Question at position 7 A perfectly competitive producer of steel rods and steel beams employs 100 workers with identical skills. If steel rods and steel beams sell for the same price, which of the following rules should the producer always follow to use the 100 workers efficiently? I. Allocate workers so that the average cost of producing beams equals the average cost of producing rods. II. Allocate workers so that the marginal product of labor is the same in both rod production and beam production. III. Allocate half the workers to rod production and half the workers to beam production. II onlyII and III onlyI, II, and IIIIII onlyI only

Question

Question at position 7  A perfectly competitive producer of steel rods and steel beams employs 100 workers with identical skills. If steel rods and steel beams sell for the same price, which of the following rules should the producer always follow to use the 100 workers efficiently? I. Allocate workers so that the average cost of producing beams equals the average cost of producing rods. II. Allocate workers so that the marginal product of labor is the same in both rod production and beam production. III. Allocate half the workers to rod production and half the workers to beam production. II onlyII and III onlyI, II, and IIIIII onlyI only

BlackTom AI · Accepted Answer

The core idea here is how a perfectly competitive firm allocates its labor across two production lines that use the same input and produce outputs priced the same.
Option I: 'Allocate workers so that the average cost of producing beams equals the average cost of producing rods.' This is not the condition for efficiency in input assignment. Average costs reflect total costs over levels of output, but efficiency in allocating a fixed amount of labor between two processes is driven by the marginal contribution of the last worker hired in each process, not by average costs.
Option II: 'Allocate workers so that the marginal product of labor is the same in both rod production and beam production.' When the price of the outputs is the same, the firm should equalize the value of the marginal product of labor across activities. Since the outputs fetch the same price, the condition reduces to equating the marginal product of labor (MPL) across the two production processes. This is the standard condition for cost-minimizing or profit-maximizing allocation of a single input between multiple production options with the same input price, so this option is correct.
Option III: 'Allocate half the workers to rod production and half the workers to beam production.' A simple 50/50 split is not generally optimal unless the two production processes have identical marginal products for every level of labor. In general, MPLs differ at different labor allocations, so a fixed half-and-half rule does not guarantee efficiency.
Option II only: Since the only condition that reliably ensures equal marginal contributions of labor across the two productions (given identical output prices) is II, this is the correct and sufficient rule for efficient allocation.
In summary, efficiency requires equalizing the marginal product of labor across the two production processes (option II). The other options rely on average costs or a fixed split, neither of which captures the true allocation condition under identical prices and a single input.

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