The firm hires until MRP equals MRC

Accept an input unit while its added revenue covers its added cost.

In a competitive labor market, one small employer takes the wage as given, so MRC equals wage. Hire the last worker for whom MRP≥ w. Diminishing marginal product makes MRP slope downward when output MR is constant. For discrete workers, exact equality is unnecessary.

MRP shifts when output price or demand changes, worker productivity changes, or the quantity and quality of complementary inputs change. A wage change causes movement along labor demand. Better machinery may raise worker productivity and labor demand if it complements labor. Automation may reduce demand for a type of labor if it substitutes for that labor.

Hiring is another marginal decision. Each worker adds MRP to revenue and MRC to cost. Hire while MRP≥ MRC and stop before the first worker whose added cost exceeds added revenue. In a smooth model, the optimum lies where the downward-sloping MRP curve meets MRC.

In a competitive factor market, one small employer can hire at the market wage without raising it, so labor supply to the firm and MRC are horizontal at w. If the MRPs of successive workers are $150, $125, $100, $75, and the wage is $90, hire three. The fourth adds only $75 while costing $90.

The wage is not compared with average revenue per worker or total revenue. Earlier workers can add much more than the wage, creating gains to the employer, while the last hired worker is near equality. The rule chooses employment. It does not require every worker to have identical productivity.

A change in the wage does not shift labor demand. It changes the quantity of labor demanded along MRP. A change in product demand shifts MRP because each worker’s output creates different revenue. Training or better complementary equipment shifts MRP by changing MP.

A product-market shock reaches hiring

Demand for catered meals falls, reducing the marginal revenue from each additional meal. Cooks’ physical MP is unchanged, but each MP is now worth less, so cook MRP shifts left and the firm hires fewer cooks at the same wage. Factor demand is derived from the output market.

With discrete workers, exact equality may not occur. Choose the last worker whose MRP covers MRC. If a worker’s MRP exactly equals MRC, hiring does not change profit, so adjacent employment levels can tie unless the item states a convention.

The employment rule is separate from wage determination. A competitive labor market sets the wage. The firm chooses how many at that wage. A monopsonist influences wage and faces an MRC above labor supply, requiring the two-step method developed later.

When workers are indivisible, equality may not occur exactly. Hire the last worker whose MRP is at least MRC, and reject the next worker whose MRP is below MRC. This discrete rule is the same marginal logic. It prevents the mistaken claim that a firm must stop only at an exact numerical equality.