Prove Roy's identity alternatively by completing the following steps: a) Using the definition of v, show that if p >> 0, and x0 : x(p0,y0), then v(p,p-x0) 2 v(p0,p0- x0),Vp >> 0 b) Conclude then that f(p) E v(p,p - x0) is minimized in 122+, at the point p : p0 c) Assuming that f is differentiable for p0_ What value should its gradient have at p0? d) Prove the identity of Roy using the previous parts