Hiring Where MRP Equals the Wage

A firm buying labor faces the same logic as any profit-maximizer: keep doing something as long as the extra benefit beats the extra cost. The benefit of one more worker is the marginal revenue product, MRP, the extra revenue that worker's output brings in. The cost is the wage, which in a competitive labor market is the same for every worker hired, so the wage also equals the marginal resource cost of labor. As long as MRP is above the wage, that worker adds more to revenue than to cost, so hiring them raises profit. Once MRP falls below the wage, that worker costs more than they earn, so hiring them shrinks profit. The firm stops exactly where MRP equals the wage, because that is the last worker who still pays for himself.

This rule makes the MRP curve double as the firm's labor demand curve. Picture the wage on the vertical axis and workers hired on the horizontal axis. At any wage, the firm scans down its MRP schedule and hires every worker whose MRP sits at or above that wage, stopping right where MRP crosses the wage line. Drop the wage and more workers clear that bar, so quantity of labor demanded rises, tracing out the same downward-sloping curve that MRP already describes. This mirrors a product market demand curve built from marginal benefit, just applied to a firm buying an input instead of a consumer buying a good.

The rule connects forward to market labor supply and backward to marginal product and marginal revenue, the two pieces that build MRP in the first place. Get comfortable multiplying marginal product by marginal revenue (or price, under perfect competition) before tackling this stopping rule.