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## Price elasticity of supply

# Elasticity of supply using a different method

## 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.