# 6.4 Other Elasticities of Demand

## Cross-price elasticity of demand

The Cross-price elasticity of demand shows us how quantity demand responds to changes in the price of related goods. Whereas before we could ignore positives and negatives with elasticities, with cross-price, this matters. Our equation is as follows:

Cross Price elasticity of demand = %change in quantity demanded of Good A ÷ % change in the price of Good B

Consider our discussion of complements and substitutes in Chapter 3. We defined complements as goods that individuals prefer to consume with another good, and substitutes as goods individuals prefer to consume instead of another good. If the price of a complement of a good rise, our demand for that good will fall, and if the price of a substitute of a good rise, our demand for the good will rise.

### For Cross-price elasticity this means:

• A complement will have a negative cross-price elasticity since if the % change in price is positive, the % change in quantity will be negative and vice-versa.
• A substitute will have a positive cross-price elasticity since if the % change in price is positive, the % change in quantity will be positive and vice-versa.

This adds another dimension to our discussion of complements/substitutes. Now we can comment on the strength of the relationship between two goods.

### Example

A cross-price elasticity of -4 suggests an individual strongly prefers to consume two goods together, compared to a cross-price elasticity of -0.5. This could represent the cross-price elasticity of a consumer for a hot dog, with respect to ketchup and relish. The consumer might strongly prefer to consume hot dogs with ketchup and loosely prefers relish.

## Income elasticity of demand

In Chapter 3, we also explained how goods can be normal or inferior depending on how a consumer responds to a change in income. This responsiveness can also be measured with elasticity by the income elasticity of demand. Our equation is as follows:

Income Elasticity of demand = % change in Quantity demanded ÷ %change in Income

### For income elasticity this means:

• A normal good will have a positive income elasticity, since if income rises (or falls), the quantity demanded also increases (or decreases).
• An inferior good will have a negative income elasticity, since if income rises (or falls), the quantity demanded decreases (or increases).

The value of our elasticity will indicate how responsive a good is to a change in income. A good with an income elasticity of 0.05, while technically a normal good (since demand increases after an increase in income) is not nearly as responsive as one with an income elasticity of demand of 5.