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In the last video we
hopefully got the intuition

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between how real interest rates

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might impact planned investment.

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We saw that if real
interest rates went up,

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then planned investment went down.

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If real interest rates went down,

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then planned investment went up.

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What we want to do in this video is

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take this conclusion right over here,

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this hopefully fairly intuitive
conclusion right over here

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and apply it to our Keynesian Cross

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and think about how real interest rates

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would effect overall planned expenditure

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and what that would do in a model

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like the Keynesian Cross,

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what that would do to our
equilibrium real GDPs.

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Just as a reminder,

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let's just draw our Keynesian Cross first,

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or parts of it.

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On this axis right over here,

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we have expenditures.

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This axis right over here,

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we have income.

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We know, from many videos now,

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that an economy is a equilibrium

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when income is equal,

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when aggregate real income

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is equal to aggregate real expenditures.

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Circular flow of GDP.

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Let's draw âŚ

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Let me make a line that's all the points

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where Y is equal to expenditures.

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Along this 45 degree line right over here.

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This is our expenditures.

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At this point right over here,

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that should be the same value

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as what our aggregate income is.

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That's part of the Keynesian Cross.

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The other part is to actually

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plot planned expenditures relative to this

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and then see where they intersect.

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What the equilibrium for that
planned expenditure line?

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I'll write it here as ...

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I've written it in the past as planned.

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I just wrote out the word.

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Planned expenditures.

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We could write it as
expenditures planned, like that.

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It's equal to our aggregate consumption.

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Our aggregate consumption,

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we can write it as a function
of disposable income.

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Y - T is disposable income.

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Aggregat income minus aggregate taxes.

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I want to be very clear here.

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This is not saying C x Y - T.

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This is saying C is a function of Y - T.

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Give my a Y - T and I will give you a C.

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For the sake of our
Keynesian Cross analysis,

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and this is kind of kind
of what you would see

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in a traditional intro class,

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we assume that we have a
linear consumption function.

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We assume that our consumption functions.

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C as a function of disposable income.

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It might be something like
our autonomous consumption

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plus our marginal propensity to consume

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times our aggregate income, minus taxes.

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This right over here
really is multiplication.

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We could distribute this C 1.

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This is just saying C
as a function of Y - T.

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That's only one part of
planned expenditures.

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Above and beyond that,

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we have planned investment.

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We're talking about the
planned side of things.

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Now we know that planned investment ...

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In the past we viewed it as a constant,

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but now we know it can actually be

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a function of real interest rates.

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Above and beyond that,

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we have government expenditures

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and then net exports.

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For some given real interest rate,

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we can plot this line.

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The consumption function right over here

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is just a line with a
positive slope that intersects

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the vertical axis at some place up here.

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It has a positive intersect.

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All of these, for given interest rate,

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these are all going to be constant.

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Our planned expenditures would
look something like this.

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It might look something like that.

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This is YP.

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Let's call this YP_1.

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This is the YP we get when we pick âŚ

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I'll just write ...

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I'll just rewrite the
whole thing over again.

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We have our consumption,

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which is a function of Y - T,

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plus the level of
planned investment at ...

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Let's say interest rate R1,

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so at some given interest rate,

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plus government spending,

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plus net exports.

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We see ...

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We've done this Keynesian Cross analysis

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several times now, already.

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This is our equilibrium level of GDP.

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This is where along our
planned expenditure line,

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where income is equal to expenditures,

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or output is equal to expenditures.

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We are equilibrium right over here.

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We're not eating into
inventories in an unplanned way

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and we're not building excessive inventory

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above and beyond what we had planned.

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Now, what I want to think about,

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what happens if interest
rates go from R1 to R2?

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What happens if interest
rates go from R1 to R2

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and in particular let's assume that R2?

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Now, we're going have
planned investment at R2

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and we're going to assume
that R2 is less than R1.

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We're essentially saying,

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what happens when interest rates go down.

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We already know.

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When interest rates go down,

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planned investment goes up.

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Everything else equal,

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if this thing shifts up,

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if this term right over
here goes from R ...

