Incentive pay

Incentive pay links a worker’s earnings to a measure of performance: output (piece rates), rank among co-workers (tournaments) or years of good behaviour (deferred compensation). Each scheme raises effort the firm cannot observe directly, and each sorts workers: pay that rewards output attracts the workers who produce the most.

The principal-agent problem

The firm (the principal) wants effort; the worker (the agent) bears its cost. The firm sees output, which depends on effort and on luck, but not effort itself. Under a time rate, pay per hour with a minimum standard, an extra unit of effort earns the worker nothing once the standard is met, so effort stops there. A pay scheme that rises with output makes the worker weigh the value of extra effort against its cost.

Piece rates and time rates

A piece rate $r$ pays $r$ dollars per unit, so daily pay is $rq$. A time rate pays $w$ a day to anyone producing at least the standard $q_{\min}$. A worker who can produce $q$ units prefers the piece rate when $rq > w$, that is when

$$q > q_c = \frac{w}{r}.$$

Piece rate per unit (r)

$20

Cut-off output q_c = 200 / r

10.0 units

Pay of a 15-unit worker on piece rates

$300

Pay of a 9-unit worker on piece rates

$180

Open in Graph Lab

Figure 1. A time-rate firm pays $200 a day for at least 8 units; a piece-rate firm pays $20 a unit. Workers who can produce more than 10 units earn more on piece rates and sort into that firm; those producing 8 to 10 units take the time rate. A higher piece rate lowers the cut-off and draws more workers to piece rates.

Two effects follow when a firm switches to piece rates. The incentive effect: the same workers produce more because extra output now pays. The sorting effect: the firm attracts and keeps more productive workers, while less productive ones leave for time-rate jobs.

Piece rates are not always best. They work when output is easy to count and individual. They fail when quality matters and is hard to measure (workers rush), when output is a team product, when luck makes pay volatile for risk-averse workers, and when workers fear the ratchet effect: a firm that sees high output may cut the rate, so workers hold output down. Rewarding one measurable task also pulls effort away from tasks that are not measured.¹

Evidence. When Safelite Glass moved windshield installers from hourly wages to piece rates, output per worker rose 44 percent.² By Lazear’s own account, only about half of the rise came from incentives; the rest came from the change in who worked there.³ In a field experiment at a tree-planting firm, piece rates raised productivity by about 20 percent.⁴ Payroll records from a British Columbia tree-planting firm imply a structural incentive effect of 22.6 percent, part of it achieved by lower quality.⁵ In a study using personnel data, productivity was at least 50 percent higher under piece rates than under relative pay, where one worker’s effort lowers co-workers’ pay.⁶

Tournaments

In a tournament workers are paid by rank: the one with the most output wins the promotion and prize $W_1$, the rest get $W_2$. Output is effort plus luck. A worker raises effort until the prize spread times the extra probability of winning equals the marginal cost of effort:

$$(W_1 - W_2)\,\frac{\partial P}{\partial e} = MC(e).$$

With two equally able workers and normally distributed luck, $\partial P/\partial e \approx 0.4/\sigma$, where $\sigma$ is the standard deviation of the luck difference between them and 0.4 is the height of the standard normal density at zero.

Prize spread W₁ - W₂ ($ thousand)

$50k

Luck: standard deviation of the luck difference, σ (units of output)

10

Equilibrium effort e*

20.0 units

Extra chance of winning per unit of effort

4.0%

Marginal benefit of effort

$2.00k

Open in Graph Lab

Figure 2. With a $50,000 prize spread and $\sigma = 10$, one more unit of effort raises the chance of winning by 4 percentage points, worth $2,000, and effort settles at 20 units. Doubling luck to $\sigma = 20$ halves effort; a larger spread raises it.

Key idea

In a tournament the spread between prizes drives effort; the level of the prizes only has to be high enough to attract workers. The more luck matters, the wider the spread must be.

A wide spread has costs. Workers who compete for one prize gain from making rivals look bad, so where cooperation matters some pay compression is efficient.⁷ Prizes also grow with rank. In an elimination tournament, winning a round brings the option to compete for later prizes; at the top no further rounds remain, so the top prize must be disproportionately large to keep effort up.⁸ That is one explanation for the jump from vice-president to CEO pay.

The level and structure of prizes in PGA Tour events affect golfers’ scores.⁹ In data on more than two hundred firms and two thousand executives a year, executive pay patterns are consistent with tournaments.¹⁰

Executive pay

A chief executive is an agent of shareholders. Jensen and Murphy estimated that CEO wealth changed by $3.25 for each $1,000 change in shareholder wealth, a weak link.¹¹ Using later data, Hall and Liebman found a strong relationship between firm performance and CEO pay, coming almost entirely from CEOs’ holdings of stock and options.¹² Pay also rewards luck: CEO pay responds as much to a dollar of performance caused by shocks beyond the CEO’s control as to any other dollar, and better-governed firms pay less for luck.¹³

In Canada, the 100 highest-paid CEOs averaged $16.2 million in 2024, 248 times the average worker’s $65,548.¹⁴ Tournament theory reads part of this as the top prize that motivates every manager below.

