Price elasticity of demand

What we are going to think about in this video is elasticity of demand. elasti-ci-ty -- elasticity of demand. And what this is, is a measure of how does the quantity demanded change, given a change in price, or how does a change in price impact the quantity demanded. So change in price -- change -- change in price change in price impact quantity (want to be careful here) quantity demanded. When you talk about demand, you are talking about the whole curve. Quantity demanded is a specific quantity. Quantity demanded. And the way that we as economists -- I'm not really an economist but since we are doing economics, we can pretend to be economists -- The way economists measure this is they measure it as a % change in, % change in Quantity over the % change in Price. And the reason that they do this, as opposed to just say, change in quantity over change in price, is because if you did change in quantity over change in price, you would have a number that is specific to the units you were using. So it would depend on whether you were doing quantity in terms of per hour, per week, or per year. And so you would have different numbers based on time frame, or the units you might use. But when you use a percentage, when you use a percentage, it is a unitless number. Because the % you're taking a change in some quantity divided by that quantity, so the units themselves actually cancel out. And the reason why it is called elasticity -- this might make some sense to you -- or the reason why I like to think it's called elasticity is I like to imagine something that's elastic, like an elastic band or a rubber band. And in a rubber band, if you pull it, depending if something, So let's say this one is inelastic. So if you pull, you're not going to be able to pull it much. It is going to be fairly stiff. It's not going to stretch a lot. While if something is inelastic, or for given amount of force, you are not able to pull it much. And if something is elastic, maybe for the same amount of force, you're going to be able to pull it a lot. So this right over here is elastic, and so the analogy maybe might make a little sense relative to applied price and demand. Something is elastic... so let me write this down Elastic, elastic. So let me write "very elastic." Very elastic if a given change in price, given price change, you have -- and especially, we'll talk about % in a little bit -- but the given change in price, you have a large change in demand. So large percentage change. Let me speak in terms of percentage. Given a % change in P, you end up having a large % change in Q. That would be very elastic. So you could imagine the P is like the force, and the Q, the quantity demanded is how far the thing can get stretched apart. And that's why we would call this very elastic, just like a very elastic rubber band. And if something is very inelastic, very in-e-lastic, if given a % change in P, you have a small, small, % change in Q. So, if -- Just like a rubber band -- for given amount of force if you are not able to pull it very much at all, then it is inelastic. If you are able to pull it a lot, it is elastic. Same thing with price and quantity. If you, for given change in price -- if a change, if the quantity demanded, if the % quantity demanded changes a lot, very elastic. If it doesn't change a lot, very inelastic. Now with that out of the way, let's actually calculate the elasticity for multiple points along this demand curve right over here. And I think that will give us a better grounding. Especially because there are a little, slightly -- um, I would call them -- unusual ways of calculating the % change in quantity and the % change of price. Just so we get the same number when we have a positive change in price, and the same as we get the negative change in price, or a negative or a positive, or a drop in price and an increase in price. So let me give myself some real estate over here, because I want to do some actual mathematics. And actually, all of this we will be reviewing in what I'm about to do and it'll give me some real estate to work with. So let me clear off all of that, and let me clear that right over here. And what I'm going to do is I'm going to calculate the elasticity of demand at several points along this demand curve right over here. And so the first one I will do at point A to point B, so let me make another column right over here. Elasticity of demand, and actually we are going to have one column that is elasticity of demand, so big E with a little subscript d, and the other one, I'll just take its absolute value. Because depending on -- sometimes people just like to think of the number which will tend to be a negative number, and sometimes people will like to look at the absolute value of it. So we will look at both and see what it actually means. So let's say our price drops from point A to point B. So from point A to point B, we have a $1, a -$1 change in price. And we have a positive, so this is a -$1 change in price, and we have a positive $2 -- haha, sorry -- a positive 2 burger per hour change in quantity demanded. So what is the elasticity of demand there? Let's write it over here; I'll do it in A's color. So the elasticity of demand, remember it is the % change in quantity, so -- % change in quantity -- let me write it -- % change in quantity over % change in price. And so we have -- what is our % change in quantity? So it is going to be the change in quantity over some base quantity. So our change in quantity is 2, so it's