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if the input into it, if the
real interest rate goes down,

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then this whole expression
is going to go up

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and so you're going to have an increase.

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You're going to have a shifting up

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of your planned expenditure

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for any level of income.

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It might look something like this.

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It would look something like this.

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This delta right over here, this ...

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Let me do it right over here.

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This distance right over here

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is going to be your change
in planned investment.

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It went up because
interest rates went down.

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We saw that in the last video.

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We saw that we got to a new level,

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or we see now that

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when you shift that up,

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that investment goes up.

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Because real interest rate went down,

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you get to a new equilibrium point.

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That equilibrium point
is a higher level ...

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it's a higher level of GDP or income.

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We know from previous videos as well,

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that this distance right over here

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is the same as our multiplier

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times the amount that
things got bumped up.

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The amount that things got bumped up

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was the change in planned investment.

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Then, we multiply that
times our multiplier.

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Our multiplier is 1 over

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the marginal propensity to save,

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or 1 over 1- the marginal
propensity to consume.

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The marginal propensity to consume ...

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We assume it's going to be constant

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in order to even be able to do this map.

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That's this piece right over there.

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That is equal to our C1.

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The main theme here,

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the real big picture
here as we go on our way

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to constructing our ISLM model,

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is really that all we're seeing ...

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when real interest rates go up,

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planned investment goes down.

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When interest rates go down ...

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which is what we saw in this
example right over here.

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Actually, let me write this down.

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Y, planned expenditures 2 at
C as a function of Y - D +.

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Our new planned investment,
at this lower interest rate,

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+ G + net exports.

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This is our Y2 right over
here, our planned expenditures.

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We saw in this example,

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when real interest rates went down,

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planned expenditures ...

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When real interest rates went down,

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planned investment went up.

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That made total planned
expenditures go up.

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That made total GDP go up.

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Now we can have another relationship,

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which is really very analogous to this.

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Really, by changing this,
we're just shifting this curve.

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Then, you have the multiplier
effect on our equilibrium output.

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The big takeaway from here is,

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if real interest rates go up,

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not only does planned investment go down,

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that would shift this entire curve down.

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Then, that would also cause

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our equilibrium real GDP to go down.

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It would go down by some multiplier,

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by the multiplier of
how much this goes down.

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If real interest rates go down,

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then planned investment,

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because of what we saw in the last video,

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goes up.

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Then, that would cause ...

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That would cause this whole ...

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That's what we did in this video.

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This curve would shift up.

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If this curve shifts up,

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our equilibrium GDP is going to be

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however much this shifted,
times the multiplier,

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so your equilibrium GDP is going to go up.

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You really have a very
similar relationship

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in terms of just how things move.

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We can plot this.

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Economist are famous for

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not always plotting the
independent variable

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the way you would want to.

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As we construct our ...

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What we're going to see is our IS curve.

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It stands for investment savings.

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What we're going to do

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and we'll talk more
about that in the future.

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We plot the convention is to put

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real interest rates on the vertical axis

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and to put real GDP right over here.

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If you want to look at this relationship,

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when we have a high real interest rate,

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we're going to have a low real GDP.

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When we have a low real interest rate,

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we're going to have a high GDP.

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It's going to make spending go up.

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If spending goes up,

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you have a multiplier effect.

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It makes our equilibrium output go up.

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Low interest rate, high real GDP,

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so you have a curve that relates.

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If you want to relate real
GDP to real interest rates

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you get a curve like this,

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and it's called the IS curve.

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IS comes for investment savings.

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We're really more focused
on the I part of it,

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the way we analyzed here.

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The whole reason, based
on the logic in this video

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and the last one as well,

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the whole reason why we
have this relationship

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is due to real interest
rates impact on investment.

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When you have high real interest rates,

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you don't have much investment.

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Also, you'll be sapping out of GDP.

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If you lower interest rates,

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then that makes you end up
having a lot more investment,

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like we saw in the last video.

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That will expand GDP by the multiplier

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that we see right over there.