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 elasticity's of demand we would see so this right over here is a vial of insulin many to 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 tight 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 the other column I will put quantity so let's say that insulin right now is going for five dollars a vial five dollars while 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 100 so this is in vials per week 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 $1.00 well what would the quantity be well they're 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 to go up or down or anything like that so in this case they'll still just buy 100 vials now what happens if the price went up a ton what happens if the price went to what happens if it 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 would 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 a billion dollars then they would just wouldn't be able to afford it but within reason they're going to buy a hundred vials per week no matter what the price is so this this is an example of perfect in elasticity perfect perfect in elasticity last tissa t 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 chase 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 the n LS that you could figure out the demand elasticity for let's say when you're going from a price of five dollars to one dollar so the price went down by four and the quantity the quantity changed by zero so your percent change in quantity percent so Delta % % % I'll write a percent change in quantity is equal to zero and then your percent is going to be over your percent change in price your percent change in price if you use the averaging method it was what it would be going down by four over an average of 250 it'll be a fairly large number but it's zero over anything is still going to be zero so it doesn't matter what that thing is over here your your elasticity of demand in this situation is zero 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 vials per week that's true when the price is that's true when the price is $5 so that's true when the price is $5 then we're going to demand 100 100 miles a week that's true when the price is $1 they're going to demand 100 miles a week and that's true if the price is $20 or $100 or whatever they're going to demand they're going to demand 100 miles 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 they're all the quantity demanded is always going to be the 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 a can of coke there and let's say starting off the can of coke let's say that they cost a dollar in each vending machine they cost a dollar in each vending machine and we're going to assume that this one remember all else equals so we're going to assume that we're going to sue that this vending machine right over here doesn't change does not change so it's just going to be consistently charging a dollar 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 in 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 if the price is $1 then you know just odds are it's going to get about half of the sales per week and let's say that ends up being let's say that ends up being I don't know let's say that ends up being a hundred cans one hundred this is in cans per week cans per week now what happens and let me put some decimals here so this is one dollar the price is one dollar sales 100 cans but we can probably this one would also sell about 100 cans per week now what happens if we have a very very small change in price so if we have if we change if we go from a dollar instead of a dollar we are at 99 cents 99 cents what's going to happen so this remember this machine right over here is not changing this is what we're talking about demand curve is for the quantity of cokes sold from this machine and the price we talked about is for this machine so this machine is even a penny cheaper and assuming that you know people there aren't lines forming and things like that people are just always to go to this machine if it's easy enough if there's no difference when you do 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 it's going to sell 200 cokes now what happens if instead of lowering the price by penny you raise the price by penny so instead of $1 your dollar a dollar one well now everyone's going to go to the other vending machine they're going to say oh we don't need a you know even a penny on it might as well walk to this one you know assuming everything else is equal so then they're going to sell they're going to sell zero and so what would the demand curve look like here well let's plot it out 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 zero this is 100 100 and then this is 200 and then this is a price of $1 that's $1 so at $1 at $1 the quantity demanded is 100 cans fair enough now at $0.99 the quantity demanded is 200 cans so 99 cents the quantity demanded is 200 so 99 cents 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 it's a dollar one a little bit over here the quantity demanded is zero the quantum and it is zero so the demand curve here is going to look something like it's going to look something like it's going to look 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 encourage you to work out the math 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 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 zero and over here the absolute value of our elasticity demand is infinity because remember its percent change in quantity of a percent change in price when you go from either from one scenario to another over here your percent change in price is very small it's roughly about one percent in this scenario right over here changing the price up or down about one percent 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 percent from that one percent 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