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A Firm Has Current and Future Marginal Productivity of Capital

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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 10%,and capital depreciates at a 15% 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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(a)uc = (r + d)pK = 0.25 × $5000 = $1250....

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