& Tornado Alley
A function F(L,K) is homogeneous of degree n if
F(λL,K)λ) = λnF(L,K)
for all λ.
Euler's Theorem is that if F(L,K) is homogeneous of degree n then
The converse of Euler's Theorem is:
An inspection of the above equations reveals that
This is a differential equation for G in terms of λ, which when expressed in differential form is:
The solution to the above equation is
The integration constant c is evaluated by setting λ equal to unity; i.e.,
Thus G(L,K) is homogeneous of degree n.
This result of course generalizes to a function of an arbitrary number of arguments.