Labour force participation and the reservation wage

The reservation wage is the lowest wage at which a person is willing to work: at that wage they are indifferent between working and not working. A person works if and only if the market wage exceeds their reservation wage. When leisure is a normal good, the reservation wage rises with non-labour income.

Two margins of labour supply

Labour supply responds at two margins. The extensive margin is the choice of whether to work at all. It is measured by the labour force participation rate, the employed plus the unemployed as a share of the working-age population (15 and over in the Canadian Labour Force Survey). The intensive margin is how much to work, measured by hours per week or per year among people who work. Survey definitions are in measuring the labour market.

The two margins respond differently to a raise. For someone already working, a higher wage has a substitution effect and an income effect that pull hours in opposite directions (income and substitution effects). For someone not working, a higher wage adds nothing to income at zero hours, so there is no income effect. It can only make work more attractive. A higher wage raises participation unambiguously, even when its effect on hours is ambiguous.

The intuition

Take the worker from the work-leisure choice: utility $U = C^{0.4}L^{0.6}$, 110 hours a week, $200 of non-labour income and a wage of $20. She works 38 hours. Now give her $1,100 a week of non-labour income, for example a share of a partner’s earnings. Before working at all she already consumes $1,100 and keeps all 110 hours of leisure. To give up the first hour she would need $15 of extra consumption. That $15 is her reservation wage: offered $12 she does not work; offered $20 she works 11 hours.

The first hour decides. With convex indifference curves, each additional hour of leisure given up must be compensated by more consumption than the hour before, so if the first hour is not worth the market wage, no later hour is.

The model

Preferences are $U(C, L)$ with convex indifference curves. The budget constraint is $C = w(T - L) + V$, where $h = T - L$ is hours of work. It has two pieces: a vertical segment at $L = T$ from zero up to $V$, and a line of slope $-w$ rising to the left from the endowment point $E = (T, V)$, the bundle with no work.

The tangency condition $MU_L/MU_C = w$ describes an interior solution, in which the person works some hours. It fails when the indifference curve through $E$ is steeper than the budget line. Then every bundle with work lies below that indifference curve, and the best choice is the corner solution at $E$: zero hours. The slope of the indifference curve at $E$ is the reservation wage:

$$w^R = \left.\frac{MU_L}{MU_C}\right|_{L = T,\ C = V}.$$

The rule: work if $w > w^R$; do not work if $w < w^R$; at $w = w^R$ the person is indifferent.

Market wage (w)

$12.00

Non-labour income per week (V)

$1,100

Reservation wage w^R

$15.00

Market wage w

$12.00

Hours worked h

0.0

Consumption C

$1,100

Open in Graph Lab

Figure 1. A worker with $U = C^{0.4}L^{0.6}$, 110 hours a week and $1,100 of non-labour income. Her reservation wage, the slope of $U_0$ at the endowment point $E$, is $15. At a market wage of $12 the budget line is flatter than $U_0$ at $E$, so the corner at $E$ is optimal and she does not work; at any wage above $15 she reaches a higher indifference curve by working.

Non-labour income raises the reservation wage

An increase in $V$ moves the endowment point straight up. If leisure is a normal good, a person with more consumption and the same leisure values an hour of leisure at more dollars, so the indifference curve through the higher endowment point is steeper at $L = T$. A steeper slope at $E$ is a higher reservation wage. For the Cobb-Douglas worker above, $w^R = 1.5V/T$: the reservation wage is proportional to non-labour income.

Market wage (w)

$12.00

Ana's reservation wage

$4.50

Ben's reservation wage

$15.00

Ana's hours

27.5

Ben's hours

0.0

Open in Graph Lab

Figure 2. Two workers with the same preferences and different non-labour income. Ana, with $330 a week, has a reservation wage of $4.50 and works 27.5 hours at a wage of $12. Ben, with $1,100, has a reservation wage of $15 and stays at his endowment point. The same market wage draws one into work and leaves the other out.

What moves participation

Participation turns on the comparison of $w$ with $w^R$, so every influence works through one side of it:

• The market wage $w$, set by skills and labour demand. A higher wage steepens the budget line.
• Non-labour income $V$: assets, a partner’s earnings, transfers. More of it raises $w^R$.
• The value of time at home: young children, home production, illness. A higher value steepens the indifference curve at $E$ and raises $w^R$.
• The costs of working, such as child care and commuting. They cut what an hour of work adds to consumption, which acts like a lower wage.
• Preferences and norms. A stronger taste for leisure means steeper indifference curves and a higher $w^R$.

