Cross Price Elasticity of Demand

Cross Price Elasticity of Demand

Substitute, complement and independent goods

The cross price elasticity of demand is useful for economists because it tells you whether two goods (A and B) are substitutes, complements or even unrelated. Think about this example:

Tea and coffee are substitutes. Let's say that tea is good A and coffee is good B. If the price of coffee falls by, say, 10% ceteris paribus, then one would expect coffee to become relatively more popular at the expense of the demand for tea. The demand for tea might fall by, say, 5%. Using the formula above, we can calculate the cross price elasticity:

Briefly, the price of coffee falls, so the demand for tea falls. This is a positive relationship, as is true for all pairs of goods that are substitutes. If the cross price elasticity of demand is positive then the two goods in question will be substitutes.

Tea and sugar are complements. Sugar is a complement to a cup of tea (for some people, anyway!). Assume that sugar is good A and tea is good B. If the price of tea fell by, say, 10% ceteris paribus, then one would expect the demand for tea to rise. This should cause the demand for sugar to rise, although not everyone has sugar in their tea, and if they do the quantities are not exactly massive, so the rise in demand for sugar is likely to be a lot smaller than the rise in demand for tea. Let's say that the demand for sugar rises by 2%. Using the formula, we have:

Put briefly, the price of tea falls, so the demand for sugar rises. This is a negative relationship, as is true for all pairs of goods that are complements. If the cross price elasticity of demand is negative then the two goods in question will be complements.

What will happen to the demand for sugar when the price of cinema admissions changes, ceteris paribus? Absolutely nothing, I should think. The two goods are completely unrelated. Using the formula:

If the cross price elasticity of demand is zero then the two goods in question will be totally unrelated (or independent).

Finally, note that the higher the value of the cross price elasticity, the stronger the relationship between the two goods in question, whether they be substitutes of complements. The nearer the figure is to zero, the more likely that the two goods are unrelated.