Elasticity and the Midpoint Method - Online Tutor, Practice Problems & Exam Prep

Understanding the midpoint method for calculating price elasticity of demand is crucial for analyzing consumer behavior. This method provides a consistent elasticity value regardless of price changes. The formula involves the percentage change in quantity demanded divided by the percentage change in price, using averages for both quantity and price. For example, if a pizza's price rises from $5 to $6, and demand drops from 2,000 to 1,400, the elasticity can indicate whether demand is elastic or inelastic. A result greater than 1 signifies elastic demand, meaning consumers are sensitive to price changes.

The Midpoint Method

Now we're going to use what's called the midpoint method to calculate elasticity, which is going to give us a consistent answer whether we're raising the price or decreasing the price. So, I've got our updated formula for our price elasticity of demand when we're using the midpoint formula, which is what we're going to use from now on, but don't let this trip you up. There's a lot going on there, but this is still just a percentage change in quantity demanded divided by the percentage change in price. Okay. We're still just dealing with that same formula. We're just changing how we calculate the percentage change in each situation. So, if you remember with percentage change, before we had the original value in the denominator, right? It was the change divided by the original value. Well instead of the original value, now we're going to use this noted sum of quantities divided by 2. This is the average quantity instead of the original quantity and over here we're going to use the ave

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?

Alright, let's try this practice problem. 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 to 280,000. Using the midpoint method, what is the price elasticity of demand, and is demand elastic or inelastic? So, we're going to go ahead and use our step-by-step formula to calculate this price elasticity. Remember that elasticity of demand is going to 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 two columns. I like to have quantity demanded and price, and let's go ahead and do step 1 where we're going to subtract our quantities and subtract our prices. So, let's circle our quantities here: 200,000 and 280,000. Remember, the order doesn't matter when we do the midpoint method. We just want to do the easiest math possible, keep the numbers positive. We're going to use absolute values anyway, always using positive numbers. So, let's go ahead and do that. First, we're going to subtract in step 1. So, let's subtract our quantities: 280,000 minus 200,000, and that's going to give us 80,000 for step 1 here. Let's do the same thing with the price. Price, I'll just use the bigger one first. It's easier: $44 minus $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 going to 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, the 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 going to get 80,000, our answer from step 1, divided by 240,000, our answer from step 3, and that's going to come out to 0.333. So, I'm going to stop at three decimals here, 0.333. Let's do the same thing with the price. Our answer from step 1 was $8 divided by our answer from step 3, which was $40. $8 divided by $40 is 0.2. So, let me go ahead and box that off and I'm going to write under it, 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 changed 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 going to be bigger than the denominator, right. So the idea is when the numerator is bigger, you're going to get a number bigger than 1, and that's conceptually what's going on here too. We've got a big change in quantity demanded compared to a smaller change in price. Demand is elastic. Cool. So, let's go ahead and move on.

Assume that the price elasticity of demand for cigarettes is 0.4. If a pack of cigarettes currently costs $6 and the government aims to decrease smoking by 20 percent, by how much should it increase the price?

• A. $1.20
• B. $2.40
• C. $3.00
• D. $4.80

Here’s what students ask on this topic:

What is the midpoint method in calculating price elasticity of demand?

The midpoint method is a technique used to calculate the price elasticity of demand, ensuring consistent results regardless of whether the price increases or decreases. It involves using the average of the initial and final quantities and prices to compute percentage changes. The formula is:

$\frac{\frac{\Delta Q}{\frac{Q}{}}}{}$₁+Q₂2ΔPP₁+P₂2

where ΔQ is the change in quantity demanded, and ΔP is the change in price. This method provides a more accurate measure of elasticity by averaging the starting and ending values.

How do you calculate price elasticity of demand using the midpoint method?

To calculate price elasticity of demand using the midpoint method, follow these steps:

1. Subtract the initial quantity from the final quantity to find ΔQ.
2. Subtract the initial price from the final price to find ΔP.
3. Calculate the average quantity: (Q1 + Q2) / 2.
4. Calculate the average price: (P1 + P2) / 2.
5. Divide ΔQ by the average quantity to find the percentage change in quantity.
6. Divide ΔP by the average price to find the percentage change in price.
7. Divide the percentage change in quantity by the percentage change in price to find the elasticity.

This method ensures consistent results regardless of the direction of the price change.

Why is the midpoint method preferred over the traditional method for calculating elasticity?

The midpoint method is preferred over the traditional method because it provides consistent elasticity values regardless of whether the price increases or decreases. The traditional method, which uses the initial values for calculations, can yield different elasticity results depending on the direction of the price change. By using the average of the initial and final quantities and prices, the midpoint method eliminates this inconsistency, offering a more accurate and reliable measure of elasticity.

What does an elasticity value greater than 1 indicate when using the midpoint method?

An elasticity value greater than 1 indicates that the demand for a product is elastic. This means that consumers are highly responsive to price changes. For example, if the price of a product increases by 10% and the quantity demanded decreases by more than 10%, the demand is considered elastic. In such cases, a small change in price leads to a relatively larger change in quantity demanded, suggesting that consumers can easily switch to substitutes or forego the product.

Can you provide an example of calculating price elasticity of demand using the midpoint method?

Sure! Let's say the price of a pizza increases from $5 to $6, and the quantity demanded decreases from 2,000 to 1,400. Using the midpoint method:

1. ΔQ = 1,400 - 2,000 = -600
2. ΔP = $6 - $5 = $1
3. Average quantity = (2,000 + 1,400) / 2 = 1,700
4. Average price = ($5 + $6) / 2 = $5.50
5. Percentage change in quantity = -600 / 1,700 ≈ -0.353 (or -35.3%)
6. Percentage change in price = $1 / $5.50 ≈ 0.182 (or 18.2%)
7. Elasticity = -0.353 / 0.182 ≈ -1.94

Since the absolute value of elasticity is greater than 1, the demand is elastic.