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Current time:0:00Total duration:10:27

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 the actual increase in output if you are a if you if you if you take all the assumptions that we took in this that the actual change in output and aggregate income was larger than the change in government spending and so you might say oh okay you know Keynesian thinking this is very left-wing this is spending the government's growing larger right here I'm more conservative I do I'm not a believer in Keynesian thinking and the reality is you actually might be whether you're on the right on the left although Keynesian economics it tends to be poo-pooed more by the the right and embraced more by the left most of the the mainstream right policies especially in the US have actually been very Keynesian they just haven't been by manipulating this variable right over here 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 so if we if we go back to just having our G so we're now back on this orange line our original planned expenditure you could based on this model right over here also shifted up by lowering taxes if you if you change your taxes to be taxes minus 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 you're multiplying this whole thing by a negative number by negative c1 c1 your marginal propensity to consume we're assuming is positive your mothers a negative out here so when you multiply it by a negative when you multiply a decrease by a negative so this is a negative change in taxes then this whole thing is going to shift up again so 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 make my graph too messy so this would be our new ex aggregate planned expenditures but the amount you would move up is by this coefficient out here cc1 negative C 1 times negative delta T so your change the amount that you would move up is negative C 1 times negative delta T if we're assume delta T is positive and so you actually have a C 1 delta T the negatives cancel out so that's actually how much it would actually move up and it's also Keynesian when you say if we increase taxes that will lower aggregate output because if you increase taxes if you increase taxes your the now all of a sudden this is a positive this is a positive and then you would shift the curve by that much and so you would actually shift the curve down and then you would get to a you would actually get to a lower equilibrium GDP so this really isn't a difference between right right-leaning fiscal policy or left or leading fiscal policy and everything that I've talked about so far at the end of the last video and this video really has been fiscal policy this has been the spending lever fiscal policy and this right over here has been kind of the taxing lever of fiscal policy if you believe either of those can affect aggregate output then you are essentially subscribing to the Keynesian model 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 the change in our output actually was some multiple of that and what I want to do now is to actually show you mathematically that it actually all works out that the multiple is actually the multiplier so if we go back to our original and this will just get a little bit math you right over here so I'm just going to rewrite it all so we have our planned expenditure just to kind of read igg our minds into the actual 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 this business right over here and we're just going to go with the original one not what I change and all this business let's just call that B that'll just make it simple for us to manipulate this so let's just call all of this business right over here B we can substitute that back in later we know we know that an economy is in equilibrium when planned expenditures is equal to output that is an economy in equilibrium so let's set this let's set planned expenditures equal to equal to aggregate output which is the same thing as aggregate expenditures with the same thing as aggregate income and so now we can just solve for our equilibrium income we can just solve for it so you get y is equal to c1 times y plus B this is going to look very familiar to you in a second subtract C 1 times Y from both sides y minus c1 y that's the left-hand side now on the right hand side obviously if we subtract c1 y it's going to go away and then we have that is equal to B and then we can factor out we can factor out the aggregate income from this so Y times 1 minus c1 is equal to B and then we divide both sides by 1 minus c1 1 minus C 1 and we get that cancels out we get I'll rewrite I'll write it right over here we get we get and now you get a little bit of a drumroll aggregate income our equilibrium equilibrium aggregate income aggregate output aggregate aggregate GDP is going to be equal to is going to be equal to well just 1 over 1 minus C 1 times B remember B was all this business up here now what was one my what is 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 this c1 right over here is our marginal propensity to consume marginal propensity to consume 1 minus our marginal propensity to consume is actually and I don't think I've actually referred to it before let me rewrite it here just we know the term so c1 is equal to our marginal propensity is equal to our marginal propensity to consume so for example if this is if this is 30% or 0.3 that means for every incremental dollar of disposable income I get I want to spend 30 cents of it now 1 minus c1 1 minus C 1 you could view this as your marginal propensity to save if I'm going to spend 30 percent that means I'm going to save 70 percent so this is just saying I'm going to save 1 minus C 1 if if I'm spending 30 percent of that incremental disposable dollar then I'm going to save 70 percent of it so this whole thing so this is a marvel procedure to consume this whole this entire denominator is a marginal propensity to save and then one over that and so 1 over 1 minus C 1 which is the same thing as 1 over the marginal propensity to save that is the multiplier we saw that a few videos ago 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 that money is income is going to spend some fraction of it based on their marginal propensity to consume and we're assuming that it's constant throughout the economy at all income levels for this model right over here and then they'll spend some of it and then the person that they spend the money on they're going to spend some fraction when you keep adding all of that infinite series up you actually get this multiplier right over here so this is equal to this is equal to our equal to our multiplier so for example if B gets shifted up if B gets shifted up by any amount let's say B gets shifted up and it could get shifted up right changes in any of this stuff right over and that exports can change planned investment can change can be shifted up or down the impact on the impact on GDP is going to be whatever that shift is times the multiplier times the multiplier we saw it before if for example if for example if C 1 is equal to is equal to 0.6 then that means that for every incremental disposable dollar people will spend 60% of it that means that the marginal propensity to save per to save is equal to 40% they're going to save 40% of any incremental disposable dollar and then the multiplier the multiplier is going to be 1 over that it's going to be 1 over 0.4 which the same thing as 1 over 2/5 which is the same thing as 5 halves which is the same thing as 2.5 so for example in this situation we just saw that that why the equilibrium Y is going to be 2.5 times whatever all of this other business is so if we change B by let's say a billion dollars and maybe we change maybe we if we increase B by a billion dollars we might increase B by a billion dollars by increasing government spending by a billion dollars or maybe having this whole term this whole term including the negative right over here become less negative by a billion dollars maybe we have planned investment increase by a billion dollars and that could actually be done a little bit with tax policy 2 by letting companies maybe depreciate their assets faster if we can increase net exports by a billion dollars essentially any way that we increase B by a billion dollars that will increase GDP by 2.5 billion dollars 2.5 times our change in B so we can write this down this way our change in Y our change in Y is going to be 2.5 times our change in B or another way to think about it when you write the expression like this you see if you said Y is a function of B then you would say look the slope is 2.5 so change in Y change in Y over change in B is equal to 2.5 but I just wanted to write this to show you that this isn't some magical voodoo what we're doing this is what we looked at it visually when we look at the Keynesian cross but there's really just described describing the same multiplier effect that we saw in previous videos and where we actually derived the actual multiplier