Skip to content

Labour economicsChapter 10: Labour unions

Unions and collective bargaining

Key facts

Key facts

dwdE∣π constant=VMPE−wE\displaystyle \left.\frac{dw}{dE}\right|_{\pi \text{ constant}} = \frac{VMP_E - w}{E}
Course
Labour economics, ECON 331
Textbook
Borjas, chapter 10
Practise this topic (16)

A union is an organization of workers that bargains collectively with employers over wages, benefits and working conditions. In the monopoly union model the union sets the wage and the firm picks employment on its labour demand curve, so a higher wage costs jobs. In the efficient contract model the two sides bargain over both the wage and employment, reach the competitive level of employment and use the wage only to divide the surplus.

Two measures are used. The union coverage rate is the share of employees who are union members or are covered by a collective agreement. The unionization rate counts members only. In 2025, 30.6 percent of Canadian employees were covered and 28.5 percent were members.

Union coverage and unionization rates, Canada

Employees aged 15 and over, annual averages

  • Union coverage rate
  • Unionization rate
Union coverage and unionization rates, Canada
Coverage exceeds membership by about two percentage points: covered non-members. Both rates fell by two to three points between 1997 and 2025.Source: Statistics Canada, Table 14-10-0129-01, Union status by geography. Retrieved 2026-10-23.
Show the data and notes

Coverage rate: employees who are union members and/or covered by a collective agreement, as a share of all employees. Unionization rate: union members only. Labour Force Survey, both genders, 10 provinces. Statistics Canada cautions that 2006 changes to LFS processing may have shifted levels; compare across 2006 with care.

PeriodUnion coverage rateUnionization rate
199733.7%30.9%
199833.0%30.5%
199932.3%29.9%
200032.3%30.1%
200132.3%30.2%
200232.2%30.1%
200332.2%30.1%
200431.7%29.8%
200532.0%29.8%
200631.6%29.2%
200731.3%29.1%
200831.0%28.8%
200931.5%29.4%
201031.4%29.3%
201130.8%28.8%
201230.9%28.9%
201330.9%28.8%
201430.2%28.1%
201530.4%28.2%
201630.0%28.0%
201730.0%28.0%
201829.6%27.6%
201929.8%27.8%
202031.0%29.1%
202130.7%28.9%
202230.4%28.2%
202330.5%28.4%
202430.2%28.3%
202530.6%28.5%

Coverage is concentrated in the public sector: 77.5 percent of public-sector employees were covered in 2025, against 15.1 percent in the private sector, down from 21.3 percent in 1997. Manufacturing coverage fell from 36.4 to 21.6 percent over the same years.1 The longer decline was among men: the share of men in unionized jobs fell from 42 percent in 1981 to 29 percent in 2012, while women’s rate stayed near 30 percent.2

Canada is far more unionized than the United States. In 2025, 11.2 percent of US wage and salary workers were represented by a union and 10.0 percent were members; the private-sector membership rate was 5.9 percent, against 13.4 percent in Canada.31

Membership is the outcome of a demand for and a supply of union jobs.

  • Demand by workers. A worker wants a union job when its package (a higher wage, better benefits, job security, a grievance procedure) is worth more than the dues and the non-union alternative. Demand rises with the union wage gain, which is largest for less-skilled workers (see union wage effects).
  • Supply of union jobs. Organizing is costly. It is cheaper in large workplaces and the public sector, and harder where employers resist and the law makes certification difficult.

The law matters. Under the Canada Labour Code the Canada Industrial Relations Board certifies a union once it is satisfied that a majority of the unit wants it, and must hold a vote only when 35 to 50 percent of employees are members, so a majority of signed members can win certification without a vote (card check).4 Alberta requires evidence of support from at least 40 percent of the unit and then a mandatory representation vote.5 Across nine Canadian jurisdictions, mandatory votes lowered certification success by about 9 percentage points relative to card check.6 When British Columbia switched from card check to votes in 1984, success rates fell by an average of 19 points and rose again when card check returned in 1993; employer opposition was about twice as effective under votes.7

A union that wins certification represents every worker in the unit, which invites free riding. The Rand formula, from Justice Ivan Rand’s 1946 arbitration award that settled the 1945 Ford strike in Windsor, requires every covered worker to pay dues whether or not they join.8

Assumptions: the firm sells its output in a competitive market, so its labour demand curve is VMPEVMP_E. Without a union it would pay the competitive wage w∗w^*, the wage workers can get elsewhere, and hire E∗E^*. The union cares about both the wage and employment, so its indifference curves in (E,w)(E, w) space slope down and are convex. The union sets the wage; the firm keeps the right to choose employment and always hires on its demand curve.

