2. The production function of a firm is given by f ( K, L) = AKOLB 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/(atB) where B = A-1/ (atB) [ (B/ a) a/ (atB) + ( a/ B)B/(a+B)]. (b) Confirm that the Lagrange multiplier is equal to marginal cost