Price Elasticity of Demand

Price Elasticity of Demand

The quantity purchased can be influenced by price and other variables. When any of the variables changes there is an effect on the quantity demanded by the consumers. The elasticity of demand enables us to calculate the rate of change in quantity demanded as a result of a change in any other variable such as the good’s own price, consumers’ incomes or prices of related products.

Price elasticity of demand measures the percentage change in quantity demanded due to the percentage change in a good’s own price. It is calculated thus:

                    % change in quantity demanded
PED =         ________________________________
                    % change in a good’s  own price

% change in quantity demanded       
=       New quantity – Old quantity            100
        ___________________________   X       ___
                       Old quantity                           1

% change in price       
=       New price – Old price           100
         _____________________  X       ___
                     Old price                        1

 

Worked example on PED
The price of apple increased from $10 to $20, resulting in a fall in quantity demanded from 1,000 units to 800 units. Calculate the PED.

Solution
New quantity = 800        Old quantity = 1,000
New price = $20              Old price = $10

PED = 800 – 1,000   X  100
            __________         ____
                 1,000               1
           _____________________
           20 – 10           100
           _______   X      ____
               10                  1
       = -20%
          _____
          +100%
      =-0.2
      =0.2 (Ignore the negative sign; it is due to the inverse relationship between price and quantity demanded)


Interpretation of PED values
PED is less than 1 (fairly inelastic demand)
The percentage in price results in a lesser percentage change in quantity demanded. This means the quantity demanded is less responsive to a price change, e.g. price increases by 100% while quantity demanded decreases by 20%. 
PED is  more than 1 (fairly elastic demand)
A percentage change in price will lead to a larger percentage change in quantity demanded. Quantity demanded is more responsive to a price change, e.g. a 10% fall in price results in a 30% rise in quantity demanded.

PED is equal to 1 (unitary elasticity)
There is an equal change in both price and quantity demanded, e.g. a 10% rise in price leads to a 10% fall in quantity demanded.

PED is equal to zero (perfectly inelastic demand)
Quantity demanded is not responsive to price change at all because quantity demanded remains unchanged regardless of price alteration, e.g. price is raised by 5% while quantity changes by 0%. The demand curve is a vertical line.

PED is equal to infinity (perfectly inelastic demand)
The price remains the same no matter the quantity demanded, e.g. a 0% increase in price and a 10% decrease in quantity demanded. In this case, the demand curve is a horizontal line.


Price elasticity of demand and total revenue
It is not always true that producers have to lower their prices in order to increase their sales revenue. The price elasticity of demand determines the ultimate outcome or effect on revenue when there is a price change. It has to do with the direction of the greater percentage change between quantity and price. For example, revenue will increase when the price moves up by 10% while quantity decreases by just 5%. However, revenue will decrease if the price rises by 10% while quantity decreases by 20%. There are more examples below.

Table 1: Effect of a fall in price on total revenue

ActionResultTotal revenueType of PED
Price falls by 20%Quantity rises by 30%IncreasesFairly elastic
Price falls by 20%Quantity rises by 5%DecreasesFairly inelastic
Price falls by 20%Quantity rises by 20%UnchangedUnitary
Price falls by 20%Quantity rises by 0%DecreasesPerfectly inelastic
Price falls by 0%Quantity rises by 10%IncreasesPerfectly elastic