Competitive labour market equilibrium

A competitive labour market has many firms and many workers, none able to influence the wage, and free entry and exit on both sides. Its equilibrium is the wage $w^*$ at which the hours workers want to supply equal the hours firms want to hire, $E^*$. That outcome maximizes the total gains from trade, and when workers or firms can move between markets, it pays the same wage in every market they link.

How the market gets there

Above $w^*$, more people want jobs than firms want to fill. Job seekers accept less and firms find they can fill vacancies for less, so the wage falls. Below $w^*$, firms cannot fill their vacancies and bid the wage up. Only at $w^*$ does everyone who wants a job at the going wage have one, while every firm hires as many workers as it wants.

Suppose an oil sands expansion raises the value of a welder’s work in Fort McMurray. Firms short of welders raise pay, the higher pay draws welders from other trades and other provinces, and the wage stops rising once the shortage is gone. Real labour markets are hit by new shocks (technology, trade, weather, demographics) before they finish adjusting, so they are rarely exactly at equilibrium. The model describes the point they are pulled toward.

Surplus and efficiency

The labour demand curve is the value of the marginal product, $VMP_E$: the most a firm would pay for each hour. The labour supply curve lists reservation wages: the least it takes to get each hour supplied. Every hour traded at $w^*$ creates two gains.

• Producer surplus (P) is the firms’ gain: the value of each hour’s output minus the wage paid for it, summed over all hours hired. It is the area below the demand curve and above the wage. Firms are the buyers in a labour market, so producer surplus plays the role that consumer surplus plays in a product market, where consumer surplus is what buyers would be willing to pay minus what they actually pay: the area below the demand curve and above the price.
• Worker surplus (Q) is the workers’ gain: the wage minus the reservation wage, summed over all hours worked. It is the area above the supply curve and below the wage.

Their sum, $P + Q$, is the total gains from trade.

Hours traded, E (thousands)

60k

Producer surplus, P

$450k

Worker surplus, Q

$270k

Deadweight loss

$0k

Total surplus, P + Q

$720k

Open in Graph Lab

Figure 1. Labour demand meets labour supply at 60 thousand hours a week and $15 an hour. Producer surplus P is $450 thousand a week and worker surplus Q is $270 thousand. At any other employment level a deadweight-loss triangle opens between the curves and total surplus falls below $720 thousand.

A gain from trade exists in a labour market whenever an hour’s value of marginal product exceeds the wage needed to get that hour supplied. Below $E^*$ such hours go unworked: demand lies above supply, and the triangle between them is lost. Above $E^*$ the reverse holds: the extra hours are worth less to firms than the time is worth to workers, so forcing them to be worked destroys value. Only at $E^*$ is every gain taken and no loss incurred.

An allocation is Pareto efficient when no one can be made better off without making someone else worse off, which means every gain from trade has been exhausted. A change that makes at least one person better off and nobody worse off is a Pareto improvement; in policy analysis the first question is whether one exists. The competitive equilibrium is Pareto efficient. That is a statement about the size of the pie, not its division: an efficient market can still leave many workers with low incomes.

Key idea

At $E^*$ the value of the last hour to the firm equals the value of the worker’s time. That equality is why the competitive outcome maximizes $P + Q$.

Many markets linked by mobility

Workers with the same skills can often sell them in several markets: different provinces, cities or industries. Suppose North pays more than South. With free mobility (no moving costs, full information), southern workers move north. Northern labour supply shifts right and southern supply shifts left, so the North wage falls and the South wage rises. Moves continue until the two wages are equal. This is the single-wage property of competitive equilibrium: markets linked by mobility pay workers of a given skill the same wage.

Workers who move from South to North (thousands)

20k

North wage, w_N

$16.00

South wage, w_S

$16.00

Firm surplus, North (per hour)

$490k

Firm surplus, South (per hour)

$90k

Value of output, both regions (per hour)

$2,180k

Open in Graph Lab

Figure 2. North pays $18 and South $14 before anyone moves. Migration shifts northern supply right and southern supply left until, after 20 thousand moves, both regions pay $16. Firm surplus (blue) rises in North and falls in South, and the combined value of output rises.

Migration redistributes surplus while it raises the total:

• North, the receiving region. The wage falls and employment rises, so producer surplus grows. Workers who were already there earn less, so their surplus shrinks. Total worker surplus in the region can still rise, because the movers add to it.
• South, the sending region. The wage rises and employment falls, so producer surplus shrinks. Workers who stay earn more. Total worker surplus in the region shrinks because fewer workers remain.
• Movers gain: they earn the common wage instead of the old southern wage.
• Both regions together gain, because each move takes a worker from a market where the value of the marginal product is low to one where it is high.

Firms can do the same arbitrage. If firms relocate from high-wage North to low-wage South, northern labour demand shifts left and southern demand shifts right, and the wages converge from the other side.

Jobs that relocate from North to South (thousands)

20k

North wage, w_N

$16.00

South wage, w_S

$16.00

North employment

50.0k

South employment

50.0k

Open in Graph Lab

Figure 3. The same two regions linked by firm mobility. As 20 thousand jobs move from North to South, labour demand shifts left in North and right in South, and both wages converge to $16.

