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### Elasticity of Demand: Price, Income and Cross-Elasticity of Demand

Elasticity measures the sensitivity of one variable to another. Specifically, it is a number that tells us the percentage change that will occur in one variable in response to a 1-percent increase in another variable. For example, the price elasticity of demand measures the sensitivity of quantity demanded to price changes. It tells us what the percentage change in the quantity demanded for a good will be following a 1-percent increase in the price of that good.

The elasticity of demand can be discussed under three heads:

• Price elasticity of demand
• Income elasticity of demand
• Cross elasticity of demand

#### PRICE ELASTICITY OF DEMAND

Price elasticity is the proportional change in quantity demanded divided by the proportional change in price.

Mathematically it can be written as:

For example, if the elasticity of demand = -2, we say that the elasticity is 2 in magnitude.

When the price elasticity is greater than 1 in magnitude, we say that demand is price elastic because the percentage decline in quantity demanded is greater than the percentage increase in price. If the price elasticity is less than 1 in magnitude, demand is said to be price inelastic. In general, the price elasticity of demand for a good depends on the availability of other goods that can be substituted for it.

When there are close substitutes, a price increase will cause the consumer to buy less of the good and more of the substitute. Demand will then highly price elastic. When there are no close substitutes, demand will tend to be price inelastic.

#### Types of Price Elasticity of Demand

In terms of degree, price elasticity of demand is classified into five categories :

(1) Perfectly elastic demand

(2) Perfectly inelastic demand

(3) Unitary elasticity of demand

(4) Elastic demand

(5) Inelastic demand

1. Perfectly elastic demand

If the demand for commodity changes though there is no change in its price, it is a case of perfectly elastic demand. In other words, if the quantity demanded keeps on increasing or decreasing in spite of the fact that the price remains constant, the elasticity of demand is said to be equal to infinity (Ed = ). The demand curve representing perfectly elastic demand is parallel to X-axis as shown in the Figure below.

For example, the demand curve under perfect competition is perfectly elastic and thus horizontal in shape. However, the perfectly elastic demand curve is hypothetical.

2. Perfectly inelastic demand. If the demand for a commodity does not change in spite of an increase or decrease in its price, we have a case of perfectly inelastic demand. This implies a situation where demand is totally unresponsive to changes in the price of the commodity. Thus elasticity of demand is zero (Ed = 0). Perfectly inelastic demand is also a hypothetical situation. In practice, there is perhaps no commodity for which demand may be perfectly inelastic under any situation.

3. Unitary elasticity of demand. If a 5 per cent increase in price is accompanied by a 5 per cent decrease in demand, the price elasticity is unity. In general terms, price elasticity of demand is unity (Ed = 1) if percentage changes in price and quantity demanded are precisely the same. Total expenditure on a commodity for which the elasticity of demand is unity always remains.  The demand curve representing the unitary elasticity of demand on each of its points assumes the shape of a rectangular hyperbola.

4. Elastic demand. In certain cases, the responsiveness of demand measured in terms of percentage change is far greater than the percentage change in the price of the commodity. This implies that if the price of a commodity rises by 10 per cent, then in response to it the demand falls by more than 10 per cent. This is known as elastic demand. Generally, the demand for luxury goods is elastic. It is often seen that the demand for these products increases considerably in response to a small reduction in their price. Conversely, if the price of a-luxury good rises, the quantity demanded decreases by a larger percentage.
5. Inelastic demand. If the demand is not much responsive to the price change, that is, a. considerable increase or decrease in the price does not result in much change in quantity demanded, the demand is inelastic. For example, with a fall in prices of a commodity by 10 per cent, the quantity demanded rises by less than 10 per cent. Demand for necessities such as agricultural goods and medicines displays such elasticity.

#### Methods of Measuring Price Elasticity of Demand

1. Percentage Method

This is the simplest method of measuring the price elasticity of demand. In this elasticity of demand is calculated by dividing the percentage change in quantity demanded by the percentage change in prices.

#### 2. Total Outlay Method

The total outlay method of measuring the elasticity of demand was originally suggested by Alfred Marshall. According to this method, the price elasticity of demand can be measured on the basis of change in total outlay or total expenditure (which is the total revenue from the point of view of the firm) in response to a change in the price of the commodity. Marshall maintains that the elasticity of demand can be of three types: (1) Unitary, (2) More than unity (i.e. elastic), and (3) Less than unity (i.e. inelastic).

###### I. Expenditure Method

Unitary elasticity. If small changes in price leave total outlay unaffected, price elasticity of demand is unity.

Elastic Demand. If a small reduction in price increases total outlay or if a small increase in price reduces total outlay, demand is elastic (i.e. it is greater than unity).

Inelastic demand. If a small reduction in price leads to a fall in total outlay or if a small increase in price increases total outlay (so that there is a positive relationship between changes in price and total expenditure), demand is inelastic. This happens in the case of necessities whose demand is not much affected by changes in prices.

#### 3. Point Elasticity of Demand Method

Let us suppose that AB is the demand curve in the Figure given below. We are interested in calculating the price elasticity of demand at the point R (initial price ON and initial quantity OM).

In this figure, elasticity of demand is zero at point B because the lower segment is zero. As we move up the demand curve, elasticity of demand increases. However, it remains less than unity in the range PB as in this entire range the lower segment is less in length as compared to the upper segment. At point P (which is the mid-point of the demand curve AB) the two segments are equal. Therefore, elasticity is unity. As we move further up, the length of the lower segment becomes more than the length of the upper segment: Accordingly as we move up from P to A, elasticity of demand increases and remains greater than unity throughout the range PA. When we reach A, the upper segment becomes zero. Therefore, elasticity of demand becomes infinite.