Deferred compensation and mandatory retirement

Lazear’s model of deferred compensation explains why pay rises with age even when productivity does not.¹⁵ The firm pays less than the value of marginal product early in the career and more later. A young worker effectively posts a bond, and a worker caught shirking is fired and loses the high late pay, so the profile deters shirking. Competition for workers forces the present value of wages to equal the present value of $VMP_E$ over the career.

Slope of the wage profile ($ per hour per year of age)

$0.40

Wage at 20

$21.00

Wage at 65

$39.00

Wage minus reservation wage at 65

$9.00

Open in Graph Lab

Figure 3. With $VMP_E$ fixed at $30 an hour, a profile rising $0.40 a year pays $21 at 20 and $39 at 65; area A equals area B, so lifetime pay matches the flat contract. At 65 the reservation wage reaches $VMP_E$, so retiring then is efficient, but the wage is still $9 above it.

Because the late wage exceeds the reservation wage at the efficient retirement age $T$, the worker would never leave voluntarily. The contract must fix the end date: mandatory retirement. The model also needs a trustworthy firm, since a firm could fire older workers once they are overpaid; reputation restrains this.

Mandatory retirement has largely disappeared. The Supreme Court of Canada upheld it for university faculty in 1990,¹⁶ but Ontario ended it in December 2006¹⁷ and federal law ended it for federally regulated employers in December 2012.¹⁸ Alberta’s human rights law protects anyone aged 18 or older from age discrimination in employment, with exceptions for bona fide retirement or pension plans.¹⁹ In the United States, mandatory retirement ended for most workers in 1987 and for tenured professors in 1994;²⁰ afterwards the retirement rates of 70- and 71-year-old faculty fell by two-thirds, to about the rate of 69-year-olds.²¹ Lazear’s model predicts this: under a rising profile, older workers are overpaid, so without a fixed end date they stay.

Median employment income by age group, Canada

2024, people with employment income, both genders

15 to 24$13,400

25 to 34$49,400

35 to 44$62,800

45 to 54$67,500

55 to 64$52,700

65 and over$13,200

Median employment income rises steeply from the 20s to the late 40s and falls after 55, consistent with both human capital and deferred compensation. This is a single-year cross-section that includes part-time workers, so it is not one cohort's profile.Source: Statistics Canada, Table 11-10-0239-01, Income of individuals by age group, gender and income source, Canada, provinces and selected census metropolitan areas. Retrieved 2026-10-23.

Show the data and notes

Canadian Income Survey. Median employment income (wages, salaries, commissions and net self-employment income) among people with employment income (zeros excluded), in 2024 dollars. Includes part-time and part-year workers, which pulls down the medians of the youngest and oldest groups.

Category	Median employment income
15 to 24	$13,400
25 to 34	$49,400
35 to 44	$62,800
45 to 54	$67,500
55 to 64	$52,700
65 and over	$13,200

Worked example

1. Sorting. A time-rate firm pays $200 a day for at least 8 units; a piece-rate firm pays $20 a unit. The cut-off is $q_c = 200/20 = 10$. Ana can produce 15 units and would earn $20 \times 15 = 300$, so she chooses the piece rate. Ben can produce 9 units and would earn 180, so he takes the time rate.

2. Tournament effort. The spread is $50,000 and $\sigma = 10$, so one more unit of effort raises the chance of winning by $0.4/10 = 0.04$. The marginal benefit is $50{,}000 \times 0.04 = 2{,}000$ dollars. With $MC(e) = 100e$ dollars, effort is $e^* = 2{,}000/100 = 20$. If $\sigma$ doubles to 20, the marginal benefit falls to $1,000 and effort to 10; restoring effort to 20 requires a $100,000 spread.

3. Deferred compensation. $VMP_E = 30$ from 20 to 65 and $w(t) = 30 + 0.4(t - 42.5)$. Pay starts at $30 - 0.4(22.5) = 21$ and ends at $30 + 0.4(22.5) = 39$. Area A $= \tfrac{1}{2}(22.5)(9) = 101.25$ equals area B, so lifetime pay equals lifetime $VMP_E$ when there is no discounting.

Common mistakes

Traps on exams

• Crediting all of a productivity gain to effort. After a switch to piece rates, part of the gain is sorting: different workers, not harder work.
• Saying tournament effort depends on the prize level. It depends on the spread; the level matters only for attracting workers.
• Thinking deferred compensation underpays workers. Lifetime pay equals lifetime $VMP_E$; only the timing differs.
• Placing mandatory retirement where $w = VMP_E$. Efficient retirement is where the reservation wage reaches $VMP_E$; the contract is needed because the wage is still above the reservation wage there.

On the exam

For deferred compensation, draw $VMP_E$ flat, the wage profile crossing it from below, and the rising reservation wage meeting $VMP_E$ at $T$. Label the equal areas A and B and the gap between the wage and the reservation wage at $T$.

Check yourself

1.

