01:01.515,0:01:03.185
when income is equal,

0:01:03.185,0:01:05.648
when aggregate real income

0:01:05.648,0:01:07.868
is equal to aggregate real expenditures.

0:01:07.868,0:01:10.357
Circular flow of GDP.

0:01:10.357,0:01:11.273
Let's draw …

0:01:11.273,0:01:13.450
Let me make a line that's all the points

0:01:13.450,0:01:16.608
where Y is equal to expenditures.

0:01:16.608,0:01:19.785
Along this 45 degree line right over here.

0:01:19.785,0:01:21.358
This is our expenditures.

0:01:21.358,0:01:22.608
At this point right over here,

0:01:22.608,0:01:24.318
that should be the same value

0:01:24.318,0:01:27.023
as what our aggregate income is.

0:01:27.023,0:01:28.524
That's part of the Keynesian Cross.

0:01:28.524,0:01:29.783
The other part is to actually

0:01:29.783,0:01:32.607
plot planned expenditures relative to this

0:01:32.607,0:01:33.941
and then see where they intersect.

0:01:33.941,0:01:37.049
What the equilibrium for that[br]planned expenditure line?

0:01:37.049,0:01:38.848
I'll write it here as ...

0:01:38.848,0:01:41.049
I've written it in the past as planned.

0:01:41.049,0:01:42.384
I just wrote out the word.

0:01:42.384,0:01:45.651
Planned expenditures.

0:01:45.651,0:01:51.858
We could write it as[br]expenditures planned, like that.

0:01:51.858,0:01:55.784
It's equal to our aggregate consumption.

0:01:55.784,0:01:57.117
Our aggregate consumption,

0:01:57.117,0:02:01.116
we can write it as a function[br]of disposable income.

0:02:01.116,0:02:02.983
Y - T is disposable income.

0:02:02.983,0:02:05.583
Aggregat income minus aggregate taxes.

0:02:05.583,0:02:07.117
I want to be very clear here.

0:02:07.117,0:02:09.522
This is not saying C x Y - T.

0:02:09.522,0:02:11.856
This is saying C is a function of Y - T.

0:02:11.856,0:02:15.116
Give my a Y - T and I will give you a C.

0:02:15.116,0:02:17.439
For the sake of our[br]Keynesian Cross analysis,

0:02:17.439,0:02:18.715
and this is kind of kind[br]of what you would see

0:02:18.715,0:02:20.359
in a traditional intro class,

0:02:20.359,0:02:23.651
we assume that we have a[br]linear consumption function.

0:02:23.651,0:02:25.716
We assume that our consumption functions.

0:02:25.716,0:02:28.649
C as a function of disposable income.

0:02:28.649,0:02:31.783
It might be something like[br]our autonomous consumption

0:02:31.783,0:02:33.939
plus our marginal propensity to consume

0:02:33.939,0:02:37.783
times our aggregate income, minus taxes.

0:02:37.783,0:02:39.916
This right over here[br]really is multiplication.

0:02:39.916,0:02:42.250
We could distribute this C 1.

0:02:42.250,0:02:46.985
This is just saying C[br]as a function of Y - T.

0:02:46.985,0:02:49.856
That's only one part of[br]planned expenditures.

0:02:49.856,0:02:51.049
Above and beyond that,

0:02:51.049,0:02:53.690
we have planned investment.

0:02:53.690,0:02:55.607
We're talking about the[br]planned side of things.

0:02:55.607,0:02:57.382
Now we know that planned investment ...

0:02:57.382,0:03:00.450
In the past we viewed it as a constant,

0:03:00.450,0:03:01.859
but now we know it can actually be

0:03:01.859,0:03:05.381
a function of real interest rates.

0:03:05.381,0:03:06.941
Above and beyond that,

0:03:06.941,0:03:09.450
we have government expenditures

0:03:09.450,0:03:11.522
and then net exports.

0:03:11.522,0:03:14.117
For some given real interest rate,

0:03:14.117,0:03:15.584
we can plot this line.

