Splitting 100 workers between rods and beams

The firm is a price taker and rods and beams sell for the same price, so the value of a worker's output is that price times the worker's marginal product. A worker should go wherever that value is higher. If one more worker in rods would add more than the last worker in beams, moving a worker from beams to rods raises total revenue at no extra labor cost. The moves stop paying off only when the marginal product of labor is the same in both lines. With equal prices, that is exactly rule II.

Rule I uses average cost instead of marginal product. Efficient choices are made at the margin, and equal average costs say nothing about whether one more worker would produce more in one line than in the other.

Rule III splits the workers evenly. That is efficient only by coincidence, if the marginal products happen to be equal at 50 and 50, so it is not a rule to follow every time.

Only II always holds.

Each choice

• A. Equal average costs compare whole lines of production, not the next worker. The decision about where to place a worker depends on what that worker adds, which is marginal product.
• B (correct). With equal prices, moving workers until the last one adds the same output in each line makes the most from the 100 workers.
• C. An even split looks fair, but the two products may use labor very differently. Half and half is efficient only if the marginal products happen to match there.
• D. II is right, but III is not a rule to follow every time. Adding it means assuming identical workers must be split evenly, which confuses identical workers with identical production processes.
• E. This accepts both the average cost rule and the even split. Neither is tied to what the next worker produces, which is the only thing that decides efficient placement.