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Current time:0:00Total duration:11:45

Details on shifting aggregate planned expenditures

Video transcript

I want to now build on what we did in the last video on the Keynesian cross and planned aggregate expenditures and fill in a little bit more on the details and think about how this could be a useful of useful conceptual tool for Keynesian thinking so let's just review a little bit I'll rebuild our planned aggregate expenditure function but I'm gonna fill in a little bit of the details so let's say that we have so this is planned planned aggregate expenditures and this is going to be equal to consumption and you'll often see it in a book written like this consumption as a function of aggregate income minus taxes and I want to be very clear here they're not saying that aggregate can they're not saying that this term should be aggregate consumption times aggregate income minus taxes they're saying that consumption is a function of this right over here the same way that we would say that F is a function of X that if you give me a y minus T or essentially if you give me a disposable income right over here I will give you a consumption and so it this actually if you actually want to deal with this directly with mathematically analytically you would have to define what this function is but I'll write it like this now and then in the next step I'll actually define what our consumption function is so this is just saying a an arbitrary consumption function and it is a function of disposable income so it's going to be your consumption function plus plus your planned investment which we're going to assume is constant plus government expenditures plus net exports plus net exports and a couple of videos ago we had built some simple models for consumption function so let's put one of those in let's say that our consumption function let's say that our consumption function so consumption aggregate consumption as a function of disposable income as a function of income minus taxes let's say that's going to be equal to some autonomous expenditure plus the marginal propensity to consume maybe I don't have to keep switching colors cuz we've seen this before plus the marginal propensity to consume times this pole possible income times disposable income so now you see that consumption aggregate consumption is being defined is being defined as a function of disposable income so that's what that notation right over there means so we could substitute this function expression with this stuff in green right over here so we can say aggregate planned expenditure aggregate planned expenditure is equal to this is our consumption function so it's equal to I'll do it in that same yellow it's equal to autonomous autonomous consumption plus the marginal propensity to consume times disposable income which is aggregate income minus taxes and then of course we have the other terms plus planned investment plus government spending plus net exports plus net exports and then we can simplify this a little bit just so that makes clear what parts of this are constant and what parts aren't what parts are kind of a function of income and we're going to for the sake of this little lesson right over here you might remember a few videos ago we can have a debate whether taxes should be a function of income or not in the real world taxes really are a function of income but for the sake of this analysis worldís assumed that like investment planned investment government spending and net exports were assumed that this for the sake of our for the sake of this presentation we're going to assume that this is constant so assume assume that this is constant this is constant so if we assume that that's a constant we can multiply and actually and if we didn't assume it's a concept we could still multiply but then we would want to redefine this in terms of Y but we can distribute the c1 and so we get we get I don't have to keep rewriting that this part right over here we have our autonomous expenditures c1 times y plus c1 times aggregate income minus the marginal propensity to consume times taxes plus all of this other stuff so actually I could just copy and paste that so plus all this other stuff so let me copy it and then let me paste it plus all of this other stuff that is equal to our planned expenditures planned expenditures and now we can think about well this part right over here this is the function this is the part that really this is how aggregate income is really driving it everything else is really a constant here so let's write it in those terms let's write it in those terms we have aggregate planned expenditures is equal to the marginal propensity to consume times our aggregate income times our aggregate income that's this term right over here I'll box it off and then everything else is a constant so Plus this the C Sub Zero which was autonomous expenditures minus C sub one times T so the marginal propensity to consume times T and these are both constants for the sake of our analysis so this whole thing is a constant and then plus all that other stuff and then plus all of that other stuff there so this might look like a really fancy complicated formula but it's actually pretty straightforward because we're assuming we're assuming for the sake of our analysis that all of this all of this right over here all of this is constant so if you were to plot this right over here it would look something like this so let us plot it so really this is almost exactly what we did in the last video but we're now filling in some details so our independent variable is going to be aggregate income or GDP however you want to view it and then our vertical acts are vertical axis is expenditures expenditures expenditures and so if we wanted to plot this the constant part this thing