Q2. Suppose that a firm's production function is given by a Cobb-Douglas function Q = ALKB, (where a, B > 0), and that the firm can purchase all the L and K it wants in competitive input markets at rental rates (prices) w and v, respectively. (a) Show that cost minimization requires wL/ a = vK/ B. (b) Now assume that A = 2, a = = 1/2, and that capital is fixed at K = K in the short run. Calculate the firm's total costs as a function of Q, w, v, and K. (c) Given Q, v, and w, how should the capital be chosen to minimize total cost? (d) Use your results from part (c) to calculate the long-run total cost of product