The union therefore chooses a point on the demand curve, as a monopolist chooses a point on its product demand curve. Its best point MM, with wage wUw_U and employment EUE_U, is where an indifference curve is tangent to the demand curve.

Monopoly union: the union sets the wage, the firm sets employment on its demand curveLabour demand w = 30 - 0.1E and a competitive wage of $22, where the firm would hire 80 workers. The union picks a wage and the firm hires off its demand curve. A union that maximizes total rent (w - w*) x E reaches its highest indifference curve at a wage of $26 and 40 workers, where the indifference curve is tangent to demand. The shaded triangle is the deadweight loss from the 40 jobs not created.
Employment EU
40
Jobs lost (80 - EU)
40
Union rent (wU - w*) × EU
$160 an hour
Deadweight loss
$80 an hour
Figure 1. Demand w=30−0.1Ew = 30 - 0.1E with a competitive wage of $22. A union that maximizes total rent (w−w∗)E(w - w^*)E reaches its highest indifference curve at MM: a wage of $26 and 40 workers instead of 80. Any other wage puts the union on a lower indifference curve; the shaded triangle is the deadweight loss of the 40 jobs not filled.

A useful special case: the union maximizes its members’ rent, (w−w∗)E(w - w^*)E, with ww read off the demand curve w(E)w(E). The first-order condition is

w(E)+E w′(E)⏟marginal revenue of a job=w∗,\underbrace{w(E) + E\,w'(E)}_{\text{marginal revenue of a job}} = w^*,

so the union behaves like a monopolist with marginal cost w∗w^*. With linear demand w=a−bEw = a - bE this gives a−2bE=w∗a - 2bE = w^*, so EU=a−w∗2b=E∗2E_U = \frac{a - w^*}{2b} = \frac{E^*}{2} and wU=a+w∗2w_U = \frac{a + w^*}{2}: employment halves and the wage is halfway between w∗w^* and the demand intercept.

The jobs between EUE_U and E∗E^* produce output worth more than w∗w^*, the value of workers’ time elsewhere. Losing them is a deadweight loss. Displaced workers move to the non-union sector and push wages down there, an effect covered in union wage effects.

The monopoly outcome leaves gains on the table. An isoprofit curve is the set of (E,w)(E, w) pairs that give the same profit π=R(E)−wE\pi = R(E) - wE, where R(E)R(E) is revenue and R′(E)=VMPER'(E) = VMP_E. Holding profit constant, R′(E) dE−w dE−E dw=0R'(E)\,dE - w\,dE - E\,dw = 0, so

dwdE∣π constant=VMPE−wE.\left.\frac{dw}{dE}\right|_{\pi \text{ constant}} = \frac{VMP_E - w}{E}.

Left of the demand curve VMPE>wVMP_E > w, so the isoprofit curve rises; right of it, it falls. Each isoprofit curve is hump-shaped with its peak on the demand curve, and lower curves mean higher profit.

At MM the firm’s isoprofit curve is flat (it peaks there) while the union’s indifference curve slopes down. The two curves cross, so a lens of contracts with more employment and a lower wage makes both parties better off.

Monopoly union vs efficient contracts: the lens of mutual gains at MAt the monopoly-union point M (wage $26, 40 workers) the union's indifference curve U_M is tangent to labour demand and the firm's isoprofit curve pi_M peaks. The shaded lens between U_M and pi_M holds every contract that makes both sides better off than M. The vertical contract curve at the competitive employment of 80 workers runs through the lens: between wages of $24 and $25 both the union and the firm gain.
Figure 2. At the monopoly-union point MM the union's indifference curve UMU_M is tangent to demand while the isoprofit curve πM\pi_M peaks. Contracts in the shaded lens beat MM for both sides; on the contract curve at 80 workers, any wage from $24 to $25 does.

An efficient contract is one where neither side can gain without the other losing: an isoprofit curve tangent to a union indifference curve. The set of tangencies is the contract curve. With a rent-maximizing union, (w−w∗)E(w - w^*)E is constant along an indifference curve, so its slope is −(w−w∗)/E-(w - w^*)/E and tangency requires

VMPE−wE=−w−w∗E⟹VMPE=w∗.\frac{VMP_E - w}{E} = -\frac{w - w^*}{E} \quad\Longrightarrow\quad VMP_E = w^*.

