In a generalization of the notion of elasticity of univariate functions (example 4.41), the elasticity the elasticity of scale of a functional f is defined by

where the symbol |t=1 means that the expression is evaluated at t = 1. In general, the elasticity of scale varies with x. Show that the elasticity of scale is constant k if and only if f is homogeneous of degree k.

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E(x) =f(t)DJ(x)는