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B1. A perfectly competitive firm has a production function given by Q = L1/3k1/3 where q is output, L is labour and K is capital. (a) Derive the conditional input demand functions of the firm. (b) Derive the long-run total cost function for the firm. Sketch the long run cost curve, labelling at least three point on it assuming the wage rate is 25 and the rental rate is 64. (c) In the short-run, the firm uses 8 units of capital. Derive the firm's short-run demand for labour and its short-run total cost function. Given a product price of P, derive the short-run supply function of the firm