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Given a perfectly competitive firm in the input and output markets where: P0 = exogenous price, Q = f(K0 , L) where dQ/dL > 0 and d2Q/dL2 < 0, the cost function where: C(K0 , L) = r0K0 + w0L; r0 = exogenous rental rate of capital, K0 = exogenous capital stock, and w0 = exogenous wage.
(a) State the firm's profit function in terms of L.
(b) Find the F.O.C. that maximizes profits at L*.
(c) Interpret the F.O.C.
(d) Find the S.O.C. that maximizes profits at Q*.
(e) Interpret the S.O.C.
(f) Find dQ*/dP0.
(g) Interpret the derivative in (f)
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