## Demand Elasticity Definition

The demand elasticity basically captures the change in demand for a product due to change in another variable, which may be the price of the product or income of the consumer.

There are two types of demand elasticity – 1) Price elasticity of demand and 2) Income elasticity of demand.

### #1 – Price Elasticity of Demand

Price elasticity of demand is defined as the measure of elasticity of demand based on price which is derived by dividing the percentage change in quantity (∆D/D) by percentage change in price (∆P/P).

**Price elasticity of demand = % change in demand / % change in price**

#### Demand Elasticity Calculation Example – I

Let us take the demand for gasoline which is the prime example of inelastic demand. Let us assume that the price of gasoline was $2.50 per liter on January 21, 20XX, which increased to $3.00 per liter on February 21, 20XX. Now, let us take the daily demand at one of a fuel pump, which down from 10,000 on January 21, 20XX to 9,950 on February 21, 20XX. Calculate the elasticity of demand price for gasoline based on the given information.

Given, P_{0} = $2.50, P_{1} = $3.00, D_{0} = 10000, D_{1} = 9950

**% Change in Demand**

Therefore, % change in demand = (D_{1} – D_{0}) ÷ (D_{1} + D_{0}) / 2

- = (9,950 – 10,000) ÷ (9,950 + 10,000) / 2
- = – 0.50%

**% Change in Price**

% change in price = (P_{1} – P_{0}) ÷ (P_{1} + P_{0}) / 2

- = ($3.00 – $2.50) ÷ ($3.00 + $2.50) / 2
- = 18.18%

Finally, Price elasticity of demand calculation = % change in demand / % change in price

= – 0.50% / 18.18%

This is very close to zero indicative of the inelastic demand of gasoline.

#### Demand Elasticity Calculation Example II

Consider that there is a soft drink manufacturing company who has recently implemented a strategy of price to boost the demand for its soft drinks. A month back, the company used to sell the soft drinks at $1.50 per bottle and the monthly consumption was nearly 50,000 bottles. Now, after the price, the company has started to sell the soft drinks at $1.25 per bottle and since then the demand has increased significantly touching up to 80,000 in the last one month. Calculate the price elasticity of demand for the soft drink based on the given information.

Given, P_{0} = $1.50, P_{1} = $1.25, D_{0} = 50,000, D_{1} = 80,000

**% Change in Demand**

- % Change in Demand = (D
_{1}– D_{0}) ÷ (D_{1}+ D_{0}) / 2 - = (80,000 – 50,000) ÷ (80,000 + 50,000) / 2
- = 46.15%

**% Change in ****Price**

- % change in price = (P
_{1}– P_{0}) ÷ (P_{1}+ P_{0}) / 2 - = ($3.00 – $2.50) ÷ ($3.00 + $2.50) / 2
- = – 18.18%

Price elasticity of demand can be calculated as,

Finally, Price elasticity of demand calculation = % change in demand / % change in price

= – 46.15% / 18.18%

This is between -1 and infinity which is indicative of the relatively elastic nature of the demand.

### #2 – Income Elasticity of Demand

Income elasticity of demand is defined as the measure of elasticity of demand based on income which is derived by dividing the percentage change in quantity (∆D/D) by percentage change in income (∆I/I)

**Income elasticity of demand calculation = % change in demand / % change in income**

Below are the examples of Income Elasticity of Demand

#### Demand Elasticity Calculation Example #I

Now, let us take an example of an inferior good to look at the impact of income on it. In an emerging country X, the economic situation has improved a lot such that the per capita income has increased during the last decade from $2,000 to $3,500. As a result of such improvement, their lifestyle has also changed as they have shifted from unbranded apparels to branded apparels. During the same period, the demand for unbranded apparel among men has dropped from 10 shirts per year to 3 shirts per year. Calculate the income elasticity of demand for unbranded apparels based on the given information.

Given, I_{0} = $2,000, I_{1} = $3,500, D_{0} = 10, D_{1} = 3

**% Change in Demand**

Therefore, % change in demand = (D_{1} – D_{0}) ÷ (D_{1} + D_{0}) / 2

= (3 – 10) ÷ (3 + 10) / 2

= – 107.69%

**% Change in Income**

And, % change in income = (I_{1} – I_{0}) ÷ (I_{1} + I_{0}) / 2

= ($3,500 – $2,000) ÷ ($3,500 + $2,000) / 2

= 54.55%

Finally, Income elasticity of demand calculation = % change in demand / % change in income

= – 107.69% / 54.55%

This is between -1 and infinity which is indicative of the relatively elastic nature of the demand.

#### Demand Elasticity Calculation Example #II

Now, let us take an example of staple food to demonstrate the impact of income on inelastic products. In the same country mentioned above, if we look at the demand for rice we will get to realize that it has changed marginally despite significant improvement in lifestyle on the back increasing per capita income. During the decade, the per capita consumption of rice has increased from 60 kgs to 61 kgs. Determine the income elasticity of demand for rice based on the given information.

Given, I_{0} = $2,000, I_{1} = $3,500, D_{0} = 60kgs, D_{1} = 61 kgs

**% Change in Demand**

Therefore, % change in demand = (D_{1} – D_{0}) ÷ (D_{1} + D_{0}) / 2

= (61 – 60) ÷ (61 + 60) / 2

= 1.65%

**% Change in Income**

% change in income = (I_{1} – I_{0}) ÷ (I_{1} + I_{0}) / 2

= ($3,500 – $2,000) ÷ ($3,500 + $2,000) / 2

= 54.55%

Finally, Income elasticity of demand calculation = % change in demand / % change in income

= 1.65% / 54.55%

This is very close to zero which is indicative of the inelastic demand nature of staple food.

### Conclusion

The above examples show how the demand for a product varies with the change in price of the product and income of the consumer. However, the change varies from product to product, such as demand for staple food is inelastic to both price and income, while demand for luxury and easily replaceable products are usually elastic in nature. It is a very important metric for companies when they intend to increase their product demand.

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