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

To calculate price elasticity of demand using the midpoint method, use the formula: $\frac{∆Q}{∆P}$, where $Q$ is quantity demanded and $P$ is price. This method ensures consistent elasticity results regardless of price changes. A calculated elasticity greater than 1 indicates elastic demand, meaning quantity demanded is sensitive to price changes, while less than 1 indicates inelastic demand.

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 percentage change in quantity demanded divided by 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 average 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 average p

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, so 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, 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 going to use absolute value anyways, always using a positive number. So let's go ahead and do that. First, we subtract our quantities, \(280,000 - 200,000\) and that's going to give us \(80,000\) for step 1 here. Let's do the same thing with the price. I'll just use the bigger one first. It's easier. \(44 - 36\) and that's a price change of $8 there. And let's move on to step 2. So, step 2, we are going to sum the quantities and sum the prices. So now it’s the same numbers, \(280,000 + 200,000\) and we get \(480,000\) for step 2 here, and for the price, \(44 + 36\) 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. \(480,000 / 2 = 240,000\). Mark that, and here the same thing, \(80 / 2 = 40\). Alright, so let’s go on to step 4. 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. Step 4 is where we're going to take our answer from step 1 and divide by the answer from step 3. So, we're going to get \(80,000 / 240,000 = 0.333\). This is our percentage change in quantity demanded. 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. \(8 / 40 = 0.2\). This is our percentage change in price. Step 5 is where we just divide these two numbers and actually get our elasticity. So let's go ahead and do that here on the left-hand side. So, elasticity of demand is going to be \(0.333 / 0.2 = 1.665\). We can confirm that this is elastic. It’s elastic because it's a number greater than 1. In step 4 we saw that the quantity demanded changed by 33.3%, while our change in price was just 20%. When the quantity demanded change is bigger, that means the numerator is bigger than the denominator. The idea is when the numerator is bigger, you're going to get a number bigger than 1, which is conceptually what's going on here as well. We've seen 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. The formula is:

$\frac{∆Q}{∆P}$

where $Q$ is the quantity demanded and $P$ is the price. Instead of using the original values, the midpoint method uses the average of the initial and final quantities and prices. This approach avoids discrepancies in elasticity calculations that can arise from different starting points.

How do you calculate the percentage change in quantity demanded using the midpoint method?

To calculate the percentage change in quantity demanded using the midpoint method, follow these steps:

1. Subtract the initial quantity from the final quantity to find the change in quantity ($∆Q$).

2. Sum the initial and final quantities and divide by 2 to find the average quantity.

3. Divide the change in quantity by the average quantity and multiply by 100 to get the percentage change.

Mathematically, it is represented as:

$\frac{∆Q}{\frac{Q}{}}$₁ + Q₂2 × 100

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 results regardless of whether the price increases or decreases. The traditional method can yield different elasticity values depending on the direction of the price change, leading to potential inaccuracies. By using the average of the initial and final quantities and prices, the midpoint method eliminates this discrepancy, ensuring a more reliable and symmetric measure of elasticity.

What does an elasticity greater than 1 indicate in the midpoint method?

An elasticity greater than 1, calculated using the midpoint method, indicates that the demand for a product is elastic. This means that the quantity demanded is highly sensitive to changes in price. In other words, a small change in price leads to a relatively larger change in the quantity demanded. Elastic demand typically occurs for goods that have many substitutes or are not necessities.

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

Sure! Let's say a pizza company raises the price of its lunch special from $5 to $6, and the weekly demand drops from 2,000 to 1,400 lunch specials. Using the midpoint method:

1. Change in quantity demanded: 2,000 - 1,400 = 600

2. Average quantity: (2,000 + 1,400) / 2 = 1,700

3. Change in price: $6 - $5 = $1

4. Average price: ($6 + $5) / 2 = $5.50

5. Percentage change in quantity demanded: (600 / 1,700) × 100 ≈ 35.3%

6. Percentage change in price: (1 / 5.50) × 100 ≈ 18.2%

7. Elasticity of demand: 35.3% / 18.2% ≈ 1.94

Since the elasticity is greater than 1, the demand is elastic.