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Analyzing planned expenditures versus actual output using the Keynesian Cross. Created by Sal Khan.
Video transcript
What I want to introduce you to in this video is the idea of a Keynesian Cross. This is one of the tools of analysis of Keynesian thinking which is really the idea that maybe every now and then the GDP, when it's at equilibrium, isn't at an optimal state. It's operating well below potential and the way that we might be able to get. If you are a follower of Keynesian thinking, the way that we can get it closer to, potential closer to full employment is by somehow affecting aggregate demand in some way. What we'll see is, we're going to build up our Keynesian Cross analysis based on what we understand from the consumption function. We're going to first start thinking about planned expenditures. We're going to think about what happens when planned expenditures deviates from actual output, from actual expenditures, right over here. This is very similar to what we're done before but we're actually thinking of it in terms of planning. Let's say we have planned expenditures, expenditures planned and we could just write the components of aggregate expenditure here. Well, you're going to have consumer spending, you're going to have investment. I'm going to be careful here, I'm going to call it planned investment. This is exactly what firms are looking to produce. The reason why I differentiate this here is because, if for whatever reason, aggregate expenditure is less than they expect then they might build up inventories and those inventories get counted as investments. Those would be excess inventories above and beyond the planned inventories. If actual demand is higher than expended then it might eat in to inventories and when inventories are eaten into it actually takes away from planned investments there would actually be kind of a, you would be eating into the total investment in that situation. That's why I'm going to differentiate between planned investment and actual investment. Then of course, you have government spending and then finally you have net exports. For the sake of the analysis of the Keynesian Cross, once again, this is a super over simplification, we're going to assume that at any given level of GDP or aggregate output that these are all constant. That these are not really dependent on aggregate output or GDP which is of course a huge over simplification. If we were to plot any of these versus aggregate income we'd say that they are really a flat line. Maybe planned investment might look something like that. Maybe government spending would look something like that. No ways at some level that's preplanned, it's exogenous to our model. It's not dependant in any way. It's an external factor. Assuming it's fixed, it's not dependent on aggregate income. So government spending looks something like that and net exports, maybe it looks something like that. The one factor that you can imagine because I said we're going to build on top of the consumption function that we're going to assume is driven by aggregate income is consumption right over here. The way that this thing will look, the way that this thing will look is you have ... So let me draw another plot right over here, draw another plot. We have aggregate income, that is going to be our independent variable and then over here we can just view this as expenditure. If we were just to plot consumer spending, we've seen that before especially if we assume a linear consumption function. What we've studied in the last few videos is all linear consumption functions and depending on how you write it, but they all look something like this. They have a positive vertical axis intercept and they have upward slope that is less than 1. Consumption by itself would look something like this, this would be consumer spending as a function of aggregate income. Then if you all all of these constants to it then your graph for aggregate planned expenditures would look something like this. if you added just in net exports it would get a little bit higher because these are constant. Any point you would add this much, if you add government a little higher than that and if you add all of them including planned investments you might get something that looks, and I'll do it in this color right over here, you might get something that looks like this. I'm just starting off with consumer spending. I'm using a linear consumption function, you don't have to, but it makes the Keynesian Cross analysis a lot more cross like and easier to analyse. If you add all what we assumed to be constant things and aggregate expenditures is going to be up here. This right over here is aggregate planned expenditures I should say. Now, we know from the circular flow in the economy that when an economy is at equilibrium, your aggregate output is equal to your aggregate expenditures or your aggregate expenditures is equal to your aggregate income. Really, at an equilibrium, these two things are going to be equal. We can actually plot a line that shows all the points that those are equal. That would be a line that has essentially a slope of 1 where Y is always equal to expenditures. It might look something like this. This is where the name Keynesian cross comes from because essentially you have planned expenditures and then right over here you have the equilibrium line or what I call the equilibrium line because these are all points where income is equal to expenditure. Right over here, income is equal to expenditure. Income is equal to expenditure. When you look at aggregate planned expenditures or you can even view this as aggregate demand as a function of aggregate income. This is actual point where the actual economy is at equilibrium where expenditures are actually equal to, where expenditures are actually equal to output. Actually, it's a little bit skewed the way I drew it but these actually should be like a square. Actually, let me see if I can draw a little bit clearer than that. Just so it will actually looks like a 45 degree line. It should really be a 45 degree line like that. That seems a little bit better. That's the point at which we are at equilibrium. Actually, I don't like that because it makes it a little bit harder to analyse. But hopefully you get the idea. This should be a line that's where expenditures is equal to aggregate income. Like this so it intersects at a point that's a little bit easier for me to analyse. Now, this is where the Keynesian Cross becomes a kind of interesting tool because we could start to think about what happens in situations. This is an equilibrium level of GDP. What happens if for whatever reason that aggregate income is higher than that equilibrium level? Let's think about scenario. Let's say we're over here. Let me do that in magenta. Let's say we're over here. Let's call that Y1. What is going on? What is going on right over here at Y1? Over here, the aggregate output which is the same thing as aggregate income is right over here. Well, this is the actually planned expenditures, is right over here. All of these excess. All of these excess above the planned demand, these are essentially going to be inventories building up. The economy is producing more than it actually needs, inventories are going to build up. Firms are not selling all of their products and that excess built up inventory is going to be reflected in investment. In this case, this delta. This delta is going to be added to your planned investment to get what the actual investment might be. When an economy is at that state then firms would say, "Oh my god! "We're building inventory more than we expected. "We're not selling our products. "We're going to lower output "so there's a natural feedback mechanism for the GDP "to go back to equilibrium." Let's think about what happens if it's below that equilibrium point. Let's say that GDP is, let's call that right over here. This is Y2. Actually, I could write it as a subscript. I don't know, I wrote a superscript there. We could call this Y2. Over here, aggregate demand at this level of output is more than what's actually being output. People want more goods and services. Right over here, this is a deficit of output and so this shows that people will be digging into inventory. That the existing inventories or the existing investment was not enough. Or, I guess another way to think it, essentially, inventories will be contracting. Let's say business was constant. I had a lemonade stand, I just keep an inventory of 5 cups of lemonade on hand and I sell a cup every hour. If all of a sudden people start buying 2 cups an hour my inventory is going to start getting depleted and so this is what's reflected. Actual output is below what's demanded. When firms start seeing that their inventories get depleted, they say, "Oh my god! "I don't want to run out of my goods and services. "Let me start producing more." Then when we're talking about inventories we're really talking about goods. So let me produce more. So output will once again want to naturally go to that feedback point. Hopefully that makes a little bit of sense. In the next few videos we'll be using the Keynesian Cross to think about the Keynesian line of reasoning. If you change one of these, how that might affect the new equilibrium level of GDP.