Measurement of Cross Elasticity of Demand Measurement of Cross Elasticity of Demand

Measurement of Cross Elasticity of Demand

Measurement of Cross Elasticity of Demand

Cross elasticity of demand can be measured by the following two methods:

1. Percentage Method

According to the percentage method, cross elasticity of demand is measured by dividing the percentage change in demand for a good X by percentage change in the price of good Y.

Let us suppose two related goods X and Y. Then,

Exy = Percentage change in demand for good X / Percentage change in the price of good Y
Exy = (△Qx/ △Py) x (Py/ Qx)


Where,
Qx = initial quantity of good X
△Qx = change in demand for good X
Py = initial price of good Y
△Py = Change in price of good Y
Exy = Cross elasticity of demand between good X and good Y

If Exy > 0, the good X and good Y are substitute goods; if Exy < 0, the good X and good Y are complementary goods, and if Exy = 0, the good X and good Y are non-related goods.

2. Arc Method

The coefficient of cross elasticity of demand between two points on a cross demand curve is called arc elasticity of demand. This method is used to measure the cross elasticity of demand when there is a greater change in price and quantity demanded. 

According to this method, cross elasticity of demand is the coefficient or average between two points along a cross demand curve. The figure below shows the measurement of cross demand between two points A and B along the cross demand curve DD.
measurement-of-cross-elasticity-of-demand-arc-method-diagram
In the above figure, DD represents the cross-demand curve of substitute goods X and Y. The cross elasticity between two points A and B is measured by using the following formula:
measurement-of-cross-elasticity-of-demand-arc-method-formula

Where,
Qx1 = Initial demand for good X
Qx2 = New demand for good X
Py1 = Initial price of good Y
Py2 = New price of good Y
Exy = Coefficient of cross elasticity of demand

If good X and good Y are complementary goods, the cross demand curve will slope downward but the method of measuring cross elasticity of demand by arc method will be the same.

If Exy > 0, the good X and good Y are substitute goods; if Exy < 0, the good X and good Y are complementary goods, and if Exy = 0, the good X and good Y are non-related goods.

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