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6. A firm has current and future marginal productivity of capital given by MPK = 10, 000 -2K + N, and marginal productivity of labor

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6. A firm has current and future marginal productivity of capital given by MPK = 10, 000 -2K + N, and marginal productivity of labor given by MPN = 50-2N + K. The price of capital is $5000, the real interest rate is 5%, and capital depreciates at a 20% rate. The real wage rate is $15. (a) Calculate the user cost of capital. (b) Find the firm's optimal amount of employment and the size of the capital stock

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