Crosselasticities

Crosselasticities refer to measures of how the quantity of one good or input responds to changes in the price of another good or input. They are used in both demand and supply analyses to capture the interdependencies across goods or production factors.

The most common type is the cross-price elasticity of demand, Exy, which is the percentage change in the quantity demanded of good x in response to a one-percent change in the price of good y. It is defined as Exy = (ΔQx/Qx) / (ΔPy/Py). The sign of Exy indicates the relationship between the goods: positive for substitutes, negative for complements, and zero for unrelated goods. The magnitude shows the strength of the linkage and can vary with the price level, income, and time horizon.

A related concept is the cross-price elasticity of supply, Esxy, which measures how the quantity supplied of good x responds to changes in the price of good y. Esxy is defined analogously to Exy. Signs and interpretation depend on production technology and market structure; positive values can occur when higher prices for one good lead producers to allocate resources toward both goods, while negative values may arise in joint-production contexts.

In multigood analyses, crosselasticities form an elasticity matrix, with own-price elasticities on the diagonal and cross-price elasticities off the diagonal. This matrix underpins demand system estimation and informs pricing, competition analysis, and policy evaluation, including tax incidence and welfare effects.

Limitations include the ceteris paribus assumption, sensitivity to the chosen time frame, and potential confounding factors. Elasticities are partial derivatives that summarize short-run relationships and may change as markets adjust.