MRP and MRC: Use the Marginal Hiring Rule
The marginal hiring rule compares the revenue from the next input unit with its full added cost. Exact equality is useful in a smooth interior model; whole-worker choices can have gaps or ties. Work through the examples, then try three original questions about hiring, equal gains and marginal payroll cost.
Accept an input unit while its added revenue covers its added cost.
Read Two Conditional Hiring Decisions
In a smooth interior model with a strictly downward-sloping MRP schedule, a small wage-taking restaurant faces a higher market wage. The new intersection remains feasible and all other relevant conditions are unchanged. Its profit-maximizing response is to
- raise employment until average product equals the wage
- keep employment fixed because the firm cannot change the wage
- reduce employment until MRP equals the higher wage
- shift market labor supply to the right
- hire every worker whose marginal product is positive
reduce employment until MRP equals the higher wage For a wage-taking employer, the market wage is marginal resource cost. A higher wage reduces the number of workers whose MRP covers that cost.
In a smooth model, a monopsonist’s MRP at current employment exceeds MRC, and a small increase in labor is feasible with no other cost changes. To increase profit locally, the firm should
- lower the product price to reduce MRP
- reduce employment until MRP rises
- keep employment fixed because the current wage is sunk
- hire additional labor
- hire only until MRP equals the wage rather than MRC
hire additional labor At that point, a feasible small increase in labor adds more revenue than cost. This establishes the direction of a local improvement. A smooth interior maximum requires the net marginal gain to change from positive to negative; a first-order equality alone is not a complete global comparison.
Video Lesson: Marginal Revenue Product and Factor Cost
A focused video lesson from Kyle Purpura.
Use the Wage Only When It Is Marginal 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.
Distinguish Schedule Changes from Wage Movements
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.
Check the Conditions for the Last-Unit Rule
For sequential, feasible worker additions whose net marginal gains decline, accept positive gains and stop before the first negative gain; a zero gain creates a tie. Compute each gain as added total revenue minus added total cost for the same period. In a smooth model, an interior maximum has MRP=MRC when the net marginal gain crosses from positive to negative. If gains are not ordered that way, compare total profit across the feasible choices instead of assuming the first rejection proves a global maximum.
Read the Original Whole-Worker Schedule
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.
Avoid Average and Total-Revenue Comparisons
Compare added revenue with added cost, not average revenue per worker or total revenue. Earlier increments may contribute more than their wage, but that difference is not automatically net profit: other production costs still matter. A labor quantity identifies a position on the stated production schedule; it need not mean that individual people have inherently different abilities. With indivisible units, the last accepted gain need not be numerically close to zero.
Read the Reference Table Conditionally
| Change | MRP curve | Hiring at a fixed wage |
|---|---|---|
| Relevant MRP schedule rises | Shifts right | More labor in the stated smooth interior model |
| Marginal productivity rises, MR unchanged | Shifts right | More labor in the stated smooth interior model |
| Complementary capital improves | Often shifts right | More labor if complementarity dominates |
| Wage rises, MRP unchanged | Movement along MRP | Less labor in the smooth interior model; discrete choices may stay unchanged |
| Technically substitutable input becomes cheaper | Substitution away from labor at fixed output | The net hiring effect also requires the output response |
Allow for Discrete Choices That Do Not Change
At a fixed MRP schedule, a change in the wage moves a wage-taking firm along its labor-demand schedule. A change in output demand can shift MRP if it changes the revenue contribution of added output. Training or complementary equipment can shift MRP when they alter marginal output and its revenue value. In discrete schedules, a small change can leave the chosen labor quantity unchanged.
Trace a Stated Product-Market Shock
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.
Recognize Adjacent Tied Choices
With discrete workers, exact equality may not occur. Under declining net gains, select the positive-gain additions. If the next addition has exactly zero net gain, accepting or rejecting it gives adjacent tied profit levels. A convention such as “include the zero-gain unit” selects one answer without making the alternative less profitable.
Separate the Hiring Rule from Wage Determination
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.
Compare Operating Choices Separately
The hiring comparison is conditional on the available production choices. A fixed cost that is identical under two hiring options cancels from their difference. A separate decision to open or shut down must include the costs that can actually be avoided; already sunk costs do not become recoverable by stopping. Do not infer that an activity should operate merely because one extra worker adds profit while it operates.
Check the Definitions and Model Assumptions
OpenStax’s labor-market theory lesson distinguishes competitive and imperfect output markets and explains hiring at a given market wage. For a whole-worker calculation, use the actual increments in total revenue and total cost. The examples here use invented figures and state their feasible choices; they do not estimate a current employer’s wages or staffing.
Find a Tie, Then Raise the Wage
Suppose four successive worker-periods add $96, $76, $56 and $36 to total revenue. Every worker-period costs $56 in full, including all relevant added costs. The firm can choose any whole number from zero through four; it operates throughout the comparison, and all other costs are the same across these choices. Which labor quantities give the largest contribution to profit?
Check your reasoning
The successive profit changes are $40, $20, $0 and −$20. Starting from zero workers, the cumulative changes are $0, $40, $60, $60 and $40. Both two and three worker-periods maximize profit among the stated choices. The third does not increase profit, but it does not reduce it either. Four is worse. Including the zero-gain third unit is a convention, not a unique maximum.
If full added cost instead becomes $66 per worker-period while the revenue schedule stays unchanged, the changes are $30, $10, −$10 and −$30. The cumulative changes become $0, $30, $40, $30 and $0, so two is now the unique best choice. The wage rise did not shift the given revenue-product schedule. It also did not have to change employment if the firm previously chose two from the tied pair.
These totals compare hiring options while operating. To compare with shutting down, include any additional avoidable costs or commitments that differ between operating and not operating. Do not replace that calculation with a claim that contribution before other costs equals net profit.
Try Three Marginal Hiring Questions
Choose one answer, then check your reasoning. These are short learning checks, not an exam score. If the controls are unavailable, the explanations remain readable below each question.
Answer B. Net increments are $40, $20, $0 and −$20. The cumulative gains are $0, $40, $60, $60 and $40. Two and three tie for the largest total.
Answer C. Subtract $66 from each revenue increment: $30, $10, −$10 and −$30. Cumulative gain peaks uniquely at $40 with two worker-periods; no exact equality is needed.
Answer D. Old payroll is 4 × $18 = $72 and new payroll is 5 × $20 = $100. Added cost is $28, including the $8 increase for existing workers. Added profit is $25 − $28 = −$3, so the quoted wage alone understates this hire’s marginal cost.
Connect the Hiring Rule to Cost and Units
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