Price elasticity of demand is a measure that shows how much quantity demanded changes in response to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price (see also Elasticity of Demand). However, as you will notice sooner or later, this formula has an annoying limitation: It will not produce distinct results when we use it to calculate the price elasticity of two different points on a demand curve. Show Fortunately, there is a simple trick we can use to avoid this issue: the so-called midpoint method to calculate price elasticities. In the following paragraphs, we will learn step-by-step how to use the midpoint formula to calculate price elasticities. But before we do that, let’s take a step back and look at why the problem we mentioned above arises in the first place. Elasticity Between Two Points on a CurveWhen we try to calculate the price elasticity of demand between two points on a demand curve as described above, we quickly see that the elasticity from point A to point B seems different from the elasticity from point B to point A. While this seems odd at first, it makes perfect sense because we generally calculate percentage changes relative to their initial value. Now, if we move from point A to point B, the initial value is at level A. However, if we move from point B to point A, the initial value is at level B. To illustrate this, let’s look at the graph below.  As you can see, at point A, the price is USD 2.00, and the quantity is 100 units. Meanwhile, at point B, price and quantity are USD 3.00 and 80 units, respectively. That means, going from point A to point B, the price increases by 50% (i.e. [3-2]/2) while quantity decreases by 20% (i.e. [80-100]/100). This indicates a price elasticity of 0.4 (i.e., 20/50). By contrast, going from point B to point A, the price only decreases by 33% (i.e. [2-3]/3) while quantity increases by 25% ([100-80]/80). This indicates a price elasticity of 0.75 (i.e., 25/33). The Midpoint FormulaAs mentioned before, we can avoid this problem by using the so-called midpoint method. Usually, when we calculate percentage changes, we divide the change by the initial value and multiply the result by 100. Unlike that, the midpoint formula divides the change by the average value (i.e., the midpoint) of the initial and final value. In the case of our example (see above) the average price is USD 2.50 (i.e. [2.00 + 3.00]/2) and the average quantity demanded is 90 (i.e. [100 + 80]/2). Thus, according to the midpoint method, a change from point A to point B (i.e. USD 2.00 to 3.00) is considered a 40% increase (i.e. [3.00 – 2.00]/2.50). Similarly, a change from point B to point A (i.e., USD 3.00 to 2.00) is considered a 40% decrease (i.e. [2.00 – 3.00]/2.50). As we can see, the percentage change is the same regardless of the direction we move. Of course, this also holds for the quantity demanded. A move from point A to point B (i.e. 100 to 80) is considered a 22% decrease (i.e. [80 – 100]/90). Similarly, a move from point B to point A (i.e., 80 to 100) is considered a 22% increase ([100 – 80]/90). With the percentage changes calculated with the midpoint method, we can now compute a distinct price elasticity of demand between points A and B. To do this, we use the following formula: The formula looks a lot more complicated than it is. All we need to do at this point is divide the percentage change in quantity demanded we calculate above by the percentage change in price. As a result, the price elasticity of demand equals 0.55 (i.e., 22/40). Please note: Unless stated otherwise, it is advisable to use the midpoint method whenever you have to calculate percentage changes and price elasticities between two points on a curve. In a NutshellPrice elasticity of demand shows how much quantity demanded changes in response to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. However, this approach does not produce distinct results when we use it to calculate the price elasticity of two different points on a demand curve (i.e., results are different based on the direction of change). The midpoint formula computes percentage changes by dividing the change by the average value (i.e., the midpoint) of the initial and final value. As a result, it produces the same result regardless of the direction of change. Therefore is advisable to use the midpoint method whenever you have to calculate percentage changes and price elasticities between two points on a curve.
