Solution
(a) Show that if f is homogeneous of degree α, then its partial derivatives are
homogeneous α-1
By (1) and (2), the partial derivatives of f are the homogeneous function with α-1
(b) Show that f is homogeneous of degree α if and only if
(*) First assume that f is homogeneous of degree α, then we obtained as following:
By (4) and (6), we obtain as following :
Do derivative both sides of equation respected to λ, then we obtained:
Then let λ=1, and the equation above become: