Consider a setting where L = 3 and a consumer whose consumption set is R (i.e., allowing for a negative demand). Suppose that the consumer's observed demand function is given by x (p, w) = P2 P3 x (p,w) = - P P3 and x3 (p, w) = W P3 (a) Show that the observed demand x(p, w) = (x1, x2, x3) is homogeneous of degree zero in (p, w) and satisfies Walras' law. (b) Show that x violates the weak axiom of revealed preference (WARP). (c) Show that v S(p, w)v = 0 for every v ER, where S(p, w) indicates the Slutsky matrix.