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If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. 1. Determinants of the price elasticity of demandConsider some determinants of the price elasticity of demand: 2. Calculating the price elasticity of demand - A step-by-step guideSuppose that during the past year, the price of a laptop computer fell from $2,300 to $2,030.During the same time period, consumer sales increased from 425,000 to 578,000 laptops.Calculate the elasticity of demand between these two price–quantity combinations by usingthe following steps. After each step, complete the relevant part of the table with theappropriate answers. (Note: For decreases in price or quantity, enter values in the Changecolumn with a minus sign.)OriginalNewAverageChangePercentageChangeQuantity425,000578,000501,500153,00030.51%Price$2,300$2,030$2,165-$270-12.47%Points:1 / 1Step 1: Fill in the appropriate values for original quantity, new quantity, original price, and newprice.
Learning Objectives
Figure 1. Just how elastic is it? We have defined price elasticity of demand as the responsiveness of the quantity demanded to a change in the price. We also explained that price elasticity is defined as the percent change in quantity demanded divided by the percent change in price. In this section, you will get some practice computing the price elasticity of demand using the midpoint method. The Midpoint MethodTo calculate elasticity, we will use the average percentage change in both quantity and price. This is called the midpoint method for elasticity and is represented by the following equations: [latex]\displaystyle\text{percent change in quantity}=\frac{Q_2-Q_1}{(Q_2+Q_1)\div{2}}\times{100}[/latex] [latex]\displaystyle\text{percent change in price}=\frac{P_2-P_1}{(P_2+P_1)\div{2}}\times{100}[/latex] The advantage of the midpoint method is that one obtains the same elasticity between two price points whether there is a price increase or decrease. This is because the formula uses the same base for both cases.
Let’s calculate the elasticity from points B to A and from points G to H, shown in Figure 2, below. Figure 2. Calculating the Price Elasticity of Demand. The price elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price. Elasticity from Point B to Point AStep 1. We know that [latex]\displaystyle\text{Price Elasticity of Demand}=\frac{\text{percent change in quantity}}{\text{percent change in price}}[/latex] Step 2. From the midpoint formula we know that [latex]\displaystyle\text{percent change in quantity}=\frac{Q_2-Q_1}{(Q_2+Q_1)\div{2}}\times{100}[/latex] [latex]\displaystyle\text{percent change in price}=\frac{P_2-P_1}{(P_2+P_1)\div{2}}\times{100}[/latex] Step 3. We can use the values provided in the figure (as price decreases from $70 at point B to $60 at point A) in each equation: [latex]\displaystyle\text{percent change in quantity}=\frac{3,000-2,800}{(3,000+2,800)\div{2}}\times{100}=\frac{200}{2,900}\times{100}=6.9[/latex] [latex]\displaystyle\text{percent change in price}=\frac{60-70}{(60+70)\div{2}}\times{100}=\frac{-10}{65}\times{100}=-15.4[/latex] Step 4. Then, those values can be used to determine the price elasticity of demand: [latex]\displaystyle\text{Price Elasticity of Demand}=\frac{6.9\text{ percent}}{-15.5\text{ percent}}=-0.45[/latex] The elasticity of demand between these two points is 0.45, which is an amount smaller than 1. That means that the demand in this interval is inelastic. Remember: price elasticities of demand are always negative, since price and quantity demanded always move in opposite directions (on the demand curve). As you’ll recall, according to the law of demand, price and quantity demanded are inversely related. By convention, we always talk about elasticities as positive numbers, however. So, mathematically, we take the absolute value of the result. For example, -0.45 would interpreted as 0.45. This means that, along the demand curve between points B and A, if the price changes by 1%, the quantity demanded will change by 0.45%. A change in the price will result in a smaller percentage change in the quantity demanded. For example, a 10% increase in the price will result in only a 4.5% decrease in quantity demanded. A 10% decrease in the price will result in only a 4.5% increase in the quantity demanded. Note also that a larger (negative) number means demand is more elastic, so that if price elasticity of demand were -0.75, the quantity demanded would change by a greater percentage than when the elasticity was -0.45.