Employment is set where the value of the marginal product equals the competitive wage, E∗E^*, whatever the bargained wage. The contract curve is vertical: a strongly efficient contract. The wage only splits the surplus, and its level depends on bargaining power.

Efficient contracts: bargaining along a vertical contract curveEvery efficient contract B is a tangency between the firm's isoprofit curve pi_B and the union's indifference curve U_B. With a union that maximizes rent above the competitive wage of $22, all tangencies lie at the competitive employment of 80 workers, so the contract curve is vertical. A higher bargained wage moves B up the contract curve: it transfers profit to the union one dollar of wage at a time and leaves employment and joint surplus unchanged. The hollow point M is the monopoly-union outcome for comparison.
Employment at B
80
Union rent at B (at M: $160)
$200 an hour
Profit at B (at M: $80)
$120 an hour
Joint surplus at B (at M: $240)
$320 an hour
Figure 3. Each efficient contract BB is a tangency between an isoprofit curve and a union indifference curve, and all of them lie at 80 workers. Raising the bargained wage from $22 to $26 moves the whole $320 surplus from the firm to the union without changing employment.

Two implications follow. First, at E∗E^* the bargained wage exceeds VMPEVMP_E, so the firm would cut jobs if it could; efficient contracts need enforceable employment rules such as staffing levels or crew sizes. Second, an efficient contract creates no deadweight loss. Abowd found that unexpected increases in union labour costs reduced shareholder wealth about dollar for dollar, as strongly efficient bargains predict.9 The efficient-bargaining model is due to McDonald and Solow.10

If both sides could predict a strike’s settlement, they could sign that agreement at once and split the wages and profits the strike would destroy. A strike is then a mistake both sides should avoid: the Hicks paradox.11 One resolution is private information. The firm knows its profitability and the union does not; a firm’s willingness to sit through a strike signals that it cannot pay more.

The Ashenfelter-Johnson model adds politics.12 Union leaders know what the firm can pay, but members expect more. A strike lowers members’ minimum acceptable settlement along a resistance curve, and the firm chooses the strike length that maximizes profit.

Ashenfelter-Johnson strike model: union resistance curve vs the firm's isoprofit lineThe union resistance curve shows the smallest wage increase members will accept after a strike of each length: 8 percent with no strike, falling toward 3 percent as the strike drags on. The firm's isoprofit lines trade strike weeks against wage increases at a fixed rate; lower lines mean higher profit. The firm chooses the strike length at which an isoprofit line is tangent to the resistance curve. The costlier a strike is to the firm, the shorter the strike; above a threshold the firm settles at once.
Strike length chosen by the firm
3.7 weeks
Settlement
5.0%
Figure 4. The firm picks the point SS on the union resistance curve that touches its lowest isoprofit line. When a strike week costs the firm the equivalent of 0.5 points of wage increase, it accepts a 3.7-week strike to settle at 5.0 percent instead of 8; when a strike week costs 1.25 points or more, it settles at once.

Card tested an asymmetric-information model on a large sample of collective agreements. Strikes were less likely when regional unemployment was high and more likely when industry selling prices were high, but negotiated wages showed no systematic relationship with strike outcomes, contrary to the model’s signalling premise.13

Canadian law limits when strikes can happen. In Alberta a strike is lawful only when no collective agreement is in force, after a majority strike vote and with notice.5 The Supreme Court of Canada held in 2015 that freedom of association in s. 2(d) of the Charter protects a right to strike.14 Since June 20, 2025, federally regulated employers may not use replacement workers to do the work of striking or locked-out employees.15

Labour demand is w=30−0.1Ew = 30 - 0.1E, so revenue is R(E)=30E−0.05E2R(E) = 30E - 0.05E^2 (the area under the demand curve). Profit is revenue minus the wage bill; other costs are fixed. The competitive wage is w∗=22w^* = 22 and the union maximizes rent (w−22)E(w - 22)E.

  1. Competitive benchmark. 30−0.1E=2230 - 0.1E = 22 gives E∗=80E^* = 80.

  2. Monopoly union. Rent is (30−0.1E−22)E=8E−0.1E2(30 - 0.1E - 22)E = 8E - 0.1E^2. Setting the derivative to zero, 8−0.2E=08 - 0.2E = 0, gives EU=40E_U = 40 and wU=30−0.1(40)=26w_U = 30 - 0.1(40) = 26. The union’s rent is (26−22)×40=160(26 - 22) \times 40 = 160 dollars an hour.

