A firm produces output y using two factors of production (Inputs), Labour L and capital K. The firm's production function is f(L,K) = 1/2 In(L)  + 1/2 In(K) . The wage rate w=4 and the rental price of capital r=4 are taken as parameters (fixed) by the firm. Solve the firm''s long run cost minimization problem (minimize costs subject to the output constraint ) to derive the firm's demand function for labour L = L(y) and for capital K =K(y) , and the firm's long run total cost function C=C(y)

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