Cross Elasticity of Demand Price of one good effecting quantity demanded of another
Cross Elasticity of Demand
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- So far we've been focused on 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 we are going to explore is how we can go cross goods.
- So we are going to talk about the cross elasticity of demand.
- And there is multiple different scenarios we can think about. But its
- really thinking about how price change in one good might affect quantity demanded in another.
- To see a example of this. Think about two airlines.
- Two competing airlines, maybe its 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 over here is a $1000 for a round trip.
- Quantity demanded is 200 tickets, let's say in a given week.
- Airline two's price is $1000 for the round trip,
- the quantity demanded is 200 tickets as well.
- Now, let's think about what will happen if Airline 1 raises its price from $1000 to $1100?
- We could even do something less dramatic than that. To $1050.
- So, a relatively small increase in price.
- Remember when we are thinking about the % price increase, we are thinking about elasticity.
- In general, we don't just say - OK. $50 on top of a $1000 is a 5% price increase.
- That's what we would in kind of everyday thinking, if you went from a $1000 to $1050.
- You would say that is a $50 increase on a base of a 1000. Or that is a 5% increase.
- When you think about elasticities, because you want to have the same % change between...
- you go from a 1000 to a 1050 or if you go from a 1050 down to a 1000.
- We actually use the average point as the base, so the percent change in this scenario...
- I'll write it in quotes because it's a little different than what you do in traditional
- mathematics, when you think about percent changes. It's you had a
- 50 change in price. Your price went up by 50
- And on our base we'll use 1025, which is the average of 1000 and 1050
- We'll say increase in price, although we'll put that increase in quote
- because we're using it on the average
- It's 4.9% increase using the midpoint as the base
- Now when that happens -- everyone today uses travel site to compare prices
- if these really are the exact same route
- going from the exact same airport to the exact same airport, leaving at the exact same time
- everyone is going to take this one now, because it's only $1000
- Even just $50, why would they ride on this airline
- So this quantity demanded is going to go to 0
- And this quantity demanded is going to go to 400
- We're not going to think about the actual capacity of the plane and all that
- We're gonna have a very simple model here
- So what was the percent change in quantity for airline 2 here?
- Well once again, our change in quantity is 200 not 400
- We went from 200 to 400, so we gained 200
- And our base, we want to use the average of 200 and 400 which is 300
- And so this is approximately 67%
- So we have, all of a sudden, our cross elasticity of demand for airline 2's tickets
- relative to A1's price
- and we get the % change in the quantity demanded for A2's tickets, which is 67%
- over the % change not in A2's price change, but in A1's price change
- That's why we call it cross elasticity. We go from one good to another
- So for simplicity, that's roughly 5%
- So you have a very high cross elasticity of demand
- If you even increase this maybe by $5, you might have had the same effect
- So you would have had a very large number here
- And that situation right here for this cross elasticity of demand is
- because these things are near perfect substitutes
- The way we set up this problem we said
- Well people don't care which one they take. They'll just go for the cheapest one
- When you have nearly perfect substitutes for each other, like this example here
- the cross elasticity of demand approaches infinity
- It gets higher and higher and higher. In theory, if these are really, really, really identical
- even if you raise a penny, people will say, why would I waste a penny?
- I would just use airline 2
- And so this number would be even lower here. So this thing might approach infinity
- And notice, this was positive. When we just in regular price elasticity of demand
- the only way that you would increase quantity for a traditional good was by lowering price
- but here we raised price on a substitute competitive product
- and we raised the demand for airline 2's product which actually makes a lot of sense
- So it wasn't a negative relationship. It's actually a positive value here
- But you could have that negative relationship using cross elasticity of demand
- This is the example of a substitute
- We could think about the example of a complement
- So what if we're talking about e-books?
- 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
- Let's say the price of an e-reader that you would need for my e-book is $100
- but let's say that the price of the e-reader goes down from $100 to $80
- So you had a $20 decrease in price
- Well, what's going to happen to my e-book, assuming its price does not change?
- Well then the quantity demanded for my e-book will go up
- So let's say the quantity demanded for my e-book goes up by 100
- because more people are going to afford this
- or they're gonna have money left over when they buy this to buy more e-books
- and so I don't even know what the price for my e-book 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 price elasticity of demand
- but you'll see that you'll actually get a negative value
- like we used to seeing for regular price elasticity of demand
- And when we do calculate, remember, you want to do your % price change in e-book quantity
- over percent change in e-reader price
- And the other thing you have to remember, you don't just take -20/100, you
- take -20 over the average of these two when you're thinking of it in the elasticity context
- So this value right over here is -20 / 90, the average of those two
- This value right over here is going to be +100 over the average of these two, which is 1050
- And so we get -- 100/1050 which gets you to about .095
- So about 9.5% change in quantity demanded for my book
- And then this denominator right here is -20 / 90
- So you get a drop of 22%
- If you divide the numerator by the denominator, it's .0952/-.22222...
- and you get -0.43
- And this make sense. If you lower the price of the e-reader, this complement product
- a product that goes along with my e-book, it increases the demand
- Just like you get with price elasticity of demand, you get a negative value over here
- What about completely two unrelated products?
- Let's say that I have basketballs
- And the price of basketballs goes from, let's say, $20 to $30
- What's going to happen to my e-book?
- Well, my e-book's not gonna change. They're gonna stay at 1000
- So my % change in the quantity demanded of my e-book is going to be zero in this example
- when we wanna do this cross elasticity of demand over my % change in basketballs
- which would be 30/25 so whatever that is
- 10/25, I should say, sorry, which is a 40% increase. So that would be
- 0/40% which equals zero
- 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 elasticity of demand
- If they're complements, you'd have a negative cross elasticity of demand
- If they're substitutes, you would have a positive and the
- closer the substitutes they are, the more
- positive your cross elasticity of demand is going to be
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