Production function for a competitive firm is Q = K2/3 L1/2. The firm ...

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Production function for a competitive firm is Q = K2/3 L1/2. The firm sells its product at $100 in a competitive market and can hire labor at a constant rate of wage of $50 per unit of time. Capital is fixed at 8,000 units. Determine the profit maximizing quantity of labor (L).

    • 8 years ago
    w = $50 Since K = 8000, Q = (8000^(2/3)) L^(1/2) = 400 L^(1/2) Marginal product of labor = 400 * (1/2) L^(-1/2) = 200 L^(-1/2) MR = p = 100 Marginal revenue product of labor = Marginal product of labor * MR = 200 L^(-1/2) * 100 = 20000 L^(-1/2) Now, set 2
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