Income Elasticity

The income elasticity of a quantity q with respect to an income y is the percentage change in q caused by a one percent change in y. Formally, this is

e = dq/dy · (y/q).

An intuitive version of this formula replaces the derivative with changes

e = ∆q/∆y · (y/q).

Reorganizing this yields

e = (∆q/q) / (∆y/y).

A common functional form is

log(q) = a + b · log(y).

or q = exp(a+b·log(y)). Differentiating using the chain rule yields

dq/dy = (b/y)·exp(a+b·log(y)) = (b/y)·q = b·(q/y).

The elasticity of q with respect to y is then b, which is constant.

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