Percentage Change and Price Elasticity of Demand - Online Tutor, Practice Problems & Exam Prep

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

So now let's see how we can actually get different elasticities using the same data. The problem here ends up being with our percentage change formula. Remember that when we were using percentage change, by the way, this is the shorthand, percentage and the delta, the triangle here is change. We would do the change over the original which was basically the new minus the original, right? That's the numerator divided by the original right. So the change divided by the original gives us the percentage change and it's actually in this denominator that we end up having our problem. So let's go ahead and see through these examples. Let's see it in action. We're going to get a different elasticity when we're raising the price and when we're decreasing the price. So let's see this example. A pizza company's lunch special currently costs $5. At this price, the weekly demand is 2,000 lunch specials. If they raise their price to $6, the weekly demand will drop to 1,400 lunch specials. What is the price elasticity of demand? Alright, so let's go ahead and start. Remember our formula for elasticity of demand was our percentage change in quantity demanded over our 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 as I've written it above, new minus original divided by original. The percentage change for quantity demanded, let's see. First I'm going to circle all our data. We've got in blue, I'll circle our quantity demanded: 2,000, and it went down to 1,400, and in red I'll do the prices. Well, I've been using red. I'll use green for the prices here, the color of money. 56, right? So let's start with our quantity demanded and we had a demand of 2,000 and it dropped to 1,400, right? So our new is 1,400 minus the 2,000 divided by the original of 2,000, right? So our original demand was 2,000. Our new demand was 1,400. What is going to be the difference here? We're gonna get negative 600 over 2,000. Right? We put that in our calculator and we're gonna get -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

Let's do the same thing for the price, right? For the price, we had a price of $5 and it went up to $6 so the new was 6 5 минус 5 5 equals 1 divided by 5. Put that in our calculator and we're gonna get 0.2. Right, that oops. Can you see that there? Alright. 6 minus 5 divided by 5. 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 our percentage change in quantity demanded, right?

Okay. So let's go ahead and solve for elasticity in this case and I'll do it in red 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 1, right, that means that it's elastic. So in this case, we got an elasticity of demand greater than 1 and elastic, 1.5. So let's go ahead in the next video. We're going to do a similar example with similar data. Check it out.

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

Alright. So now let's check out this problem. A pizza company's lunch special currently costs $6. At this price, the weekly demand is 1400 lunch specials. If they lower their price to $5, the weekly demand will increase to 2,000 lunch specials. What is the 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 increased 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 going to use still our percentage change formula. Remember that was new minus original divided by original, and just like I said, this is where we're going to end up seeing the problem is going to be in this denominator is the problem with this formula where we're going to get different answers. So let's go ahead and do 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 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, so in this case, they started at 1400 lunch specials and demand will increase to 2,000. So the new in this case is 2,000 and the original was 1400, right? They were at 1,400. They're going to 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 600 in the numerator divided by 1400. We put that in our calculator and we're going to get 0.429, I'm going to say. Okay, I'm going to cut it off at 3 decimals there. You can stop at 2 or 3. 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 going to divide by $6 there and we're going to get $5 minus $6 is negative one over $6, and remember we just get rid of the negative, right? We're going to be dealing with absolute values here. So I'm just going to get rid of that negative there. We have 1/6 which we put that in and we're going to get 0.167. Right. So there we go. That is going to be a percentage change in price. Over here, we have percentage change in quantity demanded right. Oops. Right there and right there.

Let's go ahead and put this into our elasticity of demand formula and see what answer we get. So we get 0.429 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 0.167. So let's go ahead and do that math. 0.4290.167 gives us an elasticity of demand equal to approximately 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 a price of $5 and a price of $6 and a quantity demanded of 2,000 and 1,400, 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 denominators, the original values. Notice in this first problem for the quantity demanded, our denominator was 2,000 right? Our numerator was 600 still, but our denominator was 1,400 and 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 going to 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 going to 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.