going to be equal to 2 over -- now in traditional terms, this is what I want to kind of clarify, is a little bit unusual in how we do it, but we do it so we get the same elasticity of demand whether we go from A to B or B to A, or essentially we get the same elasticity of demand along this whole part of the curve. Instead of just dividing the change in quantity divided by our starting point, what I want to do is I'm going to divide the change in quantity divided by the average of our starting and our ending points. So that is going to be 2 over -- and I'll actually do the math explicitly -- actually, no, let's just think about it. What's the average between 2 and 4? Well, the average is just going to be 3. That's the average of 2 and 4. I could write -- let me write it down just so it's clear. This right over here -- that right over here -- is 2 + 4 over 2. That's how you get 3. That's how you would calculate the average. Alright, so that is our proportionate change, and then you want to multiply by 100 -- times 100 -- to actually get a percentage. And then what is our change in price? Well, we are going to do the same thing: the percent change in price. Our change in price is -1. It is -1, over -- and once again, we don't just do -1 divided by 9 -- We do it over the average of 8 and 9, and the average of 8 and 9 is 8.5, and then multiply by 100 to get your percentage. Now these hundreds obviously cancel out and so we are going to be left with -- when you divide by a fraction, it's the same thing as multiplying by its inverse. So we are going to get 2/3 times -8.5/1 or times -8.5 -- times -8.5. Get out our calculator and it is -- so 2, well, I'll multiply 2, times -8.5 and then divided by 3, which gives us -5.6667, which is really -5 and 2/3. So I'll just write it negative -- I'll round it as -5.67. So this is approximately equal to -5.67. So right over here, it is -5.67, and this absolute value is obviously just 5.67. And I'll leave it to you to verify for yourself that you'll get the same elasticity of demand using this technique when you use the average of base of your percentage, going from 9 to 8 in price as going from 8 to 9 in price, which is different than if you used 9 as the base or the 8 as the base. So this right here is the elasticity of demand, not just of point A -- you can kind of view it as the average elasticity of demand over this little part of the curve, (which is really a line in this example) over this part of the arc. So we will write that part right over here; I'll write the absolute value. The absolute value of our elasticity of demand is 5.67. Now, let's do the other 2 sections right over here. So let's think about what happens -- let's think about what happens when we go from C to D. So our elasticity of demand there -- so from C to D, we have a change in quantity, once again, of +2, and our change in price, once again, is -1. But we will see that even though -- that the change in quantity over -- the change in quantity and the change in price is the same, we're going to have a different elasticity of demand because we'll start -- we have different starting points. Our starting points and our ending points for price are lower, and our starting and ending points for quantity are higher. So it will actually change the percentage. So let's see what we get. So our percent change in quantity -- we have a change in quantity of 2, and then our average quantity is 9 + 11, which is 20, divided by 2 is 10. All of that over change -- percent change in price -- so we have -1, -1 (let me scroll down a little bit) -1 divided by the change in... -1 divided by the average price. So -1 is the change in price and we want to divide that by the average price. Well, 5.50 plus 4.50 is 10 dollars divided by 2 is 5. So the average price is 5. And we can multiply the numerator by 100 and the denominator by 100, but that won't change anything, because we can just divide both by 100. And so this is equal to 2 over 10, times -- dividing by a fraction is the same as multiplying by its inverse -- times -5 over 1, and this is just, because 2 over 10 is the same as 1/5, 1/5 * -5/1, it is -1. So this right over here, so our elasticity of demand right over here is -1, or its absolute value is 1. So the absolute value of the elasticity of demand, right over here, is equal to 1. And let's just do one more section, and then maybe the next video, we can think a little bit about what it is telling us. So let's think, do this last section over here, just for some practice. I encourage you to pause it and try it yourself. And so, we are going to think about this section right over here. So once again, our change in quantity is +2, and our change in price is -1. And our elasticity of demand: change in quantity, 2, over average quantity, which is 17. Change in price is -1, over average price: 1 + 2 divided by 2 is $1.50, or a $1.50 is right between these two. Divided by $1.50. We don't have to multiply the numerator or the denominator by 100 because those just cancel out. So we get 2 over 17 times negative -- well we can just write this as $-1.50 over 1. And this is equal to getting our calculator back out. So this is equal to -- I'll just write, well, it's really just going to be -3 over 17, right? 2 * -1.50 is -3, over 17 is -- -3 divided by 17 -- is equal to -.1, I'll just say -.18. So here it is. -0.18, and its absolute value is 0.18. So the elasticity of demand over here is 0.18. And I'll leave you there, and in the next video, we'll think about these results a little bit.