all right sorry about that all right there was a typo in the slide and so i had to stop and re um to get back here so this is our first example suppose a price of five dollars at a price of five dollars the quantity demanded for a box of apple cinnamon cheerios at a local grocery store is 25 boxes per week at a price of six dollars the quantity demanded falls to 15 boxes per week so this is what we expect the price system goes up the quantity demanded goes down so so in this example we want to find the price elasticity of demand for apples and materials okay so remember our formula we're going to need to identify the original price the original quantity the new price the new quantity so right here suppose at a price of five dollars i'm going to call this p1 that is our initial price the quantity demanded for a box of apples and materials is 25 boxes so i'm going to call that q1 so that's our initial price our initial quantity price of six dollars that's our new price we call that p2 the demand falls to 15 boxes per week so we call that q2 okay so that's all we need to use our formula we just need to know what is p1 p2 q1 q2 and now we're ready to plug it in okay i'm going to advance a slide so i'm going to clear off those symbols okay and now i'm going to do the math and i'm going to do the math by hand for you this first time and then it will go in um and then i'll advance the slides you can see it written out so anyway i lost my cursor there for a second okay so in our formula i'm gonna rewrite the formula for right here so if it's the percentage change in quantity we're gonna do that first because that becomes our numerator and so since that's on top i wanna do that first and remember it's q2 minus q1 over the midpoint so q2 plus q1 divided by 2 and you multiply it by 100 okay and it's the same thing for the percentage change in price p2 minus p1 all over p2 plus p1 over 2 multiplied by a hundred percent to turn into a percentage and then the elasticity of demand is the percentage change in the quantity divided by the percentage change in the price and so you notice i use that similarly i should probably just said that that triangle symbol that's delta that's the greek letter delta and that is um the uh that's a math symbol for change so when i say percentage change in quantity that's what i'm writing here in math shorthand so percentage change in quantity percentage change in price sorry i should have said that earlier um but yes so that that delta just means change okay so anyway now i'm going to plug in so i have 15 minus 25 that's my numerator here divided by the midpoint so if you can look at that and immediately know i know it's halfway between 15 and 25 you can just plug that in down here but in case you can't you can always do this which is add them together and divide by two okay and then you're going to multiply the whole thing by 100 percent okay so that is so first of all let's put this equal sign here and so this is negative 10 all over 15 plus 25 is 40 divided by 2 is 20 and like i said if you immediately had said i know what's between 50 and 25 it's 20. then that would have been fine um and so we multiplied this by 100 negative 10 divided by 20 that's negative 0.5 times 100 percent so the percentage change is negative 50 percent or in other words the quantity decreased by 50 okay so now let's do it for price so i'm going to plug in p2 minus p1 that's 6 minus 5 divided by in parentheses 6 plus 5 divided by 2. and again if you know in between 6 and 5 is 5 and a half then you're fine but if you if you're not sure you want to be safe do the whole thing by all means okay we're gonna multiply this by a hundred percent so six minus five is one divided by six plus six plus five divided by 2 that's 11 divided by 2 is 5 and a half okay and when i plug in 1 divided by 5 and a half in my calculator i get 0.18181818 i get questions a lot about how many decimals should i round to honestly i don't i don't really have a rule about this you know you don't want to over round because when you over round you lose uh precision and so i wouldn't round 0.181818 to 0.2 for example um but if you left it 0.18 it would be fine i might i always like doing three decimals for some reason three decimals always feels right to me so i'm going to put out 0.182 um again it's not it's not a big deal um you know if this is a multiple choice question you might have to look at the answers and see how many decimals they are and you want to kind of keep that or else you might your answer might not match um and if you're doing this in an assignment you know two is probably fine just just just do three like it's not a rule it's just a good uh i think it's a good practice anyway and multiply this by a hundred percent and so we're left by sorry that's just a multiplication sign and so we're left with 18.2 percent okay so that is our story here is the price went up by eighteen point two percent and as a result the quantity demanded fell by fifty percent okay so our last step to finding the elasticity is just to divide the two remember it's a ratio so we do the elasticity of demand is equal to negative 50. and i'm going to not only need to put the percents here because that's going to cancel divided by 18.2 okay and i'm going to pull up my calculator real quick because i can't remember what the answer is and i can't advance the slide without erasing everything so 50 divided by 18.2 is 2.7472 so