Prove that the profits of the firm weakly decreases with input prices. More formally, suppose that the firm has a production function f, so that its profit function is x(p, w) = max pf (I) - w . I, where p denotes the output price and w denotes the input price vector. Then show that if w and w are two input price vectors such that w = w; for all j f i and w > wi, then a(p, w)