Cross elasticity of demand

WHAT IS THE CROSS ELASTICITY OF DEMAND? What is the 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.

Cross elasticity of demand (XED) measures the responsiveness of the demand for one good to changes in the price of another related good. It is the percentage change in quantity demanded of one good divided by the percentage change in the price of a related good.

Mathematically, the formula for cross elasticity of demand is:

XED = (% change in quantity demanded of good A) / (% change in price of good B)

If XED is positive, it means that the two goods are substitutes, i.e., an increase in the price of one good will lead to an increase in the quantity demanded of the other good. If XED is negative, it means that the two goods are complements, i.e., an increase in the price of one good will lead to a decrease in the quantity demanded of the other good. If XED is zero, it means that the two goods are unrelated, i.e., a change in the price of one good will not affect the quantity demanded of the other good.

In other words, cross elasticity of demand refers to the proportionate change in the number 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, the co-efficient of cross elasticity of demand =

% change in quantity demanded of commodity X

% change in the 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 follow:

• Calculate the cross elastic 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 elastic 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 of 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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