Demand for labor — short definition
– Demand for labor is the quantity of workers (or hours) firms want to hire at given wage levels. It is a derived demand: firms demand labor because labor helps produce goods or services that customers buy.
Key terms (defined on first use)
– Real wage: the wage adjusted for inflation; it measures purchasing power of pay.
– Marginal product of labor (MPL): the extra output produced when you add one more unit of labor, holding other inputs constant.
– Marginal revenue product of labor (MRPL): the extra revenue a firm obtains from hiring one additional worker. MRPL = MPL × price of output (in simple competitive-product markets).
How firms decide how many workers to hire (step-by-step)
1. Estimate how much extra output one more worker produces (MPL).
2. Multiply that MPL by the expected selling price for the extra output to get MRPL.
3. Compare MRPL to the wage (real wage) the firm must pay.
4. If MRPL > wage, hiring that worker raises profit; if MRPL wage ($60) → hiring this worker increases profit by $20.
– If a second worker had MPL = 2 (MRPL = 2 × $20 = $40), then MRPL ($40) < wage ($60) → do not hire the second worker.
So the firm would hire one additional worker but stop
once MRPL falls below the wage. In other words, the firm hires additional workers while MRPL ≥ wage; it stops when MRPL < wage.
Additional worked example (multiple hires)
Assumptions:
– Price per unit of output = $20 (competitive output market).
– Marginal product of labor (MPL) for successive workers = [6, 4, 3, 2, 1] units.
– Market wage (per worker) = $60.
Compute MRPL for each worker:
– Worker 1: MRPL = 6 × $20 = $120
– Worker 2: MRPL = 4 × $20 = $80
– Worker 3: MRPL = 3 × $20 = $60
– Worker 4: MRPL = 2 × $20 = $40
– Worker 5: MRPL = 1 × $20 = $20
Decision rule: hire while MRPL ≥ wage.
– With wage = $60 → hire workers 1, 2, and 3 (MRPLs 120, 80, 60). Stop before worker 4 because 40 < 60.
– If wage falls to $50 → hire workers 1–4 (40 ≥ 50? No: 40 < 50). Correction: with wage = $50, you would hire workers with MRPL ≥ 50; that is workers 1–3 only (120, 80, 60). Only if wage ≤ $40 would worker 4 be hired.
(Always check each MRPL against the prevailing wage. Minor arithmetic errors change hire counts; double-check calculations.)
Key formulas and definitions
– Marginal product of labor (MPL): additional units of output produced by one more worker.
– Marginal revenue of product (MRP) or MRPL (marginal revenue product of labor): MRPL = MPL × MR, where MR is marginal revenue from selling one more unit of output.
– In perfect competition (price-taker firm), MR = price (P), so MRPL = MPL × P.
– In imperfectly competitive output markets (monopoly/oligopoly), MR < P, so MRPL = MPL × MR — the firm’s demand for labor is lower for given MPL.
– Hiring rule (profit maximization): hire additional workers up to the point where MRPL = wage (or MRPL falls just below wage).
Short run vs. long run
– Short run: some inputs (commonly capital) are fixed. Firms adjust labor while capital is fixed, so MPL typically falls as more workers are added (diminishing marginal returns).
– Long run: firms can adjust all inputs (including capital and technology). Long-run demand for labor can be more elastic because firms substitute between labor and capital when relative prices change.
Factors that change (shift) labor demand
Labor demand is derived from demand for output and from firms’ production technology. Important shifters:
– Output price (P): higher P raises MRPL (if MR ≈ P), increasing labor demand.
– Productivity (MPL): improvements (training, better tech) raise MPL and labor demand.
– Cost and availability of substitute inputs (e.g., cheaper capital equipment): if capital becomes cheaper, firms may substitute away from labor, lowering labor demand.
– Taxes, subsidies, and regulations affecting employment costs (payroll taxes, minimum wages, employer mandates).
– Market structure: imperfect competition reduces MR relative to P and lowers labor demand relative to a price-taking firm.
Practical checklist for estimating how a firm will respond to a wage change
1. Determine whether the firm is a price taker for its output (competitive) or faces downward-sloping demand (imperfect competition).
2. Obtain MPL schedule (or data on productivity per additional worker).
3. Determine current price or MR for the firm’s output.
4. Compute MRPL = MPL × MR (or MPL × P for competitive firms) for successive workers.
5. Compare each MRPL to the market wage; hire while MRPL ≥ wage.
6. To analyze a policy
6. To analyze a policy change (e.g., a minimum wage, payroll tax, subsidy, or regulation) apply the following micro check-list:
– Specify the margin you care about. Is the policy a per
-worker (per hire) change, a per-hour change, or a change that varies with hours, skills, or firm size. Clear definition of the margin determines how you convert the policy into an employer cost.
7. Translate the policy into an employer cost schedule. For example:
– A payroll tax of t% on wages raises the employer’s marginal cost of hiring from w to w(1 + t) per hour (if the tax is assessed on employers). If the tax is shared, decide what fraction the employer bears versus the worker (incidence).
– A minimum wage sets a floor w_min on wages per hour; employer cost is max(w, w_min).
– A hiring subsidy of s dollars per worker reduces the employer’s marginal cost by s (if paid per hire) or by s per hour if paid per hour.
– A regulation that increases non-wage employer costs (e.g., mandatory training that costs C per hire) adds a fixed component to the marginal cost per worker or per hire depending on how it scales.
