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# Elasticity and strange percent changes

## Video transcript

in this video I want to clarify a little bit about why we calculate the percent changes when we're thinking about elasticity the way that we do so just to remind ourselves and we'll focus on price elasticity of demand although we've been exposed to other types of elasticity's already but just as a review price elasticity of demand so the ELS tissa t of demand is defined as the percent change in quantity demanded over the percent change the percent change in price so first i'll calculate the conventional way the way that you would do in a traditional microeconomics class and then i'll calculate it the way that you would just based on how you would traditionally calculate percentages and we'll see why micro economists like to do it the way that they do so first so first we'll talk about the correct way and I'll put it in quotes because correct is really just by definition really just by convention but we first think about the percent change in quantity percent change in quantity and we're going to assume we're going to calculate the elasticity of demand between point a over here point a and point B over here so what is our percent change in quantity well our absolute change in quantity going from A to B we have increased by two so we have increased by two level write it down here this is going to be two over and then this is kind of the slightly strange thing that we do when we calculate our percentages we don't say 2 over 4 we say 2 over the average of 4 and 6 2 over the average of our starting point and our ending point and the average of 4 and 6 is 5 so this is going to be we have a 40% change based on how we calculated the percentages in our in our quantity demanded and then let's do our percent change in price so this is all going to be our over our percent change in price so our absolute change in price is negative $1 negative$1 and then instead of doing it over our starting point over to we do it over the average of the two over over 150 and negative 1 over 150 is negative two thirds or right about negative negative sixty six point seven percent if we say roughly so this right over here so based on how we calculated percentages and I want to make it clear this is kind of a strange way when we do it over the midpoint of the starting and ending points but we're saying that our percent change from A to B in quantity so our percent change in quantity this right over here we are saying it is 40% and then we are saying that this percent change in price right over here is negative sixty six point seven percent now the reason why this is valuable enough obviously if you do the math right here 40 percent over negative sixty six point seven percent you're going to get some let's see you're gonna get something I think it's going to be in the six is point six something but let's actually get a calculator out to calculate it so it would be forty divided by sixty six point seven gives you it's almost 60 so it's point roughly point six zero if we were to round so this is approximately zero point two six year it was five nine seven something actually I'll just leave it that way yeah point six zero now what's cool about this or what's useful about this and this is the reason why we economists do it is you would get the same answer whether you're going from A to B or whether you're going from B to a so this is the situation where we're going from where we're going from A to B but if we were to go from B to a if we were to go from B to a it's the exact same thing if we go from B to a what is our change in quantity our change in quantity is negative two so it would be negative two over now you wouldn't do it over your starting point you do it over the average this is this is why we will get the same value regardless of what direction we go in so we get the average of four and six it's going to be five and that's going to be over now going from B to a what is our change in price our change in price is now plus one it is plus one over the average of our starting point in our ending point over 150 now these are the exact same quantities both going to be a negative number here the negative is on the bottom here the negative is on top but either way you're going to and actually this was the negative point six zero because you have a positive divided by negative and this too when you evaluate it is going to turn out to be the exact same thing it's going to be negative negative zero point six zero now if you calculated percentages in the traditional way you would not get the same value for the price elasticity of demand whether you go from A to B and B to a and just to just to show that to you I will show I'll put this in quotation marks because it was not the wrong way to do it in general in fact this is how you would calculate price changes traditionally but it's not how you do it in kind of a micro economic sense and so if you do the wrong way if you said from A to B A to B you have a you have your change your absolute change in quantity is plus two and you are and your base this is remember this is the way that it's done outside of microeconomics your base is four and then your change in price you went down one and your base you started at a so your base is two this is what you do it outside of an economics class and so you get you get this would be equal to 50% plus 50% over over negative 50% over negative 50% and you so you essentially get negative one going from A to B using a traditional way of calculating percent change now what happens if you go from B to a what happens if you go from B to a well now all of a sudden your change in quantity is negative two now you to your base is now the starting point is six your starting point is six and then your change in price once again your increasing in price by one going from B to a so this is plus one and your base is now one so you will get this is negative 33 percent roughly it's negative 1/3 so 33 point three three three it keeps repeating over over 100% sorry over 100% so this will be equal to negative point three three so notice when you calculate percentages in the traditional way you get a different answer whether you're going from A to B or whether you're going from B to a and so the whole reason why when we take the percentages we take it over the average of our starting and our end points over the average of our starting and ending points so we get the same value for the elasticity of demand along this portion of the curve you can really view it as the average elasticity of demand over this portion of the curve and if you calculate it this way it doesn't matter whether you're going from A to B or B to a