Suppose you are the production manager for Widgets, Inc. Your job is to produce

Question

3. Suppose you are the production manager for Widgets, Inc. Your job is to produce a fixed amount of output at the lowest cost possible. When you take over the position, you find that the price paid for a unit of labor is $20 (W = $20), and the price paid for a unit of capital is $50 (R = $50). You also discover that with the current mix of capital (K) and labor (L), the marginal product of labor is 10 (MPL = 10) and the marginal product of capital is 20 (MPK = 20). Is your company minimizing cost? If not, how could you change inputs to do so? Use a diagram to help explain your answer. (3 pts.)
4. In reference to the above question , assume you know the combination of inputs that minimizes cost. What would happen to this input combination if the price of labor increased? What would happen to the input combination if the price of capital decreased? Use a diagram to help explain your answer. (2 pts.)

Explanation / Answer

Cost is minimized where MPL/PL= MPK/PK (ratios of the marginal productivity and cost are the same.

So 10/20 =/ 20/50 and, no the company is not minimizing cost. It should change inputs so the ratios are the same (more labor and less capital).

If the price of labor increased you would shift to using more capital and less labor, and if the price of capital decreased you would use more capital and less labor.

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