Multiplier Effect of Investment Spending

So let's discuss how an increase in investment spending can have a multiplier effect and set off a chain reaction in consumer spending and extra spending in the economy. Let's check it out. So an increase in investment spending, let's say firms invest in new equipment and new in growing their businesses here. It's gonna cause a chain reaction in the economy. So let's see how this works out when firms increase their investment spending. This isn't gonna in turn increase the income of households, right? Because that extra spending, let's say they're growing their business, they're gonna hire new workers, right? This is going to increase the income of the households. And what happens when the household income increase? Well, as we discuss with marginal propensity to consume and marginal propensity to save, right? When you have extra income, well, you're going to consume more and you're gonna save more. So there was an increase in spending from the investment and now there's an increase in household consumption because they have more money, they're gonna increase their consumption, right? And this has to do with our marginal propensity to consume. So go back to that video, if you need a little more information earlier in this, in this topic. Um Uh so this extra consumption. Well, guess what? That's gonna lead to more income, which leads to more consumption, leading to more consumption and this chain reaction is going to continue. So let's go to an example here and let's kind of see how this follows. So we talk about investment land has increased investment spending by $5 billion. So they have this extra $5 billion dollars that gets spent which in turn is earned by by the Um excuse me? By the households and they're going to spend based on this increased income. Right? So let's let's assume that MPC equals let's say 0.75 in this example 0.75. And let's go ahead and see how this affects our consumer spending. So that extra five billion. Well that's gonna lead to extra spending. So if they have five billion of extra income and let's just ignore taxes for now. Five billion of extra income. Well they're gonna spend 75% of that, right? Five billion times 75%. Well they're gonna spend 3.75 billion. Right? So there's an extra 3.75 billion of spending at this 0.75 marginal propensity to consume. And guess what that's going to lead to another round of increased spending because of this this uh this chain reaction where now this spending has led to higher income which that income is going to be spent again. So now we can think of this right here. MPC times five billion. That's the previous step. Right? The 3.75 billion from this step. Well that's going to be spent again at the marginal propensity to consume. Right? So what is this equation simplify too? Well NPC times MPC. What happens when we multiply something by itself. NPC times NPC is the same as M. P c squared right? M p c squared times five billion. So notice what's happening now. We're taking the 3.75, the five billion times .75. And we're multiplying it by .75 again. So 3.75 times 0.75 that comes out to 2.8125 billion and it's gonna happen again. So notice what happens in the next round of consumer spending. MPC cubed times five billion. So it's gonna happen again here where we multiply that by 50.75 and now we've got another two point one, I'll say 2.1 billion and that's gonna keep going right. The 2.1 billion times 0.75 it's gonna keep happening, keep happening, keep happening over and over again. So that's what's called the multiplier effect. Where we had this initial spending of five billion leading to all this extra spending, right? Initial spending of five billion led to all this extra spending. So we can boost the economy by having this extra spending like this this initial boost of spending. Right? So this is called the multiplier effect, just like we see down here. So the multiplier effects describes how the total increase in spending is more than just the initial boost, right? Because there's this chain reaction of of extra spending. So the actual multiple, it depends on the MPC right on the marginal propensity to consume because if we look back up here right? If we had used a different marginal propensity to consume, if they had say been .9 right? If they had been spending .9 all these numbers would be bigger and they were being even bigger boost in in our spending. Right? And if it was a smaller number say they were only spending half of it. Well these numbers would be smaller as well. Cool. So the total increase in GDP is more than just the initial spending boost. It's the initial spending times this multiple here where there's the initial spending plus the multiple. The first time we hit the marginal propensity to consume and then we did it squared cubed right? Infinitely it happens infinitely. Now you guys probably don't remember this uh series analysis from mathematics but I'm gonna give you a shortcut here. You guys don't need to remember this but you do need to remember the final equation here. So the idea here is when we have this one plus M. P C plus MPC. Square. This infinite series it's actually equal to this term right here, 1/1 minus M. P. C. That is equal to what we have in the parentheses up here. You guys don't need to know how we derive that. That's the math behind it. But just trust me on that one that that infinite series can be summed up in this equation right here. Okay so what does that tell us that the initial spending boost, it's going to depend on the MPC but the total increase in GDP is gonna be a multiple of the one divided by one minus MPC. Okay, so the bigger the MPC, the smaller the denominator leading to a bigger boost. Okay, because it's gonna be a decimal in the denominator and it's going to lead to a bigger multiplier. Okay, so in our case 1/1 minus MPC When our MPC before equaled 0.75 in our example, well 0.75 If we do one divided by one minus MPC which is 0.75. 1 -0.75 is equal to 0.25. Right? one over 0.25. So what is that equal to one divided by .25 is equal to four? Right, so that tells us that the multiple is four, it's gonna be four times that size of investment. Okay, so what does that tell us is that that initial spending boost is gonna be multiplied four times to the total increase in GDP because of this chain reaction. So when we talk about this note that when we have one minus MPC that's also equal to M P s. Right? One minus M P C. Is equal to M P. S. So where this is our multiplier right here. Another way to write it. Another way to write our multiplier is like this one over M. P. S. Right? Because the one minus M. P. C. Is equal to mps are marginal propensity to save, right? But generally when we talk about the multiplier, you're gonna see it like this, they'll give you a marginal propensity to consume and you'll have to um solve for what is the total increase, or they'll just ask you what the multiplier is. So, knowing this, the key takeaway here is to know how to calculate the multiplier, using the marginal propensity to consume and to be able to calculate the total increase in spending. So knowing that let's do a quick practice problem related to our example.

So right here at the bottom, investment land has increased investment spending by $5 billion. If MPC is 0.75, what is the multiplier and the total increase in GDP. Okay, so remember this initial five billion spending is gonna set off a chain reaction. So our multiplier is going to be equal to one divided by one minus MPC. Okay, you guys want to be familiar with that equation, You're gonna want to have that one down to memory or on your equation. See sheets, whatever it is, you're definitely gonna have that one uh at the ready so 1/1 minus MPC. That's 1/1 minus 0.751 minus 0.25. Which comes out to four. Our multiplier here is four. That means that our initial spending of five billion. We multiply it by the multiplier to get the total increase. So total increase in G. D. P. Is going to equal our multiplier of four times the initial spending boost of $5 billion $20 billion dollars increase in GDP. So not only did we have that five billion. Originally that chain reaction of consumer spending led to a total $20 billion increase. So notice if the MPC had been different, we would have gotten different numbers because our multiplier would have been different, leading to a different total increase. Cool. So that's about it. Get familiar with the multiplier and then let's move on to the next video