Understanding Price Elasticity of Demand

Hi everybody, something that you might be asked to explain in an exam situation is why the elasticity, price elasticity of demand varies along the demand curve. Now, you might look at a demand curve and we make various assumptions when we draw them, right? that the elasticity is always the same along the curve, that is a wrong assumption to make. It's oversimplified. So to be hyper-technical, you've got to be aware that elasticity varies along the demand curve. And that is because there is a key distinction... between the gradient and elasticity. Gradient along the demand curve is always going to be the same. The gradient is just the slope of the line and if we draw a linear demand curve downward sloping the gradient will always be the same number. But elasticity of demand is not the gradient. Elasticity of demand looks at percentage changes in quantity demanded and percentage changes in price which gradient does not. So therefore elasticity will vary along the demand curve. What I'm going to prove here is that the top half of the demand curve is always the elastic section of the demand curve, and the bottom half is always the inelastic section of the demand curve. Let me prove that by looking at some equations on the right-hand side, some calculations here. Don't forget your equations of PED, the percentage change in QD over the percentage change in price. Remember, you Q before you P. And to work out percentage change, it's just the difference between two numbers divided by the original number and then times by 100. Okay, so let's take the first calculation. A price drop from £10 to £9. Well, if we go from £10 to £9, then quantity is increasing from 0 to 1. Alright? Let's put that in our equation. We need to work out percentage changes, remember. So the percentage change in price is a 10% reduction. The percentage increase in quantity demanded is infinite. Okay, so the difference is 1. Divide by the original, which is 0. That is going to give you infinity. Anything divided by 0... is infinity. So we have an infinite increase. Infinity divided by any number is infinity. So the top part of the demand curve represents perfect, perfectly elastic demand, okay? Infinite. Let's go to the next one. A price drop from £9 to £8. Well, at £8, the quantity demanded is 2, okay? So let's change all of this into percentage changes. So the percentage change in price was 1 over 9 times by 100. So that is a reduction. of 11.1 recurring percent. That's to say 11.11% reduction in price. And quantities increase from 1 to 2. That is a 100% increase in quantity demanded. And that gives us an elasticity of minus 9. That's greater than 1. Remember, we ignore the sign when we interpret the figure. So greater than 1, very elastic demand. So we get the point. The top path represents elastic demand. I can keep going, and you'll get the same. If you want to keep going and do the same for 8 to 7, 7 to 6, you'll work out that the end figures will show price elastic demand. So we have PED, which is greater than 1, elastic demand on the top half of the demand curve, up until we get to the midpoint of the line. So we get to the midpoint, which is here at the 5, and 5 there will take us to a quantity of 5. That is the midpoint of the line. And that midpoint is always going to be PED of 1, minus 1. one because PD is always negative. Let's prove that by looking at equation number three. A price drop from five to four. Well, four, the quantity demanded is now six. Let's put that into our equation. So the price drop from five to four, it's one over five times by a hundred and that is minus 20 percent. So it's a 20 percent reduction in price. What about the increase in QD? We've gone from five to six. That's one over five times by a hundred increase. That's a 20 percent increase in price. quantity demanded and there is our figure of minus one. So that represents unit elasticity. That is always going to be the elasticity at the midpoint of any demand curve. The bottom half of the demand curve is always going to be the inelastic portion of the demand curve. Let's understand why by looking at these two equations here. So let's take a price reduction of two pounds and at two pounds the quantity demanded is here at eight and dropping that to one pound where the quantity demanded is now. 9. Alright. Well, the price reduction from 2 to 1, well it's 1 over 2 times by 100, that is a 50% reduction in price, and the increase in quantity demand is from 8 to 9. So 1 over 8 times by 100 gives you a 12.5% increase in QD. And if we take those two figures, divide them, we get to an elasticity figure of minus 0.25. That tells you we have inelasticity. demand here. We kept going, we look at the next equation. Let's now take a price increase from 0 to 1. So this good was 3, now it's 1 pound. Well, what's happening to quantity demanded? Quantity demanded is going to fall now because there is a price increase. And it's going to fall from 10 to 9. That is a 10% reduction in quantity demanded. What's happened to the price? Well, it's increased from 0 to 1. Okay, now that is an infinite increase in price. So the difference is 1. Divided by 0, we get infinity. So that's an infinite increase in price. And any number divided by infinity, mathematical rule, is 0. So what we can put here is 0. So the very bottom of the demand curve represents perfectly inelastic demand. So at the top, perfectly elastic demand. At the bottom, perfectly inelastic demand. Right in the middle, we have unit elasticity. So we can make the conclusion that for the top... half of the demand curve we have got the elastic section. For the bottom half of the demand curve we have the inelastic section. Now if you wanted to explain why more simply in an essay or in a short question you don't need to go through all of this proof on the side here. You can keep things more simple by just saying this. For the top half of the demand curve the percentage changes in quantity demanded are always going to be greater than the percentage changes in price. That's why we get to elastic figures on the top half. Whereas on the bottom half, the percentage changes in quantity demanded are always going to be less than the percentage changes in price, which is why the figures we get are always going to be less than one for the bottom half of the demand curve. We're going to see inelastic demand for the bottom half. That's what you would say in a short question or in an essay to keep things simple. That is always true. Maybe doing a few calculations just to prove it might be a worthwhile idea, but that explains why. Now, this is also very helpful to make the distinction between PD and total revenue. So it's very clear to see here that if we just take price reductions, that total revenue is going to be maximized where there is unit elasticity, i.e. at the midpoint of the line. That's because when we hit unit elasticity, there is no longer elastic or inelastic demand taking place. If there is elastic demand, it makes sense to keep reducing price to increase total revenue. But if we go into the inelastic portion and you keep reducing... price, then we know that total revenue is going to fall. Therefore, to maximize total revenue, you want elastic demand. At that point, don't change your price either way. You have maximized your total revenue. So what you would want to draw here is you want to take the midpoint of the line, so here, unit elasticity at minus one, take that down and draw total revenue to look like this, where it's maximized at that quantity, and then it starts to fall. And this makes the point, doesn't it? That on the elastic portion, if you reduce prices, total revenue will increase. However, when you get to the inelastic portion and you continue to reduce prices, total revenue will decrease following the rules that we learned in my last video of the link between PED and total revenue. So we can link our demand curve and e-elasticity is varying along it to our total revenue curve to look like that. Hopefully that makes complete sense now, guys. You understand why PED varies along the demand curve and you can explain it. in eloquently in a short question or in an essay. Thank you so much for watching, folks. I'll see you all in the next video.