The single wage has a strong implication. Every competitive firm hires until $VMP_E = w$, so if the wage is the same everywhere, the value of the marginal product is too:

$$VMP_E^{\text{North}} = w^* = VMP_E^{\text{South}}.$$

No reallocation of workers can then raise national output: moving a worker from one market to the other loses exactly what it gains. This is allocative efficiency. It is the invisible hand at work: each worker and firm moves for private gain, and the result is the allocation that maximizes national income, which none of them set out to achieve.

Worked example

Labour demand is $w = 30 - 0.25E$ and labour supply is $w = 6 + 0.15E$, with $E$ in thousands of hours a week.

1. Find the equilibrium. $30 - 0.25E = 6 + 0.15E$, so $E^* = 24 / 0.4 = 60$ and $w^* = 30 - 0.25(60) = 15$.

2. Measure surplus. Producer surplus is the triangle between demand and the wage: $\tfrac{1}{2} \times 60 \times (30 - 15) = 450$ thousand dollars a week. Worker surplus is the triangle between the wage and supply: $\tfrac{1}{2} \times 60 \times (15 - 6) = 270$. The gains from trade total 720.

3. Show that other employment levels lose surplus. If hours are capped at 40 thousand, the last hour is worth $30 - 0.25(40) = 20$ to firms, but workers would supply it for only $6 + 0.15(40) = 12$. The lost surplus is the triangle $\tfrac{1}{2} \times (60 - 40) \times (20 - 12) = 80$.

4. Set up two regions. Now $E$ is thousands of workers. North has demand $w = 30 - 0.2E$ and supply $w = 6 + 0.2E$, so $E_N = 60$ and $w_N = 18$. South has demand $w = 22 - 0.2E$ and the same supply, so $E_S = 40$ and $w_S = 14$.

5. Let workers move. If $m$ thousand workers move north, northern supply becomes $w = 6 + 0.2(E - m)$ and southern supply $w = 6 + 0.2(E + m)$. In North, $30 - 0.2E = 6 + 0.2(E - m)$ gives $E_N = 60 + 0.5m$ and $w_N = 18 - 0.1m$. In South, $22 - 0.2E = 6 + 0.2(E + m)$ gives $E_S = 40 - 0.5m$ and $w_S = 14 + 0.1m$. The wages are equal when $m = 20$, at $w^* = 16$, with 70 thousand employed in North and 30 thousand in South.

6. Compare surplus and output. Firm surplus in North rises from $\tfrac{1}{2}(60)(30 - 18) = 360$ to $\tfrac{1}{2}(70)(30 - 16) = 490$ thousand dollars an hour; in South it falls from $\tfrac{1}{2}(40)(22 - 14) = 160$ to $\tfrac{1}{2}(30)(22 - 16) = 90$. The value of output is the area under each demand curve up to employment, $30E_N - 0.1E_N^2$ in North and $22E_S - 0.1E_S^2$ in South. It rises from $1440 + 720 = 2160$ to $1610 + 570 = 2180$ thousand dollars an hour.

Evidence

US states. Blanchard and Katz found that relative wages across US states converged steadily over the four decades they studied, and that shocks to a state’s relative wage fade within about a decade.¹ When a state loses jobs, its unemployment and participation rates return to normal within five to seven years, not because the jobs come back but because workers leave: worker migration, rather than job creation or the relocation of firms, is the main adjustment mechanism.¹ Convergence is slow. Barro and Sala-i-Martin estimated that the gap in income per person between a typical poor and a typical rich state shrinks by roughly 2 percent a year,² which implies that half of a gap takes about 35 years to close. Gaps that last that long are evidence that moving is costly.

Canada. Canadians have become much less likely to move between provinces.

Interprovincial out-migration rate, Canada

Interprovincial migrants per 1,000 population, July-to-June years

Interprovincial out-migration fell from 18.0 per 1,000 people in 1971–72 to 7.0 in 2025–26 (July-to-June years; the latest year is preliminary).Source: Statistics Canada, Table 17-10-0015-01, Estimates of the components of interprovincial migration, by age and gender, annual; Table 17-10-0005-01, Population estimates on July 1. Retrieved 2026-10-23.

Show the data and notes

Each year x covers July 1 of x to June 30 of x+1 (e.g. 2024 = 2024/2025). Rate = people who moved to another province or territory during the period ÷ Canada's population on July 1 at its start (Table 17-10-0005-01, https://doi.org/10.25318/1710000501-eng) × 1,000. For Canada as a whole, out-migrants equal in-migrants. The latest period is preliminary.

