Problem 2 Prove that the prots of the rm weakly decreases with input prices. More formally1 suppose that the rm has a production function f, so that its prot function is (13,151) : max pf[2:) m ' 1:, 133'!) Where 1:] denotes. the output price and m denote-a the input price vector. Then Show that if m and m" are two input price vectors such that w; = w;- for all j 75 z" and w; ',> mg, then 7r(p,m") 1'. 1r(p,w)