0:00:00.472,0:00:02.870
In the last video, we saw[br]how the Keynesian Cross

0:00:02.870,0:00:05.670
could help us visualize an increase in

0:00:05.670,0:00:07.691
government spending[br]which was a shift in our

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aggregate planned expenditure[br]line right over here

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and we saw how the[br]actual change, the actual

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increase in output if you take all the

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assumptions that we[br]took in this, the actual

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change in output and[br]aggregate income was larger

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than the change in government spending.

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You might say okay,[br]Keynesian thinking, this

0:00:28.539,0:00:30.400
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.[br]I'm not a believer in

0:00:34.803,0:00:36.206
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

0:00:41.461,0:00:44.464
poo-pooed more by the[br]right and embraced more

0:00:44.464,0:00:49.939
by the left, most of the[br]mainstream right policies,

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especially in the US,[br]have actually been very

0:00:51.692,0:00:52.691
Keynesian.

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They just haven't been[br]by manipulating this

0:00:54.207,0:00:56.000
variable right over here.

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For example, when people[br]talk about expanding

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the economy by lowering taxes, they are a

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Keynesian when they say[br]that because if we were

0:01:03.869,0:01:06.077
to rewind and we go back to our original

0:01:06.077,0:01:08.943
function so if we don't[br]do this, if we go back to

0:01:08.943,0:01:15.560
just having our G here,[br]we're now back on this

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orange line, our original[br]planned expenditure,

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you could, based on this[br]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[br]reason why this is going

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to shift the whole curve[br]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[br]propensity to consume, we're

0:01:43.709,0:01:45.006
assuming is positive.

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There's a negative out here.

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When you multiply it[br]by a negative, when you

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multiply a decrease by[br]a negative, this is a

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negative change in taxes,[br]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[br]up in this case and

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depending on what the[br]actual magnitude of the

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change in taxes are,[br]but you would actually

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shift up and the amount[br]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[br]planned expenditures -

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but the amount you[br]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[br]that you would move up,

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

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positive and so you[br]actually have a C1, delta T.

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The negatives cancel out[br]so that's actually how

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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[br]lower aggregate output

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because if you increase[br]taxes, now all of a

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sudden this is a positive,[br]this is a positive

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and then you would shift the curve by that

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much.

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You would actually[br]shift the curve down and

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then you would get to a[br]lower equilibrium GDP.

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This really isn't a difference between

0:03:09.011,0:03:12.902
right leaning fiscal[br]policy or left leaning

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fiscal policy and[br]everything I've talked about

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so far at the end of the[br]last video and this video

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really has been fiscal policy.

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This has been the spending[br]lever of fiscal policy

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and this right over here[br]has been the taxing lever

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of fiscal policy.

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If you believe either of those can effect

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aggregate output, then you are essentially

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subscribing to the Keynesian model.

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Now one thing that I did[br]touch on a little bit

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in the last video is[br]whatever our change is,

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however much we shift[br]this aggregate planned

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expenditure curve, the[br]change in our output

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actually was some multiple of that.

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What I want to do now is[br]show you mathematically

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that it actually all works[br]out that the multiple is

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actually the multiplier.

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If we go back to our[br]original and this will just

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get a little bit mathy[br]right over here so I'm

0:03:58.743,0:04:00.204
just going to rewrite it all.

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We have our planned[br]expenditure, just to redig

0:04:04.196,0:04:07.289
our minds into the actual expression, the

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planned expenditure is[br]equal to the marginal

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propensity to consume[br]times aggregate income

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and then you're going to have all of this

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business right over here.

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We're just going to go[br]with the original one,

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not what I changed.

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All this business, let's just call this B.

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That will just make it[br]simple for us to manipulate

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this so let's just call[br]of this business right

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over here B.

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We could substitute that back in later.

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We know that an economy is in equilibrium

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when planned expenditures[br]is equal to output.

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That is an economy in[br]equilibrium so let's set this.

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Let's set planned expenditures equal to

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aggregate output, which[br]is the same thing as

0:04:45.471,0:04:46.957
aggregate expenditures, the same thing as

0:04:46.957,0:04:49.211
aggregate income.

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We can just solve for[br]our equilibrium income.

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We can just solve for it.

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You get Y=C1xY+B, this[br]is going to look very

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familiar to you in a second.

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Subtract C1xY from both sides.

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Y-C1Y, that's the left-hand side now.

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On the right-hand side,[br]obviously if we subtract

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C1Y, it's going to go away[br]and that is equal to B.

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Then we can factor out[br]the aggregate income from

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this, so Yx1-C1=B and[br]then we divide both sides

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by 1-C1 and we get, that cancels out.

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I'll write it right over here.

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We get, a little bit of[br]a drum roll, aggregate

0:05:41.794,0:05:45.603
income, our equilibrium, aggregate income,

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aggregate output.

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GDP is going to be equal to 1/1-C1xB.

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Remember B was all this business up here.

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Now what is this?

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You might remember this[br]or if you haven't seen

0:06:03.287,0:06:04.737
the video, you might[br]want to watch the video

0:06:04.737,0:06:06.012
on the multiplier.

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This C1 right over here is our marginal

0:06:08.496,0:06:12.090
propensity to consume.

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1 minus our marginal propensity to consume

0:06:14.620,0:06:15.806
is actually - And I[br]don't think I've actually

0:06:15.806,0:06:18.041
referred to it before which[br]let me rewrite it here

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just so that you know the[br]term - so C1 is equal to

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our marginal propensity to consume.

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For example, if this is[br]30% or 0.3, that means

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for every incremental dollar of disposable

0:06:31.873,0:06:34.954
income I get, I want to spend $.30 of it.

