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what I want to do in this video is focus a little bit more on the results of the last video and make sure that they make intuitive and mathematical sense to us because something slightly strange happened we had a linear demand curve right over here which means for any given change in price right over here so in all of the examples whether we went from A to B or C to D or E to F we had a one dollar drop in price we had a one dollar drop in price one dollar drop in price and every time we had a one dollar drop in price we had a two dollar increase or we had a two unit increase in quantity demanded so we had a two unit increase in quantity demanded this is a linear demand curve but despite the fact that for each you for each dollar drop in price we had the same increase in quantity demanded the slightly maybe unintuitive thing that happened was we had a slight we had a different and actually a very different elasticity of demand and you might imagine that probably has something to do with the fact that elasticity of demand is based on percentage change in quantity relative to percentage change in price instead of just change in quantity over change in price if it was just change in quantity over change in price we would get something we would be constant but we saw very very different results and when you look closely at these so let's focus on this region between a and B right over here we had a one dollar change in price or one dollar change in price was on a relatively large base our price was already high and remember we use we use to figure out the percent change we use a dollar over the average the average of our two points so we don't do a dollar over nine because then we would have a different elasticity when we went from A to B then when we went from B to a $1 over nine versus a dollar over eight it would give you two different percentages instead we say a dollar over eight and a half so this price percent change was in the teens while this quantity percent change is going to be with 67% two over two over an average quantity of three in this region right over here so you had a relatively large actually quite large percent change in quantity over a relatively small percent change in price 67% over something that's in roughly in the mid-teens percentage and so that's why the absolute value of our elasticity of demand was a relatively large number if you don't think about the absolute value get a negative number because this is the downward this is a downwards sloping line but if you focus on the absolute value it's a the magnitude of it is a relatively large number Ella tively large percent change in quantity relative to your percent change in price and it all comes out of your quantities are low here so if you move to on a low base you're going to have a large percentage change in quantity and your prices are relatively high here so change in one isn't going to be that large of a percentage but when you have the when your absolute value of your elasticity of demand is greater than one like it is right over here so when your absolute value of your elasticity of demand is greater than one it's usually called this point in the curve is elastic or generally elastic so this is elastic elastic you get some nice percentage movements in quantity for given change percentage change in price then when you go over here our prices have gone our price is debt is lower when we're in this region between C and D so that dollar difference is going to be a larger percentage change in price and our quantities are higher so that $2 change is going to be a lower change in quantity and actually they end up being the same thing because you have a dollar change in price over an average base of five right the average between 550 and 450 is five so if a 20 percent change in price a 20 percent drop in price and you have a 20 percent increase in quantity 20 percent increase in quantity so let me write that this is in the teens over here my writing is getting too small so I won't do that so you have a 20 percent change in price and a 20 percent increase in quantity is 20 percent because you have two over the average year 2 over 10 so 20 percent increase so that's why your elasticity of demand or the magnitude of your elasticity of demand is exactly 1 and if you if your magnitude of your elasticity demand is exactly 1 we say that you have unit elasticity at that point elasticity and then finally if you go all the way down here our prices end up being quite low our prices are quite low so a dollar change is actually a huge percentage price change right our base here is our average base here is a dollar 50 in this region right over here and so a dollar over a dollar 50 it's a huge it's a huge it's actually a it's a it's a 60 it's a sixty seven percent change in price sixty seven that's right yeah one dollar is a two-thirds change in price so it's a huge percent change in price but once again now our quantity is much larger so two dollar increase isn't that large of a change in quantity so you have a smaller percent change in quantity over a large percent change in price so that means that you're relatively inelastic you're not getting you're not getting a lot of change in quantity for the the magnitude of your change in price and so if you're if the magnitude of the elasticity of demand is less than one over here we call that either relatively inelastic or just inelastic in E lastic so I'll leave you there in this video and just I want you to really kind of internalize what we're doing here especially with the math and especially understanding why the elasticity's change here get you thinking in terms of percentages and also make you hopefully you appreciate why we're taking the average of these two points when we find the denominator for the percentages instead of just taking one of the two points so that we get the same elasticity of demand either direction we go in