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Deriving the Aggregate Expenditures Model

AE Model: Graphing Macroeconomic Equilibrium


Graphing Macroeconomic Equilibrium

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All right, now, let's take what we've learned about the aggregate expenditures model. And let's put it on the graph. So what we're gonna do now is we're gonna find our macroeconomic equilibrium using the graph instead of numerical approach. Okay, So the aggregate expenditures model like we discussed, were describing the relationship between spending in the economy, which was our aggregate expenditures and our production, right? Which is our GDP real GDP. So just like I just said E equals our spending and GDP equals our production. Right? Okay. So that that's the theme of this, this uh this lesson is that we're trying to find that balance we're spending equals production. So we're gonna be defining our spending, right? Aggregate expenditures is the consumption plus the investment spending plus the government purchases plus the net exports. How we had originally defined GDP, right? Because GDP we were we were calculating it based on what was being spent in the economy, what was being consumed invested, government purchases net exports, Right? That's how we define GDP. Well, that's how we're defining aggregate expenditures at this point. Okay. So what we're gonna do is we're gonna find that level of GDP that equals our aggregate expenditures. So when we define these terms, right, we said consumption is going to have some some base number if we had no income. Well, there's still gonna be some consumption, right? There's still gotta be food purchase shelter, right? There's still these things that need to be purchased in the economy. Um And that's going to be just some constant amount, we'll say, a and we're gonna add to it as we earn more income, we spend more money. So our marginal propensity to consume is going to be our slope of the line, right? The the amount for each extra dollar we have, the amount that's going to be consumed and that's gonna be based on our disposable income, Y. D. Right? The more disposable income we have, the more we're consuming based on this marginal propensity to consume and we're gonna keep all the other ones constant. There's gonna be some constant level of investment, government purchases and net exports. Okay. And remember that these can be affected by the multiplier and I promise we're gonna get to that in future videos, but we're still just gonna keep things easy. Now we're gonna just focus on how we find our macroeconomic equilibrium on the graph and then we'll deal with how those those things can change and how that affects our equilibrium later on. All right, so let's take this down to our graph and let's go ahead and find our our macroeconomic equilibrium for this aggregate expenditures model. So, they're gonna have to give you some information in the problem like I've given you hear some level of consumption and notice they gave us a a linear equation, right? They gave us our base amount of consumption of two. This could be like two billion and then for every extra dollar that is earned, half of it is going to be spent and half of it is saved. So in this case the marginal propensity to consume is 0.5 right? So for every extra dollar, half of it is goes to consumption. Then we've got these constant levels of investment, government purchases and net exports. Alright, so those are the spending from those different areas. We've got uh firm spending of one billion government purchases of half a billion. And net exports of half a billion as well. Okay so let's go ahead and let's graph our consumption line. I just want to graph consumption just like we did with our consumption function and then we're going to add to it our investment, our government purchases and our net exports to lead up to our aggregate expenditures. Okay, so let's start here with just consumption. If we look at consumption there's two plus 0.5 Y. So when we graph this we need to know what are variables here are on the graph. Right. So in the aggregate expenditures model we're gonna have our aggregate expenditures are spending on this axis, the Y axis. And we're going to have our G. D. P. On the X. Axis. So what we're looking for is a place where these are equal. And notice I've drawn a line here across the middle. Um This dotted line across the middle is called our 45 degree line. Okay. The 45 degree line is a very important part of this graph. Because what does this what are all the points on this 45 degree line notice this point right here along the line this tells us that aggregate expenditures at this point is two billion and GDP is two billion. Right? So what does that look like to us? A point right? There is in macroeconomic equilibrium, right? Any point along this line right here. Four billion and four billion. That's macroeconomic equilibrium. Six billion. So anywhere along this line, we know we're in macroeconomic equilibrium. So the first thing you wanna do when you draw this graph is you want to have your 45 degree line because that shows us where our macroeconomic equilibrium is gonna be. All right? So what we wanna do is we want to draw our aggregate expenditures line and find where it crosses the macroeconomic the 45 degree line. Okay, because that will be the equilibrium. So let's start here with just consumption and we're gonna build up to our aggregate expenditures model. So if we're looking at just consumption, we've got this point to. Right? So if there's no income, right GDP, which is why let me put that here, GDP is why right? We call it why in this situation. I know it's on the X axis and we're calling it why they love to be confusing in economics. But GDP we we consistently will call it this variable Y So at this point where there's no G. D. P. Well there's still gonna be some consumption because people need to live, right? And as we add income. So now