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Video transcript

so far we've been focused on the elasticity of demand for only one good we've thought about how changes in the price of that good affect changes in its quantity now where we're going to explore is how we can go across goods so we're going to talk about the cross elasticity of demand cross elasticity tissa t of demand and there's multiple different scenarios we can think about but it's really thinking about how price change in one good might affect the quantity demanded in another good and to see an example of this think about two airlines to competing airlines maybe it's the same exact route going at the exact same time maybe between New York and London so airline one right over here airline two very competitive price right over here is $1,000 for a roundtrip quantity demanded is 200 tickets let's say in a given week airline - price is $1,000 for the round-trip and the quantity demanded is 200 tickets as well now let's think about what will happen what will happen if airline one raises its price raises its price from $1,000 to $1,100 to $1,100 in fact we we could even do something less dramatic than that - 1052 1050 so a relatively small increase in price and remember when we think about the percentage price increase we're thinking about elasticity's in in general we don't just say okay $50 on top of a thousand dollars that's a 5% price increase that's what we would do in kind of everyday thinking if you said you went from $1000 to 1050 you would say that's a 50% I'm sorry that is a $50 increase on the base of a thousand or that is a 5% increase but when you think about elasticity's because we want to have the same percent change between if you go from 1,000 to 1050 or if you go from 1050 down to a thousand we actually use the average point as the base so the percent change in this scenario let me write it right over here so our percent our percent change change and I'll write it in quotes because it's a little bit different than what you do in traditional automatics when you think about percent changes is you had a 50 change in price your price went up by 50 and on our base we will use 1025 which is the average of a thousand and 1050 and so that gives us a change of that gives us a change of fifty divided by 10 25 is equal to let's say let's say roughly four point nine percent so this is approximately four point nine percent will say increase in price although we're going to put that increase in quotes because we're using it on the average and we do that so that if we said it was ten fifty two thousand it would still be a four point nine percent decrease using this same idea using the midpoint as the base now when that happens you know everyone today they use these travel sites where you can compare prices and people if these really are the exact same route going from the exact same airport to the exact same to the other Airport in London leaving at the exact same time everyone is going to gravitate to this one now because it's only $1000 even just to save 50 dollars why would they ride on this airline so this quantity demand is going to go to zero and this quantity demanded is going to go to 400 and we're not going to think about the actual capacity of the planes and all that we're going to have a very simple model here so what was the percent change in quantity for airline two right over here well once again our change in quantity is two hundred not four hundred its we went from 200 to 400 so we gained two hundred and our base we want to use the average of 200 and 400 which is 300 and so this is approximately this is approximately 67% so we have all of a sudden our cross elasticity of demand for airline twos for airline twos tickets relative relative to a one's a one's price and we get the percent change in a 2's tickets the precisely the percent change in the quantity demanded for a to stick 'its which is 67 and over the percent change not in a two's price change but in a ones price change that's what we call it cross elasticity we're going from one good to another over so so that's roughly well let's just say for simplicity roughly five percent roughly five percent and so you do the math this gets us to so if you have 67 percent 67 percent divided by five percent you get to roughly thirteen point four so this is approximately thirteen point four so you have a very high cross elasticity of demand in fact if you even increase this maybe by five dollars you might have had the same effect and so you would have had a very a very large number here and that situation right here for this cross elasticity demand it's because these things are near perfect substitutes the way that we set up this problem we said well people don't care which one they take they're just going to go for the cheapest one and so when you have near substitutes near substitutes or nearly perfect substitutes nearly perfect perfect substitutes substitutes for each other like this example right here the elast the cross elasticity of demand approaches approaches infinity it gets higher and higher and higher in theory if these are really really really identical even if you raise this a penny people say well why would I waste a penny I would just use airline two and so this number would be even lower right over here and so this thing might approach a fitted infinity and notice this was a positive this was a positive when we just did regular price elasticity of demand the only way that you would increase quantity for traditional good the way you would increase quantity was by lowering price but here we raise price on a substitute competitive product and we raised demand for your product which actually or for airline twos product which actually made a lot of sense so it wasn't it wasn't a negative relationship it's actually a positive value right over here but you could have things in other you could have that negative relationship using cross elasticity demand this is an example of a substitute we could think about the example of a compliment compliment so what if what if we're talking about what if we're talking about ebooks so let's say I have some type of an e-book and the current quantity demanded in a given week I don't know is 1000 and let's say that the price of an e-reader that you would need from my eBook the current price for an e-reader is $100 but let's say that price of the e-reader goes down from $100 to I don't know goes down from $100 to $80 so you had a you had a $20 decrease in price well what's going to happen to my eBook just even holding its price it assuming it's price does not change well then the quantity demanded from my eBook will go up so let's say the quantity demanded for my eBook goes up by a hundred because more people are going to be able before this or they're going to have money left over when they buy this to buy more ebooks and so I don't even know what the price for my eBook is but at a given price point the quantity demanded will go up and so this goes to 1100 and so I'll leave it to you to calculate this elasticity price elasticity of demand but you will see that you will actually get a negative value like we're used to seeing for regular price elasticity demand and when you do calculate remember you would do you want to do your percent price change percent change in ebook ebook quantity over percent change in eReader an e-reader an e-reader price and the other thing you have to remember you don't just take negative 20 over 100 you take negative 20 over the average of these two when you're thinking of it in the elasticity context so this right over here actually maybe we'll just work it through pause it and try to do it yourself so this value right over here this one right over here is negative 20 negative 20 over 90 the average of those two and this value right over here is going to be plus 100 plus 100 over the average of these two so the average of those two is 10:50 and so we get we get so this is 100 divided by 10 50 which gets you to about 0.95 so about nine and a half percent change in quantity demanded from my book and then this this denominator right here what did I do the denominator right there is negative 20 negative 20 divided by 90 negative 20 divided by 90 so you get a drop in 12 22% and so if you divide the numerator by the denominator you get zero point nine five two divided by negative point two two two two two I'll just put a couple two is there and you get a negative point four three so this is equal to negative point four three point zero point four three and this makes sense if you lower the price of a eReader this complement product a product that goes along with my ebook it increases the demand so you just like you get with price elasticity of demand you get a negative value over here and what about completely two unrelated products so let's say let's say that I have basketballs basketballs and the price of basketballs goes from let's say they go from $20 to $30 what's going to happen to my ebook well my ebooks not going to change its going to stay at $1,000 so my percent change in the my percent change in the quantity demanded of my ebook is going to be zero in this example so we're going to have zero and we want to do this cross elasticity of demand over my percent change in basketballs which would be 30 over 25 so whatever whatever that is what is that that's like 30 over 25 that'd be a or five there would be a 10 over 25 I should say sorry which is a 40 percent increase so that would be 0 over 40 percent which equals 0 so for unrelated products products where the price change in one of them does not affect the quantity demanded in the other it makes complete sense that you have a zero cross eli city of demand if their compliments you would have a negative cross the elasticity of demand and if they're substitutes you would have a positive one and the closer the substitutes they are the more positive your cross elasticity of demand is going to be
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