right over here if we were to if I were to redefine this whole thing as B that would be where we intersect the vertical axis at B right over there I could rewrite this whole thing but that would just be a pain so I'll just call this B but this whole thing is B and then we'll you'd have an upward sloping line assuming that c1 is positive and it's going to have a slope less than 1 we're assuming that people won't be able to spend more than their aggregate income there and only spend a fraction of their aggregate income so this is going to be between 0 & 1 and so we will have our aggregate planned expenditures would be a line that might look something like this so aggregate planned expenditures and to think about our Keynesian cross you can't have an economy in equilibrium if output is not equal to if aggregate output is not equal to aggregate expenditures and so to think about all of the different scenarios where the economy is in equilibrium we draw a line at a 45-degree angle because at every point on this line output is equal to expenditures output is equal to expenditures so we get our 45-degree line looks something like this and so just as a little bit of review what this is really saying is look out of this if we have this if we have this aggregate planned expenditures this is going to be the equilibrium point this is the point where expenditure where expenditures is equal to output if we if for whatever reason the economy is performing is is outputting above that equilibrium point then output which is this line this line you could be used as output or expenditures because it's the line where they're equal to each other this is where actual output is outperforming expected expended or planned expenditures I should say and so you have all this inventory building up you have all this inventory building up and so the actual investment would be larger than the planned investment because you have all that inventory build up if output is below if output is below equilibrium then the planned expenditures were higher than output and so people are essentially the economy's have going to have to actually dig into inventory and so the actual investment is going to be lower than the planned investment it will be dug into a little bit because that negative that eating into the inventory it would be considered to be negative investment now the whole reason that I set up this whole thing this was all review maybe with a little bit more detail than what we did in the last video is to now beyond using the Keynesian cross for this kind of equilibrium analysis is to use it to kind of put in the go into the Keynesian mindset of well how can we actually change the equilibrium then because if we just change output it's natural if output is too high inventories build up people will say oh my inventories are building up I'm going to produce output will go down if inventories are being eaten too into they'll produce more and we'll go back to the equilibrium but what if the equilibrium is not where in our opinion the economy should be what if it what if it's well below full employment where what if it's well below our potential and so for example what if what if the economy's potential at full employment is something is an output that is something over here you could debate what that point is but how do you get it to there because you can't just you can't just increase the supply you can't just increase output that'll just that'll just make our inventories build up from a Keynesian point of view where you say well you want to just shift this actual curve and there's a bunch of ways in which you can shift the curve in general you can change any of these variables right over here all the things that we assumed are constant and that would shift the curve so for example the government could say hey I'm going to take you know the G was at some level what if I pop that G up what if I what if I turn that into a whatever our existing G is and then we add some change in G so they add some incremental well now this is going to be bigger by this increment right over here so maybe we'll call it this right over here so what'll happen to the curve will shift up by that increment so let's see what happens when we shift the curve up by that increment and I'll do it in that magenta color so if we shift this curve up by Delta G if we shift it up by Delta G it's going to look something like it's going to look something like this you're not changing the slope of the curve that's this right over here you're just changing its intercept so we just add a Delta G up here so this would be beep the original B plus Delta G I guess you could say it say it that way and so our new our new planned expenditures might look something like this our new planned expenditures might look something like that and that's pretty interesting because now our equilibrium point now our equilibrium point is at a significantly higher point and it's actually it's got our equilibrium point our change in our in our equilibrium so our Delta in output actually went up by more so our Delta and output our Delta and output was larger than our change is larger than our in spending so it seems like it was well worth it if you believe this analysis right here and visually the reason why it happened is because this line right here had a lower slope and so the new intersection point between it and essentially a loaf of one it has to be pushed out more and what we'll see in the last video is that this actually works out mathematically as well as consistent with kind of what we learned about the multiplier effect and that's actually the reason math kind of algebraically why this is happening why you're getting a bigger change in output then the then the incremental shift in demand and that's because of the multiplier effect and we'll see it in the next video