Elasticity of Demand : Income and Cross Elasticity and their Types

 Income Elasticity of Demand:  

     Income elasticity of demand refers to the degree of responsiveness of the quantity demanded of a commodity to a change in income of the consumers. 

    It is the ratio of proportionate change in the quantity demanded of a commodity to the proportionate change in the income of the consumers. 

   It is the measure of change in quantity demanded of a commodity, by a consumer to the change in his / her own income. 

  Income elasticity of demand is denoted by ey .

   Income elasticity of demand can be measured with the help of the following formula:

   ey = (percentage change in quantity demanded) / (Percentage change in Income) 

ey = (∆Q/ Q)  ÷ (∆ Y / Y) 

 ey = (∆Q/ Q)  × (Y / ∆Y)

ey = (∆Q / ∆Y) × ( Y/ Q) 

Where ey = income elasticity of demand 

Y = Initial income 

∆Y = Change in Income 

 Q= Initial Quantity 

 ∆Q = Change in quantity

If the value of ey of a particular product is high it becomes more responsive to the change in consumer’s income. 

Types of Income Elasticity of Demand : 

    Income elasticity of demand can be of three types –

 1. Positive income elasticity

2. Negative income elasticity

 3. Zero income elasticity

  1. Positive Income Elasticity:  

 Income elasticity of demand is said to be positive when with an increase in income of the consumer, the amount purchased of a commodity increases, and with a decrease in the income of the consumer, the amount purchased of a commodity decreases. 

    For most of the commodities, income elasticity of demand is positive because an increase in income leads to an increase in quantity  demanded. 

 Goods with positive income elasticities are called ‘normal goods’. For these normal commodities the positive income elasticity can further be classified into three categories – 

a. Income elastic 

b.  Income inelastic

c. Unitary income elasticity.

  a.  Income Elastic: 

     If the percentage change in quantity demanded of the commodity, is greater than the percentage change in income, the income elasticity will exceed unity (ey > 1). The demand for the commodity is said to be income elastic. 

    Example, the commodities of luxuries like cars, colour TVs and jewellery have high income elasticity of demand.

  b. Income Inelastic: 

    If the percentage change in quantity demanded is smaller than the percentage change in income, the income elasticity of demand will be less than unity (ey<1). This type of demand for the commodity is said to be income inelastic demand. 

  Example, the commodities of necessities like food, soap and clothes have low income elasticity of demand. 

c. Unitary income elasticity:

     If the percentage change in quantity demanded is equal to percentage change in income, the income elasticity  will be equal to unity. In this case the commodity has a unitary income elasticity. 

    Unitary income elasticity represents a dividing line between income elastic and Income inelastic demand.

2. Negative Income Elasticity of Demand :

    Income elasticity of demand is said to be negative when an increase in income leads to fall in the amount purchased of a commodity, and vise versa. 

    In case of inferior commodities, an increase in income leads to a fall in the quantity demanded, i.e., at lower income the quantity purchased or demanded is more, while at higher income the quantity’s purchased is less. Income elasticity of demand for such goods is negative. Example, income elasticity of inferior food grain like maize and bajra is negative. 

   When income increases, consumers will switch over from inferior food grains to superior food grains like rice and wheat.

 

3. Zero Income Elasticity :

    When the change in income of the consumer leads to no change in quantity demanded of the commodity, the income elasticity of demand for that commodity is said to be zero.

      Income elasticity of demand for inexpensive necessities of life is zero.  Example, salt;  any increase in income beyond a certain level may not bring about any change in demand for salt, therefore income elasticity of demand for salt is said to be zero.

Types of Income Elasticity of Demand :

 

SN		Type Of Elasticity of Demand			Description
1.		Positive Income Elasticity of Demand			Quantity demanded increases with the increase in income.
		1.	Income Elastic Demand ( ep >1)		When quantity demanded rises more than increase in income. Eg. Luxury Cars, Colour TV etc.
		2.	Income Inelastic Demand (ep < 1 )		When quantity demanded rises less than in Proportion to increase in income , eg necessities
		3.	Unitary Income Elastic Demand ( ep = 1)		When quantity demanded rises to the same proportion as rise in income
2.		Negative Income Elasticity of Demand			When quantity demanded decreases as income increases, Eg inferior goods.
3.	Zero Income Elasticity of Demand			When quantity demanded remains unchanged as income increases, eg inexpensive essential goods.

 

Cross Elasticity of Demand:  

   Cross elasticity of demand is defined as the percentage  change in quantity demanded of a commodity with the change in the price of its related commodity. 

       The degree of responsiveness of quantity demanded of one commodity to a change in the price of another commodity is called the cross elasticity of demand. It is expressed by the sign  (exy).

 exy = (% change in quantity demanded of X) / (% change in the price of Y) 

exy = (∆Q / ∆ P) × (Py/ Qx)

Where , exy = cross elasticity of demand of X  for Y

∆Qx = change in quantity demanded of commodity X 

∆Py = change in price of commodity Y

Qx = initial quantity of X 

Py = initial Price of Y 

Types of Cross Elasticity of Demand:  

Cross elasticity of demand is of three types  –

 1. Positive Cross Elasticity of Demand

2. Negative Cross Elasticity of Demand

3. Zero Cross Elasticity of Demand 

1. Positive Cross Elasticity of Demand:

   Cross elasticity of demand is said to be positive, when increase in Price of one commodity leads to an increase in the demand for the other commodity. 

    In other words, the increase in price of Y leads to an increase in the quantity demanded  for X.

   When the two goods are substitute for each other, cross elasticity will be positive because a decrease in the price of one  causes decrease in demand for the other. 

   Example, Tea and Coffee. A fall in the price of coffee (Y) increases the quantity demanded of coffee, but decreases the quantity demanded of tea (X). Therefore changes in the price of coffee and in the quantity demanded of tea will have the same sign, it  means the cross elasticity of demand is positive.

 

2. Negative Cross Elasticity of Demand:

    Cross elasticity of demand is said to be negative when a fall in the price of  one commodity lads to an increase in the demand for another commodity. 

    Or we can say, that a fall in the price of commodity Y leads to an increase in the demand for commodity X. 

     Complementary goods have negative cross elasticities. Example, bread and butter are complementary goods. A fall in the price of butter causes an increase in not only the demand of butter but in the quantity demanded of bread. 

     Therefore the changes in the price of butter and in the quantity demanded of bread will have opposite signs, and the cross elasticity is negative.

3. Zero Cross Elasticity of Demand:

    Cross elasticity of demand is said to  be  zero when a change in the price of one commodity (Y), does not affect the demand for another commodity (X).

   If the two goods are not related to each other, example, tea and TV set, the cross elasticity of demand will be zero. A change in the price of tea is not likely to influence the demand for TV set. 

 Types of Cross Elasticity of Demand :

SN	Type of Demand	Description
1.	Positive Cross Elasticity of Demand	Increase in Price of Y causes increase in quantity demanded of X
2.	Negative Cross Elasticity of Demand	Increase in Price of Y causes decrease in quantity demanded of X
3.	Zero  Cross Elasticity of Demand	When price of Y does not affect the quantity demanded of X