Calculating change in spending or taxes to close output gaps | AP Macroeconomics | Khan Academy

So we have two different economies depicted here. On the left, we have an economy where its short-run equilibrium output is above its full employment output, and so it has a positive output gap. It might seem like a good thing that your economy is just doing really, really well, even more than what is actually sustainable. But there could be negatives here as well. You might be depleting resources in an unsustainable way; you might start having uncomfortable levels of inflation.

In these situations, if you don't have your self-correcting mechanisms happen to get us back to our full employment output, a government might want to do contractionary fiscal policy. It also might be because the contractionary fiscal policy could undo some expansionary fiscal policy that was done in the past, and we'll talk more about that.

But what are examples of contractionary fiscal policy? Well, they could raise taxes. Raising taxes would decrease aggregate demand, or they could decrease spending. If you think about what it would do to these curves, it would shift our aggregate demand curve to the left. The goal would be to get back to our long-run equilibrium, so you would want to get to this aggregate demand curve 2 through your contractionary fiscal policy.

Now, if you look at the right, we have the opposite scenario here. We have a negative output gap, sometimes known as a recessionary output gap. Governments tend to get more worked up about the recessionary output gap because now people are out of work; things are not good. So what would a government want to do if the self-correction mechanisms aren't happening? Well, they might want to do expansionary fiscal policy.

Expansionary fiscal policy would involve shifting this aggregate demand curve to the right so that it looks something more like this, allowing us to get back to our full employment level of output, which would be aggregate demand 2. So what are examples of expansionary fiscal policy? What’s going to be the opposite? You could lower taxes or you could increase spending.

Let’s focus on the expansionary monetary policies and actually dig a little bit deeper into the numbers. Let's say we have an economy where our marginal propensity to consume is 0.75, and let's say that we have a negative output gap right over here of 100 billion dollars. We have a 100 billion dollar negative or recessionary output gap.

Let’s first think about the increasing spending lever. How much would we have to increase spending, given this marginal propensity to consume, to close a 100 billion dollar negative output gap? Pause this video and try to solve that.

Well, let’s just think about our multiplier. Our multiplier is going to be equal to 1 over 1 minus the MPC, so that’s 1 over 1 minus 0.75. Well, that’s 1 over 0.25, which is going to be equal to 4. If you want to close a 100 billion dollar output gap—so that's your output gap you want to close—that's going to be equal to your spending increase times your multiplier. In this case, it is times four.

If you divide both sides by four, you get that your spending increase is going to need to be 100 billion divided by 4, which is going to be 25 billion dollars. Make sense? If the government spends 25 billion dollars because of the marginal propensity to consume, you have a multiplier of 4. So you have 100 billion dollars of total spending that is going to happen in the economy because of that initial government spending of 25 billion dollars.

But what if instead the government wanted to do it by lowering taxes? What would be the amount that they would need to lower taxes, once again based on this very simplified model, in order to close this output gap? Here, we want to think about the tax multiplier.

Our tax multiplier is equal to our marginal propensity to consume times our regular multiplier. So in this case, it is going to be the negative of that because if you increase taxes, then that is going to decrease spending and vice versa. This is going to be equal to negative 0.75 times 4, which is equal to negative 3.

One way to think about it is, if we want to close a 100 billion output gap, that is going to be equal to delta T—we want to find out how much we need to increase taxes—times negative 3. If we want to solve for delta T, we divide both sides by negative 3, and we get delta T.

So let's put a little arrow here: delta T is equal to 100 billion dollars divided by negative 3, which is approximately equal to negative 33 billion dollars. Once again, why is this negative? Well, this is your increase in taxes. So if that's negative, that means you lowered taxes by 33 billion dollars.

Now, there are a couple of interesting things here, other than just the mechanics and the numbers. Notice that this number and this number are not the same, and that's a common misconception that they would be the same; that they would be equivalent if you're trying to close the same gap. Notice they aren't.

In general, if we assume everything we just assumed, if you're trying to close the same output gap, you would have to change your taxes by more than you would have to change your government spending.