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8.5. A firm produces a product with labor and capital, and its production function is described by Q = LK. The marginal products associated with

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8.5. A firm produces a product with labor and capital, and its production function is described by Q = LK. The marginal products associated with this production function are MP;, = K and MPg = L. Suppose that the price of labor equals 2 and the price of capital equals 1. Derive the equations for the long-run total cost curve and the long-run average cost curve. 8.6. A firm's long-run total cost curve is TC(Q) = 1,000Q2. Derive the equation for the corresponding long-run average cost curve, AC(Q). Given the equation of the long-run average cost curve, which of the following statements is true? a. The long-run marginal cost curve MC(Q) lies below AC(Q) for all positive quantities Q. b. The long-run marginal cost curve MC(Q) is the same as the AC(Q) for all positive quantities Q. c. The long-run marginal cost curve MC(Q) lies above the AC(Q) for all positive quantities Q. d. The long-run marginal cost curve MC(Q) lies below AC(Q) for some positive quantities Q and above the AC(Q) for some positive quantities Q. 8.7. A firm's long-run total cost curve is TC(Q) = 1,000Q?. Derive the equation for the corresponding long-run average cost curve, AC(Q). Given the equation of the long-run average cost curve, which of the following statements is true? a. The long-run marginal cost curve MC(Q) lies below AC(Q) for all positive quantities Q. b. The long-run marginal cost curve MC(Q) is the same as the AC(Q) for all positive quantities Q. c. The long-run marginal cost curve MC(Q) lies above the AC(Q) for all positive quantities Q. d. The long-run marginal cost curve MC(Q) lies below AC(Q) for some positive quantities Q and above the AC(Q) for some positive quantities Q. 8.8. A firm's long-run total cost curve is TC(Q) = 1,000Q 30Q? + Q3. Derive the expression for the corresponding long-run average cost curve and then sketch it. At what quantity is minimum efficient scale

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