we know the demand curve slope downwards because a lower price means that people want more of a good but how responsive is the quantity demanded to a change in price this is a really important concept called the price elasticity of demand sometimes written e sub p and it can be tricky but it's really important for understanding the fundamentals of a number of the topics we're going to cover including applications to business practices and tax policy i might tell you that when the price of pizza goes up by one the quantity demanded falls by 100 million that would be the slope of the demand curve how much quantity changes for a change in price but that's actually less informative than it sounds because it's sensitive to the units that i picked to define the demand curve if i used cents instead of dollars then i would tell you that demand falls by 100 million units for an increase of 100 in price since i'm using cents and i'd have a hard time comparing the responsiveness of the demand for pizza to the responsiveness of the demand for coke since i'm measuring them in different units instead we use percent changes the price elasticity of demand equals the percent change in quantity for a percent change in price and this triangle right here this capital delta just means change this tells us the responsiveness of the quantity demanded let's suppose that the quantity demanded of pizza is very sensitive to its price when the price goes up by 10 percent quantity demanded of pizza falls by thirty percent the elasticity here would be negative three negative thirty percent over positive ten percent we would call this an elastic demand when the percent change in quantity is greater than the percent change in price quantity demanded is very sensitive to price rather than messing around with negative numbers we usually just use absolute values and drop that negative and instead of saying negative 3 we would just say 3. so when the price elasticity of demand is greater than 1 in absolute value right e sub p absolute value is greater than one we call this elastic it stretches a lot for a certain amount of force the quantity changes by a big percentage for a certain change in price but what if it didn't change that much what if a ten percent change in a ten percent increase in the price of pizza led to just a 1 decrease in quantity demanded then the elasticity would be 0.1 in absolute value put absolute value signs around this this is inelastic demand and the special case where the elasticity is equal to one is called unit elastic unit for one there the percent change in quantity balances out the percent change in price so a ten percent increase in price leads to a ten percent decrease in quantity demanded now how do we calculate this in practice most economics courses spend way too much time on something called the midpoint formula or sometimes called arc elasticity that's the midpoint formula in arc elasticity which is how you find elasticity without using calculus it's a lot of grinded out plug and chug and i don't think it adds much to your understanding of the concept memorizing a formula and making sure you put the right numbers in the right place is not economics and it's not very interesting so we're not going to do it but if you see those words you know what they refer to we're going to focus on the intuition of elasticity which is what we'll need when we talk about who actually pays a tax how businesses set prices and much more so when it comes time to find an elasticity i won't ask you to do anything more complicated than dividing the percent change in quantity by the percent change in price like we did over here so let's do an example but focusing on the intuition only so we're going to have a straight line demand curve that looks like this and the formula is q equals 1000 minus 100 p if you want the exact relationship between price and quantity but we're focusing on the intuition so this over here is a price of 10 when quantity equals zero and a quantity of a thousand when the price equals zero so let's start up here at a high price like nine dollars what happens when the price goes down by a little bit let's say to eight the quantity actually goes up by a lot in percentage terms it doubles from 100 to 200 and i got these numbers just by plugging into this formula right over here so this is a really big percent change in quantity for a not very big percent change in price that's very elastic quantity changes a lot for even a small change in price quantity is very responsive to price it's stretchy it's elastic the elasticity up around here is about negative 5.6 though of course we call it 5.6 by taking the absolute value a 10 decrease in price leads to a whopping 56 percent increase in quantity or put another way a 10 increase in price leads to a 56 decrease in quantity now where did that number come from i calculated it using that midpoint formula i told you not to worry about and i still don't want you to worry about it the important thing is that the price changes by a small percentage but the quantity changes by a large percentage that's elastic but what happens when we take a look at a price that's already pretty low and again i'm getting these numbers just from plugging in to this demand curve when the price goes from two dollars to one dollar it's also a one dollar change just like it was up here but it's a much bigger percent change the price fell by half and the quantity increases by a hundred just like in the first part of the example but 100 is a much smaller percentage of quantity down here this is very inelastic demand the price changed by a lot as a percent but the quantity demanded didn't change by very much as a percent the elasticity down here is about 0.18 in absolute value which again i calculated with the midpoint formula a 10 increase in price leads to just a 1.8 percent decrease in quantity demanded or put another way a 10 decrease in price leads to a 1.8 percent increase in quantity this is a very important lesson here even though this is a straight-line demand curve so its slope is the same everywhere the elasticity changes dramatically depending on where you are so a single demand curve can be elastic in some places and inelastic in others and if we're elastic up here with a very big elasticity like 5.6 an inelastic down here with a very small elasticity like 0.18 it has to be that somewhere in between we're at exactly one or unit elastic and it will actually be exactly at the midpoint of this line now in the next video we'll go into more detail about understanding demand elasticity