And that is because there is a key distinction... between the gradient and elasticity. Gradient along the demand curve is always going to be the same. The gradient is just the slope of the line and if we draw a linear demand curve downward sloping the gradient will always be the same number. But elasticity of demand is not the gradient.

Elasticity of demand looks at percentage changes in quantity demanded and percentage changes in price which gradient does not. So therefore elasticity will vary along the demand curve. What I'm going to prove here is that the top half of the demand curve is always the elastic section of the demand curve, and the bottom half is always the inelastic section of the demand curve. Let me prove that by looking at some equations on the right-hand side, some calculations here. Don't forget your equations of PED, the percentage change in QD over the percentage change in price.

Remember, you Q before you P. And to work out percentage change, it's just the difference between two numbers divided by the original number and then times by 100. Okay, so let's take the first calculation. A price drop from £10 to £9.

Well, if we go from £10 to £9, then quantity is increasing from 0 to 1. Alright? Let's put that in our equation. We need to work out percentage changes, remember.

So the percentage change in price is a 10% reduction. The percentage increase in quantity demanded is infinite. Okay, so the difference is 1. Divide by the original, which is 0. That is going to give you infinity. Anything divided by 0... is infinity.

So we have an infinite increase. Infinity divided by any number is infinity. So the top part of the demand curve represents perfect, perfectly elastic demand, okay? Infinite. Let's go to the next one.

A price drop from £9 to £8. Well, at £8, the quantity demanded is 2, okay? So let's change all of this into percentage changes.

So the percentage change in price was 1 over 9 times by 100. So that is a reduction. of 11.1 recurring percent. That's to say 11.11% reduction in price. And quantities increase from 1 to 2. That is a 100% increase in quantity demanded.

And that gives us an elasticity of minus 9. That's greater than 1. Remember, we ignore the sign when we interpret the figure. So greater than 1, very elastic demand. So we get the point. The top path represents elastic demand. I can keep going, and you'll get the same.

