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Keynesian cross and the multiplier | Macroeconomics | Khan Academy - YouTube
Channel: Khan Academy
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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
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government spending
which was a shift in our
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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
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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
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the economy by lowering taxes, they are a
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Keynesian when they say
that because if we were
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to rewind and we go back to our original
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function so if we don't
do this, if we go back to
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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
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change in taxes are,
but you would actually
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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
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positive and so you
actually have a C1, delta T.
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The negatives cancel out
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
lower aggregate output
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because if you increase
taxes, now all of a
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sudden this is a positive,
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
shift the curve down and
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then you would get to a
lower equilibrium GDP.
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This really isn't a difference between
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right leaning fiscal
policy or left leaning
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fiscal policy and
everything I've talked about
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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
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and this right over here
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
touch on a little bit
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in the last video is
whatever our change is,
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however much we shift
this aggregate planned
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expenditure curve, the
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
show you mathematically
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that it actually all works
out that the multiple is
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actually the multiplier.
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If we go back to our
original and this will just
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get a little bit mathy
right over here so I'm
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just going to rewrite it all.
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We have our planned
expenditure, just to redig
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our minds into the actual expression, the
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planned expenditure is
equal to the marginal
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propensity to consume
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
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
simple for us to manipulate
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this so let's just call
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
is equal to output.
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That is an economy in
equilibrium so let's set this.
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Let's set planned expenditures equal to
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aggregate output, which
is the same thing as
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aggregate expenditures, the same thing as
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aggregate income.
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We can just solve for
our equilibrium income.
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We can just solve for it.
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You get Y=C1xY+B, this
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,
obviously if we subtract
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C1Y, it's going to go away
and that is equal to B.
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Then we can factor out
the aggregate income from
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this, so Yx1-C1=B and
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
a drum roll, aggregate
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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
or if you haven't seen
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the video, you might
want to watch the video
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on the multiplier.
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This C1 right over here is our marginal
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propensity to consume.
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1 minus our marginal propensity to consume
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is actually - And I
don't think I've actually
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referred to it before which
let me rewrite it here
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just so that you know the
term - so C1 is equal to
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our marginal propensity to consume.
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For example, if this is
30% or 0.3, that means
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for every incremental dollar of disposable
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income I get, I want to spend $.30 of it.
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Now 1-C1, you could view
this as your marginal
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propensity to save.
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If I'm going to spend
30%, that means I'm going
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to save 70%.
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This is just saying
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
going to save 70% of it.
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This whole thing, this is the marginal
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propensity to consume.
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This entire denominator
is the marginal propensity
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to save and then one over
that, so 1/1-C1 which
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is the the same thing
as 1/marginal propensity
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to save, that is the multiplier.
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We saw that a few videos ago.
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If you take this infinite
geometric series,
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if we just think through
how money spends, if I
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spend some money on some
good or service, the
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person who has that
money as income is going
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to spend some fraction
of it based on their
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marginal propensity to
consume and we're assuming
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that it's constant
throughout the economy at all
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income levels for this
model right over here.
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Then they'll spend some
of it and then the person
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that they spend it on,
they're going to spend
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some fraction.
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When you keep adding all
that infinite series up,
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you actually get this
multiplier right over here.
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This is equal to our multiplier.
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For example, if B gets
shifted up by any amount,
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let's say B gets shifted
up and it could get
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shifted up by changes in any of this stuff
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right over here.
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Net exports can change,
planned investments
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can change, could be shifted up or down.
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The impact on GDP is
going to be whatever that
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shift is times the multiplier.
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We saw it before.
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If, for example, if C1=0.6, that means for
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every incremental disposable
dollar, people will
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spend 60% of it.
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That means that the
marginal propensity to save
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is equal to 40%.
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They're going to save
40% of any incremental
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disposable dollar and
then the multiplier is
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going to be one over
that, is going to be 1/0.4
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which is the same thing
as one over two-fifths,
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which is the same thing
as five-halves, which
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is the same thing as 2.5.
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For example, in this
situation, we just saw that
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Y, the equilibrium Y is
going to be 2.5 times
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whatever all of this other business is.
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If we change B by, let's
say, $1 billion and
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maybe if we increase B by $1 billion.
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We might increase B by
$1 billion by increasing
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government spending by $1
billion or maybe having
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this whole term including
this negative right
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over here become less
negative by $1 billion.
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Maybe we have planned
investment increase by
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$1 billion and that could
actually be done a little
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bit with tax policy too
by letting companies
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maybe depreciate their assets faster.
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If we could increase net
exports by $1 billion.
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Essentially any way that we
increase B by $1 billion,
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that'll increase GDP by
$2.5 billion, 2.5 times
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our change in B.
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We can write this down this way.
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Our change in Y is going
to be 2.5 times our
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change in B.
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Another way to think
about it when you write
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the expression like
this, if you said Y is a
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function of B, then you
would say look the slope
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is 2.5, so change in Y over change in B is
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equal to 2.5, but I just
wanted to right this
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to show you that this isn't some magical
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voodoo that we're doing.
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This is what we looked at
visually when we looked
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at the Keynesian Cross.
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This is really just describing the same
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multiplier effect that
we saw in previous videos
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and where we actually derived
the actual multiplier.
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