Perfect inelasticity and perfect elasticity of demand

To get a better intuition for the price elasticity of demand, I thought I would take a look at some of the more extreme cases and think about what types of elasticities of demand we would see. So this right over here is a vial of insulin. Many diabetics, not all diabetics, but many diabetics need to take insulin daily. They need to inject it in order to maintain their blood sugar level. If they don't do it, bad things will happen to their body. And they might even prematurely die if they don't take their insulin on time. So let's think about what the elasticity of demand might look like for something like insulin. So in one column, I'll put price. And in the other column, I will put quantity. So let's say that insulation right now is going for $5 a vial. And we have a group of diabetics who need insulin. And they're all going to buy the insulin they need. And let's say, in this group, that turns out to be 100 vials per week. So this is in vials per week. Fair enough, that's exactly what they need to do to maintain their insulin. Now, what happens if the price changes? What happens if the price were to go down? Let's say the price were to go down to $1. Well, what would the quantity be? Well, they're not going to buy any more insulin. They're going to buy just what they need in order to maintain their diabetes. And remember, we're holding all else equal. We're not assuming any change in expectations of price. They expect price go up or down or anything like that So in this case, they'll still just by 100 vials. Now, what happens if the price went up a ton? And what happens if the price went to-- what happens if we went to $100 a vial. Well, it would be hard for them. But they need it to survive. So it's going to squeeze out any other expenses that they need to spend money on. And so they still will buy 100 vials a week. And so you could keep raising price, within reason. And they would still buy the same quantity. Obviously, if you raise it to $1 billion, then they would just wouldn't be able to afford it. But within reason, they're going to buy 100 vials per week, no matter what the price is. So this is an example of perfect inelasticity. Another way, so if you think of the physical analogy that we talked about with elasticity. It's like a brick. It doesn't matter how much, within reason once again, any amount of force pulling or pushing that a human could put on a brick, it's not going to change. It's not going to deform the brick in any way. And likewise, any change in price within reason, within reason here, isn't going to change the demand in any way. It's perfectly inelastic. And if you want to do the computation, you could look at inelas-- you could figure out the demand elasticity for, let's say, when you're going from a price of $5 to $1. So the price went down by 4. And the quantity changed by 0. So your percent change in quantity, so delta percent-- I'll write it-- percent change in quantity is equal to 0. And then, your percent is going to be over your percent change in price if you use the averaging method. It was-- it would be going down by 4 over an average of 250. It'll be a fairly large number. But at 0 over anything is still going to be 0. So it doesn't matter what that thing is over here. Your elasticity of demand in this situation is 0. And if you wanted to see what this demand curve would look like, let's plot it. So this right over here is my price axis. And that is my quantity axis. And so no matter what, let's say this is a quantity of 100 of vials per week. That's true when the price is $5. So that's true in the prices $5. They're going to demand 100 vials a week. That's true when the price is $1. They're going to demand 100 vials a week. And that's true, if the price is $20 or $100 or whatever. They're going to demand 100 vials a week. And so a perfectly inelastic demand curve would look like this. It is a vertical line. It doesn't matter what price you pick. The quantity demanded is always going to be the exact same thing. Now, let's go to another extreme. So this is perfectly inelastic. You can imagine. Well, what is perfectly elastic. Something that changes a lot if you have a small percentage change in price. And to think about that, let's look at these two vending machines. And you see that they both do sell cans of Coke. That's a can of Coke there. That is can of Coke there. And let's say, starting off, the can of Coke, let's say that they cost $1 in each vending machine. And we're going to assume that this one, remember all else equal. So we're going to assume that this vending machine right over here doesn't change. Does not change. So it's just going to be consistently charging $1 for a can of Coke. And they're sitting next to each other. And it looks like they have a little coffee machine in between right over here. So let's think about the demand curve for this, for Coca Cola in this vending machine right over here. So let's think about the price and the quantity. So I'll do-- let me do price column and quantity demanded. So let's say if the price is $1. So if the price is $1, then just odds are, it's going to get about half of the sales per week. And let's say that ends up being, I don't know, let's say that ends up being 100 cans. This is in cans per week. Now what happens? And let me put some decimals here. So this is $1.00. The price is $1.00. It sells 100 cans per week. And probably this one also would also sell about 100 cans per week. Now, what happens if we have a very, very small change in price. So if we change, if we go from $1.00, instead of $1.00, we are at $0.99. What's going to happen? So this, remember, this machine right over here is not changing. This is-- we're talking-- our demand curve is for the quantity of Cokes sold from this machine. And the price was for this machine. So if this machine is even a penny cheaper. And assuming that people, there aren't lines forming and things like that, people are just always going to go to this machine. If it's easy enough, if there's no difference, they're always going to go to this machine. So this machine will be able to get, will sell all the Cokes. So it's going to sell 200 Cokes. Now, what happens if, instead of lowering the price by a penny, you raise the price by a penny. So instead of $1.00, your at $1.01. Well, now everyone's going to go to the other vending machine. They're going to say, oh, we don't-- even a penny, might as well walk to this one. Assuming everything else is equal. So then, they're going to sell 0. And so what would the demand curve look like here. Let's plot it out. So this is the price. This right over, this axis right over here is quantity. And this is in cans per week. And so this is 0. This is 100. And then, this is 200. And then this is a price of $1. That's $1. So at $1, the quantity demanded is 100 cans. Fair enough. Now, at $0.99, the quantity demanded is 200 cans. So at $0.99, the quantity demanded is 200. So $0.99 is right below that, it's 200. So it's right over there. It's like right, right, there's a little bit lower. And $1.01 a little bit over here, the quantity demanded is 0. So the demand curve here is looks something like that. So it's going to be almost horizontal. So it's going to be approaching perfect elasticity, very small changes in price end up with these huge changes, huge changes in percent quantity demanded. And I courage to work out the math to see here, that you will get a very large number for elasticity. And so something that is, this is approaching perfect elasticity. A truly perfect elasticity would be something that is a horizontal line. So in this case, so over here, our elasticity of demand-- and I'll talk about the absolute value of it, is 0. And over here, the absolute value of our elasticity of demand is infinity. '50 Because, remember, it's percent change in quantity over percent change in price. When you go from either, from one scenario to another over here, you're percent change in price is very small. It's roughly about 1% in this scenario right over here. Changing the price up or down about 1%. But then, you see your quantity is changing, depending on which one you're looking. Your quantity is changing on the order of 50% to 100%, from that 1% change in price. So you have a huge elasticity of demand here. It would be a real-- it would actually be a number. But as you can imagine, as it becomes more and more sensitive, as quantity demanded becomes more and more sensitive to a percent change in price, this curve is going to flatten out completely. And you will have an infinite, absolute value of your elasticity of demand.