The price of widgets is currently $44 with a quantity demanded...

Question

The price of widgets is currently $44 with a quantity demanded of 200,000 units. If the price decreases to $36, the quantity demanded increases 280,000. Using the midpoint method, what is the price elasticity of demand? Is demand elastic or inelastic?

Accepted Answer

Alright so let's try this practice problem. The price of widgets is currently $$44 with a quantity demanded of 200 1,000 units. If the price decreases to 36 $$the quantity demanded increases to 280,000. Using the midpoint method, what is the price elasticity of demand and is demand elastic or inelastic? So we're gonna go ahead and use our step by step formula, to calculate this price elasticity. So remember that elasticity of demand is gonna equal our percentage change in quantity demanded over our percentage change in price and we've got that midpoint step by step that we're going to use here. So let's go ahead and set up our 2 columns. I like to have quantity demanded and price, and let's go ahead and do step 1 where we're gonna subtract our quantities and subtract our prices. So let's circle our quantities here $$200,280,000 Remember the order doesn't matter when we do midpoint method. We just want to do the easiest math possible, keep the numbers positive. We're gonna use absolute value anyways, always gonna use positive number. So let's go ahead and do that. 1st we're gonna subtract in step 1. So let's subtract our quantities. 280,000 minuteus 200,000 and that's gonna give us 80,000 for step 1 here. Let's do the same thing with price. Price, I'll just use the bigger one first. It's easier. 40 4 minuteus 36 and that's a price change of 8 $$there. And let's go on to step 2. So step 2, we are going to sum the quantities and sum the price. So now it's the same numbers 280,000 plus 200,000 and we will get 480,000 for step 2 here. And step 2 for the price, 44 plus 36 is going to be 80. Alright. Easy enough. Let's go on to step 3. Step 3, we're just gonna take our answer from step 2 and divide it by 2. So I'll draw this arrow. 480,000 divided by 2 equals 240,000. Mark that, and here same thing, 80 divided by 2 equals 40. Alright, so let's go on to step 4. So remember step 4 is where we actually calculate the percentage change in quantity demanded and the percentage change in price, which we'll use to finally calculate our elasticity. So we're on the home stretch. So let's go ahead. Step 4 is where we're going to take our answer from step 1 and divide the answer from step 3. So we're gonna get 80,000, our answer from step 1, divided by 240,000, our answer from step 3, and that's gonna come out to point 333. So I'm going to stop at 3 decimals here, 0.333. Let's do the same thing with price. Our answer from step 1 was 8 divided by our answer from step 3 was 40. 8 divided by 40 is 0 point 2. So let me go ahead and box that off and I'm gonna right under it, I'm gonna put percentage change in price. I'll do the same thing over here. This is our percentage change in quantity demanded, right. So step 5 is where we just divide these two numbers and actually get our elasticity. So let's go ahead and do that and we'll do it here on the left hand side. So elasticity of demand is going to be 0.333, divided by 0.2. Right. Divided by 0.2 and that is going to give us an elasticity of demand equal to 1.665, right, and we can confirm that this is elastic just looking at our answers to step 4, right. It's elastic because it's a number greater than 1, but we can conceptually think about it right here in step 4 right. In step 4 we saw that quantity demanded change by 0.333 which is 33%, right, 33.3% was our change in quantity demanded and our change in price was just 20 percent. So quantity demanded changed more than the percentage change in price, right. So when the quantity demanded change is bigger, that means the numerator is bigger, right. Over here if you think about it, the numerator is gonna be bigger than the denominator, right. So the idea is when the numerator is bigger, you're gonna get a number bigger than 1 and that's kind of conceptually what's going on here too. We've got big change in quantity demanded compared to a smaller change in price. Demand is elastic. Cool. So let's go ahead and move on.

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The price of widgets is currently \$44 with a quantity demanded of 200,000 units. If the price decreases to \$36, the quantity demanded increases 280,000. Using the midpoint method, what is the price elasticity of demand? Is demand elastic or inelastic?

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