Income and substitution effects

The income effect is the change in hours of work caused by a change in income with the wage held constant; if leisure is a normal good, more income means more leisure and fewer hours. The substitution effect is the change in hours caused by a change in the wage with utility held constant; a higher wage makes leisure more expensive, so it always raises hours. A wage increase triggers both, in opposite directions, so its effect on hours is ambiguous.

The intuition

A worker who wins a lottery is richer but faces the same wage: a pure income effect, which leads them to buy more of every normal good, leisure included. A worker whose wage rises from $20 to $30 is also richer, since the same hours now buy more, but each hour of leisure now costs $30 of consumption instead of $20. The first force says work less; the second says work more.

A change in non-labour income

An increase in non-labour income $V$ moves the endowment point $E = (T, V)$ straight up and shifts the budget line out in parallel. The slope, $-w$, does not change, because the price of leisure has not changed. The worker moves from $P_0$ to $P_1$ on a higher indifference curve.

A good is normal if consumption of it rises with income and inferior if it falls. The direction of the change in hours depends only on which kind of good leisure is:

• Leisure normal: leisure rises and hours of work fall.
• Leisure inferior: leisure falls and hours of work rise.

Case: 1 = leisure normal, 2 = leisure inferior

1

Hours of work at P₀

38 hours

Hours of work at P₁

26 hours

Income effect on hours

−12 hours

Open in Graph Lab

Figure 1. Non-labour income rises by $400 a week at a wage of $20, shifting the budget line up in parallel. Case 1, leisure a normal good: the new tangency $P_1$ lies to the right of $P_0$ and hours of work fall from 38 to 26. Case 2, leisure an inferior good: $P_1$ lies to the left of $P_0$ and hours rise from 38 to 50.

The course, like most of the evidence, assumes leisure is normal: an increase in non-labour income reduces hours of work.

A change in the wage

A wage increase from $w_0$ to $w_1$ leaves $V$ and $T$ unchanged, so the endowment point $E$ does not move. The budget line rotates around $E$ and becomes steeper. The worker moves from the original optimum $P$ to the new optimum $R$. The move splits into two parts:

1. Income effect, $P$ to $Q$. Draw a hypothetical budget line, $DD$, parallel to the original budget line (slope $-w_0$) and just tangent to the new indifference curve $U_1$. The tangency is $Q$. Moving from $P$ to $Q$ raises utility to the new level at the old wage: a pure change in income. With leisure normal, $Q$ has more leisure than $P$, so the income effect reduces hours.
2. Substitution effect, $Q$ to $R$. Moving along $U_1$ from slope $-w_0$ to the steeper slope $-w_1$ holds utility constant while leisure becomes more expensive. Because indifference curves are convex, the steeper tangency $R$ is to the left of $Q$: the substitution effect always raises hours when the wage rises.

The total change in hours is the sum. If the income effect is larger, hours fall when the wage rises; if the substitution effect is larger, hours rise.

Case: 1 = income effect dominates, 2 = substitution effect dominates

1

New wage (old wage $20)

$30.00

Hours of work at P

38.0 hours

Hours of work at R

34.5 hours

Income effect on hours (P to Q)

−9.5 hours

Substitution effect on hours (Q to R)

6.0 hours

Total change in hours

−3.5 hours

Open in Graph Lab

Figure 2. The wage rises from $20 to $30 and the worker moves from $P$ to $R$. $DD$ has the old slope and touches the new indifference curve at $Q$: $P$ to $Q$ is the income effect and $Q$ to $R$ the substitution effect. Case 1, income effect dominant: hours fall from 38.0 to 34.5 (income effect −9.5, substitution effect +6.0). Case 2, substitution effect dominant: hours rise to 45.8 (−11.2 and +18.9). For a wage cut both effects change sign.

Key idea

For a wage increase with leisure normal, the substitution effect raises hours and the income effect lowers them. Theory cannot say which is larger; that is an empirical question.

A wage cut runs the same logic in reverse. Leisure becomes cheaper, so the substitution effect lowers hours; the worker is poorer, so with leisure normal the income effect raises hours. Hours can rise or fall.

Change	Income effect on hours	Substitution effect on hours	Total effect on hours
Non-labour income rises (leisure normal)	Falls	None	Falls
Wage rises (leisure normal)	Falls	Rises	Ambiguous
Wage falls (leisure normal)	Rises	Falls	Ambiguous

Which effect dominates at each wage determines the shape of the individual labour supply curve, including whether it bends backward at high wages (labour supply curve and elasticity).

Intermediate microeconomics usually splits the same move the other way round, holding the original utility constant for the substitution effect and adding the income effect afterward (the Slutsky equation). The two decompositions give the same signs; ECON 331 uses the one above, with $Q$ on the new indifference curve.

