>> [music] Very well, we're back in the studio. I'm Jose Vazquez, and we are going to talk about elasticity this week. That's our topic for today for this week. And we introduce it at the barbecue restaurant. And the example we gave at that time, let's say you own a restaurant, barbeque restaurant like the one we, we were last time, and you wanted to increase the price of your sandwiches. Let's say, a friend of yours say, well why don't you increase the price of your sandwiches and that way you can make more money? And then your response is well, well, I may or may not. Because if you increase the price of your sandwiches two things could happen, right? Either you sell the, about the same number of sandwiches that you actually were selling before, and if that's the case, then, yeah, your revenue, your money, the money you made making sandwiches or selling sandwiches go up. But the other alternative is that when you increase the price of your sandwiches and the demand curve is downward sloping, you actually lose most of your customers or a lot of your customers proportional to the increase in price. And if that the case, then your money that you collect from selling sandwiches actually, actually go down. So it is not necessarily true that an increase in the price of your product will lead to more revenue. It depends of what happens to the quantity. So the, the variable that or the, the type of response or measure that we want here is a measure of how the quantity or, or your consumption for your sandwiches change as a result of a price change. And that's what we call an elasticity in economics. And the first one we'll do is that one, which is the price elasticity of demand, alright? So a good way to define this is by using a little bit of math or not math but a form of formal equation in, with, with numbers and fractions, right? So we can say that the price elasticity of demand for any product for x, we can use this little symbol here Ex. Write it a little bigger here, Ex. That's the price elasticity of demand for a good x sandwich. It's going to be equal to the percentage change in the quantity consume of x over the percentage change in the price of x, alright? So that is a very easy way of defining what do we mean by elasticity. And remember this is actually, this could be an elasticity for anything, right? Elasticity is simply a measure of the rate of change, and we can have it for any variable. In this particular section, we are really interested in the, the price, how the price of a good affects the quantity consumption of that good, so we are talking about the price elasticity of demand. But it could be in economics we'll deal with a lot of, many different elasticities, as we deal with in this, in this week and later throughout the course. Now we can summarize this a little better but, by instead of using the word change, we use a mathematical operator. And we say that is the percentage change. We going to use this triangle delta to represent change. And that compact equation for elasticity now is simply this, alright? It's a percentage change in the price in the quantity of x as a result of the percentage change in the price of x. Now remember that this is probably always going to be negative, because a demand curve is downward sloping. And you increase the price, the quantity consumed goes down, and if you decrease the price, the quantity consumed goes up. So the relationship between these two variables is inverse, so therefore the result of this operation here is going to be a negative number, alright? But we'll talk a little bit more about that in a second. So let's do an example, alright? Let's say that you're thinking about increasing the price of your sandwiches of x by, let's say, 10%. And you're trying to decide, if I increase the price of my sandwiches by 10%, would I be making more money or less money out of my sandwiches? Well it depends on how much the quantity changes, right? You have basically three different options here. The quantity can actually the quantity will go down for sure. So the quantity could go down by more than 10%, by less than 10%, or by exactly 10%, right? So one situation is that the quantity actually goes down let's say by about 5%, alright? So this is a negative change here. So what does that mean? Well that means that when you put those, those numbers into our equation here, right? The elasticity of x equals percentage change in Q of x over percentage change in the price of x. What you're going to have is that a, a percentage change of 10% here actually led to an reduction in quantity consumption by 5%, alright? So what does that mean? Will your revenue go up or down? Well probably go up right? We'll go, we'll, we'll, we'll go more in detail in a second. But your, your, the increase in price was proportionately more than a reduction in quantity. Basically that what we have here. So your reduction ins, in consumption was not proportionately, it was proportionately smaller than the percentage change in the price. So when that happens and the result here that you're going to have is 0.5, right? So, that's going to be the measure of elasticity. And notice that it doesn't have any units. It's just a number. So we can, this number is very useful, right? Because now we can say that if, if the number, if the absolute value of this number end up being less than 1, then this is not a very responsive com, demand, right? Or the other, the other possibility that you can have is that you in, you increase the price of your product by 10% and your consumption goes down, instead of by 5%, let's say it goes down by 15%. Well in that situation, you plug in that number to our elasticity equation here. Percentage change in quantity of x over the percentage change in the price of x. This is still 10, right? But here now we had is 15. So this is actually now going to be a number that is actually larger than 1, right? So therefore, when a number is larger than 1 in absolute terms, right? It's always going to be negative, but in absolute terms, then we can say that this, this, this demand is very responsive to a change in price. And now we can use that to classify our elasticities. Kind of thought we can talk about this later, right? Let's do that here. Okay, so let's, let's use this, this fraction and the numbers we got to classify elasticity with particular terms that we can communicate with each other, because this, this very responsive and not very responsive, is kind of confusing, right? We have to have an actual measure so we can talk about different goods, are whether they are or not very responsive or not. And the word that economists use is not necessarily a weird word. It's elastic or inelastic. And we say that the price elasticity of a good is elastic when the absolute value of, of the elasticity, right, is going to be larger than 1, alright? In this case, if, if our, if you increase the price of your product by 10% and you get a reduction of 15%, then that means that if you plug that into the equation what you get is minus 1.5. The absolute value of that is 1.5. That means that that's an elastic sandwich, or the price elasticity of that sandwich is elastic. It's very responsive, right? So elastic is, is what we call very responsive. Responsive. Alright, the other way is you increase a price on your product, product by 10% and you get a reduction of 5%, which is less than 10%. But when you plug that into the equation, what you get is a number that in absolute terms is, is less than 1. So we're going to call that inelastic, right? Not very responsive. And that's going to happen when the absolute value of your elasticity, right, of E, is less than 1. So in this case, this is actually the case. When the per, when the percentage change in your consumption of reduction of a price change, of a price increase is less than the percentage change in the price. Or you can have a situation, it's not very likely, but you could have a situation in which the percentage changing quantities eh, equal to the percentage changing price, and that we call a unitary, right? When the absolute value of E, elasticity, is actually equal to 1. Alright, so let's, that's kind of the way we going to classify elasticity so that you and I can talk about this, right? We can say that a good has a price elastic demand when the value of the price elasticity is larger than 1 in absolute terms. We say that a good's had a price inelastic demand when the absolute value of the term elasticity is less than 1. And we say that it's unitary when the absolute value of the price elasticity's equal to 1. Now let's go back and use that to, to answer our real question which is, should you increase the price of your product or not? Which is, what is the exact relationship between this classification and total revenue? [music] >> Produced by OCE, Atlas Digital Media, at the University of Illinois, Urbana-Champaign.