The price elasticity of demand which is popularly just referred to as price elasticity is a measure of the rate of response of quantity demanded when price changes (Backman ,1953). We have the following data to work with.
Old price of a gallon of paint=$3.00
New price of a gallon of paint =$3.50
Old quantity demanded= 35 gallons of paint per month.
New quantity demanded= 20 gallons of paint per month.
Calculation of elasticity entails first a computation of percentage change in quantity demanded per month and percentage change in price.
Calculating the percentage change in quantity demanded per month
The formula used to calculate the percentage change in quantity demanded is
[ Quantity demanded ( New) -Quantity demanded (Old) ] / Quantity demanded (old) . (Backman, 1953)
[20-35] / 35 = -15/35 = -0.4286
The percentage change in quantity demanded is thus = -0.4286 in decimal form. This translates to -42.86% .
Calculating the percentage change in price:
[Price (New) - price(Old)] / Price (Old).
50 - 3.00] / 3.00 = ( 0.50/3.00) = 0.1667. = 16.67%
Since we have already calculated the percentage change in quantity demanded and the percentage change in price , we now calculate the price elasticity of demand.
Calculating the price Elasticity of demand.
Price elasticity of demand = (% Change in Quantity Demanded) / (% Change in Price). (Backman ,1953)
Substituting using the calculated values:
PEOD = - 0.4286/0.1667 = - 42.86% /16.67% = -2.5711.
When analyzing price elasticity , we take the absolute value hence we ignore the negative sign. Thus in our case , the price elasticity of demand when the price increases from $3.00 to $3.50 is 2.5711.
If price Elasticity of demand > 1 then Demand is price Elastic ( Demand is responsive to price changes).
If price Elasticity of Demand = 1 then Demand is said to be Unit Elastic.
If Price Elasticity of demand is < 1 then Demand is price Inelastic (Demand is not responsive to price changes) . (Backman ,1953)
In our calculation we have obtained a price elasticity of demand = 2.
5711. which is greater than 1 . This shows that our Demand for paint is price Elastic.
Interpretation of the price Elasticity of Demand.
Since we have obtained an high price Elasticity of Demand, our Demand for paint is very sensitive to price changes. When the price of paint goes up , a great deal less of it is bought and when the price goes down , a great deal more of it is bought.