optimisation math

3. Suppose that a firm uses L as an input, and its production function changes with L and a parameter a. Thus its profit is given by T = pf(L. a) WL. where f is differentiable and increasing in a, and where p. w > 0. Using Envelope Theo- rem. find the derivative of the firm's maximal profit with respect to a and determine the sign of the derivative. 1 3. Suppose that a firm uses L as an input, and its production function changes with L and a parameter a. Thus its profit is given by T = pf(L. a) WL. where f is differentiable and increasing in a, and where p. w > 0. Using Envelope Theo- rem. find the derivative of the firm's maximal profit with respect to a and determine the sign of the derivative. 1