AP Syllabus focus: ‘A firm hires labor up to the point where the market wage equals marginal revenue product.’
Firms in competitive labor markets choose employment by comparing what an extra worker adds to revenue with what that worker costs. The hiring rule links labor decisions directly to profit maximization.
Competitive labor markets and the wage
In a perfectly competitive labor market, an individual firm is a wage taker: it can hire any number of workers at the going market wage without affecting that wage. Because the firm cannot influence the wage, the key decision is how many workers to employ at that wage.
The firm’s labor decision uses marginal analysis:
Hiring another worker increases total revenue by increasing output.
Hiring another worker increases total cost by adding labor expense.
Marginal revenue product (MRP) as labor demand
A firm’s labor demand is determined by the additional revenue generated by each additional worker.
Marginal revenue product of labor (MRP): the change in a firm’s total revenue from hiring one more worker, holding other inputs constant.
MRP typically diminishes as more workers are hired because of diminishing marginal returns in the short run: with some inputs fixed (like capital), additional workers add less and less extra output, reducing the extra revenue created per worker.
Marginal resource cost (MRC) in a competitive labor market
To decide whether hiring is worthwhile, the firm compares MRP to the extra cost of hiring one more worker.
Marginal resource cost of labor (MRC): the change in a firm’s total cost from hiring one more worker.
In a competitive labor market:
MRC equals the wage for each additional worker because the wage is constant for the firm.
The firm does not need to raise wages for existing workers when hiring an additional worker (this is specific to competitive, wage-taking conditions).
The firm’s hiring rule: hire until
The profit-maximizing employment level occurs where the extra benefit of hiring (MRP) equals the extra cost (MRC). Since MRC = W in a competitive labor market, the rule becomes: hire labor up to the point where the market wage equals marginal revenue product, matching the AP syllabus wording.
= marginal revenue product of labour, dollars of revenue per additional worker
= marginal product of labour, additional units of output per additional worker
= marginal revenue, dollars of revenue per additional unit of output
= market wage, dollars of cost per additional worker
This rule can be understood with marginal profit:
If , hiring one more worker increases profit (extra revenue exceeds extra cost).
If , hiring one more worker decreases profit (extra cost exceeds extra revenue).
If , the firm is at the profit-maximizing quantity of labor (no further gain from changing employment by one worker).
Why the rule identifies the firm’s labor demand curve
For a wage-taking firm, the MRP curve is the firm’s labor demand curve because:
At each possible wage, the firm chooses the quantity of labor where .
A lower wage makes it profitable to hire additional workers (the intersection with MRP occurs at higher labor).
A higher wage makes it profitable to hire fewer workers (the intersection with MRP occurs at lower labor).
Graphically (conceptually), the firm compares:
A wage-taking firm faces a horizontal market wage line and hires labor up to the quantity where that wage intersects the firm’s marginal revenue product (often labeled in perfect competition). The intersection identifies the profit-maximizing employment level because it is where the extra benefit of the last worker equals the extra cost. Source
A horizontal wage line at the market wage (because the firm is a wage taker).
A downward-sloping MRP curve (because MRP tends to fall as more labor is employed).
Interpreting the rule carefully
“Hire up to the point where … equals …” means “up to and including the last profitable worker”
In discrete terms (hiring whole workers):
The firm hires each additional worker as long as that worker’s MRP is at least as large as the wage.
The “last worker hired” is the last worker for which MRP is not below W.
What must be held constant
The hiring rule assumes:
The firm is holding other inputs constant when evaluating the extra output from one more worker.
The wage is taken as given by the market (competitive labor market condition).
The firm is using the same output-market conditions when interpreting MR inside MRP.
Common interpretation pitfalls to avoid
Do not confuse MRP (a revenue change) with MP (a physical output change); MRP incorporates both productivity and revenue per unit.
Do not treat the wage as a measure of worker “value”; the rule is about profit-maximizing employment, not fairness or total contribution.
Do not compare wage to total revenue or average revenue; the decision is strictly marginal.
FAQ
With continuous hours, the same logic applies at the margin.
The firm adjusts hours until the marginal hour satisfies $MRP = W$.
If hours can be finely adjusted, equality is more exact; with whole workers, you often apply “hire the last worker with $MRP \ge W$”.
This affects interpretation, not the underlying rule.
Marginal profit from an extra worker is $MRP - W$.
If $MRP - W > 0$, the worker increases profit.
If $MRP - W < 0$, the worker reduces profit.
If $MRP - W = 0$, the firm has no incentive to change employment at the margin.
This restates the hiring rule in profit terms.
MRP can fall because it depends on productivity and revenue per unit, not on wages.
If marginal product declines as more workers share fixed inputs, then output added per worker falls.
If marginal revenue from extra output decreases, revenue added per worker falls.
Either channel reduces MRP as employment rises.
The rule $W = MRP$ holds in both horizons, but what changes is what is “fixed.”
Short run: some inputs are fixed, so diminishing marginal returns often make $MRP$ fall quickly.
Long run: the firm can adjust more inputs, potentially sustaining marginal product and shifting the relevant $MRP$ schedule.
The optimisation condition is the same; the underlying MRP may differ.
It implies the firms have different $MRP$ schedules.
Possible sources include:
Different production technologies (different $MP_L$ at each employment level).
Different ability to generate marginal revenue from added output (different $MR$).
Different constraints on combining labour with other inputs.
At the same $W$, the firm with higher $MRP$ at each labour quantity hires more labour.
Practice Questions
(2 marks) In a perfectly competitive labour market, state the firm’s profit-maximising hiring rule using the wage and marginal revenue product.
1 mark: Identifies the relevant comparison as wage (or MRC) versus marginal revenue product (MRP).
1 mark: States the rule correctly: hire up to the quantity of labour where (or equivalently where with ).
(5 marks) Explain why a wage-taking firm’s labour demand curve is its marginal revenue product curve. In your answer, refer to how the firm decides whether to hire an additional worker.
1 mark: States that the firm is a wage taker so the wage is constant for the firm (horizontal at ).
1 mark: Explains the decision rule: hire if and stop when (or hire until ).
1 mark: Links wage changes to employment changes: a lower makes more workers profitable, a higher makes fewer workers profitable.
1 mark: Concludes that the quantity of labour chosen at each wage is where intersects , so the relationship between and traces the curve.
1 mark: Notes that slopes downward (typically due to diminishing marginal returns), supporting a downward-sloping labour demand curve.
