What is Cross elasticity of demand?

WHAT IS CROSS ELASTICITY OF DEMAND

What is Cross elasticity of demand? this may be defined as the degree of responsiveness of demand for a commodity to changes in the price of another commodity.

 In other words, cross elasticity of demand refers to the proportionate change in the quantity of goods (X) demanded over the proportionate change in the price of another good (Y) demanded.

Cross elasticity of demand is applicable mainly to goods that are close substitutes as well as complementary goods. For example, the demand for butter will increase if there is an increase in the price of margarine.

Measurement of cross elasticity of demand

Cross elasticity of demand can be measured or calculated by using the co-efficient of cross elasticity of demand.

Thus, co-efficient of cross elasticity of demand =

% change in quantity demanded of commodity X

% change in price of commodity Y

=          %DQdX

            %DPY

Worked           example

The table below shows the response of quantity demanded to changes in prices of two types of commodities. Use the table to answer the questions that follows:

CommodityChanges in Price CommodityChanges in quantity demanded
 Original price (6)New  price (6)Maltonic MacleanOriginal Quantity (kg)New quantity (kg)
Maltina Close up50 5080 60 200 120300 150
  • Calculate the cross elasticity’s of demand for:
  • Maltina and Maltonic
  • Close Up and Maclean
  • Are their elasticity elastic or inelastic? State your reasons.

Solution

1(a)      Cross elasticity of demand for Maltina  and Maltonic

            Let X = Maltonic, Y = Maltina

  • Percentage change in quantity demanded  of Maltonic (X)

=          New Qd – Orinial Qd             x          100

                        Original Qd                 1

=          300 – 200        x          100

            200                              1

=          100      x          100

            200                  1

=          50%

  • Percentage change in the price of Maltina (Y)

=          Old price – Original price       x          100

                        Original price              1

=          80 – 50            x          100

            50                                1

=          30        x          100

            50                    1

=          60%

Cross elasticity of Maltonic of Maltina

=          50%

            60%     =          0.83

  • Cross elasticity of demand for Maclean and Close-Up. Let X = Maclean, Y = Close Up (i) % change in quantity demanded of Maclean (X)

=          New Qd – Orinial Qd             x          100

                        Original Qd                 1

=          150 – 120        x          100

            120                              1

=          30        x          100

            120                  1

=          25%

  •  % change in the price of Close Up (Y)

=          New price – Original price      x          100

                        Original price              1

=          60 – 50            x          100

            50                                1

=          10        x          100

            50                    1

=          20%

Cross elasticity of demand for Maclean and Close Up

=          %∆Qs(X)

            %∆P(Y)

=          25%

20%     =          1.25

2(a) The cross elasticity for Maltina and Maltonic is inelastic because the elasticity, which is 0.83. is less than 1.

  • The cross elasticity for Maclean and Close Up is elastic because the elasticity, which is 1.25, is greater than 1.

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