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

## What is the Demand Elasticity Formula?

The term “demand elasticity” refers to the change in a product’s demand due to changes in other economic factors, primarily consumer income and product price. In other words, demand elasticity measures the impact of a variety of factors on the demand of the subject product. The two major types of demand elasticity are – 1) Income elasticity of demand and 1) Price elasticity of demand.

The formula for income elasticity of demand can be expressed by dividing the % change in demand (∆D/D) by the % change in real consumer income (∆I/I). Mathematically, it is represented as,

**Income Elasticity of Demand = [(∆D/D)] / [(∆I/I)]**

or

**Income Elasticity of Demand = [(D _{f} – D_{i}) / (D_{f} + D_{i})] / [(I_{f} – I_{i}) / (I_{f} + I_{i})]**

where,

**D**= Initial Demand_{i}**D**= Final Demand_{f}**I**= Initial Real Income and_{i}**I**= Final Real Income_{f}

The formula for price elasticity of demand can be expressed by dividing the % change in demand (∆D/D) by the % change in the product price (∆P/P). Mathematically, it is represented as,

**Price Elasticity of Demand = [(∆D/D)] / [(∆P/P)]**

or

**Price Elasticity of Demand = [(D _{f} – D_{i}) / (D_{f} + D_{i})] / [(P_{f} – P_{i}) / (P_{f} + P_{i})]**

where,

**D**= Initial Demand_{i}**D**= Final Demand_{f}**P**= Initial Price and_{i}**I**= Final Price_{f}

**Examples of Demand Elasticity Formula (With Excel Template)**

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

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#### Demand Elasticity Formula – Example #1

**Let us take the example of rice’s per capita consumption to illustrate the concept of income elasticity of demand. In a certain country, the per capita income has increased from $2,000 to $3,000 during the last decade. During the same period, rice’s per capita consumption has increased from 60 kg to 63 kg. Calculate the income elasticity of demand in this case.**

**Solution:**

% Change in Demand is calculated using the formula given below

**% Change in Demand (∆D/D) = [(D _{f} – D_{i})] / [(D_{f} + D_{i}) / 2]**

- % Change in Demand = [(63 – 60)] / [(63 + 60) / 2]
- % Change in Demand =
**4.88%**

% Change in Income is calculated using the formula given below

**% Change in Income (∆I/I) =[(I _{f} – I_{i})] / [(I_{f} + I_{i}) / 2]**

- % Change in Income = [($3,000 – $2,000)] / [($3,000 + $2,000) / 2]
- % Change in Income =
**40.00%**

Income Elasticity of Demand is calculated using the formula given below

**Income Elasticity of Demand = % Change in Demand (∆D/D) / % Change in Income (∆I/I)**

- Income Elasticity of Demand = 4.88% / 40.00%
- Income Elasticity of Demand =
**0.12**

0.12, which indicates the inelastic nature of demand.

#### Demand Elasticity Formula – Example #2

**Let us take the example of a soft drink manufacturing company to illustrate the concept of price elasticity of demand. Last month the company was able to sell 50,000 bottles of soft drinks at $1.50 per bottle. However, in the current month, the company has revised the price to $1.45 per bottle and expects to achieve month-end sales of 60,000. Calculate the price elasticity of demand.**

**Solution:**

% Change in Demand is calculated using the formula given below

**% Change in Demand (∆D/D) = [(D _{f} – D_{i})] / [(D_{f} + D_{i}) / 2]**

- % Change in Demand = (60,000 – 50,000) / [(60,000 + 50,000) / 2]
- % Change in Demand =
**18.18%**

% Change in Price is calculated using the formula given below

**% Change in Price (∆P/P) = [(P _{f} – P_{i})] / [(P_{f} + P_{i}) / 2]**

- % Change in Price = [($1.45 – $1.50)] / [($1.45 + $1.50) / 2]
- % Change in Price =
**-3.39%**

Price Elasticity of Demand is calculated using the formula given below

**Price Elasticity of Demand = % Change in Demand (∆D/D) / % Change in Price (∆P/P) **

- Price Elasticity of Demand = 18.18% / (-3.39%)
- Price Elasticity of Demand =
**-5.36**

-5.36 which indicates the elastic nature of demand

### Explanation

By using the following steps, we can derive the income elasticity of the demand formula:

**Step 1:** Firstly, figure out the real income at the start of a period and the demand at that income level. They are denoted by I_{i} and D_{i,} respectively.

**Step 2:** Next, figure out the real income at the end of the period and the demand at that income level. They are denoted by I_{f} and D_{f,} respectively.

**Step 3:** Next, compute the % change in demand by dividing the difference between the initial quantity and the final quantity by the average of the initial quantity and the final quantity.

**% Change in Demand = [****(D _{f} – D_{i})] / [(D_{f} + D_{i}) **

**/ 2]**

**Step 4:** Next, compute the % change in real income by dividing the difference between the initial income and the final income by the average of the initial income and the final income.

**% Change in Income = [****(I _{f} – I_{i})] / [(I_{f} + I_{i}) **

**/ 2]**

**Step 5:** Finally, we can derive the income elasticity of demand formula by dividing the % change in demand (step 3) by the % change in income (step 4) as shown below.

**Income Elasticity of Demand = [(D _{f} – D_{i}) / (D_{f} + D_{i})] / [(I_{f} – I_{i}) / (I_{f} + I_{i})]**

Similarly, the formula for price elasticity of demand can be derived by replacing the real income with product price.

**Price Elasticity of Demand = [(D _{f} – D_{i}) / (D_{f} + D_{i})] / [(P_{f} – P_{i}) / (P_{f} + P_{i})]**

### Relevance and Use of Demand Elasticity Formula

It is important to understand the concept of demand elasticity as it can be used to build various businesses strategy such as discount offers and luxurious substitute products in case of price elasticity of demand.

Based on price elasticity, businesses decide on the pricing policy for pursuing different target markets. On the other hand, income elasticity of demand can be used to categorize goods into two broad categories – normal goods and inferior goods.

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