let's say there's 22 billion of income, right? Or two billion of G. D. P. Well that's going to affect our consumption, right? So if we have GDP equals two, well then what happens to consumption, consumption is gonna equal to plus 0.5 times two. Right, because we're spending half of all of the income. Right? So every we're just assuming all of income is disposable income at this point and we're spending half of it, right? Because we plug that into our equation and we're gonna get consumption equals three at that point. Right? So as we add uh GDP half of it is going to consumption. So we would say that at a GDP of two consumption would equal three. Right? So we would end up having a line that continues along that form, right? If we went up to four G. D. P. Well we would be right here for and that line would continue just like that. Right? So this is how we would find the equation of a line and we would end up with a line that looks something like this for our um consumption function. Right? So this right here is our consumption function and I'm going to call it C C for consumption. But now what happens when we add investment to it? Right? This is just consumption, we're looking for our aggregate expenditures in total. So if we add investment to it. Well, that would be our consumption function of two plus 0.5 Y Plus our investment of one. Right, so what does that equal? It's going to equal three plus 0.5. Y. Right, because the two plus the one equals three and then we have the 0.5. Y. So notice all that investment did was increase our our y intercept here, our intercept on the on the y axis up to three. So just by adding investment, remember these are gonna be constant. So all they're gonna do is bump the line up, bump it up, bump it up. Okay, so let's go ahead and do our our uh investment here and investment. It would be three when there's no GDP or our consumption plus investment would be three when there's no GDP and it would go up at the same rate, right, When there's two billion of GDP it would add one more there, one more there. Right. So notice these lines are parallel because the slope is the same for these two lines. So we're just having the line shift upward. So this line, C plus I C plus i is just a little further up. And that's what's gonna happen with the aggregate expenditures model. We have consumption and we're just adding these investment, government purchasing that export their all constant. They're just gonna shift the line up a little bit. Cool. So let's go ahead and do the next one. I'll do it in blue again. City plus I plus G. We've got two plus 0.5 Y. That's our consumption plus investment of one plus government purchases of 0.5. Well that gets us to 3.5. Right to plus one plus 0.5 is 3.5 plus 0.5. Y. So notice don't get too caught up in the math here. The main the main idea is that we're just moving the line up, that's all of that. These extra pieces due to the puzzle here, they're just moving the line up. So we would go to 3.53 point five would have the same slope When we when we plug in those numbers, we're just gonna follow the same slope. The slope hasn't changed. Right. 0.5 here, there's nothing else affecting the slope of the line and we're just moving up. So here would be r. c. plus I plus G would be right here. And then finally we add in net exports. We have all four pieces of the puzzle together and we get two plus 0.5 Y. Is our consumption plus investment of one plus government purchase of 0.5 plus net exports of 0.5 gets us to a final um aggregate expenditures of two plus one plus 0.5 plus 0.5 is four plus 0.5 Y. Right so notice all this is done again is just bump us up uh the graph so finally I'll do this one in red. We're gonna have at four is our intercept here and it's gonna be moving up like this. So notice that this line here is our aggregate expenditures line. So this final line right here is aggregate expenditures. So here I'm gonna put A. E. Equals C plus I plus G. Plus and X. Okay so all we did was build up to the aggregate expenditures. I just went through that process just because I wanted to show you that all of these components just push the consumption function up. Okay our our investment government purchases and exports all they do is shift that consumption function up the graph. Last thing there is left to do on this graph is find our macroeconomic equilibrium. I said it a while ago. Where is our macroeconomic equilibrium gonna be? It's gonna be where that aggregate expenditures line crosses the 45 degree line. Right so if we look for our aggregate expenditures, I know we've got a lot of lines going here now but this top one here is our aggregate expenditures line, where does it cross? Our 45 degree line is right up here, right up here. So notice just consumption cross there but by adding investment government purchases net exports here is our macroeconomic equilibrium amount of G. D. P. And that's where spending is say eight billion and our production is eight billion. Right? So now we know at this level of consumption, this level of investment, this level of net exports, this level of government purchases the correct amount of production that would be an equilibrium is eight billion. Right? Eight billion is the is the magic number here. And all we're looking for is where does that aggregate expenditures line across the 45 degree line? Nothing too crazy here. So, right behind me as a summary macroeconomic equilibrium where the E. C. Plus I plus G plus N. X. Final line crosses the 45 degree line. Okay, so the first step you always want to do in these graphs, if your professor doesn't do it for you, is draw that 45 degree line. And then we're going to find where our aggregate expenditures touches it. Generally you're just gonna have your aggregate expenditures in total. But I wanted to build up to it so you can kind of see the whole process. Cool. Alright, now that we've got our macroeconomic equilibrium on the graph, let's go ahead and move on to the next