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Types of Elasticity of Demand: Price Elasticity of Demand, Income Elasticity of Demand and Cross Elasticity of Demand
Price Elasticity of Demand
What is the difference between price elasticity of demand and elasticity of demand? The answer is that there is no difference between price elasticity of demand and elasticity of demand. By the term ‘elasticity of demand’, we generally refer to price elasticity of demand; because, price of a commodity is the most important factor that affects its demand.
Price elasticity of demand (e_{p}) = Percentage change in quantity demanded / Percentage change in price
Suppose the percentage decrease in the price of the commodity is 25% and the percentage increase in the quantity demanded is 50%.
Hence,
e_{p} = 50%/25% = 2
Note that the price elasticity is always negative because of the inverse relationship between price and quantity demanded (law of demand). However, as a conventional way, we ignore the negative sign when calculating the price elasticity.
Instead of the term ‘percentage change’, we can use the term proportionate change also.
Therefore,
e_{p} = Proportionate change in quantity demanded / Proportionate change in price
Symbolically,
e_{p} = (ΔQ/Q)/(ΔP/P) ; alternatively e_{p} = (ΔQ/Q) × (P/ΔP)
By rearranging e_{p} = (ΔQ/ΔP) × (P/Q)
Illustration:
(a) When the price of oranges is $5, the quantity demanded is 20 KGs.
(b) When the price of oranges is $4, the quantity demanded is 24 KGs.
Thus, P = 5, Q = 20; ΔP = 1, ΔQ = 4
e_{p} = (ΔQ/ΔP) × (P/Q) = (4/1) × (5/20) = 1
This means, the elasticity of demand is unity. The numerical value of price elasticity can be anything from zero to infinity.
Degrees of price elasticity of demand
The price elasticity of demand can be any value between zero and infinity. As you see, the price elasticity of demand is just a numerical value. How do you interpret it? There are three important numerical values of price elasticity. They are:
1. e_{p}= ∞
 It represents perfectly elastic demand. It means that the quantity demanded is most responsive to price.
 Shape of demand curve is horizontal. It means that at a particular price, buyers are ready to buy all commodities. If there is even a slight change in the price, the quantity demanded will be zero.
2. e_{p} = 0
 It represents infinitely inelastic demand. It means that the quantity demanded is not at all responsive to price.
 Shape of demand curve is vertical. It implies that the quantity demanded is fixed and does not respond to the price changes.
3. e_{p} = 1
 It implies proportionate change in price and quantity demanded of a commodity.
 Shape of demand curve is a rectangular hyperbola.
Other cases:
1. 0 < e_{p} < 1
 It implies that price elasticity of demand is between zero and one.
 Inelastic demand
 A decrease in price results in a less than proportionate increase in quantity demanded
 Shape of demand curve is quite steep.
2. ∞ > e_{p} > 1
 It implies that price elasticity of demand is between one and infinity
 Elastic demand
 A decrease in price results in a more than proportionate increase in quantity demanded
 The demand curve will be flatter.
Range of variation of price elasticity of demand
The following table summarizes the different kinds of price elasticity:
Table 1
Numerical Value
 Terminology
 Description
 Shape of the Demand Curve
 Examples


1. Price Elasticity = ∞
 Perfectly elastic
 A consumer will buy all the quantity of the commodity at this price and nothing else at some other price.
 Horizontal
 

2. Price Elasticity = 0
 Perfectly inelastic
 Demand remains unchanged whatever be the change in price
 Vertical
 Medicines

3. Price Elasticity = 1
 Unitary elastic
 % ΔQ = % ΔP
 Rectangular hyperbola
 

4. 0 < Price Elasticity < 1
 Inelastic
 % ΔQ < % ΔP
 Flatter
 Essential goods

5. ∞ > Price Elasticity > 1
 Elastic
 % ΔQ > % ΔP
 Steeper
 Luxuries and comforts

Income Elasticity of Demand
Price is one of the important determinants of demand. At the same time, we cannot ignore other factors that influence demand for a commodity. One of such factors is consumer’s income. Under income elasticity of demand, we are going to study the relationship between consumer’s income and quantity demanded. Income elasticity of demand measures the degree of change in the consumer’s demand for a commodity when there is a change in his income.
As consumer’s income increases, the demand also increases and vice versa. Therefore, the relationship between consumer’s income and quantity demanded is positive.
Symbolically,
Income elasticity of demand (e_{y}) = Percentage change in the quantity demanded of X / Percentage change in the income of the consumer
= (ΔX/X) / (ΔY/Y) = (ΔX/ΔY) × (Y/X);
Where,
X = Commodity
Y = income
Illustration:
Suppose a consumer’s demand for a commodity increases from 10 units per week to 20 units per week when his income rises from $200 to $300.
e_{y }= (ΔX/ΔY) × (Y/X) = (10/100) × (200/10) = 2
The numerical value of income elasticity of demand may be positive or negative. A positive value implies that an increase in income is associated with an increase in the quantity of goods purchased. For instance, normal goods always have a positive income elasticity of demand.
A negative value implies that there is an inverse relationship between income and the quantity of commodity purchased. For instance, income elasticity of demand is negative for inferior goods. If your income increases, you obviously will go for better products. Therefore, the demand for inferior goods reduces. Because of this reason, income elasticity of demand is negative for inferior goods.
Table 2 shows the positive income elasticity of different commodities.
Table 2
Commodities
 Coefficient of income elasticity
 Impact on expenditure


Necessities
 Less than unity (income elasticity < 1)
 Less than proportionate change in expenditure

Comforts
 Almost equal to one (income elasticity = 1)
 Almost proportionate change in expenditure

Luxuries
 Greater than unity (income elasticity > 1)
 More than proportionate change in expenditure

Types of income elasticity of demand
The following are the five types of income elasticity:
1. e_{y} > 1
 It represents high income elasticity
 The change in quantity demanded is greater than the change in income
2. e_{y} = 1
 It represents unitary income elasticity
 It refers to a case in which the change in quantity demanded is equal to the change in income
3. e_{y} < 1
 It represents low income elasticity
 It indicates a situation in which the change in quantity demanded is less than the relative change in income.
4. e_{y} = 0
 It represents zero income elasticity
 It implies that a change in income will have no effect on the quantity demanded.
5. e_{y}_{}< 0
 It represents negative income elasticity
 It shows that an increase in consumer’s income is accompanied by a fall in the quantity demanded.
Cross Elasticity of Demand
Consider two commodities, namely commodity X and commodity Y. Cross elasticity of demand measures the percentage change in the quantity demanded of commodity X when there is a change in the price of commodity Y.
Symbolically,
Cross elasticity of demand (e_{c}) = Percentage change in the quantity demanded of commodity X / Percentage change in the price of commodity Y
= (ΔQ_{x}/Q_{x}) / (ΔP_{y}/P_{y}) = (ΔQ_{x}/ ΔP_{y}) × (P_{y}/Q_{x})
Where,
ΔQ_{x} = change in the quantity of X
ΔP_{y} = change in the price of Y
P_{y }= price of Y
Q_{x} = quantity of x
Illustration:
Let us consider coffee and tea. Suppose an increase of 5% in the price of coffee results in a 10% increase in the quantity demanded of tea.
The cross elasticity of demand = (100/5) × (10/100) = 2
The numerical value of the cross elasticity of demand for commodity X can be positive or negative. It depends upon the nature of relationship between commodity X and commodity Y.
© 2013 Sundaram Ponnusamy
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