When we were considering the problem of excise taxes and who bears what burden? We understood that it had a lot to do with responsiveness of quantity demanded to prices. Imagined the following. Suppose you are running a store, we'll put price on the vertical axis and quantity on the horizontal axis. Suppose that you had a deal where you found out at seven dollars per unit, you would sell 100 of these units in a day. It's a retail output. You've got seven dollars for some product and selling 100 units a day. Somebody says, "Hey, you know what? We should have a sale. Let's put a sign on the door that says 50 percent off all day Thursday." So, you say, "Okay. I understand what that is, that's going to be $3.50." Now, suppose as a result of reducing it from $7 to $3.50, you move from the original point which we'll call X, to this point, which we'll call Y, that's like 101 units. So, as a result of dropping our price 50 percent you get a one percent increase in volume. Is that possible? Sure. You could imagine a demand curve that's just pretty steep like this. Now, that's probably not a very smart move. Having a 50 percent off sale, what all it does is increase the traffic through your door by one percent, that's going to be pretty painful on your cash register at the end of the day. Now, alternatively, you could have that same sale. Suppose that you sold some point Z, which we'll say is 1,000 units. Is that possible? Sure. The demand curve could be one that looks just like this D1. That curve, which is much flatter than the steeper D0, that curve is quite possible, it's realistic. You can see in that case, your 50 percent reduction in price, led to a tenfold increase in the amount of volume through your door. So, if you're running a retail outlet, and you're thinking about whether you're going to run ads in the newspaper for having X off air on Sunday's newspaper, you've got to have kind of an idea about what this looks like. Understanding this responsiveness is very important to understanding rather you should be having these types of sales or perhaps even just thinking about inching your price up a bit, because very few people move away from your market. Economists have a term for this, elasticity of demand. Economists call this elasticity of demand, and elasticity of demand is the responsiveness of quantity demanded to changes in price. We have a definition for this, that's E, which for us is elasticity, is equal to the percentage change in quantity over the percentage change in price. This is elasticity to us. What it basically says, and just thinking about the ratio of the impact on quantity for any impact on price. You're thinking about that work ratio, it's very important. I'm going to give you a classification of these, and we'll call this classification. Remember, E, which is elasticity, is equal to the ratio of the percentage change in quantity over the percentage change in price. Our classification says that it's inelastic if the absolute value of E is less than one. These vertical bars on either side of the variable name E, meaning absolute value. Just drop the sign, which is looking at the raw number. So, what's absolute value mean? Absolute value just means, whatever the sign of that- you compute that ratio and just drop the sign. The sign is always positive. Now, why do we do this? Well, economists can be sometimes a little bit lazy about doing simple arithmetic. Look at this ratio. What's the sign of that ratio? Well, since we've already established that demand curve is downward sloping. Anytime, prices going up, quantity is going down. Anytime, prices going down, quantity is going up. We have that inverse relationship between price and quantity. So, the sign of that ratio is always going to have a positive change in the numerator and a negative change in the denominator or the other way around. So, the sign of the total ratio is going to be negative every time. So, instead of working with negative numbers, we just do absolute value. We say that it's inelastic if the absolute value is less than one. Let's write out the full classification, and then we'll spend some time thinking about it. We say it is elastic if the absolute value is greater than one, it's elastic. We say it is unit elastic if the absolute value is exactly equal to one. So, what's the big deal about this one? Everything seems to hinge about whether it's equal to one, greater than one, and less than one. The big deal here is that we're talking about a ratio. So, number one is always important in the ratio because it tells you whether the numerator or the denominator is stronger. If the absolute value was greater than one, it means that the impact in the numerator, which would be change in quantity, is much bigger than the impact in the denominator, which is changing price. If it's less than one, it means that the numerator effect, that is the change in quantity, is smaller than the denominator effect. Think about some arbitrary curve I'm going to draw here. Again, we have price on the vertical axis, quantity on the horizontal axis. Think about that demand curve that we drew for gasoline, that demand curve for gasoline looked pretty steep. What that meant was, that we can have very big swings in price, that's the denominator. Very big swings in price will lead to hardly any change in quantity, and think about this example. Suppose this is the original price and this is the original quantity, and suppose price went up dramatically, it doubled from $2 a gallon to $4 a gallon. Well, that would be a huge increase in the denominator, and the numerator would have what effect? Hardly any. People don't cut back very much on gasoline in this. So, there's very little change in quantity for a wild change in price. That means the denominator can get really large compared to a small numerator. That would be a situation that looks like this, the ratio of the change in quantity over the change in price is less than one. So, let's get a little bit more concrete about this, and let's just draw two curves, then I'll ask you a question. So, let's go over here, and put a couple axis systems up. We have one, which we'll call market one has a demand that looks like this. We have another one, which we'll call market two, which has a demand that looks like this. If I were to ask you to think which one of these would you call elastic or which would you call inelastic? Well, hopefully, you'll see that in fact, this product is the one that's going to be inelastic, because you can have wild swings in price and hardly any change in quantity. If we remember, our formula for elasticity is equal to the percentage change in quantity, divided by the percentage change in price. That ratio is going to be less than one when the curve is very steep. On the other hand, over here, you could have very little change in price, could cause huge changes in quantity. You'd have just a little bitty drop in price from here to here, would change quantity from here all the way down to here. So, in that market, the denominator can be small, but the numerator's going to be very big. That of course, fits our story about elasticity with the absolute value of that ratio is greater than one.