  3. Profit at the monopoly point. R(40)=1,200−80=1,120R(40) = 1{,}200 - 80 = 1{,}120, minus the wage bill 26×40=1,04026 \times 40 = 1{,}040, leaves πM=80\pi_M = 80.

  4. Deadweight loss. 12(26−22)(80−40)=80\tfrac{1}{2}(26 - 22)(80 - 40) = 80 dollars an hour.

  5. Efficient contracts. Employment returns to 80 and joint surplus is R(80)−22×80=2,080−1,760=320R(80) - 22 \times 80 = 2{,}080 - 1{,}760 = 320, which is 160+80160 + 80 plus the recovered deadweight loss of 80.

  6. Wages that beat MM for both sides. The union needs (w−22)×80≥160(w - 22) \times 80 \ge 160, so w≥24w \ge 24. The firm needs 2,080−80w≥802{,}080 - 80w \ge 80, so w≤25w \le 25. Any wage between $24 and $25 with 80 workers makes both better off than MM.

Exercise: demand w=40−0.2Ew = 40 - 0.2E and w∗=24w^* = 24

E∗=80E^* = 80. The rent-maximizing union picks EU=40E_U = 40 and wU=32w_U = 32, with rent 8×40=3208 \times 40 = 320. Revenue is R(E)=40E−0.1E2R(E) = 40E - 0.1E^2, so πM=1,440−1,280=160\pi_M = 1{,}440 - 1{,}280 = 160 and the deadweight loss is 12(8)(40)=160\tfrac{1}{2}(8)(40) = 160. At 80 workers, R(80)=2,560R(80) = 2{,}560. The union needs w≥24+320/80=28w \ge 24 + 320/80 = 28; the firm needs 2,560−80w≥1602{,}560 - 80w \ge 160, so w≤30w \le 30.

1.

In the monopoly union model, the union sets a wage wUw_U above the competitive wage w∗w^*. Which describes the outcome?

2.

Where does a firm's isoprofit curve reach its peak in a graph with employment on the horizontal axis and the wage on the vertical axis?

3.

A union maximizes total rent (w−w∗)E(w - w^*)E and bargains with the firm over both the wage and employment. The contract curve is vertical at the competitive employment level E∗E^*. What does this imply?

Practise more questions on this topic

  1. Statistics Canada, Table 14-10-0132-01, Union status by industry, annual Labour Force Survey estimates. ↩ ↩2

  2. Galarneau, D. and T. Sohn (2013). Long-term trends in unionization. Insights on Canadian Society, Statistics Canada catalogue no. 75-006-X. ↩

  3. US Bureau of Labor Statistics, Union Members — 2025, news release, February 18, 2026. ↩

  4. Canada Labour Code, R.S.C. 1985, c. L-2, sections 28 and 29. ↩

  5. Alberta Labour Relations Code, R.S.A. 2000, c. L-1, sections 33, 34 and 73. ↩ ↩2

  6. Johnson, S. (2002). Card check or mandatory representation vote? How the type of union recognition procedure affects union certification success. Economic Journal, 112(479), 344 to 361. IDEAS. ↩

  7. Riddell, C. (2004). Union certification success under voting versus card-check procedures: Evidence from British Columbia, 1978 to 1998. ILR Review, 57(4), 493 to 517. doi:10.1177/001979390405700402. ↩

  8. Dion, G. and D. Panneton, Rand Formula, The Canadian Encyclopedia. ↩

  9. Abowd, J. M. (1989). The effect of wage bargains on the stock market value of the firm. American Economic Review, 79(4), 774 to 800. IDEAS. ↩

  10. McDonald, I. M. and R. M. Solow (1981). Wage bargaining and employment. American Economic Review, 71(5), 896 to 908. IDEAS. ↩

  11. Hicks, J. R. (1932). The Theory of Wages. London: Macmillan. ↩

  12. Ashenfelter, O. and G. E. Johnson (1969). Bargaining theory, trade unions, and industrial strike activity. American Economic Review, 59(1), 35 to 49. IDEAS. ↩

  13. Card, D. (1990). Strikes and wages: A test of an asymmetric information model. Quarterly Journal of Economics, 105(3), 625 to 659. NBER working paper 2550. ↩

  14. Saskatchewan Federation of Labour v. Saskatchewan, 2015 SCC 4. ↩

  15. Employment and Social Development Canada, Protecting Canadian labour: Replacement workers legislation now in force, June 20, 2025. ↩