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# Calculating change in spending or taxes to close output gaps

Recall that the tax multiplier and expenditure multiplier magnify the effect of any change in spending or taxes. In this video, we use that fact to calculate the amount of spending or tax change necessary to close output gaps.

## Want to join the conversation?

- why not shift SRAS curve when change the taxes?(2 votes)
- The government intervention most likely to affect SRAS would be regulations.(1 vote)

- Using the same $100B scenario, how would the equation differ using the MPS rather than MPC?(0 votes)
- I think you might have misunderstood how MPS and MPC are used here. MPC and MPS are used to calculate the spending multiplier or tax multiplier. For example, both MPC and MPS are used to calculate the tax multiplier.(2 votes)

## Video transcript

- [Instructor] 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 cap. And it might seem like a good thing that your economy's 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. And so 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, contractionary fiscal policy. And 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, contractionary fiscal policy, you could raise taxes. That would decrease aggregate demand. Or, you could decrease spending. And 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 two 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. And governments tend to get more worked up about the recessionary output gap because now people are out of work. Things are not good. And so what would a
government want to do if the self-correction mechanisms
aren't happening? Well, they might wanna do
expansionary fiscal policy. And so they would wanna shift
this aggregate demand curve to the right so that it looks
something more like this. So we'd get back to our full
employment level of output. So that would aggregate demand two. And what are examples of
expansionary fiscal policy? Well, it's gonna be the opposite. You could lower taxes or you could increase spending. So let's focus on this, 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 a hundred billion dollars. So we have one hundred
billion dollar negative, or recessionary, negative 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 one hundred 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 one over one minus the MPC. So that's one over one minus 0.75. Well that's one over 0.25, which is going to be equal to four. And so if you want to close a hundred billion dollar spending
gap, or sorry, output gap, so that's your output gap you wanna close. That's going to be equal
to your spending increase. So spending increase
times your multiplier. So in this case, it is times four. So if you divide both sides by four, you get your spending increase
is going to need to be hundred billion divided by four is going to be 25 billion dollars. Makes sense. If you spend, if the government
spends 25 billion dollars, because of the marginal
propensity to consume, you have a multiplier four, so you have a hundred
billion dollars of more 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. Well here, we wanna think
about the tax multiplier. Our tax multiplier is equal to our marginal propensity to
consume times our multiplier. So in this case, it's
actually the negative of that because if you increase taxes, then that is going to decrease
spending and vice versa. And so this is going to be equal to negative 0.75 times four, which is equal to negative three. And so one way to think about it is if we wanna close a hundred
billion dollar output gap, that is going to be equal to delta t, how much we increase taxes,
times negative three. If we wanna solve for delta t, we divide both sides by negative three. And we get delta t, so let's
put a little arrow here. Delta t is equal to 100 billion dollars divided by negative three, which is approximately equal
to -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. So lower taxes by 33 billion dollars. Now there's 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.