Reservation wages differ across people. The participation rate at a given market wage is therefore the share of the population whose reservation wage is below it, and the participation curve traces out the distribution of reservation wages.

Market wage (w)

$18.00

Median reservation wage

$16.00

Participation rate

62.2%

Change from the original curve

0.0 points

Open in Graph Lab

Figure 3. With reservation wages spread around a median of $16, 62 percent of people participate at a market wage of $18. Anything that raises reservation wages across the population, such as more non-labour income or costlier child care, shifts the curve up and lowers participation at every wage.

Key idea

A person works if and only if the market wage exceeds the reservation wage, the slope of the indifference curve at the endowment point. More non-labour income raises the reservation wage; a higher market wage can only draw people into work.

Worked example

Maya’s utility is $U = C^{0.4}L^{0.6}$ and she has $T = 110$ hours a week.

1. Find the MRS. $\dfrac{MU_L}{MU_C} = \dfrac{0.6\,C^{0.4}L^{-0.4}}{0.4\,C^{-0.6}L^{0.6}} = 1.5\,\dfrac{C}{L}$.

2. Evaluate it at the endowment point. With $V = 1{,}100$: $w^R = 1.5 \times \frac{1{,}100}{110} = 15$.

3. Compare with a market wage of $12. Since $12 < 15$, she does not work: $h = 0$ and $C = 1{,}100$. The interior formula confirms the corner: $L^* = 0.6\,(wT + V)/w = 0.6 \times 2{,}420/12 = 121$, more hours of leisure than exist.

4. At $20 she works. $L^* = 0.6 \times (2{,}200 + 1{,}100)/20 = 99$, so $h = 11$ and $C = 1{,}100 + 20 \times 11 = 1{,}320$.

5. Cut her non-labour income to $330. Now $w^R = 1.5 \times 330/110 = 4.50$, and at $12 she works: $L^* = 0.6 \times (1{,}320 + 330)/12 = 82.5$, so $h = 27.5$.

Exercise: the work-leisure example

With $200 of non-labour income, $w^R = 1.5 \times 200/110 = 2.73$. At a wage of $20 she works: $L^* = 0.6 \times (2{,}200 + 200)/20 = 72$, so $h = 38$, as on the work-leisure page.

Evidence: the rise in women’s participation

Labour force participation rate by gender, Canada

Annual averages, population aged 15 and over

• Men
• Women

Women's participation rose by about 17 points between 1976 and 2008 and has stayed near 61 percent since; men's fell by about 8 points between 1976 and 2025.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 averages of monthly Labour Force Survey estimates. The LFS recorded sex before 2022 and gender from 2022; Statistics Canada combines them in one series. From 2022 "Men" and "Women" are its Men+ and Women+ categories, each of which includes some non-binary persons. 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.

Period	Men	Women
1976	77.7%	45.7%
1977	77.6%	46.5%
1978	77.9%	47.9%
1979	78.4%	49.4%
1980	78.3%	50.6%
1981	78.4%	52.0%
1982	77.0%	52.1%
1983	76.9%	53.0%
1984	76.7%	53.8%
1985	76.7%	54.9%
1986	76.9%	55.7%
1987	76.8%	56.5%
1988	76.6%	57.4%
1989	76.8%	58.1%
1990	76.1%	58.5%
1991	75.0%	58.4%
1992	73.9%	57.8%
1993	73.3%	57.7%
1994	73.1%	57.5%
1995	72.5%	57.5%
1996	72.2%	57.5%
1997	72.2%	57.8%
1998	72.1%	58.4%
1999	72.4%	58.9%
2000	72.3%	59.4%
2001	72.3%	59.8%
2002	73.0%	60.9%
2003	73.4%	61.9%
2004	73.2%	62.0%
2005	72.8%	61.7%
2006	72.7%	61.9%
2007	72.7%	62.4%
2008	72.9%	62.5%
2009	72.3%	62.4%
2010	71.9%	62.4%
2011	71.8%	62.0%
2012	71.6%	62.0%
2013	71.4%	62.1%
2014	71.0%	61.5%
2015	71.0%	61.3%
2016	70.6%	61.2%
2017	70.7%	61.4%
2018	70.3%	61.3%
2019	70.5%	61.6%
2020	69.0%	59.8%
2021	69.9%	61.0%
2022	69.6%	61.4%
2023	70.0%	61.7%
2024	69.7%	61.2%
2025	69.5%	61.1%

Women’s participation in Canada rose from 45.7 percent in 1976 to 62.5 percent in 2008; men’s fell from 77.7 percent to 69.5 percent by 2025. In the model the rise for women comes from higher market wages, lower reservation wages, or both.

