Cross Elasticity Of Demand

 MICROECONOMICS
We have seen in the earlier section that in defining  the  demand relationship we have assumed Other things to remain constant. One of the factors which has been assumed to remain constant is the prices of other commodities. When the price of related commodities like complementary goods or substitutes Change what will be its impact on the demand? Two commodities X and Y are said to be complements if With an increase in the price of X not only the demand for X but the demand for Y also goes down. For example we can consider Pen  and ink, Tea  and sugar, car and petrol are complements. On the other hand two commodities X and Y are said to be substitutes if with an increase in the price of X the demand for Y increases. For example Coca-cola and Pepsi ,electricity and gas, travel by rail and travel by road are substitutes. We study impact of a change in the price of one good on account of a change in the price of another good which is a complement or substitute.

Cross elasticity of Demand is defined  as :The degree of responsiveness of demand  for  commodity X on account of a change in the Price of  Commodity Y.

From the definition it follows that

Exy  = (Percentage change in quantity demanded of x)/( Percentage change in the price of Y)

In mathematical terms it can be represented as:

Exy ==   ( ∆Qx/∆py)(Py/Qx)

Let us consider an example.If the price of coffee rises from Rs.6/- to Rs.7/- per cup and as a result the consumer's demand for tea increases from 60 cups to 70 cups,then the cross elasticity of demand of tea(x) for coffee(y) can be found out as follows: ∆Qx =70-60 =10 Qx =60 ∆py =7-6 =1 Py = 6

Cross elasticity of demand = Exy =   ( ∆Qx/∆py)(Py/Qx) =(10/1)(6/60) =1 We can see that with an increase in the price of coffee(Y) the demand for tea (X) has increased.The two commodities are considered as substitutes. In this case the consumer substitutes tea for coffee.

If  Exy is greater than zero, X and Y are substitutes  because  an increase  in Py  leads to an increase in Qx as  X is substituted  for Y in consumption. On the other hand if  Exy  is  less than zero, X and Y are complements because an increase in Py leads to a reduction in  Qy and  Qx  both.

The following diagram indicates the effect of change in price of good Y (Price of X remaining the same) on the demand for good X.With a decrease in the price of good Y from OP1 to OP2 the demand for good Y declines from OQ1 to OQ2 and the demand for X  also declines from OM1 to OM2. The two commodities X and Y are said to be complements.

There are certain points to be taken note of with respect to cross elasticity of demand.
 * Exy need not be equal to Eyx because the responsiveness of Qx to change in price of Y need not be  equal the responsiveness of Qy to a change in the price of X.
 * A high positive cross elasticity is associated with high degee of similarity between  commodities.
 * The above definition of substitutes and complements is sometimes referred to as gross definition since it refers to the market  response.

a.Classify the commodities in your own consumption basket as normal goods,luxury goods and inferior goods.

b.Are the commodities mentioned below normal goods ,luxury goods or inferior goods ? Give reason for your answer.

Salt,camera,fruits,milk,Two wheeler,Cigarettes,medicines,Picasso's painting,Laptop.

Colgate sells its standard size toothpaste for Rs.30.Its sales have been on an average 8000 units per month over the past year. Recently its close competitor Binaca reduced the price of the same standard size from Rs.40 to Rs.35.As a result ,Colgate sales declined by 1200 units per month.
 * Calculate the Cross elasticity of demand between the two products.
 * What does your estimate indicate about the relationship between rhe two products?