## Calculating Price Elasticity of Demand

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

**Calculating the Price Elasticity of Demand**

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

\(\begin{array}{rcl}\text{% change in quantity}& =& \cfrac{3,000–2,800}{(3,000+2,800)/2}× 100\\ & =& \cfrac{200}{2,900}× 100\\ & =& 6.9\\ \text{% change in price}& =& \cfrac{60-70}{(60+70)/2}× 100\\ & =& \cfrac{–10}{65}× 100\\ & =& -15.4\\ \text{Price Elasticity of Demand}& =& \cfrac{6.9\%}{-15.4\%}\\ & =& 0.45\end{array}\)

Therefore, the elasticity of demand between these two points is \(\cfrac{6.9\%}{–15.4\%}\) which is 0.45, an amount smaller than one, showing that the demand is inelastic in this interval. Price elasticities of demand are *always* 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, while remembering 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.

### Finding the Price Elasticity of Demand

Calculate the price elasticity of demand using the data in this figure for an increase in price from G to H. Has the elasticity increased or decreased?

Step 1. We know that:

\(\begin{array}{rcl}\text{Price Elasticity of Demand}& =& \cfrac{\text{% change in quantity}}{\text{% change in price}}\end{array}\)

Step 2. From the **Midpoint Formula** we know that:

\(\begin{array}{rcl}\%\text{ change in quantity}& =& \cfrac{{\text{Q}}_{2}–{\text{Q}}_{1}}{({\text{Q}}_{2}+{\text{Q}}_{1})/2}× 100\\ \%\text{ change in price}& =& \cfrac{{\text{P}}_{2}–{\text{P}}_{1}}{({\text{P}}_{2}+{\text{P}}_{1})/2}× 100\end{array}\)

Step 3. So we can use the values provided in the figure in each equation:

\(\begin{array}{rcl}\text{% change in quantity}& =& \cfrac{1,600–1,800}{(1,600+1,800)/2}×100\\ & =& \cfrac{–200}{1,700}×100\\ & =& –11.76\\ \text{% change in price}& =& \cfrac{130–120}{(130+120)/2}×100\\ & =& \cfrac{10}{125}×100\\ & =& 8.0\end{array}\)

Step 4. Then, those values can be used to determine the price elasticity of demand:

\(\begin{array}{rcl}\text{Price Elasticity of Demand}& =& \cfrac{\text{% change in quantity}}{\text{% change in price}}\\ & =& \cfrac{–11.76}{8}\\ & =& 1.47\end{array}\)

Therefore, the elasticity of demand from G to H 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 these two points was 0.45. Demand was 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**.