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A function F(L,K) is homogeneous of degree n if
Euler's Theorem is that if F(L,K) is homogeneous of degree n then
The converse of Euler's Theorem is:
Proof:
Note that
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
Thus
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.