i'm going to put it as 2.75 okay and that is my answer okay a couple of things i want to point out about this answer okay first off i was about to say i didn't actually do negative 2.75 negative 50 divided by 18.2 i'm sure some of you watching this thought hey where's that negative go and that was the point i was about to make if you follow along in the book you will notice the negative disappears it does and it doesn't actually explain it very well but what they do is in the book they will take the absolute value of the elasticity so they will take the absolute value of that negative 2.75 and that makes it 2.75 if you've not taken enough math to know what absolute value it means don't worry about it just means taking the negative and turning it positive uh the reason they do that is because if you think about the price elasticity of demand okay it's the percentage change in quantity divided by the percentage change in price if the price is going up like in this example the quantity is going down so you're going to have a negative number in the numerator a positive number here so your elasticity is going to be negative if on the other hand the price is going down then we expect the quantity to be going up so if you have a positive number here you have a negative number down here and the elasticity again will be negative so it's always negative and so the book thinks you know what let's we can just ignore the negative and think about the plot just think of that the whole number and that way we can be more easy for us to compare magnitudes like which number is bigger which elasticity is bigger we can compare the magnitudes easier if we don't have to deal with the negative okay i don't subscribe to that personally i think it should stay negative that's how i was taught that's how most textbooks i believe teach it and i think there's good reason so my reasoning for keeping the negative is by the end of this chapter we're going to see some elasticities that are not negative yes the price elasticity of demand is going to stay negative but we're going to have other versions that can oscillate between positive and negative and understanding why one's positive and one's negative i think is crucial and so ignoring this negative i don't think fits with that uh that teaching element that i think is important okay so i'm going to keep it negative in all of my examples now i am not dastardly enough to give you a multiple choice question where your answer has a negative and a positive like negative 2.75 and positive 2.75 and i'm asking you who to believe near the book it's not gonna happen okay i'm also if you do if i do put a question like this in a short answer version where you have to write out your answer i will um accept both answers positive or negative that's fine if you do the book wait that's okay so don't worry about this affecting your grade i think it's important for comprehension for understanding what's going on in the economics of this instead of just the math to keep it negative that's me it's negative because as one of these two elements goes up the other is going down as one goes down the other goes up okay that is why it's negative and so i want to embrace that okay the other thing i want to say is let's uh this notice that the elasticity is not a percentage this is just a hint a lot of people want to take that 2.75 multiply by 100 the end and give me an answer of 275 percent don't do that we do the percentages in the steps because we're talking about the percentage change in quantity we're doing that talking about the percentage change in price but elasticity is the ratio it's not a percentage so please do not convert it into a percentage okay and the last thing let's talk about what that answer means so it's always going to be negative but let's talk about the magnitude let's talk about 2.75 let's talk about the number okay the first thing is it's greater than one okay i'll explain in more detail what that means in a bit but right away i want you to look at and say hey that's greater than one why because if we look at the ratio a number greater than one when you're doing any sort of division any sort of ratio means the top number is bigger than the bottom number and that's what happened here the change in quantity is greater than the change in price so remember we talked about elasticity meaning elastic meaning you can change your decisions well how did consumers react to an eighteen point two percent price hike fifty percent drop in quantity demanded that's a pretty strong reaction we're going to call that in a little bit elastic demand okay so um that's the first thing i wanted to point out now we're going to move on to another example and here's what i want you to do i'm going to put this example in another video i didn't want to stop sharing my screen i don't know why i did that i'm going to put this example in the next video but i'm going to put this up right here i want you to try it on your own i don't want you just to go to the next video and see the answer and watch me do it i want you to do it first because this is the first real matthew like you gotta get your hands dirty okay so do it pause this video do that answer uh and then when you're ready to check your answer and you're ready to go on the next problem see how you did okay that's my suggestion um i'm an econ professor i'm not a cop do it do whatever you want i will see you for the next video