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Current time:0:00Total duration:9:33

Elasticity of supply using a different method

Video transcript

we've been talking a lot about elasticity's of demand so you are probably wondering can we think about elasticity's of supply and as you can imagine the answer is of course we can and it's interesting to think about how does the quantity 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 at a price of $1 the quantity supplied is going to be 10 and this is going to be in gallons 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 quantity supplied goes to goes to 16 gallons per week so what is the elasticity of supply roughly over this period right over here so the elasticity elasticity of supply and you can imagine how we're going to calculate is going to be the percent change in quantity supplied supplied over our percent change in price so what is our percent change in price well we went from 1 to 2 dollars 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 in when we're traditionally finding a percent change because we want to have the same percent change whether we go from 1 to 2 and s from 2 to 1 so instead the convention when we when we think about elasticity 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 a dollar fifty or you could say a dollar fifty is right in between these two things and one over a dollar fifty this is about this is 67% roughly so this is approximately 67 we have approximately a 67 percent change in price based on how we just calculate it remember we're using the midpoint as our base and then our percent change in quantity supplied percent change in quantity supplied that's this so this right over here we went from 10 to 16 so we had plus 6 over a base of midpoint between 10 and 16 is 13 10 plus 6 is 26 divided by 2 is 13 6 over 13 which is going to be 40-something percent get a calculator out so we have 6 divided by 13 gives us 46 percent so this is this right over here is 46% so we have when we had based on the way we calculated a 67% increase in price we had a 46% increase in quantity supplied so this is a 46% increase in quantity supplied and so we can 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 we can get so that's going to be that divided by point it's actually 0.666 6 it keeps going on forever gives us 2 point 6 9 so this gives us an elasticity of supply of zero point six nine maybe Becca stated approximately zero point six nine which tells us that we get a we get a smaller percent at least at this price point right over here we get a smaller percent change in quantity supplied then our percent change in price now let's think about like we did with when we thought about the elasticity of demand let's think about different scenarios so let's think about let's think about a scenario that is any elastic that may be perfectly inelastic so let's say that price price and quantity so let's take let's take me for example I make videos I love making videos this is what I want to spend my days doing and and I don't care how much you pay me or how little you pay me I guess if you paid me enough that would maybe that's been living a little bit more time making videos but let's just assume that I don't I'm completely I know whether you pay me a penny a video or zero per video or whether you pay me a thousand dollars per video I'm going to just make the same number of videos every day so this is this right over here is videos 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 paying me $1,000 I am what's 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 perfectly in elastic supply curve so this is perfectly perfectly in E elastic supply curve now you could have the other scenario 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 you can 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 cost you the exact same to produce one or the other so in that situation so let's say that the price of wheat per and let's say we're using comparable units so the price of wheat wheat is for you know adjusting for units and all of that let's say it's ten dollars I don't know for 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 we're thinking about corn and so if corn so if if let's say corn is right at ten dollars and it right at ten dollars when they're both at ten dollars I will produce so let me make this clear so price of corn price of corn is $10 and the quantity of corn maybe I know I produce 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 if the price of course let me put this so this is a 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 ten dollars and five cents per bushel all of a sudden I'm going to shift all my wheat production to corn production so this is going to go to zero and then this is going to go to 4,000 so then we're going to go so just 1005 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 995 I would shift all my production to wheat and I wouldn't produce any corn and so there you see that we have a very the 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 this is approaching approaching perfect perfect 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 wonder about 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 prices increasing when this is 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 a curve supply curve that has unit elasticity than it is to construct a normal demand curve that has unit elasticity