Elasticity of Demand

Dughorm

Hi folks,

This bugs me - elasticity of demand is sometimes shown as having an impact on the slope of the demand curve. E.g. half way down the page on this link they show a very elastic demand curve being almost horizontal.

Then in other places you see the one demand curve with different portions of it representing, elastic, unit and inelastic demand - like half way down the page (Right hand side) on this link

How can the same elasticity both be causing the demand curve to have a certain slope and yet change depending on which part of the demand curve you're looking at?

Cheers!

andrew

Dughorm wrote: »

Hi folks,

This bugs me - elasticity of demand is sometimes shown as having an impact on the slope of the demand curve. E.g. half way down the page on this link they show a very elastic demand curve being almost horizontal.

Then in other places you see the one demand curve with different portions of it representing, elastic, unit and inelastic demand - like half way down the page (Right hand side) on this link

How can the same elasticity both be causing the demand curve to have a certain slope and yet change depending on which part of the demand curve you're looking at?

Cheers!

I think in the second graph you reference, it's referring to the elasticity of total revenue, not the elasticity of demand.

Dughorm

andrew wrote: »

I think in the second graph you reference, it's referring to the elasticity of total revenue, not the elasticity of demand.

Hi Andrew, thanks for your reply.

I can't say I've heard of the "elasticity of total revenue" before, to me the reason of elasticity of demand was to determine how a %change in price affects %change in quantity demanded - if PED was >1 the price effect is greater than the quantity demanded effect and total revenue would increase with a decrease in price.

On reflection, I saw on the wiki link
"It is important to realize that price-elasticity of demand is not necessarily constant over all price ranges. The linear demand curve in the accompanying diagram illustrates that changes in price also change the elasticity: the price elasticity is different at every point on the curve."

Of course, if PED = infinity we have a perfectly elastic (horizontal) demand curve and PED at each point on the demand curve is the same. Similarly with PED = O there is a perfectly inelastic (vertical) demand curve.

I think the point of the diagram in the first link is to show that when the demand curve gets nearer to the horizontal, all points on the demand curve (which have their own unique PED) are becoming more elastic, and vice versa.

Any more thoughts welcome!

Time Magazine

Hi there.

There are two components of the formula for PED. Moving between any two points on the demand curve and defining Pm as the price at the midpoint between the two points and Qm as the quantity at the midpoint, then:

[latex]PED = \frac{\Delta Q}{\Delta P} \times \frac{Pm}{Qm}[/latex]

1. The first component, the change in Q divided by the change in P, is basically a slope. (Technically it's the inverse of the slope, but let's just call it a slope.)
2. The second component, Pm over Qm, is an adjustment factor.

So PED is clearly closely related to slope of a line. In particular, it's the slope of the line multiplied by the adjustment factor.

However, if you hold Pm and Qm constant -- for example if you have two lines going through the same point (Qm, Pm) -- then the slope will tell you everything you need to know about which curve is more elastic at that point. This is the case of the picture in your first link:



All those lines are going through the same point, so obviously the adjustment factor is the same for any line at that point. What's left over in the PED formula is the different slopes. For this reason, looking at any two demand curves that pass through the same point, the flatter curve is the more elastic one at that point.

So that's when you hold the adjustment factor constant. What about the other case, when you hold the slope constant?

If you have a linear demand curve (i.e. if demand is a straight line, which would never happen in the real world), then by definition of "straight line" the slope is constant anywhere on that line. Then what happens to PED?

Well, starting from very high up on the demand curve, your adjustment factor is huge because P is high and Q is low. That means that PED is relatively large, i.e. elastic. Down near the bottom of the curve, P is low and Q is high, making the adjustment factor a small number. That means that the PED is relatively small, i.e. inelastic. That's where we get the idea of elasticity not being constant as we move along a straight line demand curve.

Another fun fact from the special case of linear demand curves: PED is exactly unit elastic at the midpoint of the line. (Don't confuse this midpoint with the midpoint in the PED formula. This midpoint is the middle of the whole line. For example, if the line hits the price axis at 100, then the midpoint is wherever the line is when the price is 50.) Anything above that point and PED>1 (elastic), and anywhere below PED<1 (inelastic).

andrew

Time Magazine wrote: »

Hi there.

There are two components of the formula for PED. Moving between any two points on the demand curve and defining Pm as the price at the midpoint between the two points and Qm as the quantity at the midpoint, then:

[latex]PED = \frac{\Delta Q}{\Delta P} \times \frac{Pm}{Qm}[/latex]

1. The first component, the change in Q divided by the change in P, is basically a slope. (Technically it's the inverse of the slope, but let's just call it a slope.)
2. The second component, Pm over Qm, is an adjustment factor.

So PED is clearly closely related to slope of a line. In particular, it's the slope of the line multiplied by the adjustment factor.

However, if you hold Pm and Qm constant -- for example if you have two lines going through the same point (Qm, Pm) -- then the slope will tell you everything you need to know about which curve is more elastic at that point. This is the case of the picture in your first link:



All those lines are going through the same point, so obviously the adjustment factor is the same for any line at that point. What's left over in the PED formula is the different slopes. For this reason, looking at any two demand curves that pass through the same point, the flatter curve is the more elastic one at that point.

So that's when you hold the adjustment factor constant. What about the other case, when you hold the slope constant?

If you have a linear demand curve (i.e. if demand is a straight line, which would never happen in the real world), then by definition of "straight line" the slope is constant anywhere on that line. Then what happens to PED?

Well, starting from very high up on the demand curve, your adjustment factor is huge because P is high and Q is low. That means that PED is relatively large, i.e. elastic. Down near the bottom of the curve, P is low and Q is high, making the adjustment factor a small number. That means that the PED is relatively small, i.e. inelastic. That's where we get the idea of elasticity not being constant as we move along a straight line demand curve.

Another fun fact from the special case of linear demand curves: PED is exactly unit elastic at the midpoint of the line. (Don't confuse this midpoint with the midpoint in the PED formula. This midpoint is the middle of the whole line. For example, if the line hits the price axis at 100, then the midpoint is wherever the line is when the price is 50.) Anything above that point and PED>1 (elastic), and anywhere below PED<1 (inelastic).

Welcome back!