AE Model and the Multiplier

So I promised you we were gonna discuss the multiplier effect in the aggregate expenditure model and the time is finally here, let's go ahead and check out that multiplier effect. So the multiplier effect, it describes how an initial boost in spending. So there's a we had some level of investment spending of some level of government purchases. Well, it's going to boost our GDP much higher. So it's gonna be a much higher increase to G. D. P. Than what our initial spending boost is. And that's the multiplier effect, right? There's gonna be some amount of increase in say investment and that amount of increase is going to be multiplied several times to the amount of extra GDP that we see. Okay, so let's go ahead and see how it works in the model in the aggregate expenditures model, just like before we're still thinking of our aggregate expenditures as our spending, our GDP as our production, right, spending and production here and now we're we're in the full economy where we've got consumption investment, government purchases, net exports, these are all of our spending, right? We've got spending on consumption plus investment plus government purchases plus net exports. And when we discussed the consumption function, right, we have defined consumption as some base amount of consumption, right? Regardless of GDP, even if nothing is produced, we're gonna be consuming something to survive plus our marginal propensity to consume, times are disposable income, right? Times are disposable income. So as we have more income, it's gonna increase our consumption and we keep all the other ones constant, there's gonna be some constant level of investment, constant level of government purchases and constant level of net exports. And these constants can be affected by the multiplier effect. If we were to change any of these constants, Well, they're going to have a big effect on our on our um on our GDP through the multiplier effect. So let's see how that happens here on our graph, our aggregate expenditures graph. So we have our same information where we had two plus 0.5 Y. For our consumption investment was 10.5 and 0.5 government purchases and net exports. So we had graft our aggregate expenditures curve our aggregate expenditures for right? And what we're gonna do is we're gonna pump up our investment spending. So in this case we're gonna start with our original graph where our investment was equal to one. We're gonna pump it up in this graph. So let's let's start with the old one. So C plus I plus G plus N. X. We would add all these constants. Two plus one plus 0.5 plus 0.5 would give us four Plus 0.5 Y. Right, that would be our aggregate expenditures line, right, this is our aggregate expenditures is all of those added together. So two plus 0.5 Y plus one would make this three plus 0.53 point five plus 0.5. Makes it four. Right? So four plus 0.5 Y. And that was the aggregate expenditures line that we saw in the previous video, right where we started at four. Right? This is four. Regardless of anything being produced. There's still gonna be four there in our aggregate expenditures. And this being G. D. P down here. And then as we add uh GDP well, that's going to increase our consumption. Which increases our aggregate expenditures. So for every two in GDP, right, if we add two to G. D. P we would put a two in here and it would add two times 0.5 is one. It would make it five. Right? So we saw that the slope was something like this for every two of GDP half of that goes to consumption. So this is the slope of that line right here. So we're gonna have Now I want to make a note that this 0.5 could be any number, This is the number. In my example, it could be 0.80 point 60.2. Whatever that marginal propensity to consume is in that society. Right? So the first thing you might have to do is plug in a couple of different numbers for why to be able to graph this line, right? You might plug in two for y and figure out what that point is on the graph, plug in three. And then you connect the dots to make the line. Okay, So there's our original aggregate expenditures. and I'm gonna put a E Old right there for our original aggregate expenditures. And now what we're gonna do is in this society we're going to pump up our investment spending so and a boost to investment spending from 1-2. So we're saying instead of one amount of investment spending $1 billion $2 billion one billion. Right? So the change let me go like this. So the new investments to which is a change a change of one billion. Right? We've added one billion of investment spending here from one billion. We've added another billion. Okay so it went up by one billion. How is that going to affect our equilibrium? G. D. P. So in this case instead of having two plus one plus 0.5 plus 0.5 we're having two plus two plus 0.5 plus 0.5. Right because now we have two investment so it's gonna be two plus two plus 0.5 plus 0.5 is five plus 0.5 Y. Right so that's that change of one billion We added we added one more billion to our aggregate expenditure. So now we've got a new aggregate expenditures line which is five plus 0.5 Y and what's that going to do on our graph? So I'll do this one in blue notice we're gonna have five right here. Five on our graph when there's no no GDP nothing being produced, there's still 55 billion of spending. And then it's gonna go up at that same rate of 0.5 Y. So since there's one billion more in investment spending we might expect there to be one billion more of GDP. But that's not what's gonna happen. So let's look at where this crosses our aggregate expenditures line crosses the The 45° line and notice what we've got. Now, aggregate expenditures new. So now that we've got that boosted one billion extra investment spending. Well, our original our old old equilibrium was right here and that was at a at a GDP of eight. Right? So G. D. P. And aggregate expenditures were eight at the old equilibrium. But what about now at the new equilibrium the new equilibrium is up here at the very corner of our graph at 10. Right. So even though we only increased our investment spending by one billion. Well, guess what? Our GDP went up by two billion. So by increasing one billion of investment spending it actually had a twofold effect on our aggregate expenditures. So this twofold effect could be a different number but in this case it's two fold, it's always going to be some number greater than one, right? There's always gonna be some multiplier effect going on. And this is our new equilibrium here at 10 billion. Right. So there's two billion more two billion more G. D. P. And the reason for this has to do with the slope of the line by pushing the line up one well the slope of the line, it took longer for it to reach that 45 degree line where we got to our equilibrium right? It didn't just take one more, it took two more. It actually has to do because of that. This this marginal propensity to consume of 0.5 is affecting the line. You can imagine if we had a different marginal propensity to consume what might look something like this. Right? We might have a different slope of the line if we had lines like this and then a new line like this. Right. It all has to do with that slope is what how much the multiplier is going to affect it. Right. So the multiplier effect has to do with the slope of the line and that's what we have here at the bottom, the total increase in GDP. So the total increase in GDP is going to be that initial boost of spending. So in our case that the initial boost was one billion times one minus 1/1 minus the MPC. So in our case the MPC and the NPC is always going to be the slope of the line of the aggregate expenditures line 1 -0.5. So that gives us one over 0.5 times one billion. And that this right here, this is the multiplier And the total amount of extra spending is going to be the multiplier times the initial spending boost. So one over 0.5 If we pull out our calculators, one divided by 0.5 let me get out of the way Is to write this equals two times 1 billion Which equals two billion. Right? So too is the multiplier and this has to do with taking the the the slope of the line, that marginal propensity to consume and doing one divided by one minus the slope of the line. And that gives us the multiplier. Why is this important? Well it tells us it tells us that by increasing one of our constants, increasing our investments, our government purchases were able to have a big boost in in our real GDP right, we're able to increase our GDP by a lot more than that initial spending. So you can think about maybe a situation of a recession, maybe the economy is in recession and and the government wants to help push us out of the recession. Maybe the government makes a bunch of purchases, maybe the government hires a bunch of people builds a bunch of highways, right? Something like that. They take on a huge project that boost the GDP. Right, because now the government spend more money but not only that the consumers spend more money because they're earning income and they're spending that income. Right? That's that multiplier effect that not only is there the government purchases but that it affects consumption as well. Okay so the multiplier is right here this variable one divided by one minus M. P. C. And if you want to find the total change, you're gonna have to multiply it by what was the change in the spending, right? Are spending was it went from one billion to two billion? So there was an extra one billion of spending their. Cool. Alright. So that's how the multiplier effect works into our expenditures model. When we have an initial boost in one of our constants investment, government purchase or net exports, it's going to have a multiple effect on our equilibrium GDP. Cool. Alright, let's go ahead and move on to the next video.