Derived Demand and Marginal Revenue Product

Why firms demand labor

A bakery does not hire a worker because labor is enjoyable to own. It hires because workers help produce bread that customers are willing to buy. Demand for an input is therefore derived demand: it comes from demand for the output the input helps create.

This link explains why a fall in bread sales can reduce bakers' employment even when their skills and preferences have not changed. It also connects product markets, production technology, and wages in one decision.

From marginal product to dollar value

The marginal product of labor, $MP_L$, is the additional output produced by one more unit of labor, holding other inputs fixed. With diminishing marginal returns, $MP_L$ usually falls as more workers share a fixed kitchen, machine, or shop floor.

The marginal revenue product of labor, $MRP_L$, is the extra revenue created by the next worker:

$MRP_L = MR \times MP_L$

For a firm that takes its output price as given, marginal revenue equals price, so:

$MRP_L = P \times MP_L$

MRP is measured in money per worker-period, which makes it comparable with the wage for that same period.

The hiring rule

Suppose the wage is the additional cost of employing one worker. Hiring raises profit when $MRP_L > W$, leaves profit unchanged when $MRP_L = W$, and lowers profit when $MRP_L < W$. The firm should hire units of labor up to the point where the next worker's MRP no longer covers the wage.

This is a marginal rule, not a claim that every worker literally receives the revenue personally created by a labeled unit. Workers cooperate with capital and coworkers; the ordered units are a way to compare employment levels.

Worked example: a neighborhood bakery

Bread sells for $6 per tray, and each baker earns$42 per shift.

The bakery hires three bakers. The third adds $48 of revenue for$42 of cost, but the fourth would add only $36. Stopping at three maximizes the contribution of labor to profit.

What shifts labor demand?

A higher output price raises every worker's MRP and shifts labor demand right. Better complementary capital or technology can raise marginal product and also shift demand right. A lower product demand, a lower output price, or cheaper substitute inputs can shift labor demand left. A wage change is different: it changes the quantity of labor demanded along the existing MRP schedule.

Misconceptions and limits

Do not compare physical marginal product directly with a money wage; convert output into revenue first. Do not hire whenever total revenue rises, because employment also raises cost. And do not treat measured MRP as pure personal merit: team production, bargaining institutions, discrimination, and imperfect information can separate pay from productivity.

In practice, a retailer uses this logic when scheduling another cashier for a busy hour. The relevant question is whether faster service and retained sales add more revenue than the shift costs.

Worker:              1   2   3   4   5
Marginal product:    9   7   5   3   1 trays/day

The firm's MRP schedule gives one side of a labor market. Next we combine employers' demand with workers' willingness to supply labor to determine employment and wages.