Cross elasticity of demand
The Cross Elasticity of Demand is the relation between percentage change in the quantity demanded of a good to the percentage change in the price of a related good.
According to J.S. SLOMAN," Cross elasticity of demand refers to the responsiveness of demand for one good to a change in the price of another."
The Cross Elasticity of Demand between Good A and B is:-
Eba= Percentage change in the quantity of B/ Percentage change in price of A
Let us suppose that when the price of tea is Rs.8 per kg, 100 kg of coffee is bought but when the price rises to Rs.10, the demand for coffee increases to 120 kg. According to the formula, the coefficient of cross elasticity of demand is:-
Eba= (100-120)/ (100+120) * (8+10)/ ( 8-10) = -20/220*18/-2=9/11
There are 2 types of related goods :- Substitutes and Complementaries
CROSS ELASTICITY OF SUBSTITUTES
In the case of substitutes, the cross elasticity is POSITIVE and LARGE. The higher the coefficient Eba, the better substitutes the goods are. If the price of butter RISES, it will lead to INCREASE in the demand for jam. Similarly, a fall in the price of butter will cause a decrease in the demand for jam.
If a change in the price of Good A leads to more than proportionate change in the demand for Good-B, the cross elasticity is HIGH (Eba>1).
**** draw panel (a) diagram
In the above figure Price of Good-A is taken on Y- axis and the quantity of Good-B on X-axis. The change in the amount demanded of Good-B is more than proportionate to the change in price of A. The cross elasticity is HIGH. Such goods are CLOSE SUBSTITUTES.
The cross elasticity of demand is UNITY ( Eba=1) when a change in the price of Good-A causes the same proportionate change in the quantity of Good-B. This is illustrated in the diagram below.
***draw diagram
The cross elasticity is Less Than Unity (Eba<1) when the quantity demanded of Good-B changes less than proportionately in response to the change in the price of Good-A as in the diagram below. It means that Good-A and B are POOR SUBSTITUTES for each other.
****draw diagram
When the change in price of Good-A has no effect whatsoever on the demand for Good-B , the cross elasticity of demand is ZERO. The diagram below shows that with the change in the price of A, from a to a1 the demand for B remains UNCHANGED as OD(Eba=0). Such goods are UNRELATED to each other, like butter and mango.
***draw diagram
In case of two goods are PERFECT SUBSTITUTES, the cross elasticity of demand will be INFINITE, Eba= infinity. A fall in price of butter may reduce the demand for jam to nothing. The demand curve for Good-B will coincide with Y-axis./
***draw diagram
Though the cross elasticity of demand for Substitutes varies between Zero and Infinity, it may also be NEGATIVE. If the price of A falls, the demand for A being inelastic, then less of A will be puurchase because it is cheaper, and more of B will be bought.
***draw diagram
In the above diagram, a fall in price of Good-A from a1 to a leads to a rise in the demand for B from b1 to b. The slope of the DD curve shows NEGATIVE CROSS ELASTICITY.
CROSS ELASTICITY OF COMPLEMENTARY GOODS
If two goods are complementary(jointly demanded), a rise in the price of one leads to a fall in the demand for the other. Rise in the prices of cars will bring a fall in their demand together with the demand for petrol. Since price and demand vary in the opposite direction, the Cross Elasticity of Demand is NEGATIVE.
If the change in quantity demanded B is exactly in the same proportion as the change in the price of A, the Cross Elasticity is UNITY( Eba=1) as in the figure below.
****draw diagram
In the case of Complementary Goods, Cross Elasticity is Greater than Unity ( Eba>1). When the change in the demand for Good-B is more than proportionate to the change in price of Good-A as shown in figure below.
****draw diagram
The Cross Elasticity is Less Than Unity (Eba<1), when the change in quantity of B is less in response to a change in the price of A, as shown in figure below.
****draw diagram
The Cross elasticity of demand is ZERO(Eba=0), when the change in price of A causes no change whatsoever in the purchases of B. In the diagram below, a fall in the Price of Good-A from a to a1, leaves the demand OD of Good-B unchanged. This is in the case of UNRELATED GOODS.
***draw diagram
It is INFINITY when an infinitesimal change in the Price of A causs an infinitely large change in the purchase of B .The price of A remains almost the same (OD) and the demand for B increases from b to b1 in the diagram below.