Worked example

A worker has $U = C^{0.4}L^{0.6}$, $T = 110$ hours and non-labour income of $200, and earns $20 an hour, so from the work-leisure model $L^* = 0.6(wT + V)/w$ and $C^* = 0.4(wT + V)$. At the start, $L = 72$, $h = 38$ and $C = 960$.

1. Non-labour income rises to $600. $L = 0.6(2{,}200 + 600)/20 = 84$, so hours fall from 38 to 26. The income effect is $-12$ hours: leisure is a normal good.

2. Instead, the wage rises to $30 with $V = 200$. $L = 0.6(3{,}300 + 200)/30 = 70$, so hours rise from 38 to 40 and consumption to $0.4 \times 3{,}500 = 1{,}400$ dollars. This is $R$.

3. Find $Q$. $Q$ is on the new indifference curve where the MRS equals the old wage. Since $MRS = 1.5\,C/L$, the tangency at $20 requires $C/L = 40/3$. Setting $C^{0.4}L^{0.6}$ at $Q$ equal to its value at $R$, $(\tfrac{40}{3}L)^{0.4}L^{0.6} = 1{,}400^{0.4}\,70^{0.6}$, gives $L_Q = 70 \times 1.5^{0.4} = 82.33$ hours, so $h_Q = 27.67$.

4. Decompose. Income effect: $27.67 - 38 = -10.33$ hours. Substitution effect: $40 - 27.67 = +12.33$ hours. Total: $+2$ hours. The substitution effect dominates, as it always does for this utility function when $V > 0$.

Evidence

Lottery winners. A lottery prize is non-labour income assigned at random among players, the cleanest test of the income effect. Among Massachusetts lottery players, Imbens, Rubin and Sacerdote found that unearned income reduces labour earnings, with a marginal propensity to consume leisure of about 11 percent: each extra dollar of unearned income cuts earnings by about 11 cents, with larger effects for people aged 55 to 65.¹ Among Swedish lottery players, winning a prize modestly reduces earnings; the drop is immediate, persistent, and similar across age, education and sex.² Both findings say leisure is a normal good, and both say the income effect is modest.

Hours over the long run. Across countries, hours worked have fallen by a little under half a percent a year for about 150 years as wages grew. Boppart and Krusell show that this is what happens when the income effect of higher wages slightly outweighs the substitution effect; the postwar United States, where hours stopped falling, is the exception.³

Average annual hours actually worked per worker

Selected OECD countries, all workers

• Canada
• United States
• France
• Germany
• Japan
• United Kingdom

Average annual hours actually worked per worker fell in all six countries between 1970 and 2025: in Canada from 1,925 to 1,687, in Germany from 1,960 to 1,332 and in Japan from 2,243 to 1,598. The OECD advises comparing trends over time, not levels across countries.Source: OECD Data Explorer, Average annual hours actually worked per worker (OECD.ELS.SAE, DSD_HW@DF_AVG_ANN_HRS_WKD). Retrieved 2026-10-23.

Show the data and notes

Total hours actually worked in the year ÷ average number of people in employment (employees and self-employed). The OECD advises using these data to compare trends over time, not levels across countries, because national sources and methods differ. Rounded to whole hours, the OECD's published precision.

