Please help to solve the following question. Please step by step. Thank you.

(a) Suppose f(x, y, z) is a function of three variables satisfying f (Xx, Xy, X z) = Xk f(x, y, z), (1) for every ) E R. Show that of Ox of = kf (x, y, z) Hint: Define new variables u = Ax, w = ly, and v = \\z and differentiate with respect to 1. Now, use the fact that the relationship holds for any J E R. (b) Now, show that if f satisfies eq. (1), then fx(Xx, ly, Az) = 1k -1fx(x, y, z) fy (Ax, Ay, Az) = 15 -1fy(2, y, 2) fz (Xx, Ay, Az) = 15-1fz (2, y, 2) (c) In economics, the three factor Cobb-Douglas production function is P = LO KBMY, where P is the total production, L is the amount of labour, K is the amount of capital, M is the amount of materials, and a, B, y E R are constants. Show that this production function satisfies the property in part (a). Give an interpretation of the result in part (b) if a t Sty = 1 (constant returns to scale)