0:03:15.584,0:03:17.190
The consumption function right over here

0:03:17.190,0:03:20.984
is just a line with a[br]positive slope that intersects

0:03:20.984,0:03:24.857
the vertical axis at some place up here.

0:03:24.857,0:03:26.383
It has a positive intersect.

0:03:26.383,0:03:28.316
All of these, for given interest rate,

0:03:28.316,0:03:29.941
these are all going to be constant.

0:03:29.941,0:03:34.050
Our planned expenditures would[br]look something like this.

0:03:34.050,0:03:37.318
It might look something like that.

0:03:37.318,0:03:40.608
This is YP.

0:03:40.608,0:03:43.182
Let's call this YP_1.

0:03:43.182,0:03:46.247
This is the YP we get when we pick …

0:03:46.247,0:03:47.450
I'll just write ...

0:03:47.450,0:03:49.190
I'll just rewrite the[br]whole thing over again.

0:03:49.190,0:03:50.916
We have our consumption,

0:03:50.916,0:03:53.716
which is a function of Y - T,

0:03:53.716,0:03:56.858
plus the level of[br]planned investment at ...

0:03:56.858,0:04:00.048
Let's say interest rate R1,

0:04:00.048,0:04:01.856
so at some given interest rate,

0:04:01.856,0:04:03.857
plus government spending,

0:04:03.857,0:04:07.524
plus net exports.

0:04:07.524,0:04:08.650
We see ...

0:04:08.650,0:04:10.051
We've done this Keynesian Cross analysis

0:04:10.051,0:04:11.916
several times now, already.

0:04:11.916,0:04:14.783
This is our equilibrium level of GDP.

0:04:14.783,0:04:17.251
This is where along our[br]planned expenditure line,

0:04:17.251,0:04:20.784
where income is equal to expenditures,

0:04:20.784,0:04:22.450
or output is equal to expenditures.

0:04:22.450,0:04:25.191
We are equilibrium right over here.

0:04:25.191,0:04:28.999
We're not eating into[br]inventories in an unplanned way

0:04:28.999,0:04:31.398
and we're not building excessive inventory

0:04:31.398,0:04:34.597
above and beyond what we had planned.

0:04:34.597,0:04:35.998
Now, what I want to think about,

0:04:35.998,0:04:43.731
what happens if interest[br]rates go from R1 to R2?

0:04:43.731,0:04:47.315
What happens if interest[br]rates go from R1 to R2

0:04:47.315,0:04:50.665
and in particular let's assume that R2?

0:04:50.665,0:04:54.796
Now, we're going have[br]planned investment at R2

0:04:54.796,0:04:58.316
and we're going to assume[br]that R2 is less than R1.

0:04:58.316,0:04:59.265
We're essentially saying,

0:04:59.265,0:05:01.731
what happens when interest rates go down.

0:05:01.731,0:05:02.597
We already know.

0:05:02.597,0:05:04.856
When interest rates go down,

0:05:04.856,0:05:08.798
planned investment goes up.

0:05:08.798,0:05:09.932
Everything else equal,

0:05:09.932,0:05:11.933
if this thing shifts up,

0:05:11.933,0:05:14.999
if this term right over[br]here goes from R ...

0:05:14.999,0:05:18.149
if the input into it, if the[br]real interest rate goes down,

0:05:18.149,0:05:21.332
then this whole expression[br]is going to go up

0:05:21.332,0:05:23.423
and so you're going to have an increase.

0:05:23.423,0:05:25.080
You're going to have a shifting up

0:05:25.080,0:05:26.465
of your planned expenditure

0:05:26.465,0:05:28.996
for any level of income.

0:05:28.996,0:05:31.198
It might look something like this.

0:05:31.198,0:05:34.079
It would look something like this.

0:05:34.079,0:05:37.196
This delta right over here, this ...

0:05:37.196,0:05:38.665
Let me do it right over here.

0:05:38.665,0:05:40.398
This distance right over here

0:05:40.398,0:05:44.263
is going to be your change[br]in planned investment.