Period	Out-migrants per 1,000
1971	18.0
1972	17.8
1973	19.5
1974	18.1
1975	16.2
1976	15.2
1977	15.4
1978	15.0
1979	15.3
1980	15.6
1981	14.4
1982	12.2
1983	11.0
1984	10.6
1985	11.1
1986	11.6
1987	12.2
1988	12.2
1989	13.1
1990	11.4
1991	11.3
1992	10.7
1993	10.1
1994	9.8
1995	10.0
1996	9.9
1997	10.3
1998	9.2
1999	9.4
2000	8.8
2001	9.4
2002	8.8
2003	8.3
2004	8.9
2005	8.9
2006	9.4
2007	9.2
2008	8.4
2009	7.7
2010	7.6
2011	8.2
2012	7.5
2013	7.8
2014	8.0
2015	7.8
2016	7.2
2017	7.1
2018	6.9
2019	7.6
2020	6.6
2021	9.1
2022	8.8
2023	8.3
2024	7.3
2025	7.0

Statistics Canada attributes part of the decline to population aging, but finds that mobility fell at all ages, and points to Canada’s relative prosperity, which narrowed unemployment gaps between provinces and raised incomes in the provinces people used to leave.³ Its later projections work adds the rise of dual-earner couples, higher household debt and information technology as likely contributors.⁴

Unemployment rate by province, 2025

Annual average, population aged 15 and over

Canada6.8%

Newfoundland and Labrador10.1%

Prince Edward Island8.0%

Nova Scotia6.6%

New Brunswick7.1%

Quebec5.6%

Ontario7.7%

Manitoba5.9%

Saskatchewan5.2%

Alberta7.2%

British Columbia6.2%

Unemployment rates in 2025 ranged from 5.2 percent in Saskatchewan to 10.1 percent in Newfoundland and Labrador.Source: Statistics Canada, Table 14-10-0327-01, Labour force characteristics by gender and detailed age group, annual. Retrieved 2026-10-23.

Show the data and notes

Annual average of monthly Labour Force Survey estimates, both genders. The Labour Force Survey covers the 10 provinces; it excludes the territories, people living on reserves, full-time members of the Canadian Armed Forces and people living in institutions.

Category	Unemployment rate
Canada	6.8%
Newfoundland and Labrador	10.1%
Prince Edward Island	8.0%
Nova Scotia	6.6%
New Brunswick	7.1%
Quebec	5.6%
Ontario	7.7%
Manitoba	5.9%
Saskatchewan	5.2%
Alberta	7.2%
British Columbia	6.2%

In the frictionless model, gaps like these would draw workers toward the low-unemployment provinces until they closed. They remain because moving costs money and time and means leaving family and community. The decision to move as an investment is covered in migration and job turnover.

Common mistakes

Traps on exams

• Calling the firms’ area consumer surplus. Firms buy labour, but the labour-market convention (and Borjas) calls their gain producer surplus. Worker surplus is the sellers’ gain.
• Shifting only one curve in a two-region question. Each migrant leaves one supply curve and joins the other, so both shift, in opposite directions. With firm mobility, both demand curves shift.
• Equalizing employment instead of wages. Mobility equalizes wages, and therefore the value of the marginal product, not the number of jobs in each region.
• Reading every wage gap as disequilibrium. Gaps survive in equilibrium when moving is costly or jobs differ in their amenities.
• Treating efficiency as fairness. Pareto efficiency says nothing about how the surplus is shared.

On the exam

For two regions, draw two panels side by side on the same wage scale. Mark the starting wages, shift supply right in the high-wage region and left in the low-wage region, and show both wages meeting at $w^*$. Shade producer surplus (under demand, above the wage) and worker surplus (above supply, below the wage) before and after, then say in one line who gains and who loses.

Check yourself

1.

What does worker surplus measure in a competitive labour market?

1The total amount by which the wage exceeds the reservation wages of the people who work2The total wages paid to workers3The value of workers' time outside the labour market4The amount by which the value of the marginal product exceeds the wage

Check answer

2.

Why is the competitive equilibrium in a labour market Pareto efficient?

1Every hour whose value of marginal product exceeds its reservation wage is worked, and no hour for which the reverse holds is worked2It maximizes employment, and more employment always raises welfare3Every worker receives the same surplus, so no one can be made better off4Firms pay each worker the value of the average product of labour

Check answer

3.

Workers migrate from a low-wage region (South) to a high-wage region (North) until wages are equal. Both markets are competitive. Which statements are true? Select all that apply.

Select all that apply.

1Producer surplus rises in North2Producer surplus rises in South3Workers who were already employed in North are worse off4Workers who stay in South are better off5The combined value of output in the two regions falls

Check answer

Practise more questions on this topic

Sources

1. Blanchard, O. J. and L. F. Katz (1992). Regional evolutions. Brookings Papers on Economic Activity, 1992(1), 1 to 75. Brookings. ↩ ↩²

2. Barro, R. J. and X. Sala-i-Martin (1991). Convergence across states and regions. Brookings Papers on Economic Activity, 1991(1), 107 to 182. Brookings. ↩

3. Statistics Canada (2008). A portrait of the mobility of Canadians between 2001 and 2006. In Report on the Demographic Situation in Canada: 2005 and 2006, catalogue no. 91-209-X. Statistics Canada. ↩

4. Dion, P. (2019). Chapter 8: Projection of interprovincial migration. In Population Projections for Canada (2018 to 2068), Provinces and Territories (2018 to 2043): Technical Report on Methodology and Assumptions, Statistics Canada catalogue no. 91-620-X. Statistics Canada. ↩