64 Calculating Price Elasticities Using the Midpoint Formula
64 Calculating Price Elasticities Using the Midpoint Formula
Learning Objectives
- Calculate price elasticity using the midpoint method
- Differentiate between slope and elasticity
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 Method
To 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.
Exercise: Calculating the Price Elasticity of Demand
Let’s calculate the elasticity from points B to A and from points G to H, shown in Figure 2, below.
Elasticity from Point B to Point A
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 (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 t