Period	Canada	United States	France	Germany	Japan	United Kingdom
1970	1,925	1,949	1,993	1,960	2,243	1,775
1971	1,912	1,936	1,990	1,929	2,239	1,740
1972	1,904	1,933	1,937	1,906	2,228	1,709
1973	1,898	1,934	1,920	1,877	2,201	1,760
1974	1,891	1,903	1,888	1,838	2,137	1,725
1975	1,872	1,882	1,863	1,801	2,112	1,720
1976	1,862	1,884	1,889	1,813	2,128	1,704
1977	1,834	1,888	1,850	1,796	2,129	1,687
1978	1,836	1,879	1,819	1,777	2,123	1,669
1979	1,841	1,877	1,816	1,765	2,126	1,661
1980	1,827	1,859	1,806	1,746	2,121	1,619
1981	1,812	1,855	1,786	1,724	2,106	1,567
1982	1,789	1,847	1,714	1,713	2,104	1,581
1983	1,779	1,867	1,696	1,700	2,095	1,568
1984	1,789	1,884	1,690	1,689	2,108	1,583
1985	1,795	1,883	1,654	1,666	2,093	1,613
1986	1,797	1,875	1,648	1,647	2,097	1,615
1987	1,807	1,884	1,659	1,624	2,096	1,605
1988	1,808	1,884	1,667	1,619	2,092	1,642
1989	1,802	1,895	1,651	1,596	2,070	1,631
1990	1,797	1,878	1,645	1,573	2,031	1,617
1991	1,775	1,868	1,638	1,554	1,998	1,615
1992	1,772	1,867	1,635	1,565	1,965	1,583
1993	1,769	1,876	1,627	1,540	1,905	1,577
1994	1,778	1,887	1,623	1,537	1,898	1,586
1995	1,775	1,886	1,579	1,529	1,884	1,586
1996	1,790	1,887	1,575	1,516	1,892	1,586
1997	1,802	1,894	1,574	1,506	1,865	1,586
1998	1,797	1,892	1,565	1,503	1,842	1,582
1999	1,795	1,889	1,561	1,490	1,810	1,572
2000	1,789	1,880	1,542	1,465	1,821	1,558
2001	1,775	1,860	1,523	1,457	1,809	1,563
2002	1,757	1,854	1,490	1,448	1,798	1,543
2003	1,747	1,844	1,493	1,443	1,799	1,534
2004	1,757	1,845	1,517	1,443	1,785	1,534
2005	1,747	1,842	1,519	1,432	1,777	1,544
2006	1,745	1,847	1,503	1,452	1,786	1,536
2007	1,745	1,842	1,525	1,454	1,785	1,541
2008	1,742	1,830	1,532	1,447	1,771	1,525
2009	1,710	1,799	1,520	1,407	1,714	1,516
2010	1,715	1,810	1,528	1,425	1,733	1,507
2011	1,711	1,820	1,534	1,427	1,728	1,515
2012	1,721	1,827	1,528	1,406	1,745	1,531
2013	1,714	1,825	1,513	1,396	1,734	1,534
2014	1,709	1,830	1,504	1,400	1,729	1,542
2015	1,710	1,831	1,504	1,402	1,719	1,525
2016	1,705	1,822	1,507	1,396	1,714	1,541
2017	1,694	1,820	1,492	1,388	1,709	1,536
2018	1,704	1,826	1,500	1,381	1,680	1,536
2019	1,693	1,823	1,504	1,372	1,644	1,537
2020	1,658	1,800	1,391	1,314	1,597	1,364
2021	1,691	1,819	1,469	1,341	1,607	1,498
2022	1,693	1,810	1,498	1,343	1,607	1,532
2023	1,694	1,805	1,503	1,339	1,611	1,524
2024	1,697	1,796	1,509	1,334	1,617	1,538
2025	1,687	1,800	1,498	1,332	1,598	1,533

Common mistakes

Traps on exams

• Moving the endowment point when the wage changes. $E = (T, V)$ stays put; the budget line rotates around it. Only a change in $V$ moves $E$.
• Putting $Q$ on the wrong curve. In the course’s decomposition, $Q$ is on the new indifference curve, tangent to a line with the old slope.
• Concluding that a raise must increase hours. Only the substitution effect is certain to raise hours; with leisure normal, the income effect works against it.
• Calling the effect of a change in $V$ a substitution effect. A change in non-labour income leaves the price of leisure unchanged, so it has only an income effect.

On the exam

Draw the old and new budget lines through $E$, the two indifference curves, and $DD$ parallel to the old line. Label $P$, $Q$ and $R$, mark the income effect ($P$ to $Q$) and the substitution effect ($Q$ to $R$) along the leisure axis, and finish with one sentence saying which is larger and what happens to hours $h = T - L$.

Check yourself

1.

The wage rises and leisure is a normal good. Which statement about the effect on hours of work is correct?

1The substitution effect raises hours, the income effect lowers them, and the total effect is ambiguous2Both effects raise hours, so hours rise3Both effects lower hours, so hours fall4The substitution effect lowers hours and the income effect raises them

Check answer

2.

The wage falls and leisure is a normal good. What happens to hours of work?

1The substitution effect lowers hours and the income effect raises them, so hours may rise or fall2Hours must fall, because work now pays less3Hours must rise, because the worker is poorer4Nothing, because the endowment point does not move

Check answer

3.

Leisure is a normal good and a worker's wage rises. Which outcomes are consistent with the labour-leisure model? Select all that apply.

Select all that apply.

1Hours of work rise2Hours of work fall3Hours of work do not change4The worker reaches a lower indifference curve

Check answer

Practise more questions on this topic

Sources

1. Imbens, G. W., Rubin, D. B. and Sacerdote, B. I. (2001). Estimating the effect of unearned income on labor earnings, savings, and consumption: Evidence from a survey of lottery players. American Economic Review, 91(4), 778 to 794. doi:10.1257/aer.91.4.778. ↩

2. Cesarini, D., Lindqvist, E., Notowidigdo, M. J. and Östling, R. (2017). The effect of wealth on individual and household labor supply: Evidence from Swedish lotteries. American Economic Review, 107(12), 3917 to 3946. doi:10.1257/aer.20151589. ↩

3. Boppart, T. and Krusell, P. (2020). Labor supply in the past, present, and future: A balanced-growth perspective. Journal of Political Economy, 128(1), 118 to 157. NBER working paper 22215. ↩