(a) Let f: R R+ be a a firm's differentiable production function satisfying the usual assumptions. Suppose that x ER is a vector of inputs and that we R are the factor prices. Let p E R+ denote the output price. The profit of the firm is given by: (p,w) = max [pf (x) - wx]. x Derive and explain Shephard's lemma: ; -xi (p, w).