# PRICE ELASTICITY OF DEMAND

##### ELASTICITY

We studied that when price falls, quantity demanded would increase. While we know this qualitative effect exists for most goods and services, managers and business analysts are often more interested in knowing the magnitude of the response to a price change i.e. by how much? There are many situations in which one might want to measure how sensitive the quantity demanded is to changes in a product’s price. Economists and other business analysts are frequently concerned with the responsiveness of one variable to changes in some other variable. It is useful to know, for example, what effect a given percentage change in price would have on sales. The most widely adopted measure of responsiveness is elasticity. Elasticity is a general concept that economists, business people, and government officials rely on for such measurement. For example, the finance minister might be interested in knowing whether decreasing tax rates would increase tax revenue. Likewise, it is often useful to measure the sensitivity of changes in demand to changes in one of the determinants of demand, such as income or advertising.

Elasticity is defined as the ratio of the percentage change in quantity demanded to the percentage change in some factor (such as price or income) that stimulates the change in quantity. The reason for using percentage change is that it obviates the need to know the units in which quantity and price are measured. For example quantity could be in kilograms, grams, litres or gallons and price could be in dollars, rupees, euro etc. A measure of elasticity based on units would lead to confusion and misleading comparisons across different products. The use of percentage change makes the measure of elasticity independent of units of measurement and hence easy to understand.

Elasticity is the percentage change in some dependent variable given a one-percent change in an independent variable, ceteris paribus. If we let Y represent the dependent variable, X the independent variable, and E the elasticity, then elasticity is represented as

E = % change in Y / % change in X

There are two forms of elasticity: arc elasticity and point elasticity. Arc elasticity reflects the average responsiveness of the dependent variable to changes in the independent variable over some interval. The numeric value of arc elasticity can be found as follows:

Although economists use a great variety of elasticities, the following three deserve particular attention because of their wide application in the business world: price elasticity, income elasticity, and cross-price elasticity. We discuss these in detail in the subsequent sections.

#### THE PRICE ELASTICITY OF DEMAND

Price elasticity of demand measures the responsiveness of the quantity sold to changes in the product’s price, ceteris paribus. It is the percentage change in sales divided by a percentage change in price. The notation Ep will be used for the arc price elasticity of demand, and ep will be used for the point price elasticity of demand. If the absolute value of Ep (or ep ) is greater than one, a given percentage decrease (increase) in price will result in an even greater percentage increase  (decrease) in sales.1 In such a case, the demand for the product is considered elastic; that is, sales are relatively responsive to price changes. Therefore, the percentage change in quantity demanded will be greater than the percentage change in the price. When the absolute value of the price elasticity of demand is less than one, the percentage change in sales is less than a given percentage change in price. Demand is then said to be inelastic with respect to price. Unitary price elasticity results when a given percentage change in price results in an equal percentage change in sales. The absolute value of the coefficient of price elasticity is equal to one in such cases. These relationships are summarized as follows:

If |ep| or |Ep |> 1, demand is elastic

If |ep| or |Ep| < 1, demand is inelastic

If |ep| or |Ep| = 1, demand is unitarily elastic

##### ARC PRICE ELASTICITY

Consider the hypothetical prices of some product and the corresponding quantity demanded, as given in Table-1. We could calculate the arc price elasticity between the two lowest prices i.e. between Rs. 30 and Rs. 10 as follows:

We would say that demand is price elastic in this range because the percentage change in sales is greater than the percentage change in  price. You can calculate arc elasticity over any price range. As an exercise estimate the arc elasticity between the extremes of the demand function shown in Table-1, i.e. between Rs. 90 and Rs. 10. Satisfy yourself that he absolute value of arc elasticity between these two points is 1.

* You should note that since the demand curve is downward sloping, i.e. price and quantity are inversely related; the price elasticity of demand will always be negative. Thus the change in quantity will be in the opposite direction to the change in price. We usually ignore the negative sign and consider absolute values for price elasticity to ease understanding of the concept.

##### POINT PRICE ELASTICITY

This example shows that the price elasticity of demand may (and usually does) vary along any demand function, depending on the portion of the function for which the elasticity is calculated. It follows that we usually cannot make such statements as “the demand for product X is elastic” because it is likely to be elastic for one range of prices and inelastic for another. Usually at high prices demand is elastic, while at lower prices demand tends to be inelastic. Intuitively, this is so because lowering price from very high levels is likely to stimulate demand much more  compared to lowering prices when price is already low. As an illustration, consider the prices of cellular phones (handsets) when these were first introduced in the Indian market at prices ranging between Rs. 25,000 to Rs. 30,000 per handset. Demand was limited to the higher end of the market. As these prices fell, demand was stimulated and resulted in increasing penetration in the middle and lower end segments, indicating an elastic response.