Consider the following production function: f(k,l)= 10kl/ (k+l) (a) Derive the conditional input demand functions. (b) Derive the long-run total cost, marginal cost and average cost functions. (c) State and verify Shephard's lemma for the functions derived in (a) and (b). (d) When wk = 4 and wl = 1, plot the long-run total cost, average cost and marginal cost functions. (3) Assume the production function f(x1,... ,xn) has constant returns to scale. For fix input prices w = (w1 , . . . , wn ), argue that the total cost functions satisfies C(q) = A q, where A is a constant that depends on w