Chapter 86: Workplace Incentives, Efficiency Wages, Tournaments, and Contracts. The Encyclopedia of Economic Principals, interactive companion

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

Monitoring, joblessness, and the effort decision

When does the threat of dismissal make a worker exert effort?

The wage premium disciplines only through the rent a dismissal destroys. Faster reemployment shrinks that rent; better monitoring raises the chance of losing it.

$Equation, written in LaTeX: qR\geq c.$

$Equation, written in LaTeX: R=3(500)=1{,}500\text{ units}.$

$Equation, written in LaTeX: qR=0.20(1{,}500)=300\text{ units}.$

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c = 300 is the monthly effort cost, q the probability shirking is detected and R the rent lost on dismissal: the 500-unit monthly premium times the expected jobless months.

Predict first. If the jobless spell drops to one month, does Lee still exert effort at q = 0.20?

Your prediction Yes No

Detection probability

Expected jobless months

Figure: Monitoring, joblessness, and the effort decision. Two bars: expected forfeiture 300 units beside the effort cost of 300 units. — Detection probability: 0.2, Expected jobless months: 3
Constructed example: the chapter's hypothetical values are c = 300, the 500 premium, q = 0.20 and 0.60 and spells of 3 and 1 months; q = 0.40 and a 2-month spell are added.

Rent lost R: 1,500
Expected forfeiture qR: 300
Effort cost c: 300
Discipline: Just binds (tie)

Hypothetical warehouse from the chapter. With 3 expected jobless months the rent at stake is 3 x 500 = 1,500 units, and detection at 0.20 makes the expected forfeiture 0.20 x 1,500 = 300 against an effort cost of 300, so the constraint just binds (a tie) and effort is only weakly supported.

Worked steps

R = 3 x 500 = 1,500 units
qR = 0.20 x 1,500 = 300 units
Compare: 300 = 300, so the constraint just binds (a tie) and effort is only weakly supported

Use the idea

Read a wage premium together with monitoring and reemployment prospects, never alone.

Where the conclusion applies

No discounting, a fixed premium and detection probability, and dismissal as the only sanction.

Check your understanding: With q = 0.40 and two jobless months, does discipline hold?

R = 1,000 and qR = 400 > 300, so effort is supported.

Chapter 86 source: section "Efficiency-wage discipline mechanism".

Demonstration 2 of 4

The no-shirking wage floor

How high must pay be to prevent shirking, and when does that floor exceed what the job is worth?

The floor rises when an outside job is easy to find and falls when shirking is more likely to be caught. A tight labor market can push the floor above what the job produces.

$Equation, written in LaTeX: w\geq b+c+\frac{(r+s+a)c}{q}.$

$Equation, written in LaTeX: w_{NS}=36+4+\frac{(0.05+0.10+0.50)4}{0.25}=50.4.$

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b = 36 is the value of unemployment, c = 4 the effort cost, r = 0.05 the discount rate, s = 0.10 the separation rate, a the job-finding rate and q the detection hazard (thousands per year).

Predict first. If job finding doubles to 1.00, does the floor exceed the job's value of 54?

Your prediction Yes No

Detection hazard q

Job-finding rate a

Figure: The no-shirking wage floor. One stacked bar: 36 unemployment value, 4 effort cost and a rent term of 10.4, totalling 50.4, against a job value line at 54. — Detection hazard q: 0.25, Job-finding rate a: 0.5
Constructed example: the chapter's hypothetical values are b = 36, c = 4, r = 0.05, s = 0.10, a = 0.50 and 1.00, q = 0.25 and 0.50 and the job value 54; a = 0.75 is added.

Rent term: 10.4
No-shirking wage w_NS: 50.4
Feasible against 54: Yes

Hypothetical workplace from the chapter (thousands per year). With detection 0.25 and job finding 0.50, w_NS = 36 + 4 + 0.65 x 4 / 0.25 = 50.4, so the floor of 50.4 is below the job's value of 54 and the contract is feasible.

Worked steps

r + s + a = 0.05 + 0.10 + 0.50 = 0.65
Rent term = 0.65 x 4 / 0.25 = 10.4
w_NS = 36 + 4 + 10.4 = 50.4
Compare with 54: the floor of 50.4 is below the job's value of 54 and the contract is feasible

Use the idea

In a hot labor market, expect either higher pay, more monitoring or other sanctions to keep effort; the same wage no longer disciplines.

Where the conclusion applies

Risk neutrality, the stated units and value equations, and constant rates.

Check your understanding: With q = 0.50 and a = 0.75, what is w_NS?