Calculate the price elasticity of demand using the data in Figure 2 for an increase in price from G to H. Does the elasticity increase or decrease as we move up the demand curve? Step 1. We know that [latex]\displaystyle\text{Price Elasticity of Demand}=\frac{\text{percent change in quantity}}{\text{percent change in price}}[/latex] Step 2. From the midpoint formula we know that [latex]\displaystyle\text{percent change in quantity}=\frac{Q_2-Q_1}{(Q_2+Q_1)\div{2}}\times{100}[/latex] [latex]\displaystyle\text{percent change in price}=\frac{P_2-P_1}{(P_2+P_1)\div{2}}\times{100}[/latex] Step 3. We can use the values provided in the figure in each equation: [latex]\displaystyle\text{percent change in quantity}=\frac{1,600-1,800}{(1,600+1,800)\div{2}}\times{100}=\frac{-200}{1,700}\times{100}=-11.76[/latex] [latex]\displaystyle\text{percent change in price}=\frac{130-120}{(130+120)\div{2}}\times{100}=\frac{10}{125}\times{100}=8.0[/latex] Step 4. Then, those values can be used to determine the price elasticity of demand: [latex]\displaystyle\text{Price Elasticity of Demand}=\frac{\text{percent change in quantity}}{\text{percent change in price}}=\frac{-11.76}{8}=1.45[/latex] The elasticity of demand from G to H is 1.47. The magnitude of the elasticity has increased (in absolute value) as we moved up along the demand curve from points A to B. Recall that the elasticity between those two points is 0.45. Demand is inelastic between points A and B and elastic between points G and H. This shows us that price elasticity of demand changes at different points along a straight-line demand curve. Let’s pause and think about why the elasticity is different over different parts of the demand curve. When price elasticity of demand is greater (as between points G and H), it means that there is a larger impact on demand as price changes. That is, when the price is higher, buyers are more sensitive to additional price increases. Logically, that makes sense. Elasticity Is Not SlopeIt’s a common mistake to confuse the slope of either the supply or demand curve with its elasticity. The slope is the rate of change in units along the curve, or the rise/run (change in y over the change in x). For example, in Figure 2 above, for each point shown on the demand curve, price drops by $10 and the number of units demanded increases by 200. So the slope is –10/200 along the entire demand curve, and it doesn’t change. The price elasticity, however, changes along the curve. Elasticity between points B and A was 0.45 and increased to 1.47 between points G and H. Elasticity is the percentage change—which is a different calculation from the slope, and it has a different meaning. When we are at the upper end of a demand curve, where price is high and the quantity demanded is low, a small change in the quantity demanded—even by, say, one unit—is pretty big in percentage terms. A change in price of, say, a dollar, is going to be much less important in percentage terms than it will be at the bottom of the demand curve. Likewise, at the bottom of the demand curve, that one unit change when the quantity demanded is high will be small as a percentage. So, at one end of the demand curve, where we have a large percentage change in quantity demanded over a small percentage change in price, the elasticity value will be high—demand will be relatively elastic. Even with the same change in the price and the same change in the quantity demanded, at the other end of the demand curve the quantity is much higher, and the price is much lower, so the percentage change in quantity demanded is smaller and the percentage change in price is much higher. See Figure 3, below: Figure 3. Elasticity changes along the demand curve. At the bottom of the curve we have a small numerator over a large denominator, so the elasticity measure will be much lower, or inelastic. As we move along the demand curve, the values for quantity and price go up or down, depending on which way we are moving, so the percentages for, say, a $1 difference in price or a one-unit difference in quantity, will change as well, which means the ratios of those percentages will change, too.
These next questions allow you to get as much practice as you need, as you can click the link at the top of the questions (“Try another version of these questions”) to get a new version of the questions. Practice until you feel comfortable with this concept. elasticity: an economics concept that measures the responsiveness of one variable to changes in another variable midpoint method: measures the average elasticity over some part of the demand (or supply) curve more elastic: the calculated elasticity is greater in absolute value, meaning the quantity response is greater to the same change in price Contribute!Did you have an idea for improving this content? We’d love your input. Improve this pageLearn More |
Using the midpoint method, the elasticity of demand for laptops is about
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