# Price Elasticity of Demand

Price elasticity of demand (PED) is the measure of responsiveness of consumers to change in price of a product. The consumer responsiveness to price change of a product is the degree to which they change their demand for a product if its price changes by certain amount. When consumers are more responsive, they increase or decrease their demand for a product by higher amount in response to a smaller respective decrease or increase in the product price.

Price elasticity of demand is represented by E_{d} and it is calculated using the following formula:

$$ Price\ Elasticity\ of\ Demand\ (E_d) \\= \frac{\%\ Change\ in\ Quantity\ Demanded}{\%\ Change\ in\ Price\ of\ Product} $$

Where, percentage change in quantity demanded and price in the above formula are calculated by dividing change in quantity demanded / price by initial quantity demanded / price respectively. The above formula has a drawback. Suppose the price increases from $8 to $10 per unit. The percentage change of price will be 2/10 = 20%. But when the price decreases back from $10 to $8 per unit, the percentage change in price will be 2/8 = 25%. Therefore, price elasticity of demand calculated will be different for two equal and opposite changes in price or quantity demanded.

In order to calculate an accurate value of price elasticity of demand, we can use the mid-point formula given below:

$$ E_d = \frac{Q_f − Q_i}{(Q_f + Q_i) ÷ 2} ÷ \frac{P_f − P_i}{(P_f + P_i) ÷ 2} $$

Where Q_{i} and Q_{f} are the initial and final quantities demanded respectively; and P_{i} and P_{f} are the initial and final prices respectively.

The price elasticity of demand equals the slope of demand curve. According to the law of demand, there is an inverse relationship between price and quantity demanded; therefore the slope of demand curve and thus the price elasticity of demand will always be negative. However, economists usually ignore the negative sign of price elasticity of demand.

## 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