Suppose, for example, that the price of a pecan pie increases by 10 percent (say $1.00 to $1.10 per slice). This increase in price is likely to cause the demand of hot fudge sundaes to change. The cross elasticity of demand answers the question: Does demand increase or decrease, and if so, by how much? If the demand increases by 10 percent (say from 100 hot fudge sundaes to 110 hot fudge sundaes), then pecan pie is a substitute good for hot fudge sundaes. If the demand decreases by 10 percent (say from 100 hot fudge sundaes to 90 hot fudge sundaes), then pecan pie is a complement good for hot fudge sundaes. If the demand does not change, then pecan pie is an independent good relative to hot fudge sundaes.

A Summary Formula

cross elasticity of demand

=

percentage change in demand for good 1 percentage change in price of good 2

However, in practice, the cross elasticity of demand is calculated as the percentage change in "quantity" resulting from the percentage change the price of another good. In other words, the calculation is based on the change in quantity from one value to another.

Substitute and Complement

• Substitute Good: A substitute good exists if an increase in the price of one good causes an increase in demand for the other good. This is seen as a positive value for the cross elasticity of demand, or a coefficient of elasticity of C > 0.


• Complement Good: A complement good exists if an increase in the price of one good causes a decrease in demand for the other good. This is seen as a negative value for the cross elasticity of demand, or a coefficient of elasticity of C < 0.


• Independent Good: An independent good exists if a change in the price of one good has no affect on the demand for another good. This is seen as a zero value for the cross elasticity of demand, or a coefficient of elasticity of C = 0.

Although some goods might intuitively appear to be substitute, complement, or independent goods, economists generally let cross elasticity calculations make the actual determination. One of the more important applications of these calculations is in the area of market control',500,400)">market control and antitrust laws. Because government frowns on markets controlled by a single firm, it is very important to know if the buyers of the good produced by one firm have any reasonable substitute alternatives. If there are NO close substitutes, that is, all cross elasticities are approximately zero, then the firm producing the good probably falls into the monopoly category of market structures and is subject to antitrust scrutiny.

Three Other Elasticities

• Price Elasticity of Demand: On one side of the market is the price elasticity of demand. This is the relative response of quantity demanded to changes in the price. It is specified as the percentage change in quantity demanded to a percentage change in price.


• Price Elasticity of Supply: On the other side of the market is the price elasticity of supply. This is the relative response of quantity supplied to changes in the price. It is also analogously specified as the percentage change in quantity supplied to a percentage change in price.


• Income Elasticity of Demand: This is the relative response of demand to changes in income, or the percentage change in demand due to a percentage change in income. This elasticity quantifies the buyers' income demand determinant.