## 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)

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.

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:

**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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