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# Connecting the keynesian cross to the IS curve

Introduction to the Investment/Savings curve. Created by Sal Khan.

## Want to join the conversation?

- Who controls real interest rates, and what use would it be to keep them high? Wouldn't you keep them as low as possible?(6 votes)
- The central bank controls interest rates. They fluctuate this to alter the money supply in the economy as per the aims of the government (monetary policy).

If the government wants to stimulate the economy to increase the GDP, they would lower interest rates (reflationary monetary policy) so as to makes loans cheaper (more investment) and to make savings less attractive (more consumption). This would lead to a rise in the money supply thereby causing an increase in aggregate demand

On the other hand, if the government wants to combat inflation, (deflationary monetary policy) they will KEEP interest rates HIGH. this would discourage loans and make savings more attractive . The money supply in the economy will then decrease, causing a fall in aggregate demand. Producers would then drop prices to meet equilibrium and this is deflation of the economy.(15 votes)

- Why does Sal say planned expenditures are YP2, not EP2?(6 votes)
- It does seem odd, but YP is equal EP - as total expenditures in an economy equals total income. I searched Google and did find other instances of YP used as equivalent to planned expenditure.(5 votes)

- Why is the curve graphing the relation between real interest rates and investment called the IS or
**Investment**-**Saving**curve ? What does the term "saving" represent here ?(5 votes) - what is the difference between IS-LM model and AD-AS model?(1 vote)
- The IS-LM model relates interest rates to output, while the AD-AS model relates price level to output.(4 votes)

- In one book I read, it said income=income+transfer payments-taxes. It would make it more elaborate I guess. What are your views on it?(2 votes)
- That would be disposable income. In most macroeconomic models "T" isn't really just taxes. It's defined as T=taxes-transfers. Transfers includes of course everything from, in the US, food stamps and social security to unemployment benefits and pensions.

So really, disposable income is just Y-T. But T is defined as the difference between taxes and transfer payments.(2 votes)

- As interest rate changes, investment was changing. But with the change in invt., will the Expenditure curve necessarily shift as parallel?(1 vote)
- Yes, the investment increases by the same amount, regardless of GDP.(1 vote)

- Shouldn't it be a plane ? the interest rate axis, Y axis, and the EXP axis ?(1 vote)
- Think of all economic factors as being in an infinite dimensional space. Each factor may or may not affect each other. We are all connected to each other and everthing we do affects the whole. Reducing elements is the way to simplify so one can attempt to understand and make a prediction based on history.(1 vote)

- If (r) goes down and planned investments goes up would not savings be affected as well, in that it would go up?(1 vote)
- thank you for making it so simple for understanding. I was not able to get hang on it from last 2 months. You guys are awesome!

#CFAPrep(1 vote) - Why is the change in the level of income because of the investment multiplier? How exactly is the multiplier related to it?(1 vote)
- the multiplier measures the rate of change of income as a result to a change in investment(1 vote)