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Now 1-C1, you could view[br]this as your marginal

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propensity to save.

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If I'm going to spend[br]30%, that means I'm going

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to save 70%.

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This is just saying[br]I'm going to save 1-C1.

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If I'm spending 30% of that incremental

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disposable dollar, then I'm[br]going to save 70% of it.

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This whole thing, this is the marginal

0:06:56.470,0:06:57.536
propensity to consume.

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This entire denominator[br]is the marginal propensity

0:07:00.545,0:07:06.138
to save and then one over[br]that, so 1/1-C1 which

0:07:06.138,0:07:08.544
is the the same thing[br]as 1/marginal propensity

0:07:08.544,0:07:11.136
to save, that is the multiplier.

0:07:11.136,0:07:12.475
We saw that a few videos ago.

0:07:12.475,0:07:14.207
If you take this infinite[br]geometric series,

0:07:14.207,0:07:16.203
if we just think through[br]how money spends, if I

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spend some money on some[br]good or service, the

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person who has that[br]money as income is going

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to spend some fraction[br]of it based on their

0:07:23.536,0:07:25.739
marginal propensity to[br]consume and we're assuming

0:07:25.739,0:07:27.802
that it's constant[br]throughout the economy at all

0:07:27.802,0:07:30.909
income levels for this[br]model right over here.

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Then they'll spend some[br]of it and then the person

0:07:33.612,0:07:35.000
that they spend it on,[br]they're going to spend

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some fraction.

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When you keep adding all[br]that infinite series up,

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you actually get this[br]multiplier right over here.

0:07:41.749,0:07:48.738
This is equal to our multiplier.

0:07:48.738,0:07:54.408
For example, if B gets[br]shifted up by any amount,

0:07:54.408,0:07:57.316
let's say B gets shifted[br]up and it could get

0:07:57.316,0:07:59.138
shifted up by changes in any of this stuff

0:07:59.138,0:08:00.076
right over here.

0:08:00.076,0:08:01.789
Net exports can change,[br]planned investments

0:08:01.789,0:08:04.397
can change, could be shifted up or down.

0:08:04.397,0:08:08.627
The impact on GDP is[br]going to be whatever that

0:08:08.627,0:08:12.425
shift is times the multiplier.

0:08:12.425,0:08:13.733
We saw it before.

0:08:13.733,0:08:23.190
If, for example, if C1=0.6, that means for

0:08:23.190,0:08:25.806
every incremental disposable[br]dollar, people will

0:08:25.806,0:08:27.209
spend 60% of it.

0:08:27.209,0:08:31.773
That means that the[br]marginal propensity to save

0:08:31.773,0:08:33.871
is equal to 40%.

0:08:33.871,0:08:36.137
They're going to save[br]40% of any incremental

0:08:36.137,0:08:42.233
disposable dollar and[br]then the multiplier is

0:08:42.233,0:08:45.806
going to be one over[br]that, is going to be 1/0.4

0:08:45.806,0:08:48.192
which is the same thing[br]as one over two-fifths,

0:08:48.192,0:08:51.292
which is the same thing[br]as five-halves, which

0:08:51.292,0:08:53.959
is the same thing as 2.5.

0:08:53.959,0:08:58.190
For example, in this[br]situation, we just saw that

0:08:58.190,0:09:01.876
Y, the equilibrium Y is[br]going to be 2.5 times

0:09:01.876,0:09:04.407
whatever all of this other business is.

0:09:04.407,0:09:08.043
If we change B by, let's[br]say, $1 billion and

0:09:08.043,0:09:12.211
maybe if we increase B by $1 billion.

0:09:12.211,0:09:14.536
We might increase B by[br]$1 billion by increasing

0:09:14.536,0:09:17.314
government spending by $1[br]billion or maybe having

0:09:17.314,0:09:20.294
this whole term including[br]this negative right

0:09:20.294,0:09:24.470
over here become less[br]negative by $1 billion.

0:09:24.470,0:09:26.204
Maybe we have planned[br]investment increase by

0:09:26.204,0:09:29.010
$1 billion and that could[br]actually be done a little

0:09:29.010,0:09:31.036
bit with tax policy too[br]by letting companies

0:09:31.036,0:09:33.074
maybe depreciate their assets faster.

0:09:33.074,0:09:35.743
If we could increase net[br]exports by $1 billion.

0:09:35.743,0:09:38.804
Essentially any way that we[br]increase B by $1 billion,

0:09:38.804,0:09:44.181
that'll increase GDP by[br]$2.5 billion, 2.5 times

0:09:44.181,0:09:45.375
our change in B.

0:09:45.375,0:09:48.003
We can write this down this way.

0:09:48.003,0:09:54.140
Our change in Y is going[br]to be 2.5 times our

0:09:54.140,0:09:55.471
change in B.

0:09:55.471,0:09:56.873
Another way to think[br]about it when you write

0:09:56.873,0:09:59.733
the expression like[br]this, if you said Y is a

0:09:59.733,0:10:02.073
function of B, then you[br]would say look the slope

0:10:02.073,0:10:08.027
is 2.5, so change in Y over change in B is

0:10:08.027,0:10:11.110
equal to 2.5, but I just[br]wanted to right this

0:10:11.110,0:10:12.339
to show you that this isn't some magical

0:10:12.339,0:10:13.804
voodoo that we're doing.

0:10:13.804,0:10:15.958
This is what we looked at[br]visually when we looked

0:10:15.958,0:10:17.043
at the Keynesian Cross.

0:10:17.043,0:10:19.628
This is really just describing the same

0:10:19.628,0:10:22.803
multiplier effect that[br]we saw in previous videos

0:10:22.803,0:10:26.803
and where we actually derived[br]the actual multiplier.