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we are now going to discuss price elasticity of demand which sounds like a very fancy concept but really it's a way for economists to sense how sensitive is quantity to change in prices and in this video we're going to denote it as a capital e so e price elasticity of demand and the easy way to think about it is it is your percent change in I'll use the Greek letter Delta shorthand for change in your percent change in quantity over your percent change in price and so you might say wait how does this relate to the everyday idea of elasticity well imagine two bands so let's imagine an inelastic band in elastic right over here and let's imagine an elastic band right over here so in an inelastic band if we apply some amount of force you're not going to be able to stretch it much it might stretch a little bit what an elastic band if you apply that same amount of force you might be able to stretch it a lot more and so the analogy here is we're not using force but we're saying how much does quantity stretch for a given amount of price change and so something where the quantity changes a lot for a given price change would be very elastic so this the magnitude of this will be larger and if the percent change in quantity doesn't change a lot for a given percent change in price well then we're dealing with an inelastic price elasticity of demand and we'll be able to internalize these more as we work through the numbers and actually let's do that for this demand schedule that we have right over here and it's visualized as our demand curve in the vertical axis we have price of burgers and then in our horizontal axis we have quantity in terms of burgers per hour and so let's just use this definition of price elasticity of demand to calculate it across different points on our demand curve so let me make a new column here so price elasticity of demand and the way I'm going to do it is really the simplest method for calculating this in other videos we can go into more in-depth methods like the midpoint method and I'll show you the weakness in what we're doing right here but for the sake of say an AP economics microeconomics course this would be sufficient so let's think about our price elasticity of demand as we go from point A to point B well remember that's just going to be our percent change in quantity over our percent change in price so what is our percent change in quantity well we're starting at a quantity of two so put that in our denominator and we're going from two to four so we are adding two so we have 2 over two we could multiply that times one hundred percent if we like so this would give us we have a hundred percent change in quantity over now what was the corresponding change in price percent change in price so our corresponding percent change in price our initial price is nine and we go from nine to eight so we're going down by one and then we multiply that times one hundred percent so this is going to be about a negative 11 percent change in price and this math is reasonably straightforward because the hundred percents cancel out this is just a 1 1 over negative 1/9 is just going to be equal to negative 9 so you have a negative 9e lasted price elasticity of demand so before I interpret that more let's look at the price elasticity of demand at other points or starting from other points two other points on this curve so let's think about it going from actually let's think about it going from E to F so as we go from E to F we're going to do the same exact exercise what is our percent change in quantity well our initial quantity is 16 and we're going from 16 to 18 so we have a change in two of two so 2 over 16 times 100 percent that is our percent change in quantity and what is our percent change in price well our initial price is two and we're going from two to one so we have a price change of negative one times 100% and so what you see here is this is 1/8 times 100% this would be 12.5% up here so this is 12.5% up there and then this over here is going to be negative 50 percent so when price went down by 50% you had a 12 and a half percent increase in quantity 12.5% is 1/4 of 50% so this is going to give us a price elasticity a price elasticity of demand of negative 0.25 so there's a couple of interesting things that you might already be realizing one is even though our demand curve right over here is a line it actually has a constant slope you see that the price elasticity of demand changes depending on different parts of the curve now the reason why this is is really just boils down to math when we're going from A to B our initial prices were relatively high so even though you had a price decrease of 1 it was from an initial price of 9 so your percentage change in price looked fairly low while your percentage change in quantity was high because you're going from a low quantity of 2 and you're adding 2 to it so you had a hundred percent change in quantity when you go to the other end of our curve and you go from E to F it's the other way around your price starting point is low so your percent change in price when you decrease price by one it looks like a fairly large magnitude while your percent change in quantity when you go from E to F because you are already at a quantity of 16 adding 2 to that is not that large of a percentage now another thing you might be appreciating is if we tried to calculate the price elasticity of demand up here on the curve and instead of going from A to B if we went from bead a we would have gotten a different value because our initial prices and quantities would have been different our initial price we would have put an 8 over here and our initial quantity we would have put a four over here and we would have gotten a different value and that's one of the negatives of the technique which is arguably the simplest technique that I just used there's other techniques like the midpoint technique that can give you a more consistent result whether you're going from A to B or B to a but I won't cover it just yet but let's think now about how to interpret this and the best way to interpret it is to think about the absolute value of the price elasticity of demand so over here the absolute value of our price elasticity of demand is equal to nine and then over here the absolute value of our price elasticity of demand is equal to 0.25 and a general rule of thumb is if your absolute value of your price elasticity of demand is less than one you are dealing with an inelastic in elastic elastic situation and if your price elasticity of demand the absolute value of it is greater than one you're dealing with an elastic situation why does that make sense well in this first scenario it's saying for a given percentage change in price you have a smaller percent change in quantity while here for a given percent in price you're going to have a larger than that percentage change in your quantity so once again it goes back to these rubberband analogies so when we're going from A to B the absolute value of our price elasticity of demand is definitely larger than one so economists would consider this to be an elastic situation while when we go from point A to point EV our price elasticity of demand or the absolute value of it is definitely less than one so this is going to be an in elastic situation

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