AE Model and the Multiplier - Online Tutor, Practice Problems & Exam Prep

The multiplier effect illustrates how an initial increase in spending, such as investment or government purchases, leads to a greater overall increase in GDP. This occurs through the marginal propensity to consume (MPC), which determines how much additional income is spent. The multiplier is calculated as $\frac{1}{1-\mathrm{MPC}}$. For example, a $1 billion increase in investment can result in a $2 billion increase in GDP, demonstrating the significant impact of fiscal policy on economic growth.

AE Model and the Multiplier

So I promised you we were going to 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 level of investment spending or a level of government purchases. Well, it's going to boost our GDP much higher. So it's going to be a much higher increase in GDP than what our initial spending boost is, and that's the multiplier effect, right? There's going to be some amount of increase in, say, investment, and that amount of increase is going to be multiplied several times 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 in the full economy where we've got consumption, investment, government purchases, and 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 discuss the consumption function, right? We had defined consumption as some base amount of consumption regardless of GDP. Even if nothing is produced, we're going to be consuming something to survive plus our marginal propensity to consume times our disposable income, right? Times our disposable income. So as we have more income, it's going to increase our consumption. And we keep all the other ones constant. There's going to 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 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 2 + 0.5y for our consumption, and investment was 1, 0.5 for government purchases and 0.5 for net exports. So we had graphed our aggregate expenditures curve. And what we're going to do is we're going to pump up our investment spending. So we start with our original graph where our investment was equal to 1. And we're going to pump it up in this graph. So let's start with the old one. So c + g + mx, we would add all these constants. 2 + 0.5 + 0.5 would give us 4 + 0.5y. Right? That would be our aggregate expenditures line, right? This is our aggregate expenditures is all of those added together. So 2 + 0.5y + 1 would make this 3 + 0.53.5 + 0.5 makes it 4, right? So 4 + 0.5y. And this was the aggregate expenditures line that we saw in the previous video, right? Where we started at 4, right? This is 4 regardless of anything being produced. There's still going to be 4 there in our aggregate expenditures. And this being GDP down here. As we add GDP, well that's going to increase our consumption, which increases our aggregate expenditures. So for every 2 in GDP, right? If we add 2 to GDP, we would put a 2 in here and it would add 2 times 0.5 is 1. It would make it 5. Right? So we saw that the slope was something like this. For every 2 of GDP, half of that goes to consumption. So this is the slope of that line right here.

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 0.8, 0.6, 0.2, 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 Y to be able to graph this line, right? You might plug in 2 for Y and figure out what that point is on the graph, plug in 3 and then you connect the dots to make the line. Okay? So there's our original aggregate expenditures. And I'm going to put AE old right there for our original aggregate expenditures. And now what we're going to do is, in this society, we're going to pump up our investment spending. So and a boost to investment spending from 1 to 2. So we're saying instead of one amount of investment spending, $1,000,000,000, we're saying there's $2,000,000,000 of investment spending. We've essentially added 1,000,000,000. Right? So the change let me go like this. So the new investments too, which is a change. A change of 1,000,000,000, right? We've added 1,000,000,000 of investment spending here from 1,000,000,000 we've added another 1,000,000,000, okay? So it went up by 1,000,000,000. How is that going to affect our equilibrium GDP? So in this case, instead of having 2 + 1 + 0.5 + 0.5, we're having 2 + 2 + 0.5 + 0.5, right? Because now we have 2 investment. So it's going to be 2 + 2 + 0.5 + 0.5 is 5 + 0.5y, right? So that's that change of 1,000,000,000. We added we added 1 more 1,000,000,000 to our aggregate expenditure. So now we've got a newXvpenditures line which is 5 +0.5y. And what's that going to do on our graph? So I'll do this one in blue. Notice, we're going to have 5 right here. 5 on our graph when there's no GDP, nothing being produced. There's still 55,000,000,000 of spending, and then it's going to go up at that same rate of 0.5y. So since there's 1,000,000,000 more in investment spending, we might expect there to be $1,000,000,000 more of GDP, but that's not what's going to happen. So let's look at where this crosses our aggregate expenditures line crosses the 45 degree line. And notice what we've got now. Aggregate expenditures new. So now that we've got that boosted 1,000,000,000 extra investment spending, well, our original, our old old equilibrium was right here. And that was at a GDP of 8, right? So GDP and aggregate expenditures were 8 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 1,000,000,000, well guess what our GDP went up by 2,000,000,000. So by increasing 1,000,000,000 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 twofold. It's always going to be some number greater than 1, right? There's always going to be some multiplier effect going on, and this is our new equilibrium here at 10,000,000,000, right? So there's 2,000,000,000 more. 2,000,000,000 more GDP, and the reason for this has to do with the slope of the line. By pushing the line up 1, 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 2 more. It actually has to do because of that this marginal propensity to consume of 0.5 is affecting the line. You could 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 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 the total increase in GDP is going to be that initial boost of spending. So, in our case, the initial boost was 1,000,000,000 times 1 minus one over 1 minus the MPC. So, in our case, the MPC and the MPC is always going to be the slope of the line of the aggregate expenditures line. 1 minus 0.5, so that gives us 1 over 0.5 times 1,000,000,000, and 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, 1 divided by 0.5. Let me get out of the way. Is 2, right? This equals 2 times 1,000,000,000 which equals 2,000,000,000. Right? So 2 is the multiplier. And this has to do with taking the slope of the line that marginal propensity to consume and doing 1 divided by 1 minus the slope of the line and that gives us the multiplier. Why is this important? Well, it tells us that by increasing one of our constants, increasing our investment, our government purchases, we're able to have a big boost in our real GDP, right? We're able to increase our GDP by a lot more than that initial spending. So you could think about maybe a situation of a recession, maybe the economy is in recession 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 boosts the GDP, right? Because now the government spends 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, 1 divided by 1 minus MPC, and if you want to find the total change, you're going to have to multiply it by what was the change in the spending, right? Our spending was it went from 1,000,000,000 to 2,000,000,000 so there was an extra 1,000,000,000 of spending there. Cool? Alright. So that's how the multiplier effect works into our aggregate 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.

