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Cost minimizing level of capital

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A ?rms production process uses labor, L, and capital, K, and materials, M, to produce an output, Q according to the function Q = KLM, where the marginal products of the three inputs are MPL = KM,MPK = LM, and MPM = KL. The wage rate for labor is w = 2, the rental rate of capital is r = 1, and the cost of materials is m = 4 per unit. What is the long run cost minimizing level of capital that the ?rm must use to produce a target level of output, Q = 1000?

Reference no: EM131217829

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