2. The production function of a firm is given by f ( K, L) = AKIB and factor prices for the inputs capital K and labour L are r and w, respectively. The price of output is p. (a) Using the Lagrangian approach for profit maximization, show that the firm's cost func- tion is C(q) = B (qrawB) 1/(a+B) where B = A-1/ (atB) [(B/ a) a/ (atB) + ( a/ B)B/ (atB)]. (b) Confirm that the Lagrange multiplier is equal to marginal cost. (c) What is the optimal quantity if i. atB> 1? ii. a + 3 = 1? iii. a + 3