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Elasticity of supply using a different method

Thinking about elasticity of supply. Created by Sal Khan.

Video transcript

We've been talking a lot about elasticities of demand, so you were probably wondering, can we think about elasticities of a supply? And, as you can imagine, the answer is, of course we can. And it's interesting to think about how does the percent change in quantity supplied relate to percent change in prices? So for example, let's say we have a lemonade stand of some sort. So this is price on that axis. That is quantity on that axis. And let's say that our supply curve looks something like that. Obviously, the higher the price, the more quantity we're willing to supply. And let's say at a price of $1, the quantity supplied is going to be 10. And this is going to be in gallons per week. So the quantity supplied is going to be 10 gallons per week. And let's say that if the price goes to $2, so when the price goes to $2, the quantity supplied goes to 16 gallons per week. So what is the elasticity of supply roughly over this period right over here? So the elasticity of supply. And you can imagine how we're going to calculate it. It's going to be the percent change in quantity supplied over our percent change in price. So what is our percent change in price? Well, we went from $1 to $2. So this part right over here is going to be, we went up by $1. So we went up by $1 per gallon. So it's going to be up by $1. And we don't use 1, we don't use our starting point as our base like we would do when we're traditionally finding a percent change, because we want to have the same present change whether we go from 1 to 2 as from 2 to 1. So instead, the convention when we think about elasticities is use the midpoint of these two or use the average of these two. So 1 plus 2 is 3, 3 divided by 2 is 1.5. So it's 1 over $1.50, or you could say $1.50 is right in between these two things. And 1 over $1.50, this is about 67% roughly. So this is approximately 67. We have approximately a 67% change in price based on how we just calculated. Remember, we're using the midpoint as our base. And then our percent change in quantity supplied, that's this. So this right over here. We went from 10 to 16. So we have plus-6 over a base of, midpoint between 10 and 16, is 13. 10 plus 16 is 26, divided by 2 is 13. 6/13, which is going to be 40-something percent. Get a calculator out. So we have 6 divided by 13 gives us 46%. So this right over here is 46%. So we have, when we had, based on the way we calculated it, it's 67% increase in price, we had a 46% increase in quantity supplied. So this is a 46% increase in quantity supplied. And so we could see it's going to be 40. Our elasticity of supply is going to be 46% over 67%. So it's going to be something less than 1. So that's going to be that divided by-- it's actually 0.6666 and it keeps going on forever-- gets us to 0.69. So this gives us an elasticity of supply of 0.69. And maybe I should say approximately 0.69, which tells us that we get a smaller percent. At least at this price point right over here, we get a smaller percent change in quantity supplied than our percent change in price. Now, let's think about-- like we did when we thought about the elasticities of demand-- let's think about different scenarios. So let's think about a scenario that is inelastic, that is maybe perfectly inelastic. So let's say that price and quantity. So let's take me for example. I make videos. I love making videos. This is what I want to spend my days doing. And I don't care how much you pay me or how little you pay me. I guess if you paid me enough, maybe I'd spend even a little bit more time making videos. But let's just assume that I don't. Whether you pay me a penny a video or zero per video, or whether you pay me $1,000 per video, I'm going to just make the same number of videos every day. So this right over here is videos per day on average. And this is the price per video. And let's say no matter how much you pay me, whether you pay me nothing or you pay me $1,000, I am just going to produce, on average, let's just say, three videos a day. So then you have this right over here. You have a perfectly inelastic supply curve. So this is perfectly inelastic supply curve. Now, you could have the other scenario where you are a farmer. So let me do price and quantity. Now, you have the other scenario where you're a farmer and you can either do crop A or crop B. Maybe it's corn and wheat. And you can easily swap between the two. And let's just assume for simplicity it costs you the exact same to produce one or the other. So let's say that the price of wheat per-- and let's say we're using comparable units. So the price of wheat is, adjusting for units and all of that, let's say it's $10, I don't know, per bushel or something like that. We just want to simplify it for the sake of our model right over here. But this right over here, we're thinking about the corn. We're thinking about corn. Let's say corn is right at $10. And right at $10, when they're both at $10, I will produce-- so let me make this clear. So price of corn is $10, and the quantity of corn-- maybe, I don't know, I produce 2,000 bushels. And I know these prices are way off for what the real price per bushel of corn or wheat is. And same thing. My quantity for wheat right here is 2,000. Now, if the price of corn were to go marginally up-- so let me put this. So this is our graph for corn. So this is $10 and this is 2,000 bushels per year or something. So let's say that's where we are right over there. Now, if the price for corn goes marginally up, if the price for corn goes up to even $10.05 per bushel, all of a sudden, I'm going to shift all of my wheat production to corn production. So this is going to go to 0, and then this is going to go to $4,000. So at just $10.05, we're going to go all the way to $4,000. And likewise, if this price were to go down, if this were to go to, like, $9.95, I would shift all of my production to wheat and I wouldn't produce any corn. And so there you see that the demand curve is getting very flat. And you can see, based on very, very small percent changes in prices, I have very large percent changes in quantity supplied. So this right over here is approaching perfect elasticity. Huge changes in quantity supplied, elasticity, for small percent changes in price. Now, the cool thing about elasticity of supply is it's actually much easier to make a curve that has unit elasticity or even, if you want to think about it, constant elasticity. But if you want to have unit elasticity, the easiest curve I can draw for unit elasticity is going to look like this. Well, actually, this is the curve for unit elasticity. It will literally be a curve that looks like that. And the reason why it works in this case is because it's upward-sloping. As price increases, so does quantity increase for the supply curve. So at any point here, the two are going to be proportional. So a given change in quantity and a given change in price, they're going to represent the same percentages, because, as price is increasing, when you have large price or when you have medium price, you have medium quantity. When you have large price, you have large quantity. So these steps are going to be the same percentage of either one of them. When you have small prices, you have small quantities. And so it's much easier to construct a supply curve that has unit elasticity than it is to construct a normal demand curve that has unit elasticity.