# Elasticity of Demand

A change in the price of a commodity affects its demand. We can find the elasticity of demand, or the degree of responsiveness of demand by comparing the percentage price changes with the quantities demanded. In this article, we will look at the concept of elasticity of demand and take a quick look at its various types.

## Elasticity of Demand

To begin with, let’s look at the definition of the elasticity of demand: “Elasticity of demand is the responsiveness of the quantity demanded of a commodity to changes in one of the variables on which demand depends. In other words, it is the percentage change in quantity demanded divided by the percentage in one of the variables on which demand depends.”

The variables on which demand can depend on are:

• Price of the commodity
• Prices of related commodities
• Consumer’s income, etc.

Let’s look at some examples:

1. The price of a radio falls from Rs. 500 to Rs. 400 per unit. As a result, the demand increases from 100 to 150 units.
2. Due to government subsidy, the price of wheat falls from Rs. 10/kg to Rs. 9/kg. Due to this, the demand increases from 500 kilograms to 520 kilograms.

In both cases above, you can notice that as the price decreases, the demand increases. Hence, the demand for radios and wheat responds to price changes.

## Types of Elasticity of Demand

Based on the variable that affects the demand, the elasticity of demand is of the following types. One point to note is that unless otherwise mentioned, whenever the elasticity of demand is mentioned, it implies price elasticity.

### Price Elasticity

The price elasticity of demand is the response of the quantity demanded to change in the price of a commodity. It is assumed that the consumer’s income, tastes, and prices of all other goods are steady. It is measured as a percentage change in the quantity demanded divided by the percentage change in price. Therefore,

$$\text{Price Elasticity} = E_p = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$$

Or,

$$E_p = \frac{\frac{\text{Change in Quantity} \times 100}{\text{Original Quantity}}}{\frac{\text{Change in Price} \times 100}{\text{Original Price}}}$$

$$= \frac{\text{Change in Quantity}}{\text{Original Quantity}} \times \frac{\text{Original Price}}{\text{Change in Price}}$$

### Income Elasticity

The income elasticity of demand is the degree of responsiveness of the quantity demanded to a change in the consumer’s income. Symbolically,

$$E_I = \frac {\text{Percentage change in quantity demanded}}{\text{Percentage change in income}}$$

### Cross Elasticity

The cross elasticity of demand of a commodity X for another commodity Y, is the change in demand of commodity X due to a change in the price of commodity Y. Symbolically,

$$E_c = \frac{\Delta q_x}{\Delta p_y} \times \frac{p_y}{q_x}$$

Where, $$E_c$$ is the cross elasticity, $$\Delta q_x$$ is the original demand of commodity X, $$\Delta q_x$$ is the change in demand of X, $$\Delta p_y$$ is the original price of commodity Y, and $$\Delta p_y$$ is the change in price of Y.

## Solved Questions on Elasticity of Demand

Q1.  The price elasticity of demand is defined as the responsiveness of :

1. price to a change in quantity demanded.
2. quantity demanded to a change in price.
3. price to a change in income.
4. quantity demanded to a change in income.

Answer: By definition, The elasticity of demand is the change in demand due to the change in one or more of the variable factors that it depends on. Therefore, options a and c are incorrect, since they talk about the responsiveness of a price.

The responsiveness of the quantity demanded to the change in income is called Income elasticity of demand while that to the price is called Price elasticity of demand. Therefore, the correct answer is option B.

Q2: The price of a commodity decreases from Rs.6 to Rs. 4. This results in an increase in the quantity demanded from 10 units to 15 units. Find the coefficient of price elasticity.

Ans: The Coefficient of price elasticity $$= E_p = \frac{\Delta q}{\Delta p} \times \frac{p}{q}$$

Where, q is quantity, p is price and Δ is the change.

Therefore, we have

$$\Delta q = 15 – 10 = 5$$

$$\Delta p = 6 – 4 = 2$$

Hence,

$$= E_p = \frac{5}{2} \times \frac{6}{10} = 1.5$$

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