0:05:44.263,0:05:46.996
It went up because[br]interest rates went down.

0:05:46.996,0:05:49.329
We saw that in the last video.

0:05:49.329,0:05:51.931
We saw that we got to a new level,

0:05:51.931,0:05:53.369
or we see now that

0:05:53.369,0:05:54.743
when you shift that up,

0:05:54.743,0:05:55.600
that investment goes up.

0:05:55.600,0:05:57.200
Because real interest rate went down,

0:05:57.200,0:05:59.684
you get to a new equilibrium point.

0:05:59.684,0:06:02.768
That equilibrium point[br]is a higher level ...

0:06:02.768,0:06:06.184
it's a higher level of GDP or income.

0:06:06.184,0:06:08.101
We know from previous videos as well,

0:06:08.101,0:06:10.133
that this distance right over here

0:06:10.133,0:06:12.768
is the same as our multiplier

0:06:12.768,0:06:15.599
times the amount that[br]things got bumped up.

0:06:15.599,0:06:17.408
The amount that things got bumped up

0:06:17.408,0:06:20.099
was the change in planned investment.

0:06:20.099,0:06:22.532
Then, we multiply that[br]times our multiplier.

0:06:22.532,0:06:24.684
Our multiplier is 1 over

0:06:24.684,0:06:27.017
the marginal propensity to save,

0:06:27.017,0:06:31.132
or 1 over 1- the marginal[br]propensity to consume.

0:06:31.132,0:06:33.102
The marginal propensity to consume ...

0:06:33.102,0:06:35.398
We assume it's going to be constant

0:06:35.398,0:06:37.199
in order to even be able to do this map.

0:06:37.199,0:06:39.266
That's this piece right over there.

0:06:39.266,0:06:42.531
That is equal to our C1.

0:06:42.531,0:06:44.266
The main theme here,

0:06:44.266,0:06:48.017
the real big picture[br]here as we go on our way

0:06:48.017,0:06:50.532
to constructing our ISLM model,

0:06:50.532,0:06:52.266
is really that all we're seeing ...

0:06:52.266,0:06:54.665
when real interest rates go up,

0:06:54.665,0:06:56.278
planned investment goes down.

0:06:56.278,0:06:57.696
When interest rates go down ...

0:06:57.696,0:07:00.126
which is what we saw in this[br]example right over here.

0:07:00.126,0:07:01.662
Actually, let me write this down.

0:07:01.662,0:07:08.198
Y, planned expenditures 2 at[br]C as a function of Y - D +.

0:07:08.198,0:07:11.778
Our new planned investment,[br]at this lower interest rate,

0:07:11.778,0:07:13.817
+ G + net exports.

0:07:13.817,0:07:17.454
This is our Y2 right over[br]here, our planned expenditures.

0:07:17.454,0:07:18.788
We saw in this example,

0:07:18.788,0:07:20.721
when real interest rates went down,

0:07:20.721,0:07:23.192
planned expenditures ...

0:07:23.192,0:07:24.691
When real interest rates went down,

0:07:24.691,0:07:26.120
planned investment went up.

0:07:26.120,0:07:29.387
That made total planned[br]expenditures go up.

0:07:29.387,0:07:31.985
That made total GDP go up.

0:07:31.985,0:07:34.054
Now we can have another relationship,

0:07:34.054,0:07:36.190
which is really very analogous to this.

0:07:36.190,0:07:38.941
Really, by changing this,[br]we're just shifting this curve.

0:07:38.941,0:07:42.587
Then, you have the multiplier[br]effect on our equilibrium output.

0:07:42.587,0:07:43.720
The big takeaway from here is,

0:07:43.720,0:07:46.024
if real interest rates go up,

0:07:46.024,0:07:49.121
not only does planned investment go down,

0:07:49.121,0:07:51.690
that would shift this entire curve down.

0:07:51.690,0:07:53.525
Then, that would also cause

0:07:53.525,0:07:57.191
our equilibrium real GDP to go down.

