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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