A firm is making a long-run planning decision. It wants to decide on t

A firm is making a long-run planning decision. It wants to decide on the optimal size of plant and labor force. It is considering building a medium-sized plant and hiring 100 workers.

Engineering estimates suggest that at those levels, the marginal product of capital will be 100 and the marginal product of labor will be 75. If the wage rate is $5 and the rental rate on capital is $10, is the firm making the right decision? Support your answer.

ANSWER

No, the firm is not making the right decision. Minimizing cost (maximizing output) requires that (MPL/w) = (MPK/r). 100/10 < 75/5, so the firm should plan to build a smaller plant and employ more workers, all other things equal.