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# Introduction to price elasticity of demand

AP Micro: MKT‑3 (EU), MKT‑3.E (LO), MKT‑3.E.1 (EK), MKT‑3.E.2 (EK), MKT‑3.E.3 (EK)

## Video transcript

- [Instructor] We are now going to discuss price elasticity of demand, which sounds like a very fancy concept, but really, it's a way for economists to sense how sensitive is quantity to change in prices. And in this video, we're gonna denote it as a capital E, so E, price elasticity of demand. And the easy way to think about it is it is your percent change in, I'll use the Greek letter delta as shorthand for change in here, percent change in quantity over your percent change in price. And so, you might say, wait, how does this relate to the everyday idea of elasticity? Well, imagine two bands. So, let's imagine an inelastic band, inelastic, right over here, and let's imagine an elastic band right over here. So, in an inelastic band, if we apply some amount of force, you're not going to be able to stretch it much, it might stretch a little bit, while an elastic band, if you apply that same amount of force, you might be able to stretch it a lot more. And so, the analogy here is we're not using force, but we're saying how much does quantity stretch for a given amount of price change? And so, something where the quantity changes a lot for a given price change would be very elastic. So, this, the magnitude of this will be larger. And if the percent change in quantity doesn't change a lot for a our given percent change in price, well, then we're dealing with an inelastic price elasticity of demand. And we'll be able to internalize these more as we work through the numbers. And actually, let's do that for this demand schedule that we have right over here, and it's visualized as our demand curve. In the vertical axis, we have price of burgers; and then in our horizontal axis, we have quantity, in terms of burgers per hour. And so, let's just use this definition of price elasticity of demand to calculate it across different points on our demand curve. So, I'm gonna make a new column here, so price elasticity of demand. And the way I'm gonna do it is really the simplest method for calculating this. In other videos, we can go into more in-depth methods, like the midpoint method. And I'll show you the weakness in what we're doing right here. But for the sake of, say, an AP economics, microeconomics course, this would be sufficient. So, let's think about our price elasticity of demand as we go from point A to point B. Well, remember, that's just going to be our percent change in quantity over our percent change in price. So, what is our percent change in quantity? Well, we're starting at a quantity of two, so I'll put that in our denominator. And we're going from two to four, so we are adding two. So, we have two over two, we could multiply that times 100% if we like. So, this would give us, we have 100% change in quantity over, now what was the corresponding change in price, percent change in price? So, our corresponding percent change in price, our initial price is nine, and we go from nine to eight, so we're going down by one. And then we multiply that times 100%. So, this is going to be about a negative 11% change in price. And this math is reasonably straightforward because the 100%s cancel out, this is just a one. One over negative 1/9 is just going to be equal to negative nine. So, you have a negative nine price elasticity of demand. So, before I interpret that more, let's look at the price elasticity of demand at other points, or starting from other points to other points on this curve. So, let's think about it going from, actually let's think about it going from E to F. So, as we go from E to F, we're going to do the same exact exercise. What is our percent change in quantity? Well, our initial quantity is 16. And we're going from 16 to 18, so we have a change of two. So, two over 16 times 100%, that is our percent change in quantity. And what is our percent change in price? Well, our initial price is two. And we're going from two to one, so we have a price change of negative one times 100%. And so, what you see here is this is 1/8 times 100%, this would be 12.5% up here. So, this is 12.5% up there, and then this, over here, is going to be negative 50%. So, when price went down by 50%, you had a 12.5% increase in quantity. 12.5% is 1/4 of 50%, so this is going to give us a price elasticity of demand of negative 0.25. So, there's a couple of interesting things that you might already be realizing. One is even though our demand curve right over here is a line, it actually has a constant slope, you see that the price elasticity of demand changes, depending on different parts of the curve. Now, the reason why this is, is really just boils down to math. When we're going from A to B, our initial prices were relatively high. So, even though you had a price decrease of one, it was from an initial price of nine. So, your percentage change in price looked fairly low, while your percentage change in quantity was high 'cause you're going from a low quantity of two, and you're adding two to it, so you had 100% change in quantity. When you go to the other end our curve, and you go from E to F, it's the other way around. Your price starting point is low, so your percent change in price, when you decrease price by one, it looks like a fairly large magnitude; while your percent change in quantity when you go from E to F because you are already at a quantity of 16, adding two to that is not that large of a percentage. Now, another thing you might be appreciating is if we tried to calculate the price elasticity of demand up here on the curve, and instead of going from A to B, if we went from B to A, we would've gotten a different value because our initial prices and quantities would have been different. Our initial price, we would've put an eight right over here, and our initial quantity, we would've put a four over here, and we would've gotten a different value. And that's one of the negatives of the technique, which is arguably the simplest technique, that I just used. There's other techniques, like the midpoint technique, that can give you a more consistent result, whether you're going from A to B or B to A, but I won't cover it just yet. But let's think, now, about how to interpret this. And the best way to interpret it is to think about the absolute value of the price elasticity of demand. So, over here, the absolute value of our price elasticity of demand is equal to nine, and then, over here, the absolute value of our price elasticity of demand is equal to 0.25. And a general rule of thumb is if your absolute value of your price elasticity of demand is less than one, you are dealing with an inelastic, inelastic, elastic situation; and if your price elasticity of demand, the absolute value of it, is greater than one, you're dealing with an elastic situation. Why does that make sense? Well, in this first scenario, it's saying for a given percentage change in price, you have a smaller percent change in quantity; while here, for a given percent in price, you're going to have a larger than that percentage change in your quantity. So, once again, it goes back to these rubber band analogies. So, when we're going from A to B, the absolute value of our price elasticity of demand is definitely larger than one. So, economists would consider this to be an elastic situation; while when we go from point E to point F, our price elasticity of demand, or the absolute value of it, is definitely less than one, so this going to be an inelastic situation.