Keynesian cross and the multiplier발음듣기
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Keynesian cross and the multiplier
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In the last video, we saw how the Keynesian Cross could help us visualize an increase in government spending which was a shift in our aggregate planned expenditure line right over here and we saw how the actual change,발음듣기
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the actual increase in output if you take all the assumptions that we took in this, the actual change in output and aggregate income was larger than the change in government spending.발음듣기
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You might say okay, Keynesian thinking, this is very left wing, this is the government's growing larger right here.발음듣기
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Whether you're on the right or the left, although Keynesian economics tends to be poo-pooed more by the right and embraced more by the left, most of the mainstream right policies, especially in the US, have actually been very Keynesian.발음듣기
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For example, when people talk about expanding the economy by lowering taxes, they are a Keynesian when they say that because if we were to rewind and we go back to our original function so if we don't do this, if we go back to just having our G here,발음듣기
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we're now back on this orange line, our original planned expenditure, you could, based on this model right over here, also shift it up by lowering taxes.발음듣기
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If you change your taxes to be taxes minus some delta in taxes, the reason why this is going to shift the whole curve up is because you're multiplying this whole thing by a negative number, by negative C1.발음듣기
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There's a negative out here. When you multiply it by a negative, when you multiply a decrease by a negative, this is a negative change in taxes, then this whole thing is going to shift up again.발음듣기
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You would actually shift up. You would actually shift up in this case and depending on what the actual magnitude of the change in taxes are, but you would actually shift up and the amount that you would shift up -발음듣기
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I don't want to make my graph to messy so this is our new aggregate planned expenditures - but the amount you would move up is by this coefficient down here, C1, -C1 x -delta T.발음듣기
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You're change, the amount that you would move up, is -C1 x -delta T, if we assume delta T is positive and so you actually have a C1, delta T.발음듣기
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It's also Keynesian when you say if we increase taxes that will lower aggregate output because if you increase taxes, now all of a sudden this is a positive, this is a positive and then you would shift the curve by that much.발음듣기
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This really isn't a difference between right leaning fiscal policy or left leaning fiscal policy and everything I've talked about so far at the end of the last video and this video really has been fiscal policy.발음듣기
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This has been the spending lever of fiscal policy and this right over here has been the taxing lever of fiscal policy.발음듣기
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If you believe either of those can effect aggregate output, then you are essentially subscribing to the Keynesian model.발음듣기
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Now one thing that I did touch on a little bit in the last video is whatever our change is, however much we shift this aggregate planned expenditure curve, the change in our output actually was some multiple of that.발음듣기
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What I want to do now is show you mathematically that it actually all works out that the multiple is actually the multiplier.발음듣기
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If we go back to our original and this will just get a little bit mathy right over here so I'm just going to rewrite it all.발음듣기
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We have our planned expenditure, just to redig our minds into the actual expression, the planned expenditure is equal to the marginal propensity to consume times aggregate income and then you're going to have all of this business right over here.발음듣기
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That will just make it simple for us to manipulate this so let's just call of this business right over here B.발음듣기
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Let's set planned expenditures equal to aggregate output, which is the same thing as aggregate expenditures, the same thing as aggregate income.발음듣기
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On the right-hand side, obviously if we subtract C1Y, it's going to go away and that is equal to B.발음듣기
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Then we can factor out the aggregate income from this, so Yx1-C1=B and then we divide both sides by 1-C1 and we get, that cancels out.발음듣기
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We get, a little bit of a drum roll, aggregate income, our equilibrium, aggregate income, aggregate output.발음듣기
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Now what is this? You might remember this or if you haven't seen the video, you might want to watch the video on the multiplier.발음듣기
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1 minus our marginal propensity to consume is actually - And I don't think I've actually referred to it before which let me rewrite it here just so that you know the term - so C1 is equal to our marginal propensity to consume.발음듣기
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For example, if this is 30% or 0.3, that means for every incremental dollar of disposable income I get, I want to spend $.30 of it.발음듣기
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If I'm spending 30% of that incremental disposable dollar, then I'm going to save 70% of it.발음듣기
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This entire denominator is the marginal propensity to save and then one over that, so 1/1-C1 which is the same thing as 1/marginal propensity to save, that is the multiplier.발음듣기
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If you take this infinite geometric series, if we just think through how money spends, if I spend some money on some good or service, the person who has that money as income is going to spend some fraction of it based on their marginal propensity to consume,발음듣기
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and we're assuming that it's constant throughout the economy at all income levels for this model right over here.발음듣기
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Then they'll spend some of it and then the person that they spend it on, they're going to spend some fraction.발음듣기
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When you keep adding all that infinite series up, you actually get this multiplier right over here.발음듣기
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For example, if B gets shifted up by any amount, let's say B gets shifted up and it could get shifted up by changes in any of this stuff right over here.발음듣기
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We saw it before. If, for example, if C1=0.6, that means for every incremental disposable dollar, people will spend 60% of it.발음듣기
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They're going to save 40% of any incremental disposable dollar and then the multiplier is going to be one over that, is going to be 1/0.4 which is the same thing as one over two-fifths, which is the same thing as five-halves, which is the same thing as 2.5.발음듣기
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For example, in this situation, we just saw that Y, the equilibrium Y is going to be 2.5 times whatever all of this other business is.발음듣기
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We might increase B by $1 billion by increasing government spending by $1 billion or maybe having this whole term including this negative right over here become less negative by $1 billion.발음듣기
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Maybe we have planned investment increase by $1 billion and that could actually be done a little bit with tax policy too by letting companies maybe depreciate their assets faster.발음듣기
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Essentially any way that we increase B by $1 billion, that'll increase GDP by $2.5 billion, 2.5 times our change in B.발음듣기
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Another way to think about it when you write the expression like this, if you said Y is a function of B, then you would say look the slope is 2.5, so change in Y over change in B is equal to 2.5, but I just wanted to right this to show you that this isn't some magical voodoo that we're doing.발음듣기
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