# Cross & income elasticity of demand

### Cross & income elasticity of demand

#### Lessons

Cross Elasticity of Demand

To measure the responsiveness of substitutes and complements of goods, we use the cross elasticity of demand.

The cross elasticity of demand measures the change of demand from one good to a change in price of a substitute or complement. In other words,

Cross - price elasticity = $\frac{\% \;change \;in \;quantity \;demanded}{\% \;change \;in \;price \;of \;substitute \;or \;complement}$

The formula for cross elasticity of demand is

Cross - price elasticity = $\frac{(Q_{x_2}-Q_{x_1})/Q_{x_{avg}}}{(P_{y_2}-P_{y_1})/P_{y_{avg}}}$

If the cross elasticity of demand is positive, then the it is a substitute. This means when the price of the substitute increases, then the demand for the good increases.

If the cross elasticity of demand is negative, then the it is a complement. This means when the price of the complement increases, then the demand for the good decreases.

Income Elasticity of Demand

The income elasticity of demand is the responsiveness of the demand for a good to a change in income. In other words,

Income - price elasticity = $\frac{\% \;change \;in \;quantity \;demanded}{\% \;change \;in \;income}$

The formula for income elasticity of demand is

Income - price elasticity = $\frac{(Q_{2}-Q_{1})/Q_{_{avg}}}{(I_{2}-I_{1})/I_{_{avg}}}$

If the income elasticity of demand is greater than 1, then the good is normal and income elastic. In addition, the percentage of income spent on the good increases as income increases.

If the income elasticity of demand is less than 1 and positive, then the good is normal and income inelastic. In addition, the percentage of income spent on the good decreases as income increases.

If the income elasticity of demand is negative, then the good is inferior. This means when income increases, the demand for the good decreases.
• Introduction
Cross & Income Elasticity of Demand Overview:
a)
Cross Elasticity of Demand
• Formula for Cross Elasticity of Demand
• Do not take the absolute value
• Positive  →  goods are substitutes
• Demand curve for good shifts rightward
• Negative  →  goods are complements
• Demand curve for good shifts leftward

b)
Cross Elasticity of Demand
• Formula for Income Elasticity of Demand
• Do not take the absolute value
• Positive  →  goods are normal
• Negative  →  goods are inferior