A firm switches its installers from hourly pay to a piece rate and output per worker rises 44 percent. Which interpretation is correct?

1Part of the rise is an incentive effect (the same workers produce more) and part is sorting (the firm attracts and keeps more productive workers)2The whole rise is an incentive effect, because the workers' skills did not change3The whole rise is sorting, because effort does not respond to pay4The rise must reflect lower quality, because piece rates always reduce quality

Check answer

2.

In a two-person promotion tournament the winner gets $120,000 and the loser $80,000. The firm raises both prizes by $20,000. What happens to effort?

1It does not change, because the prize spread is still $40,0002It rises, because both prizes are higher3It falls, because the loser's prize is now more attractive4It doubles, because total prize money rose by $40,000

Check answer

3.

In Lazear's deferred compensation model, why does the contract need mandatory retirement?

1At the efficient retirement age the wage still exceeds the worker's reservation wage, so the worker would not leave voluntarily2At the efficient retirement age the worker's productivity falls to zero3Older workers are paid less than the value of their marginal product, so the firm wants to keep them4The worker's reservation wage exceeds the wage after age 40

Check answer

Practise more questions on this topic

Sources

1. Holmström, B. and P. Milgrom (1991). Multitask principal-agent analyses: Incentive contracts, asset ownership, and job design. Journal of Law, Economics, and Organization, 7 (special issue), 24 to 52. doi:10.1093/jleo/7.special_issue.24. ↩

2. Lazear, E. P. (2000). Performance pay and productivity. American Economic Review, 90(5), 1346 to 1361. doi:10.1257/aer.90.5.1346. ↩

3. Lazear, E. P. (2000). Personnel economics and economic approaches to incentives. HKCER Letters, 61. ↩

4. Shearer, B. (2004). Piece rates, fixed wages and incentives: Evidence from a field experiment. Review of Economic Studies, 71(2), 513 to 534. doi:10.1111/0034-6527.00294. ↩

5. Paarsch, H. J. and B. Shearer (2000). Piece rates, fixed wages, and incentive effects: Statistical evidence from payroll records. International Economic Review, 41(1), 59 to 92. IDEAS. ↩

6. Bandiera, O., I. Barankay and I. Rasul (2005). Social preferences and the response to incentives: Evidence from personnel data. Quarterly Journal of Economics, 120(3), 917 to 962. doi:10.1093/qje/120.3.917. ↩

7. Lazear, E. P. (1989). Pay equality and industrial politics. Journal of Political Economy, 97(3), 561 to 580. doi:10.1086/261616. ↩

8. Rosen, S. (1986). Prizes and incentives in elimination tournaments. American Economic Review, 76(4), 701 to 715. IDEAS. The model of rank-order pay is from Lazear, E. P. and S. Rosen (1981), Rank-order tournaments as optimum labor contracts, Journal of Political Economy, 89(5), 841 to 864. ↩

9. Ehrenberg, R. G. and M. L. Bognanno (1990). Do tournaments have incentive effects? Journal of Political Economy, 98(6), 1307 to 1324. doi:10.1086/261736. ↩

10. Main, B. G. M., C. A. O’Reilly III and J. Wade (1993). Top executive pay: Tournament or teamwork? Journal of Labor Economics, 11(4), 606 to 628. doi:10.1086/298309. ↩

11. Jensen, M. C. and K. J. Murphy (1990). Performance pay and top-management incentives. Journal of Political Economy, 98(2), 225 to 264. doi:10.1086/261677. ↩

12. Hall, B. J. and J. B. Liebman (1998). Are CEOs really paid like bureaucrats? Quarterly Journal of Economics, 113(3), 653 to 691. doi:10.1162/003355398555702. ↩

13. Bertrand, M. and S. Mullainathan (2001). Are CEOs rewarded for luck? The ones without principals are. Quarterly Journal of Economics, 116(3), 901 to 932. doi:10.1162/00335530152466269. ↩

14. Macdonald, D. (2026). Living the high life: A record-breaking year for CEO pay in Canada. Canadian Centre for Policy Alternatives. ↩

15. Lazear, E. P. (1979). Why is there mandatory retirement? Journal of Political Economy, 87(6), 1261 to 1284. doi:10.1086/260835. ↩

16. McKinney v. University of Guelph, [1990] 3 S.C.R. 229. ↩

17. Ending Mandatory Retirement Statute Law Amendment Act, 2005, S.O. 2005, c. 29, in force December 12, 2006. ↩

18. Keeping Canada’s Economy and Jobs Growing Act, S.C. 2011, c. 24, sections 165 to 169, in force December 15, 2012. ↩

19. Alberta Human Rights Act, R.S.A. 2000, c. A-25.5, sections 7 and 44. ↩

20. Age Discrimination in Employment Amendments of 1986, Pub. L. 99-592, 100 Stat. 3342. ↩

21. Ashenfelter, O. and D. Card (2002). Did the elimination of mandatory retirement affect faculty retirement? American Economic Review, 92(4), 957 to 980. doi:10.1257/00028280260344542. ↩