# Price Elasticity of Demand Formula  ## Formula to Calculate Price Elasticity of Demand

The of demand is the measure of elasticity of demand based on price which is calculated by dividing the percentage change in quantity (∆Q/Q) by percentage change in price (∆P/P) which is represented mathematically as

Price Elasticity of Demand = Percentage Change in Quantity (∆q/q) / Percentage Change in Price (∆p/p)

Further, the equation for price elasticity of demand can be elaborated into

Price Elasticity of Demand = [(Q1 – Q0) / (Q1 + Q0)] / [(P1 – P0)/(P1 + P0)]

Where Q0 = Initial quantity, Q1 = Final quantity, P0 = Initial price and P1 = Final price

For eg:
Source: Price Elasticity of Demand Formula (wallstreetmojo.com)

### Price Elasticity of Demand Calculation (Step by Step)

Price Elasticity of Demand can be determined in the following four steps:

1. Identify P0 and Q0 which are the initial price and quantity respectively and then decide on the target quantity and based on that the final price point which is termed as Q1 and P1 respectively.

2. Now work out the numerator of the formula which represents the percentage change in quantity. It is arrived at by dividing the difference of final and initial quantities (Q1 – Q0) by summation of the final and initial quantities (Q1 + Q0) i.e. (Q1 – Q0) / (Q1 + Q0).

3. Now work out the denominator of the formula which represents the percentage change in price. It is arrived at by dividing the difference of final and initial prices (P1 – P0) by summation of the final and initial prices (P1 + P0) i.e. (P1 – P0) / (P1 + P0).

4. Finally, the price elasticity of demand is calculated by dividing the expression in Step 2 by expression in Step 3 as shown below. ### Examples

You can download this Price Elasticity of Demand Formula Excel Template here – Price Elasticity of Demand Formula Excel Template

#### Example #1

Let us take the simple example of gasoline. Now let us assume that a surged of 60% in gasoline price resulted in a decline in the purchase of gasoline by 15%. Using the above-mentioned formula the calculation of price elasticity of demand can be done as:

• Price Elasticity of Demand = Percentage change in quantity / Percentage change in price
• Price Elasticity of Demand = -15% ÷ 60%
• Price Elasticity of Demand = -1/4 or -0.25

#### Example #2

Let us assume that there is a company that supplies vending machines. At present, the vending machines sell soft drinks at \$3.50 per bottle. Now at this price, consumers buy 4,000 bottles per week. In order to increase sales, it has been decided to decrease the price to \$2.50 which will increase sales to 5,000 bottles. Now, the calculation of price elasticity of demand can be done as below:

Given, Q0 = 4,000 bottles, Q1 = 5,000 bottles, P0 = \$3.50 and P1 = \$2.50

Therefore,

• Price Elasticity of Demand = (5,000 – 4,000) / (5,000 + 4,000) ÷ (\$2.50 – \$3.50) / (\$2.50 + \$3.50)
• Price Elasticity of Demand = (1 / 9) ÷ (-1 / 6)
• Price Elasticity of Demand = -2/3 or -0.667

#### Example #3

Now let us take the case of a beef sale in the US in the year 2014. Due to certain food shortages, the prices of cattle surged. In January 2014, a family of four consumed around 10.0 lbs of beef at a price point of \$3.47/lb. Due to the price surge, the price went up to \$4.45/lb by the end of October 2014 which brought down the consumption to 8.5 lbs. Now, the calculation of the price elasticity of demand can be done as below:

Given, Q0 = 10.0 lbs, Q1 = 8.5 lbs, P0 = \$3.47 and P1 = \$4.45

Therefore,

• Price Elasticity of Demand = (8.5 – 10.0) / (8.5 + 10.0) ÷ (\$4.45 – \$3.47) / (\$4.45 + \$3.47)
• Price Elasticity of Demand = (-0.081) ÷ (0.124)
• Price Elasticity of Demand = -0.653

### Price Elasticity of Demand Calculator

You can use the following price elasticity of demand calculator.

 Percentage Change in Quantity Percentage Change in Price PED Formula =

PED Formula =
 Percentage Change in Quantity = Percentage Change in Price
 0 = 0 0

### Relevance and Use

It is of paramount importance for a business to understand the concept and relevance of price elasticity of demand to understand the relationship between the price of a good and the corresponding demand at that price. Price elasticity of demand can be used to decide the pricing policy for different markets and for various products or services.

In case the quantity demanded fluctuates a lot when prices vary a little, then the product is said to be elastic. This often happens in the case of products or services which has many alternatives and as such the consumers relatively price sensitive. In such a scenario either the business will be careful in setting the price or target a different market where the fluctuation is low.

In case the quantity demanded changes by a very small margin despite a significant change in prices, then the product is said to be inelastic. This happens when there is a lack of good substitutes for the product or service and as such the consumers are willing to buy at relatively higher prices. A business will be able to price the product much more comfortable in such a market condition.

### Price Elasticity of Demand in Excel (with excel template)

Now let us take the case mentioned in price elasticity of demand example #3 to illustrate the same in the excel template below. The table gives a snapshot of the monthly variation in price and consumption of a family of four for the period of January 2014 to October 2014 and calculates the monthly price elasticity of demand.

In the below given excel template, we have used the price elasticity of demand formula to find the Monthly Price Elasticity of Demand.

So the Calculation of Monthly Price Elasticity of Demand will be-

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