63 Calculating Elasticity and Percentage Changes
What you’ll learn to do: explain the price elasticity of demand and price elasticity of supply, and compute both using the midpoint method
Remember, elasticity measures the responsiveness of one variable to changes in another variable. In the last section we looked at price elasticity of demand, or how much a change in price affects the quantity demanded. In this section we will dig deeper by learning how to calculate elasticity using the midpoint method. We’ll also introduce the idea of elasticity of supply. Supply can also be elastic, since a change in price will influence the quantity supplied.
Learning Objectives
- Mathematically differentiate between elastic, inelastic, and unitary elasticities of demand
- Calculate percentage changes, or growth rates
- Differentiate between the midpoint elasticity approach and the point elasticity approach in calculating elasticity
Calculating Elasticity
The formula for calculating elasticity is:
[latex]\displaystyle\text{Price Elasticity of Demand}=\frac{\text{percent change in quantity}}{\text{percent change in price}}[/latex].
Let’s look at the practical example mentioned earlier about cigarettes. Certain groups of cigarette smokers, such as teenage, minority, low-income, and casual smokers, are somewhat sensitive to changes in price: for every 10 percent increase in the price of a pack of cigarettes, the smoking rates drop about 7 percent. Plugging those numbers into the formula, we get
[latex]\displaystyle\text{Price Elasticity of Demand}=\frac{\text{percent change in quantity}}{\text{percent change in price}}=\frac{-7\%}{10\%}=-0.7[/latex]
Try It
Inelastic, Elastic, and Unitary Demand
So what does the number -0.7 tell us about the elasticity of demand? The negative sign reflects the law of demand: at a higher price, the quantity demanded for cigarettes declines. All price elasticities of demand have a negative sign, so it’s easiest to think about elasticity in absolute value, ignoring the negative sign. The fact that the result is less than one is more important than the negative sign. It tells us that the size of the quantity change is less than the size of the price change (i.e. the numerator in the elasticity formula is less than the denominator). This tells us that it would take a relatively large price change in order to cause a relatively small change in quantity demanded. In other words, consumer responsiveness to a change in price is relatively small. Therefore, when the elasticity is less than 1, we say that demand is inelastic.
The data above indicate that the demand for cigarettes by teenagers, minority, low income and casual smokers is relatively inelastic. Addicted adult smokers, though, are even less sensitive to changes in the price—most are willing to pay whatever it takes to support their smoking habit. We can say that their demand is even more inelastic than low income or casual smokers.
Different products have different price elastici