8. Recompute the hiring rule with the new cost:
– For competitive firms: hire additional labor while MPL × P ≥ employer marginal cost.
– For firms with downward-sloping demand: hire while MPL × MR ≥ employer marginal cost.
– If cost depends on hours or has a fixed-per-hire component, compare expected incremental revenue to incremental cost taking hours and probability of retention into account.
9. Consider behavioral and general-equilibrium adjustments:
– Short run versus long run. Short-run labor demand holds capital and technology fixed; long-run demand allows substitution between labor and capital (machines, software) and changes in firm scale.
– Worker responses. Workers may accept lower hours, change labor force participation, or acquire different skills.
– Market responses. Output prices may change if the policy affects costs across many firms; demand for the product can fall, feeding back into labor demand.
10. Quantify effects using elasticities and passes-through:
– Labor demand elasticity (η) measures percent change in employment from a 1% change in wage. Use empirical estimates for your industry or similar sectors.
– If you know the employer cost change Δc and the initial employment L0, the approximate change in employment is ΔL ≈ η × (Δc / c0) × L0, where c0 is initial employer cost per unit of labor (be clear whether elasticities are defined with respect to gross wage, employer cost, or net-of-tax wage).
– For payroll taxes and shared incidence, adjust Δc to reflect employer’s effective cost increase.
Worked numeric example — competitive firm, per-hour analysis
– Assumptions:
– Output price P = $10 per unit (firm is a price taker).
– Marginal product of labor (MPL) for successive workers (units of output per hour): worker1=6, worker2=5, worker3=4, worker4=3, worker5=2.
– Pre-policy hourly wage w = $30.
– Employer faces a payroll tax t = 20% paid entirely by the employer.
Step A — Compute marginal revenue product of labor (MRPL):
– MRPL = MPL × P.
– Worker1 MRPL = 6 × 10 = $60.
– Worker2 MRPL = 5 × 10 = $50.
– Worker3 MRPL = 4 × 10 = $40.
– Worker4 MRPL = 3 × 10 = $30.
– Worker5 MRPL = 2 × 10 = $20.
Step B — Employer cost per worker before tax = $30. Hire if MRPL ≥ 30:
– Hire workers 1, 2, 3, 4 (MRPLs 60, 50, 40, 30). Not worker5.
Step C — Employer cost per worker after 20% payroll tax = w × (1 + t) = 30 × 1.20
= Step C continued — Employer cost per worker after payroll tax =
Employer cost per worker = w × (1 + t) = 30 × 1.20 = $36.
Hire if MRPL ≥ employer cost after tax (36):
– MRPLs: 60, 50, 40, 30, 20 → hire workers 1, 2, 3 (MRPLs 60, 50, 40).
– Worker 4 (MRPL = 30) and worker 5 (MRPL = 20) are not hired.
Employment falls from 4 workers to 3 workers (ΔL = −1, a 25% decline in this small example).
= Step D — Accounting and incidence (numeric checks) =
– Employer total payroll outlay before tax = 4 workers × $30 = $120.
– Employer total payroll outlay after tax = 3 workers × $36 = $108.
– Government payroll-tax revenue = t × w × L_after = 0.20 × $30 × 3 = $18.
– Workers’ total gross wages before tax = 4 × $30 = $120; after = 3 × $30 = $90.
Interpretation:
– The statutory tax is levied on the employer, so the employer’s per-worker cost rose from $30 to $36.
– Because the employer reduces hiring, aggregate wages received by workers fall (from $120 to $90) even though the wage per employed worker was held constant at $30 in this example.
– Economic incidence (who ultimately bears the burden) depends on adjustments in employment and wages. Here, employers pay the tax directly per hire, but the decline in employment shifts part of the economic burden to workers through lost jobs and lost total earnings.
= Key checklist to analyze a payroll tax effect on labor demand =
1. Compute MRPL (marginal revenue product of labor) = MPL × output price.
2. Compute employer cost per worker before and after tax = w and w × (1 + t).
3. Compare MRPL to post-tax employer cost to decide hires.
4. Calculate changes in employment, employer outlays, government revenue, and aggregate worker earnings.
5. Note that if wages can adjust, re-solve allowing w to move; the burden will generally be shared between employers and workers according to supply/demand elasticities.
Assumptions in this worked example:
– Wage per employed worker (w = $30) is fixed and does not adjust in response to the tax.
– Output price and MPL schedule are exogenous and unchanged.
– Small discrete workforce for clarity; continuous labor markets use the same logic with marginal conditions.
Educational disclaimer:
This explanation is educational, not individualized investment or policy advice. Real labor markets can behave differently; consider supply elasticities and wage adjustments when applying this framework.
Sources and further reading:
– Investopedia — Demand for Labor (definition and examples): https://www.investopedia.com/terms/d/demand_for_labor.asp
– Internal Revenue Service — Employment Taxes (overview of payroll taxes): https://www.irs.gov/businesses/small-businesses-self-employed/employment-taxes
– U.S. Bureau of Labor Statistics — Occupational Employment and Wage Statistics: https://www.bls.gov/oes/
– Federal Reserve Bank of St. Louis — How payroll taxes affect wages (policy discussion): https://www.stlouisfed.org/on-the-economy/2016/december/how-payroll-taxes-affect-wages