**Elastic Demand Formula (Table of Contents)**

## What is the Elastic Demand Formula?

The term “Elastic Demand” refers to the strong movement witnessed in a product’s demand owing to changes in some other economic factors, primarily product price and consumer income. In other words, the slight change in either producer price or consumer income will result in a huge change in the demand for the subject product. So, product demand is called to be elastic only when the elasticity of demand is more than one. Based on the driving economic factors, there are two major types of elasticity of demand:

1. Price Elasticity of Demand

2. Income Elasticity of Demand

The price elasticity of demand is known as elastic demand when the percentage increase in demand is greater than the percentage decline in the product price. Mathematically, it is represented as,

**(D**

_{1}– D_{0}) / (D_{1}+ D_{0}) > – (P_{1}– P_{0}) / (P_{1}+ P_{0})Where

**D**Starting Demand_{0}:**D**Closing Demand_{1:}**P**Starting Price_{0}:**P**Closing Price_{1}:

The income elasticity of demand is known as elastic demand when the percentage increase in demand is greater than the percentage increase in consumer income. Mathematically, it is represented as,

**(D**

_{1}– D_{0}) / (D_{1}+ D_{0}) > (I_{1}– I_{0}) / (I_{1}+ I_{0})Where

**D**Starting Demand_{0}:**D**Closing Demand_{1}:**I**Starting Income_{0}:**I**Closing Income_{1}:

**Example of Elastic Demand Formula (With Excel Template)**

Let’s take an example to understand the calculation of Elastic Demand in a better manner.

#### Elastic Demand Formula – Example #1

**Let us take the example of a company, which manufactures soft drinks, to illustrate the concept of price elasticity of demand. Recently the company reduced the price from $1.50 per bottle to $1.45 per bottle which resulted in a sales increase from 40,000 bottles to 50,000. Based on the given information, calculate if the demand for soft drinks is elastic or not.**

**Solution:**

Percentage Increase in Demand is calculated using the formula given below

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**Percentage Increase in Demand = 2 * (D _{1} – D_{0}) / (D_{1} + D_{0})**

- Percentage Increase in Demand = 2 * (50,000 – 40,000) / (50,000 + 40,000)
- Percentage Increase in Demand =
**22.2%**

Percentage Decrease in Price is calculated using the formula given below

**Percentage Decrease in Price = 2 * (P _{0} – P_{1}) / (P_{1} + P_{0})**

- Percentage Decrease in Price = 2 * ($1.50 – $1.45) / ($1.45 + $1.50)
- Percentage Decrease in Price =
**3.4%**

So, it can be seen that the percentage increase in demand is greater than the percentage decrease in price. Therefore, it is an example of elastic demand.

Price Elasticity of Demand is calculated as

#### Elastic Demand Formula – Example #2

**Let us take the example of the demand for ice cream and illustrate how it changes with the change in consumer income. As the per capita income increased from $2,000 to $2,500, the per capita per year consumption of ice cream increased from 10lbs to 15lbs. Based on the given information, calculate if the demand for ice cream is elastic or not.**

**Solution:**

Percentage Increase in Demand is calculated using the formula given below

**Percentage Increase in Demand = 2 * (D _{1} – D_{0}) / (D_{1} + D_{0})**

- Percentage Increase in Demand = 2 * (15 – 10) / (15 + 10)
- Percentage Increase in Demand =
**40.0%**

Percentage Increase in Income is calculated using the formula given below

**Percentage Increase in Income = 2 * (I _{1} – I_{0}) / (I_{1} + I_{0})**

- Percentage Increase in Income = 2 * ($2,500 – $2,000) / ($2,500 + $2,000)
- Percentage Increase in Income =
**22.2%**

So, it can be seen that the percentage increase in demand in greater than the percentage increase in income. Therefore, its demand for ice cream is elastic in nature.

Income Elasticity of Demand is calculated as

### Explanation

The formula for Elastic Demand can be calculated by using the following steps:

**Step 1:** Firstly, calculate the increase in demand for the subject product which is denoted by (D_{1} – D_{0)}, such that D_{1} > D_{0}.

**Step 2:** Next, calculate the average demand of the product which is denoted by (D_{1} + D_{0})/2.

**Step 3:** Next, calculate the percentage increase in demand by dividing the increase in demand (step 1) by the average demand (step 2) of the product.

**Percentage Increase in Demand = 2 * ****(D _{1} – D_{0}) / (D_{1} + D_{0})**

**Step 4:** Next, calculate the decrease in producer price of the product which is denoted by (P_{0} – P_{1)}, such that P_{1} < P_{0}

**Step 5:** Next, calculate the average price of the product which is denoted by (P_{1} + P_{0})/2.

**Step 6:** Next, calculate the percentage decrease in price by dividing the decrease in price (step 4) by the average price (step 5) of the product.

**Percentage Decrease in Price = 2 * ****(P _{0} – P_{1}) / (P_{1} + P_{0})**

**Step 7:** Finally, the formula for elastic demand due to producer price is when the percentage increase in demand (step 3) is greater than the percentage decline in the product price (step 6) as shown below.

**2 * ****(D _{1} – D_{0}) / (D_{1} + D_{0}) > **

**2 ***

**(P**

_{0}– P_{1}) / (P_{1}+ P_{0})**(D**_{1}– D_{0}) / (D_{1}+ D_{0}) >**–****(P**_{1}– P_{0}) / (P_{1}+ P_{0})

Similarly, the formula for elastic demand due to consumer income can be derived by replacing the percentage decrease in producer price by the percentage increase in consumer income.

**(D _{1} – D_{0}) / (D_{1} + D_{0}) > (I_{1} – I_{0}) / (I_{1} + I_{0})**

### Relevance and Use of Elastic Demand Formula

It is an interesting topic if you belong to the pricing team of a company or part of the financial planning wing of the government. Based on elastic demand, the pricing team can make changes in the product price (such as discounts, offers, etc.) in order to get the desired demand drive. On the other hand, the government can implement policy changes (such as reduction of taxes) to boost consumer income which will eventually percolate to increasing demand.

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