• Market wages. Women’s pay rose relative to men’s. Among full-time employees, women’s average hourly wage went from 83 percent of men’s in 1997 to about 90 percent in 2025.¹
• Fewer children. Children raise the value of time at home. Using the sex mix of a family’s first two children as a natural experiment, Angrist and Evans find that a third child reduces mothers’ labour supply, by less than simple comparisons suggest, with no effect among more-educated women and effects that fade by the time the child is about 13.²
• Household technology. Greenwood, Seshadri and Yorukoglu argue that the spread of labour-saving appliances freed married women’s time from home production and helps explain their rising participation over the twentieth century.³
• The pill. Goldin and Katz link the spread of oral contraception among young unmarried women around 1970 to a jump in women entering long professional programs and to later marriage: the pill lowered the cost of investing in a career.⁴
• Norms. Goldin dates a “quiet revolution” from the late 1970s in women’s career expectations and identity.⁵ Fernández, Fogli and Olivetti find that men raised by working mothers are more likely to have working wives, so attitudes toward women’s work passed between generations.⁶
• Child care. Quebec’s $5-a-day child care, introduced in 1997 and extended to younger children over the following years, was followed by a large rise in the labour supply of married mothers.⁷ Cheaper care lowers the cost of working, which pushes the net wage of mothers of young children above their reservation wages.

Most of women’s wage response is at the extensive margin; the size of that response is on the labour supply curve and elasticity page.

Common mistakes

Traps on exams

• Applying tangency at a corner. If the interior formula gives more leisure than $T$ (negative hours), the answer is zero hours. Compare $w$ with $w^R$ first.
• Getting the direction wrong. More non-labour income raises the reservation wage when leisure is normal. It does not let someone “afford to accept less”.
• Giving a raise an income effect at zero hours. For a non-worker a higher wage only pivots the budget line around $E$. It can draw them in; it cannot push them out.
• Confusing the reservation wage with the market or minimum wage. The reservation wage is personal: it comes from preferences and the endowment point.

On the exam

Draw the budget constraint with its vertical piece at $L = T$ and mark $E$. Draw the indifference curve through $E$ and a dashed tangent to it labelled “slope $= -w^R$”. A budget line flatter than that tangent means no work; a steeper one means the person works, at a tangency to the left of $E$.

Check yourself

1.

Leisure is a normal good. A person's non-labour income $V$ rises (an inheritance, or a partner's raise). What happens to the person's reservation wage?

1It rises, so the person is less likely to work at any given market wage2It falls, because the person can now afford to accept a lower wage3It does not change, because the reservation wage depends only on preferences4It rises only if the market wage also rises

Check answer

2.

True or false: for someone who is not working, a rise in the market wage has an income effect that can make them less willing to enter the labour force.

1True2False

Check answer

3.

At a person's endowment point, the indifference curve is steeper than the budget line. What does the person choose?

1Not to work, because the first hour of work is worth less to them than its pay2To work until the indifference curve becomes tangent to the budget line3To work full time, because the budget line is flatter than the indifference curve4It cannot be determined without knowing the person's non-labour income

Check answer

Practise more questions on this topic

Sources

1. Statistics Canada, Table 14-10-0064-01, Employee wages by industry, annual: average hourly wages of full-time employees aged 15 and over, women divided by men. A raw ratio that does not adjust for occupation, experience or hours. ↩

2. Angrist, J. D. and Evans, W. N. (1998). Children and their parents’ labor supply: Evidence from exogenous variation in family size. American Economic Review, 88(3), 450 to 477. NBER working paper 5778. ↩

3. Greenwood, J., Seshadri, A. and Yorukoglu, M. (2005). Engines of liberation. Review of Economic Studies, 72(1), 109 to 133. IDEAS record. ↩

4. Goldin, C. and Katz, L. F. (2002). The power of the pill: Oral contraceptives and women’s career and marriage decisions. Journal of Political Economy, 110(4), 730 to 770. Harvard repository copy. ↩

5. Goldin, C. (2006). The quiet revolution that transformed women’s employment, education, and family. American Economic Review, 96(2), 1 to 21. doi:10.1257/000282806777212350. ↩

6. Fernández, R., Fogli, A. and Olivetti, C. (2004). Mothers and sons: Preference formation and female labor force dynamics. Quarterly Journal of Economics, 119(4), 1249 to 1299. IDEAS record. ↩

7. Baker, M., Gruber, J. and Milligan, K. (2008). Universal child care, maternal labor supply, and family well-being. Journal of Political Economy, 116(4), 709 to 745. NBER working paper 11832. ↩