***draw diagram
According to J.S. SLOMAN," Cross elasticity of demand refers to the responsiveness of demand for one good to a change in the price of another."
The Cross Elasticity of Demand between Good A and B is:-
Eba= Percentage change in the quantity of B/ Percentage change in price of A
Let us suppose that when the price of tea is Rs.8 per kg, 100 kg of coffee is bought but when the price rises to Rs.10, the demand for coffee increases to 120 kg. According to the formula, the coefficient of cross elasticity of demand is:-
Eba= (100-120)/ (100+120) * (8+10)/ ( 8-10) = -20/220*18/-2=9/11
There are 2 types of related goods :- Substitutes and Complementaries
CROSS ELASTICITY OF SUBSTITUTES
In the case of substitutes, the cross elasticity is POSITIVE and LARGE. The higher the coefficient Eba, the better substitutes the goods are. If the price of butter RISES, it will lead to INCREASE in the demand for jam. Similarly, a fall in the price of butter will cause a decrease in the demand for jam.
If a change in the price of Good A leads to more than proportionate change in the demand for Good-B, the cross elasticity is HIGH (Eba>1).
**** draw panel (a) diagram
In the above figure Price of Good-A is taken on Y- axis and the quantity of Good-B on X-axis. The change in the amount demanded of Good-B is more than proportionate to the change in price of A. The cross elasticity is HIGH. Such goods are CLOSE SUBSTITUTES.
The cross elasticity of demand is UNITY ( Eba=1) when a change in the price of Good-A causes the same proportionate change in the quantity of Good-B. This is illustrated in the diagram below.
***draw diagram
The cross elasticity is Less Than Unity (Eba<1) when the quantity demanded of Good-B changes less than proportionately in response to the change in the price of Good-A as in the diagram below. It means that Good-A and B are POOR SUBSTITUTES for each other.
****draw diagram
When the change in price of Good-A has no effect whatsoever on the demand for Good-B , the cross elasticity of demand is ZERO. The diagram below shows that with the change in the price of A, from a to a1 the demand for B remains UNCHANGED as OD(Eba=0). Such goods are UNRELATED to each other, like butter and mango.
***draw diagram
In case of two goods are PERFECT SUBSTITUTES, the cross elasticity of demand will be INFINITE, Eba= infinity. A fall in price of butter may reduce the demand for jam to nothing. The demand curve for Good-B will coincide with Y-axis./
***draw diagram
Though the cross elasticity of demand for Substitutes varies between Zero and Infinity, it may also be NEGATIVE. If the price of A falls, the demand for A being inelastic, then less of A will be puurchase because it is cheaper, and more of B will be bought.
***draw diagram
In the above diagram, a fall in price of Good-A from a1 to a leads to a rise in the demand for B from b1 to b. The slope of the DD curve shows NEGATIVE CROSS ELASTICITY.
CROSS ELASTICITY OF COMPLEMENTARY GOODS
If two goods are complementary(jointly demanded), a rise in the price of one leads to a fall in the demand for the other. Rise in the prices of cars will bring a fall in their demand together with the demand for petrol. Since price and demand vary in the opposite direction, the Cross Elasticity of Demand is NEGATIVE.
If the change in quantity demanded B is exactly in the same proportion as the change in the price of A, the Cross Elasticity is UNITY( Eba=1) as in the figure below.
****draw diagram
In the case of Complementary Goods, Cross Elasticity is Greater than Unity ( Eba>1). When the change in the demand for Good-B is more than proportionate to the change in price of Good-A as shown in figure below.
****draw diagram
The Cross Elasticity is Less Than Unity (Eba<1), when the change in quantity of B is less in response to a change in the price of A, as shown in figure below.
****draw diagram
The Cross elasticity of demand is ZERO(Eba=0), when the change in price of A causes no change whatsoever in the purchases of B. In the diagram below, a fall in the Price of Good-A from a to a1, leaves the demand OD of Good-B unchanged. This is in the case of UNRELATED GOODS.
***draw diagram
It is INFINITY when an infinitesimal change in the Price of A causs an infinitely large change in the purchase of B .The price of A remains almost the same (OD) and the demand for B increases from b to b1 in the diagram below.
***draw diagram
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