Formula to Calculate Price Elasticity
Price elasticity typically refers to price elasticity of demand that measures the response of demand of a particular item to the change in its price. The formula for price elasticity can be derived by dividing the percentage change in quantity by the percentage change in price. Mathematically, it can be calculated as,
or
- Qi = Initial quantity
- Qf = Final quantity
- Pi = Initial price and
- Pf = Final price
Price Elasticity Calculation (Step by Step)
- Step 1: Firstly, determine the initial price and quantity demanded of the item under consideration. The initial price and demand are denoted by Pi and Qi respectively.
- Step 2: Next, determine the final price and quantity demanded of the item. The final price and demand are denoted by Pf and Qf respectively.
- Step 3: Next, calculate the percentage change in quantity demanded by dividing the change in demand by the average demand. The change in quantity is the difference between final and initial demands (Qf – Qi) while the average demand is (Qf + Qi)/2. Therefore, the percentage change in demand is expressed as – 2 * (Qf – Qi) / (Qf + Qi).
- Step 4: Next, calculate the percentage change in price by dividing the change in price by the average price. The percentage change in price is expressed as – 2 * (Pf – Pi) / (Pf + Pi).
- Step 5: Finally, the price elasticity can be derived by the percentage change in quantity demanded (step 3) by the percentage change in price (step 4) as shown below.
Price Elasticity = (Qf – Qi) / (Qf + Qi) ÷ (Pf – Pi) / (Pf + Pi)
Examples
Example #1
Let us take the example of chocolate ice-cream to understand the concept of price elasticity. If the price of the ice-cream surged 20% in the last week that resulted in a decline in demand for the same to the tune of 30%. Calculate the price elasticity based on the given information.
Use the following information to calculate price elasticity.
- Percentage change in Demand: -30%
- Percentage change in price: 20%
Now, the price elasticity can be calculated by using the above formula as,
- Price Elasticity = Percentage change in demand / Percentage change in price
- = -30% / 20%
Price Elasticity will be –
- Price Elasticity = -1.50
Therefore, the ice-cream demand exhibited a price elasticity of -1.5.
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Example #2
Let us take the example of a company which is into the business of soft drinks production. Currently, the company sells its soft drinks at $4.00 per bottle which is drawing weekly demand of 3,000 bottles. Today the management of the company has decided to cut down the price by $0.50 per bottle which is expected to increase the weekly demand up to 4,000 bottles. Calculate the price elasticity based on the given information.
Use the following information to calculate price elasticity.
- Initial Demand of Bottles(Qi): 3,000
- Final Demand of Bottles(Qf): 4,000
- Initial price per Bottle (Pi): $4.00
- Final price per Bottle (Pf): $3.50
Now, the price elasticity can be calculated as,
- Price elasticity = (Qf – Qi) / (Qf + Qi) ÷ (Pf – Pi) / (Pf + Pi)
- = (4,000 – 3,000) / (4,000 + 3,000) ÷ (3.50 – 4.00) / (3.50 + 4.00)
- = (1,000 / 7,000) ÷ (-0.5 / 7.5)
Price Elasticity of weekly demand will be –
- Price Elasticity = -2.14
Therefore, the price elasticity of the weekly demand of the soft drinks is -2.14.
Example #3
Let us take the example of the beef sale in the US in the year 2014 to illustrate how price elasticity works in the real world. On the back ongoing food shortage, the prices of cattle surged from $3.47/lb to $4.45/lb. in a span of 10 months. As a result of the price surge, the usual consumption of a family of four reduced from 10.0 lbs to 8.5 lbs. Calculate the price elasticity of the beef demand.
Use the following information to calculate price elasticity.
- Initial Deman(Qi): 10.0
- Final Demand(Qf): 8.5
- Initial Price: (Pi): $3.47
- Final Price (Pf): $4.45
Now, the price elasticity can be calculated as,
- Price elasticity = (Qf – Qi) / (Qf + Qi) ÷ (Pf – Pi) / (Pf + Pi)
- = (8.5 – 10.0) / (8.5 + 10.0) ÷ (4.45 – 3.47) / (4.45 + 3.47)
- = (-1.5 / 18.5) ÷ (0.98 / 7.92)
Price elasticity of the beef demand will be –
- Price Elasticity = -0.66
Therefore, the price elasticity of the beef demand was -0.66 during the food crisis of 2014.
Price Elasticity Calculator
You can use the following price elasticity calculator.
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Relevance and Use
From the perspective of any business, the understanding of price elasticity is very important as it helps in assessing the relationship between the price of a good and the corresponding demand at that price. Goods for which the quantity demanded changes significantly with the change in price are known to have elastic demand. This characteristic is exhibited by-products or services which have easily available alternatives and as such the consumers relatively price sensitive.
On the other hand, goods for which quantity demanded does not change a great deal despite a significant change in price are known to have inelastic demand. This characteristic is exhibited when there is a lack of substitutes for the product or service and as such the consumers are willing to buy at relatively higher prices.
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