Greetings, in our earlier video we talked a bit about how when you're dealing with the response of market to an excise tax, the relative jump in prices that reflect this excise tax depends a lot on sort of the shape of the demand curve. Sometimes quantity demanded is relatively unresponsive to price increases, that's the gasoline market. If prices go up for gasoline, people buy just about the same amount of gasoline, a little bit less, but just about the same amount of gasoline. When prices go down, people buy a little bit more gasoline. They might go ahead and take a weekend trip over to Bloomington, which is about an hour away from here, and try some different restaurants or something like that. So there's a little bit of flexibility. So what we want to do in this particular video, is to introduce a formal description about this idea of responsiveness of quantity demanded. Okay, so economists have a phrase for this, and the phrase for how we measure responsiveness of quantity demanded is something called price elasticity. And price elasticity, as you can see by this definition, I'll read it here, percentage change in quantity demanded divided by the percentage change in price. Percentage change in quantity demanded divided by the percentage change in price. And so we're going to write that as the following, elasticity equals percentage change in quantity divided by the percentage change in price. So this is a measure to how much quantity actually changes for any arbitrary change in prices. Okay, and in order to use this we need to get a little bit more clear about, what we'll call, classifications for the system. All right, so we're going to go to the next page, and I'm going to rewrite for you this formula for elasticity. Elasticity is the percentage change in quantity over the percentage change in price, and we have these sets of classifications. There's three of them. And it's going to get a little bit, we have a little bit of jargon to work our way through. The three classifications are inelastic. And then we have one called elastic. Some demand curves we call inelastic, some demand curves we call elastic, and some demand curves we say are unit elastic. And these classifications depend on the size of this particular ratio. And so, we're going to say that they're elastic if, and here comes a little bit of the jargon, the absolute value of that ratio, okay, if the absolute value of that ratio is less than one. Now, what is that? What's this mean right here? What is this? What does this term mean? We got these two vertical bars around it. Well, if you have had good training in mathematics, you know that means absolute value. If you had training and forgot it, or maybe never saw this, all absolute value says is, drop the sign. Absolute values says, I just want to know the size of the number, I don't care whether it's plus or minus. Now, the reason economists do this is because, as I said earlier, economists are lazy at mathematics. Okay, a little bit sloppy about it. They say, well, I just don't want to deal with negative numbers. See one of the things about this is, if you look up at the elasticity, look at that definition of elasticity, percentage change in quantity over percentage change in price. Every time the numerator, anytime take the denominator, suppose you raise price, the denominators got positive increase in price. What's going to happen to the amount of sales? They're going to go down. You remember from your little, and I'll remind you here, the little cloud above your head that says that quantity and price are inversely related along the demand curve. Anytime price goes up, quantity falls. Anytime price goes down, quantity increases. So that means, if the sign of the denominator is positive, the sign of the numerator is negative. Well, if you have a ratio where the sign of the numerator is different than the sign of the denominator, that ratio is a negative number. Okay, and so since demand curves are always having that slope, that means all elasticities are negative. And so, economists just say, well, instead of dealing with negative numbers, which sometimes makes my head hurt, let's just say, we'll use absolute value. And it will say, if elasticity, the absolute value of elasticity is greater than one, we call it elastic. And finally, if the absolute value of that ratio is equal to one, we call it unit elastic. So what's the big deal about this number one? What's this big deal about number one? Why do we have all these definitions that hinge upon the relative size of absolute value to the number one? Well, the reason is because any time you have a ratio, one is a very important number because it tells you which one is stronger. If the numerator, that's the thing on the top, if the numerator's stronger than denominator, then that ratio is going to be above one. If the numerator is bigger number than the denominator, in absolute value sense, then that's going to be greater than one, that means there's a big quantity effect for any price change. Conversely, if the denominator's stronger that means that the number in the, down here, if that's bigger than up here, it means you can have wild price changes and very little impact on quantity. So that's kind of like our story that we had, what this says is, that in situations like this, the demand curve is going to be pretty steep. You can have wild changes in prices, that's the denominator. You could have wild changes in prices, and very little change in quantity because no matter what happens along price here, there's very little change in quantity. On the other hand, situation like this, That's a relatively flat curve, looks something like this, maybe should put a D here so we know what we're talking about, demand curve. In this situation, okay, you can have very small price changes can cause huge jumps in quantity. So the denominator can be small changes, but the numerator's going to have big changes, that's called elastic. And of course, unit elastic is when the denominator and the numerator change at exactly the same percentage. Okay, so this classification is really important. You can go out and look up elasticity, economists have studied elasticity for just about everything. What's the elasticity for beer? What's the elasticity for tomatoes? What's the elasticity for corn? What's the elasticity for gasoline, for oil, you name it? People have done published papers showing some sort of rigorous test of what the shape of that demand curve is, and what these numbers would be. Okay, good.
