Derive marginal rate of technical substitution for the firm

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Let the production function of a firm be Q(L, K) = 100L + 10K. The MPL = 100 and the MPK = 10, for all levels of L and K.

(a) Derive the marginal rate of technical substitution for the firm.

(b) Let w = $10 for 0 < L = 10, and w = $20 for L > 10. Let r = $10. Graph the cost-minimization problem for the firm at Q = 1000. What amounts of L and K will the firm demand?

(c) Suppose that a labor union proposes to double the wage for 0 < L = 10, so as to make the w = $20 for all levels of L. Describe the cost-minimization problem for this firm. Should the currently employed workers support this effort-why or why not?

Reference no: EM13222909

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