82 Reading: Calculating Price Elasticities
Introduction
Remember, all elasticities measure the responsiveness of one variable to changes in another variable. In this section, we will focus on the price elasticity of demand and the price elasticity of supply, but the calculations for other elasticities are analogous.
Let’s start with the definition:
Price elasticity of demand is the percentage change in the quantity of a good or service demanded divided by the percentage change in the price.
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.
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 1, 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.
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%,