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1. A firm has a production function described as follows: "Weekly output is equal to the square root of the minimum of the amount of capital and the number of hours of labor used per week." Suppose that the cost of a unit of capital is r and the price of a unit of labor is w and the level of output is y. Write down the long-run total cost as a function of w, r, and y.
2. The production function of a competitive firm is described by the equation y = 4x11/2 x21/2. The factor prices are p1 = $1 and p2 = $36 and the firm can hire as much of either factor it wants at these prices. The firm's marginal cost is
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