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Current time:0:00Total duration:9:57

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 planned investment went down if real interest rates went down then planned investment 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 affect overall planned expenditure and then what that would do in a model like the Keynesian cross what that would do to our equilibrium real GDP so just as a reminder so let's just draw our Keynesian cross first or parts of it so on this axis right over here we have expenditures expenditures this axis right over here we have income and we know for many videos now that an economy is in equilibrium when income is equal when aggregate income aggregate real income is equal to aggregate real expenditures so circular flow of GDP so let's draw let me make a line that's all the points where Y is equal to expenditures so along this 45-degree line right over here so this is our expenditures at this point right over here that should be the same value as what our aggregate income is now 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 is the equilibrium point on that planned expenditure line and I'll write it here as I've written it in the past as planned I just wrote out the word planned planned expenditures we could write it even as we could write it as it as expenditures planned like that and it's equal to it's equal to our aggregate consumption and our aggregate consumption we can write it as a function of disposable income Y minus T is disposable income aggregate income minus aggregate taxes and I want to be very clear here this is not saying C times y minus T this is saying C is a function of Y minus T give me a Y minus T and we'll give you a C and for the sake of our Keynesian cross analysis and this is kind of what you'd see in a traditional intro class we assume that we have a linear consumption function so we assume that our consumption function so 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 so this right over here really is multiplication we could really distribute the C one this is just saying C as a function of Y minus T so that's only one part of planned expenditures above and beyond that we have investment planned investment we're talking about the planned side of things and now we know that planned investment in the past we viewed it as we viewed it as a constant but we're now we know it can actually be a function a function of real interest rates and then above and beyond that we have government expenditures and then net exports so for some given real interest rate we can plot this line the consumption function right over here is just a is just a line with a positive slope that intersects the Y vertical axis at some place up here some has a positive intercept and so all of these for given interest rate these are all going to be constant and so our planned expenditures would look something like this so it might look something like that so this is y P let's call this YP underscore one and this is the YP we get when we pick and I'll just write so I'll just rewrite the whole thing over again so we have our consumption which is a function of y minus t plus the level of planned investment at let's say interest rate r1 so it's some at some given interest rate plus government spending plus net plus net exports and we see we've done this Keynesian cross analysis several times now already this is our equal equilibrium level of GDP this is where along our planned expenditure line where income is equal to expenditures or our output is equal to expenditures we have a balance we are at equilibrium right away or we aren't having and we're not eating into inventories an unplanned way and we're not building excessive in inventories above and beyond what we had planned now what I want to think about what happens if interest rates what happens if interest rates go from r1 to r2 so what happens if interest rates go from r1 to r2 and in particular in particular let's assume that r2 so now we're going to have planned investment at r2 and we're going to assume that r2 is less than R 1 so we're essentially saying what happens when interest rates go down well we already know when interest rates go down planned investment planned investment goes up so all 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 rates 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 expenditures for any level of income and so it might look something like this it would look something like this so this Delta right over here this let me do it right over here so this distance right over here is going to be your change in planned investment and it went up because interest rates went down we saw that in the last video and 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 and that equilibrium point is a higher level it's a higher level of GDP or income and 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 so the amount that things got bumped up was the change in planned investment and then we'd multiply that times our multiplier and our multiplier is 1 over the marginal propensity to save or 1 over 1 minus the marginal propensity to consume and the marginal propensity to consume if we assume and we assume it's going to be constant in order to even be able to do this math that's this piece right over there so that is equal to our c1 but the main theme here though real big picture here as we as we go on our way to constructing our is LM model is really that all we're seeing look interest rates 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 so actually let me write this down so why so planned expenditures - it's C as a function of Y minus T plus our new planned investment at this lower interest rate plus G plus net exports this is our y2 right over here our planned expenditures so we saw in this example when real interest rates went down planned expenditures B when real interest rates went down planned investment went up and that made planned that made total planned expenditures go up and that made total GDP go up so now we can have a another relationship which is really very analogous to this because really by changing this we're just shifting this curve and then you have the multiplier effect on our equilibrium output so 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 and then that would also cause our equilibrium real GDP to go down and 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 and then that would cause that would cause this hole that's what we did in this video this curve would shift up and if this curve shifts up our equilibrium GDP is going to be however much this shifted times the multiplier and so your equilibrium GDP is going to go up so you really have a very similar relationship in terms of just how things move and we can plant we can plot this and economists are famous for not always plotting the independent variable that where you would want to so as we construct our what we're going to see is our is curve and 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 and to put real GDP right over here and so 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 and when we have a low real interest rate we're going to have a high GDP because it helps it's going to make spending go up spending goes up you have a multiplier effect makes our equilibrium output go up so low interest rates high real GDP and 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 and is comes for investment savings but we're really more focused on the eye part of it the way we analyzed here because 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 and that also you also you'll be sapping out of GDP if you lower interest rates then that makes you get end up having a lot more investment like we saw in the last video and that will expand GDP by the multiplier that we see right over there