0:07:57.191,0:07:59.078
It would go down by some multiplier,

0:07:59.078,0:08:01.501
by the multiplier of[br]how much this goes down.

0:08:01.501,0:08:03.500
If real interest rates go down,

0:08:03.500,0:08:04.999
then planned investment,

0:08:04.999,0:08:06.388
because of what we saw in the last video,

0:08:06.388,0:08:07.417
goes up.

0:08:07.417,0:08:09.001
Then, that would cause ...

0:08:09.001,0:08:09.986
That would cause this whole ...

0:08:09.986,0:08:11.119
That's what we did in this video.

0:08:11.119,0:08:12.720
This curve would shift up.

0:08:12.720,0:08:13.916
If this curve shifts up,

0:08:13.916,0:08:16.520
our equilibrium GDP is going to be

0:08:16.520,0:08:20.084
however much this shifted,[br]times the multiplier,

0:08:20.084,0:08:23.916
so your equilibrium GDP is going to go up.

0:08:23.916,0:08:26.627
You really have a very[br]similar relationship

0:08:26.627,0:08:28.916
in terms of just how things move.

0:08:28.916,0:08:31.083
We can plot this.

0:08:31.083,0:08:33.119
Economist are famous for

0:08:33.119,0:08:35.707
not always plotting the[br]independent variable

0:08:35.707,0:08:37.499
the way you would want to.

0:08:37.499,0:08:38.787
As we construct our ...

0:08:38.787,0:08:40.217
What we're going to see is our IS curve.

0:08:40.217,0:08:42.467
It stands for investment savings.

0:08:42.467,0:08:43.301
What we're going to do

0:08:43.301,0:08:44.719
and we'll talk more[br]about that in the future.

0:08:44.719,0:08:46.317
We plot the convention is to put

0:08:46.317,0:08:48.986
real interest rates on the vertical axis

0:08:48.986,0:08:53.217
and to put real GDP right over here.

0:08:53.217,0:08:54.717
If you want to look at this relationship,

0:08:54.717,0:08:56.918
when we have a high real interest rate,

0:08:56.918,0:09:00.253
we're going to have a low real GDP.

0:09:00.253,0:09:02.885
When we have a low real interest rate,

0:09:02.885,0:09:04.253
we're going to have a high GDP.

0:09:04.253,0:09:06.253
It's going to make spending go up.

0:09:06.253,0:09:07.051
If spending goes up,

0:09:07.051,0:09:08.156
you have a multiplier effect.

0:09:08.156,0:09:10.127
It makes our equilibrium output go up.

0:09:10.127,0:09:12.460
Low interest rate, high real GDP,

0:09:12.460,0:09:15.125
so you have a curve that relates.

0:09:15.125,0:09:18.031
If you want to relate real[br]GDP to real interest rates

0:09:18.031,0:09:19.726
you get a curve like this,

0:09:19.726,0:09:21.697
and it's called the IS curve.

0:09:21.697,0:09:24.526
IS comes for investment savings.

0:09:24.526,0:09:26.531
We're really more focused[br]on the I part of it,

0:09:26.531,0:09:27.927
the way we analyzed here.

0:09:27.927,0:09:30.364
The whole reason, based[br]on the logic in this video

0:09:30.364,0:09:31.865
and the last one as well,

0:09:31.865,0:09:33.994
the whole reason why we[br]have this relationship

0:09:33.994,0:09:37.793
is due to real interest[br]rates impact on investment.

0:09:37.793,0:09:39.326
When you have high real interest rates,

0:09:39.326,0:09:41.031
you don't have much investment.

0:09:41.031,0:09:45.531
Also, you'll be sapping out of GDP.

0:09:45.531,0:09:47.125
If you lower interest rates,

0:09:47.125,0:09:50.260
then that makes you end up[br]having a lot more investment,

0:09:50.260,0:09:51.260
like we saw in the last video.

0:09:51.260,0:09:53.793
That will expand GDP by the multiplier

0:09:53.793,0:09:57.000
that we see right over there.