What is the solution to the firms long-run cost minimization

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Consider the production function in Learning- By-Doing Exercise 7.6: Q = L + K + M.For this production function, the marginal products of labor, capital, and materials are MPL = 1/(2 L), MPK = 1/(2 K), and MPM = 1/(2 M). Suppose that the input prices of labor, capital, and materials are w = 1, r = 1, and m = 1, respectively.

a)Given that the firm wants to produce Q units of output, what is the solution to the firm's long-run cost- minimization problem?

b)Given that the firm wants to produce Q units of output, what is the solution to the firrm?s short-run cost- minimization problem when K = 4? Will the firm want to use positive quantities of labor and materials for all levels of Q? (c)Given that the firm wants to produce 12 units of output, what is the solution to the firrm's short-run cost- minimization problem when K = 4 and L = 9? Will the firm want to use a positive quantity of materials for all levels of Q?

Reference no: EM13218893

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