If you want to keep going and do the same for 8 to 7, 7 to 6, you'll work out that the end figures will show price elastic demand. So we have PED, which is greater than 1, elastic demand on the top half of the demand curve, up until we get to the midpoint of the line. So we get to the midpoint, which is here at the 5, and 5 there will take us to a quantity of 5. That is the midpoint of the line. And that midpoint is always going to be PED of 1, minus 1. one because PD is always negative. Let's prove that by looking at equation number three.

A price drop from five to four. Well, four, the quantity demanded is now six. Let's put that into our equation. So the price drop from five to four, it's one over five times by a hundred and that is minus 20 percent.

So it's a 20 percent reduction in price. What about the increase in QD? We've gone from five to six.

That's one over five times by a hundred increase. That's a 20 percent increase in price. quantity demanded and there is our figure of minus one.

So that represents unit elasticity. That is always going to be the elasticity at the midpoint of any demand curve. The bottom half of the demand curve is always going to be the inelastic portion of the demand curve.

Let's understand why by looking at these two equations here. So let's take a price reduction of two pounds and at two pounds the quantity demanded is here at eight and dropping that to one pound where the quantity demanded is now. 9. Alright.

Well, the price reduction from 2 to 1, well it's 1 over 2 times by 100, that is a 50% reduction in price, and the increase in quantity demand is from 8 to 9. So 1 over 8 times by 100 gives you a 12.5% increase in QD. And if we take those two figures, divide them, we get to an elasticity figure of minus 0.25. That tells you we have inelasticity. demand here. We kept going, we look at the next equation.

Let's now take a price increase from 0 to 1. So this good was 3, now it's 1 pound. Well, what's happening to quantity demanded? Quantity demanded is going to fall now because there is a price increase. And it's going to fall from 10 to 9. That is a 10% reduction in quantity demanded. What's happened to the price?

Well, it's increased from 0 to 1. Okay, now that is an infinite increase in price. So the difference is 1. Divided by 0, we get infinity. So that's an infinite increase in price.

And any number divided by infinity, mathematical rule, is 0. So what we can put here is 0. So the very bottom of the demand curve represents perfectly inelastic demand. So at the top, perfectly elastic demand. At the bottom, perfectly inelastic demand.

Right in the middle, we have unit elasticity. So we can make the conclusion that for the top... half of the demand curve we have got the elastic section.

For the bottom half of the demand curve we have the inelastic section. Now if you wanted to explain why more simply in an essay or in a short question you don't need to go through all of this proof on the side here. You can keep things more simple by just saying this. For the top half of the demand curve the percentage changes in quantity demanded are always going to be greater than the percentage changes in price. That's why we get to elastic figures on the top half.

Whereas on the bottom half, the percentage changes in quantity demanded are always going to be less than the percentage changes in price, which is why the figures we get are always going to be less than one for the bottom half of the demand curve. We're going to see inelastic demand for the bottom half. That's what you would say in a short question or in an essay to keep things simple. That is always true.

Maybe doing a few calculations just to prove it might be a worthwhile idea, but that explains why. Now, this is also very helpful to make the distinction between PD and total revenue. So it's very clear to see here that if we just take price reductions, that total revenue is going to be maximized where there is unit elasticity, i.e. at the midpoint of the line.

That's because when we hit unit elasticity, there is no longer elastic or inelastic demand taking place. If there is elastic demand, it makes sense to keep reducing price to increase total revenue. But if we go into the inelastic portion and you keep reducing...

price, then we know that total revenue is going to fall. Therefore, to maximize total revenue, you want elastic demand. At that point, don't change your price either way.

You have maximized your total revenue. So what you would want to draw here is you want to take the midpoint of the line, so here, unit elasticity at minus one, take that down and draw total revenue to look like this, where it's maximized at that quantity, and then it starts to fall. And this makes the point, doesn't it? That on the elastic portion, if you reduce prices, total revenue will increase.

However, when you get to the inelastic portion and you continue to reduce prices, total revenue will decrease following the rules that we learned in my last video of the link between PED and total revenue. So we can link our demand curve and e-elasticity is varying along it to our total revenue curve to look like that. Hopefully that makes complete sense now, guys. You understand why PED varies along the demand curve and you can explain it. in eloquently in a short question or in an essay.

Thank you so much for watching, folks. I'll see you all in the next video.

Transcript for:Understanding Price Elasticity of Demand

Transcript for:
Understanding Price Elasticity of Demand