Derived Demand vs Marginal Revenue Product

One hiring table shows the derived link and the MRP rule at the same time

A bakery sells in a competitive output market at $5 a loaf, and its first four workers add 10, 8, 6, and 4 loaves an hour. Marginal revenue product runs $50, $40, $30, $20. At a wage of $35 the bakery hires two workers, because the third adds $30 of revenue and costs $35. Now demand for bread rises and the price goes to $8. Nothing about the workers changed, nobody was trained, and the marginal product schedule is identical, yet marginal revenue product becomes $80, $64, $48, $32, and the bakery hires three at the same $35 wage. The shift in labor demand came entirely out of the output market. That is derived demand stated as a mechanism instead of a slogan, and marginal revenue product is the number that records it. Read the two ideas as one chain: demand for the good sets the price, the price sets marginal revenue, marginal revenue times marginal product gives MRP, and MRP is what the firm holds against the wage.

The MR inside MRP = MP × MR is where most of the lost points live

Marginal revenue equals price only when the firm sells in a perfectly competitive output market. Give the same bakery a local monopoly and the arithmetic changes. Its third worker still adds 6 loaves and the price at the current output is still $8, but selling those extra loaves forces the price down on every loaf, so marginal revenue there is $5, not $8. Marginal revenue product for that worker is $30 rather than $48, and at a wage of $35 she is not hired. A firm with output-market power hires fewer workers at every wage for the same reason it produces less output. When the output market is competitive, MRP equals marginal product times price, which some textbooks call the value of the marginal product, and the two labels agree. When it is not competitive, they separate, and multiplying by price on that stem produces the wrong number and the wrong hiring level. Read the description of the output market before you multiply, because the stem always tells you.

A free-response chain that starts in the goods market and ends at the wage

A common stem drops a shock into the output market and asks what happens in the factor market. Write the chain in order and each link earns its own point. Demand for electric cars falls, so the price of cars falls, so marginal revenue falls, so the marginal revenue product of assembly labor falls at every quantity, so labor demand shifts left, so the equilibrium wage and the quantity of labor hired both fall. Two traps sit inside that chain. First, a change in the wage by itself moves you along the MRP curve and does not shift it, so never redraw labor demand for a wage change. Second, a productivity gain from new equipment or training raises marginal product and shifts MRP right even when the output price never moves. Both shifters, output price and productivity, sit inside the formula, which is the argument for memorizing MRP in its multiplied form rather than as a loose rule about labor.

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