Different Answers when Increasing or Decreasing Prices! (Part 1)

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So now let's see how we can actually get different elasticity. He's using the same data. The problem here ends up being with our percentage change formula. Remember that when we were using percentage change. Um By the way this is the shorthand right percentage and the delta, the triangle here is change. Uh We would do the change over the original which was basically the new minus the original. Right? That's the that's the numerator divided by the original. Right? So the change divided by the original, gives us the percentage shape and it's actually in this denominator that we end up having a problem. So let's go ahead and see uh through these examples. Let's see let's see it in action. We're gonna get a different elasticity when we're raising the price and when we're decreasing the price. So let's see this example. Pizza Companies lunch special Currently costs $5 at this price. The weekly demand is 2000 lunch specials. If they raised their price to $6, the weekly demand will drop to 1400 lunch specials. What is the price elasticity of demand. Alright so let's go ahead and start remember um our formula for elasticity of demand was our percentage change in quantity demanded over a percentage change in price. Right so let's go ahead and start with the quantity demanded. And I'm gonna go here and we're gonna use our percentage change formula just like I've written there above new minus original, divided by original. So the percentage change for quantity demanded. Let's see um First I'm gonna circle all our data we've got in blue, I'll circle our quantity demanded 2000 and it went down to 1400 and in red. I'll do the prices. Well I've been using red I'll use green for the prices here. Color of money. Five and six. Right? So let's start with our quantity demanded. Okay. And we had a demand of 2000 and it dropped to 1400. Right? So our new is 1400 minus the 2000 divided by the original of 2000. Right? So our original demand was 2000. Our new demand was 1400. What is going to be? The difference here? We're gonna get negative 600 over 2000. Right? We put that in our calculator and we're gonna get 0.3. Right? And this will be a negative 0.3. Right? But remember we're gonna drop all the negatives and positives because we're always gonna get one of them negative. So we're just gonna say 0.3 absolute value. And let's do the same thing for price. Right? For price, we had a price of $5 and it went up to $6. So the new was six minus the original of five divided by the original of five. Right? So six minus five is one divided by five. Put that in our calculator and we're gonna get 0.2 right? That. Oops, can you see that there? Alright six minus five divided by five. So it gives us 1/5 and we're gonna get 0.2 here for our percentage change in price. And we had 0.3 here for a percentage change in quantity demanded. Right, Okay, so let's go ahead. And sulfur elasticity in this case and I'll do it in right here. So elasticity of demand is going to equal that percentage change in quantity demanded. 0.3 divided by our percentage change in price, which was 0.2. Right. And what does that give us? It's going to give us 1.5. So our elasticity in demand in this case was 1.5. Right? And when we get an elasticity of demand greater than one, right? That means that it's elastic. So in this case We got an elasticity of demand greater than one and an elastic 1.5. So let's go ahead. In the next video, we're gonna do a similar example with similar data. Check it out

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Different Answers when Increasing or Decreasing Prices! (Part 2)

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Alright so now let's check out this problem, A pizza companies lunch special currently cost $6 at this price. The weekly demand is 1400 lunch specials. If they lower their price to $5 the weekly demand will increase to 2000 lunch specials. What is price elasticity of demand? And you should be able to notice that we've got the same numbers here, right? Except in this case we started at a price of $6 and We're decreasing to $5 in the previous problem. Up here we started at a price of $5 and increase to $6. But the quantity demanded are all the same. Right? It's just which direction we're moving. So let's go ahead and solve our price elasticity of demand here. Right? We're gonna use still our percentage change formula. Remember that was new minus original divided by original. And just like I said um this is where we're gonna end up seeing the problem is going to be in this denominator. Um is the problem with this formula where we're gonna get different answers. So let's go ahead and do our uh our price elasticity. So elasticity of demand is going to equal percentage change in quantity demanded. Over percentage change in price. Right? So let's go ahead and do like we did before, we'll get our our quantities here and our prices we'll use green. Alright so let's go ahead and start with quantity demanded. Let's get our percentage change in quantity demanded. Alright um so in this case uh they started at 1400 lunch specials And demand will increase to 2000. So the new in this case, excuse me. The new is 2000 and the original was 1400. Right? They were at 1400. They're gonna decrease the price which will increase quantity demanded. So new minus original divided by the original which in this case was 1400 and we are going to get uh 600 in the numerator divided by 1400. We put that in our calculator and we're going to get 0.429. I'm gonna say okay I'm gonna cut it off at three decimals there, you can stop at two or three. We're just rounding and for price let's go ahead and do the same thing. So price, we had a new price of $5. Right? In this case they're lowering their price to $5. They had an original price of $6 and we're gonna divide by six there and we're gonna get five minus six is negative, 1/6. Um and remember we just get rid of the negative, right we're gonna be dealing with absolute values here. So I'm just gonna get rid of that negative there. We have 16 which we put that in and we're gonna get 0.1 and I'm gonna go to three decimals here as well. 1670.167. Right so there we go that is gonna be a percentage change in price over here, We have percentage change in quantity demanded. Right, whoops right there And right there, let's go ahead and put this in to our elasticity of demand formula and see what answer we get. So we get .429 is going to be in our numerator. I'll do it in blue just to keep it even. And in our denominator we will have .167. So let's go ahead and do that. Math. .429 divided by .167 gives us an elasticity of demand Equal to 2.569. So look at this. In this case we've got 2.569 before we got 1.5 right? We've gotten different answers in both cases and we used the same numbers, we used price of five and a price of six and a quantity demanded of 21,400, right? The numbers stayed the same. But we got a different answer whether we were going up in price or down in price and we don't want that. We want a consistent answer. Right? This problem came from what was in our, in our denominators, the original values. Notice in in this first problem for the quantity demanded um our denominator was 2000, right? Our numerator was 600 still but our denominator was 2000 and down here notice our numerator was 600. But our denominator was 1400 that's the problem, we're seeing the same thing is going to happen with price. We have different denominators in either case, so what we're gonna end up doing is taking an average and putting that in the denominator instead. So let's go ahead to the next video where I'm gonna show you a step by step method to do the averaging and get a consistent answer when we solve these problems. So let's go ahead and do that now.