# Price Elasticity of Demand

Price elasticity of demand measures the sensitivity of quantity demanded to change in price. It is calculated by dividing the percentage change in quantity demanded by the percentage change in price. If the price elasticity of demand is (a) higher than 1, demand is considered elastic, (b) equal to 1, demand is unit-elastic and (c) lower than 1, demand is inelastic.

Price elasticity of demand is the most popular measure of demand elasticity, other being income elasticity of demand and cross elasticity of demand. Understanding price elasticity of demand is important for a company in determining the price that optimizes its revenue. It tells us whether an increase in price will result in an increase in revenue. It also tells us whether price discrimination strategy can be applied by a company.

## Calculation

Price elasticity of demand equals percentage change in quantity demanded divided by percentage change in price:

$$\text{E} _ \text{d}=\frac{\frac{\text{Q} _ \text{1}-\text{Q} _ \text{0}}{\text{Q} _ \text{0}}}{\frac{\text{P} _ \text{1}-\text{P} _ \text{0}}{\text{P} _ \text{0}}}=\frac{\text{Q} _ \text{1}-\text{Q} _ \text{0}}{\text{P} _ \text{1}-\text{P} _ \text{0}}\times\frac{\text{P} _ \text{0}}{\text{Q} _ \text{0}}$$

Where Q1 is the new quantity demanded, Q0 is the initial quantity demanded, P1 is the new price and P0 is the initial price.

### Mid-point Formula

As illustrated in the graph below, the price elasticity changes as we move along the demand curve. If the difference between Q1 and Q0 or P1 and P0 is high, the mid-point formula for calculation of price elasticity of demand is a better indicator. The mid-point price elasticity is calculated using the following formula:

$$\text{E} _ \text{d}=\frac{\text{Q} _ \text{1}-\text{Q} _ \text{0}}{\frac{{\text{Q} _ \text{1}+\text{Q}} _ \text{0}}{\text{2}}}\div\frac{\text{P} _ \text{1}-\text{P} _ \text{0}}{\frac{{\text{P} _ \text{1}+\text{P}} _ \text{0}}{\text{2}}}=\frac{\text{Q} _ \text{1}-\text{Q} _ \text{0}}{\text{P} _ \text{1}-\text{P} _ \text{0}}\times\frac{\frac{{\text{P} _ \text{1}+\text{P}} _ \text{0}}{\text{2}}}{\frac{{\text{Q} _ \text{1}+\text{Q}} _ \text{0}}{\text{2}}}$$

Price elasticity of demand for a demand represented by demand function of the form Q = A – bP can be determined using the following formula:

$$\text{E} _ \text{d}=\text{b}\times\frac{\text{P} _ \text{0}}{\text{Q} _ \text{0}}$$

Where b = (Q1 – Q0)/(P1 – P0).

### Graphical Method

Price elasticity of demand can also be worked out using graphs.

Price elasticity at any point on a straight demand curve equals the length of the curve below the point (at which price elasticity is measured) divided by the length of the curve above the point. In case of a curved demand curve, price elasticity of demand can be arrived at by drawing a tangent to the curve at the point and then using the method mentioned above.

The graph below shows calculation of price elasticity using ratio of the two segments of the demand curve. At Point B, the ratio of the lower segment i.e. BC is divided by the ratio of the upper segment i.e. AB.

### Elasticity of Demand and Revenue

Total revenue of a producer equals the product of quantity demanded and price. Change in revenue due to a change in price depends on the price elasticity of demand of the product. Following are the effect on total revenue under different price elasticity scenarios:

• If demand is elastic, price elasticity of demand is greater than 1 and a one percentage increase in price will result in more than one percentage change in quantity demanded.
• If demand is inelastic, price elasticity of demand is lower than 1 and a one percentage increase in price will result in less than one percentage change in quantity demanded.
• If demand is unit-elastic, price elasticity is equal to 1 and a one percentage increase in price will result in exactly one percentage change in quantity demanded.

## Example

Calculate the price elasticity of demand when the price changes from $9 to$7 and the quantity demanded changes from 10 units per consumer per month to 14 units per consumer per month. Use the mid-point formula.

Solution

Percentage change in quantity demanded
= (14 − 10) ÷ {(14 + 10) ÷ 2}
≈ 33.33%

Percentage change in price
= ($7 −$9) ÷ {($7 +$9) ÷ 2}
= -25%

Price elasticity of demand ≈ 33.33% ÷ −25% ≈ −1.33 or simply 1.33