## Video transcript

In the last video we
hopefully got the intuition between how real interest rates might impact planned investment. We saw that if real
interest rates went up, then planned investment went down. If real interest rates went down, then planned investment went up. What we want to do in this video is take this conclusion right over here, this hopefully fairly intuitive
conclusion right over here and apply it to our Keynesian Cross and think about how real interest rates would effect overall planned expenditure and what that would do in a model like the Keynesian Cross, what that would do to our
equilibrium real GDPs. Just as a reminder, let's just draw our Keynesian Cross first, or parts of it. On this axis right over here, we have expenditures. This axis right over here, we have income. We know, from many videos now, that an economy is a equilibrium when income is equal, when aggregate real income is equal to aggregate real expenditures. Circular flow of GDP. Let's draw … Let me make a line that's all the points where Y is equal to expenditures. Along this 45 degree line right over here. This is our expenditures. At this point right over here, that should be the same value as what our aggregate income is. That's part of the Keynesian Cross. The other part is to actually plot planned expenditures relative to this and then see where they intersect. What the equilibrium for that
planned expenditure line? I'll write it here as ... I've written it in the past as planned. I just wrote out the word. Planned expenditures. We could write it as
expenditures planned, like that. It's equal to our aggregate consumption. Our aggregate consumption, we can write it as a function
of disposable income. Y - T is disposable income. Aggregat income minus aggregate taxes. I want to be very clear here. This is not saying C x Y - T. This is saying C is a function of Y - T. Give my a Y - T and I will give you a C. For the sake of our
Keynesian Cross analysis, and this is kind of kind
of what you would see in a traditional intro class, we assume that we have a
linear consumption function. We assume that our consumption functions. C as a function of disposable income. It might be something like
our autonomous consumption plus our marginal propensity to consume times our aggregate income, minus taxes. This right over here
really is multiplication. We could distribute this C 1. This is just saying C
as a function of Y - T. That's only one part of
planned expenditures. Above and beyond that, we have planned investment. We're talking about the
planned side of things. Now we know that planned investment ... In the past we viewed it as a constant, but now we know it can actually be a function of real interest rates. Above and beyond that, we have government expenditures and then net exports. For some given real interest rate, we can plot this line. The consumption function right over here is just a line with a
positive slope that intersects the vertical axis at some place up here. It has a positive intersect. All of these, for given interest rate, these are all going to be constant. Our planned expenditures would
look something like this. It might look something like that. This is YP. Let's call this YP_1. This is the YP we get when we pick … I'll just write ... I'll just rewrite the
whole thing over again. We have our consumption, which is a function of Y - T, plus the level of
planned investment at ... Let's say interest rate R1, so at some given interest rate, plus government spending, plus net exports. We see ... We've done this Keynesian Cross analysis several times now, already. This is our equilibrium level of GDP. This is where along our
planned expenditure line, where income is equal to expenditures, or output is equal to expenditures. We are equilibrium right over here. We're not eating into
inventories in an unplanned way and we're not building excessive inventory above and beyond what we had planned. Now, what I want to think about, what happens if interest
rates go from R1 to R2? What happens if interest
rates go from R1 to R2 and in particular let's assume that R2? Now, we're going have
planned investment at R2 and we're going to assume
that R2 is less than R1. We're essentially saying, what happens when interest rates go down. We already know. When interest rates go down, planned investment goes up. Everything else equal, if this thing shifts up, if this term right over
here goes from R ... if the input into it, if the
real interest rate goes down, then this whole expression
is going to go up and so you're going to have an increase. You're going to have a shifting up of your planned expenditure for any level of income. It might look something like this. It would look something like this. This delta right over here, this ... Let me do it right over here. This distance right over here is going to be your change
in planned investment. It went up because
interest rates went down. We saw that in the last video. We saw that we got to a new level, or we see now that when you shift that up, that investment goes up. Because real interest rate went down, you get to a new equilibrium point. That equilibrium point
is a higher level ... it's a higher level of GDP or income. We know from previous videos as well, that this distance right over here is the same as our multiplier times the amount that
things got bumped up. The amount that things got bumped up was the change in planned investment. Then, we multiply that
times our multiplier. Our multiplier is 1 over the marginal propensity to save, or 1 over 1- the marginal
propensity to consume. The marginal propensity to consume ... We assume it's going to be constant in order to even be able to do this map. That's this piece right over there. That is equal to our C1. The main theme here, the real big picture
here as we go on our way to constructing our ISLM model, is really that all we're seeing ... when real interest rates go up, planned investment goes down. When interest rates go down ... which is what we saw in this
example right over here. Actually, let me write this down. Y, planned expenditures 2 at
C as a function of Y - D +. Our new planned investment,
at this lower interest rate, + G + net exports. This is our Y2 right over
here, our planned expenditures. We saw in this example, when real interest rates went down, planned expenditures ... When real interest rates went down, planned investment went up. That made total planned
expenditures go up. That made total GDP go up. Now we can have another relationship, which is really very analogous to this. Really, by changing this,
we're just shifting this curve. Then, you have the multiplier
effect on our equilibrium output. The big takeaway from here is, if real interest rates go up, not only does planned investment go down, that would shift this entire curve down. Then, that would also cause our equilibrium real GDP to go down. It would go down by some multiplier, by the multiplier of
how much this goes down. If real interest rates go down, then planned investment, because of what we saw in the last video, goes up. Then, that would cause ... That would cause this whole ... That's what we did in this video. This curve would shift up. If this curve shifts up, our equilibrium GDP is going to be however much this shifted,
times the multiplier, so your equilibrium GDP is going to go up. You really have a very
similar relationship in terms of just how things move. We can plot this. Economist are famous for not always plotting the
independent variable the way you would want to. As we construct our ... What we're going to see is our IS curve. It stands for investment savings. What we're going to do and we'll talk more
about that in the future. We plot the convention is to put real interest rates on the vertical axis and to put real GDP right over here. If you want to look at this relationship, when we have a high real interest rate, we're going to have a low real GDP. When we have a low real interest rate, we're going to have a high GDP. It's going to make spending go up. If spending goes up, you have a multiplier effect. It makes our equilibrium output go up. Low interest rate, high real GDP, so you have a curve that relates. If you want to relate real
GDP to real interest rates you get a curve like this, and it's called the IS curve. IS comes for investment savings. We're really more focused
on the I part of it, the way we analyzed here. The whole reason, based
on the logic in this video and the last one as well, the whole reason why we
have this relationship is due to real interest
rates impact on investment. When you have high real interest rates, you don't have much investment. Also, you'll be sapping out of GDP. If you lower interest rates, then that makes you end up
having a lot more investment, like we saw in the last video. That will expand GDP by the multiplier that we see right over there.