Here’s what students ask on this topic:

What is the multiplier effect in the aggregate expenditure model?

The multiplier effect in the aggregate expenditure (AE) model describes how an initial increase in spending, such as investment or government purchases, leads to a greater overall increase in GDP. This occurs because the initial spending generates additional income, which is then spent by consumers, creating a ripple effect throughout the economy. The size of the multiplier depends on the marginal propensity to consume (MPC), which is the fraction of additional income that is spent. The multiplier is calculated using the formula:

$\frac{1}{1-\mathrm{MPC}}$

For example, if the MPC is 0.5, the multiplier would be 2, meaning a $1 billion increase in investment could result in a $2 billion increase in GDP.

How do you calculate the multiplier in the AE model?

The multiplier in the aggregate expenditure (AE) model is calculated using the marginal propensity to consume (MPC). The formula for the multiplier is:

$\frac{1}{1-\mathrm{MPC}}$

For instance, if the MPC is 0.6, the multiplier would be:

$\frac{1}{1-0.6}=2.5$

This means that an initial increase in spending of $1 billion would lead to a total increase in GDP of $2.5 billion.

What role does the marginal propensity to consume (MPC) play in the multiplier effect?

The marginal propensity to consume (MPC) is crucial in determining the size of the multiplier effect. The MPC represents the fraction of additional income that consumers spend rather than save. A higher MPC means that consumers spend a larger portion of any additional income, leading to a larger multiplier effect. The multiplier is calculated using the formula:

$\frac{1}{1-\mathrm{MPC}}$

For example, if the MPC is 0.8, the multiplier would be 5, indicating that an initial increase in spending would have a fivefold impact on GDP. Conversely, a lower MPC results in a smaller multiplier effect.

How does an increase in government spending affect GDP through the multiplier effect?

An increase in government spending affects GDP through the multiplier effect by initiating a chain reaction of increased income and consumption. When the government spends more, it directly boosts aggregate demand, leading to higher production and income. This additional income is then spent by consumers, further increasing aggregate demand. The total increase in GDP is determined by the multiplier, which is calculated as:

$\frac{1}{1-\mathrm{MPC}}$

For instance, if the MPC is 0.75, the multiplier is 4. Therefore, a $1 billion increase in government spending would result in a $4 billion increase in GDP, demonstrating the significant impact of fiscal policy on economic growth.

What is the relationship between the multiplier effect and fiscal policy?

The multiplier effect and fiscal policy are closely related because fiscal policy actions, such as changes in government spending and taxation, can significantly influence the economy through the multiplier effect. When the government increases spending or cuts taxes, it boosts aggregate demand, leading to higher production and income. This initial increase in spending is magnified by the multiplier effect, which is determined by the marginal propensity to consume (MPC). The formula for the multiplier is:

$\frac{1}{1-\mathrm{MPC}}$

For example, if the MPC is 0.6, the multiplier is 2.5, meaning that a $1 billion increase in government spending could lead to a $2.5 billion increase in GDP. This illustrates how fiscal policy can have a powerful impact on economic growth.