Calculating Price Elasticity of Demand

Let’s calculate the elasticity between points A and B and between points G and H shown in Figure 1.

First, apply the formula to calculate the elasticity as price decreases from $70 at point B to $60 at point A:

[latex]\begin{array}{rcl}\text{% change in quantity}& = & \frac{2,800 - 3,000}{\frac{3,000 + 2,800}{2}} \times 100 \\ & = & \frac{-200}{2,900} \times 100 \\ & = & -6.9  \end{array}[/latex]

[latex]\begin{array}{rcl}\text{% change in price}& = & \frac{70 - 60}{\frac{60 + 70}{2}} \times 100 \\ & = & \frac{10}{65} \times 100 \\ & = & 15.4  \end{array}[/latex]

[latex]\begin{array}{rcl}\text{Price Elasticity of Demand}& = & |\frac{\text{% change in quantity}}{\text{% change in price}}|  \\ & = & |\frac{-6.9}{15.4}| \\ & = & |-0.45| \\ & = & 0.45\end{array}[/latex]

Therefore, the elasticity of demand between these two points 0.45, an amount smaller than one, showing that the demand is inelastic in this interval. Price elasticities of demand would always be negative since price and quantity demanded always move in opposite directions (on the demand curve). By convention, we always talk about elasticities as positive numbers. So mathematically, we take the absolute value of the result. We will ignore this detail from now on and simply remember to interpret elasticities as positive numbers.

This means that, along the demand curve between point 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. Price elasticities of demand are negative numbers indicating that the demand curve is downward sloping, but are read as absolute values. The following Work It Out feature will walk you through calculating the price elasticity of demand.

Calculating the Price Elasticity of Supply

Assume that an apartment rents for $650 per month and at that price 10,000 units are rented as shown in Figure 2. When the price increases to $700 per month, 13,000 units are supplied into the market. By what percentage does apartment supply increase? What is the price sensitivity?

Using the Midpoint Method,

[latex]\begin{array}{rcl}\text{% change in quantity}& = & \frac{13,000 - 10,000}{\frac{10,000 + 13,000}{2}} \times 100 \\ & = & \frac{3,000}{11,500} \times 100 \\ & = & 26.1  \end{array}[/latex]

[latex]\begin{array}{rcl}\text{% change in price}& = & \frac{700 - 650}{\frac{650 + 700}{2}} \times 100 \\ & = & \frac{50}{675} \times 100 \\ & = & 7.4  \end{array}[/latex]

[latex]\begin{array}{rcl}\text{Price Elasticity of Supply}& = & \frac{\text{% change in quantity}}{\text{% change in price}}  \\ & = & \frac{26.1}{7.4} \\ & = & 3.53\end{array}[/latex]

Again, as with the elasticity of demand, the elasticity of supply is not followed by any units. Elasticity is a ratio of one percentage change to another percentage change—nothing more—and is read as an absolute value. In this case, a 1% rise in price causes an increase in quantity supplied of 3.5%. The greater than one elasticity of supply means that the percentage change in quantity supplied will be greater than a one percent price change. If you’re starting to wonder if the concept of slope fits into this calculation, read the following Clear It Up box.