36 + 4 + 0.90 x 4 / 0.50 = 40 + 7.2 = 47.2.

Chapter 86 source: section "No-shirking efficiency wage".

Demonstration 3 of 4

Back-loaded pay as a bond

How does paying less early and more late deter shirking?

Early shortfalls finance a late premium, so a worker caught shirking loses a claim worth more than the outside path. The bond works only if detection is likely enough and the firm's promise is credible.

$Equation, written in LaTeX: c\leq q(V_{t+1}-V_{t+1}^{out}).$

$Equation, written in LaTeX: 0.25(15{,}000)=3{,}750\text{ units}.$

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Maria produces 60,000 a year and is paid 45,000, 55,000 and 80,000. V_t+1 is the remaining promised pay, V_t+1^out the outside path, q the detection probability and c the effort cost saved by shirking.

Predict first. Does q = 0.10 still deter shirking that saves 3,000?

Your prediction Yes No

Detection probability

Effort cost saved by shirking

Figure: Back-loaded pay as a bond. Left: pay of 45, 55 and 80 thousand against flat productivity of 60. Right: expected forfeiture 3,750 beside effort saved 3,000. — Detection probability: 0.25, Effort cost saved by shirking: 3000
Constructed example: the chapter's hypothetical values are the pay path, productivity 60,000, the 15,000 claim, q = 0.25 and 0.10 and 3,000 saved; q = 0.40 and 4,000 saved are added.

Claim at stake: 15,000
Expected forfeiture: 3,750
Effort cost saved: 3,000
Verdict: Effort

Hypothetical three-year job from the chapter. Back-loaded pay leaves 15,000 units at stake after year one; with detection 0.25 the expected forfeiture is 0.25 x 15,000 = 3,750 against 3,000 of effort saved, so the bond supports effort.

Worked steps

Remaining promised pay = 55,000 + 80,000 = 135,000; outside path = 2 x 60,000 = 120,000
Claim at stake = 135,000 - 120,000 = 15,000
Expected forfeiture = 0.25 x 15,000 = 3,750
Compare: 3,750 > 3,000, so the bond supports effort

Use the idea

Check both sides of a deferred-pay scheme: the worker's expected loss from shirking and the firm's temptation to dismiss before paying the premium.

Where the conclusion applies

No discounting, fixed productivity and outside pay, and an enforceable final-year payment.

Check your understanding: With q = 0.25 and effort saved of 4,000, does the bond hold?

0.25 x 15,000 = 3,750 < 4,000, so shirking pays.

Chapter 86 source: section "Deferred-compensation bonding".

Demonstration 4 of 4

Prize spreads: effort and sabotage

How does widening the prize spread change productive effort and sabotage?

A wider spread raises the return to anything that improves the chance of winning, including harming the rival. Restoring effort under noise can activate destructive behavior.

$Equation, written in LaTeX: \Delta W\frac{\partial\Pr(i\text{ wins})}{\partial e_i},$

$Equation, written in LaTeX: 0.10(8{,}000)=800\text{ units}.$

$Equation, written in LaTeX: 0.03(16{,}000)=480\text{ units},$

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Delta W is the prize spread (winner minus loser pay). A productive action costs 600 and raises the chance of winning by the slope set here; sabotage costs 300, raises it by 0.03 and destroys 1,000 units of customer value.

Predict first. Doubling the spread to 16,000 under high noise (slope 0.05): which behaviors pay?

Your prediction Productive action only Sabotage only Both

Prize spread

Productive slope (noise)

Productive return: 800
Productive action: Taken
Sabotage return: 240
Sabotage: Not taken

Hypothetical managers from the chapter with a prize spread of 8,000. The productive action returns 0.10 x 8,000 = 800 against a cost of 600, so it is taken; sabotage returns 0.03 x 8,000 = 240 against 300, so it is not taken. Each act of sabotage also destroys 1,000 units of customer value.

Worked steps

Productive: 0.10 x 8,000 = 800 > 600, taken
Sabotage: 0.03 x 8,000 = 240 < 300, not taken

Use the idea

Before widening a prize spread, list the cheapest ways to raise one's rank and check which of them destroy value.

Where the conclusion applies

Linear win-probability slopes held locally valid; costs and harm as stated.

Check your understanding: At a spread of 12,000 and slope 0.05, are the productive action and sabotage chosen?

Productive 0.05 x 12,000 = 600, exactly its cost (indifferent); sabotage 0.03 x 12,000 = 360 > 300, chosen.

Chapter 86 source: section "Tournament incentives".

Monitoring, joblessness, and the effort decision

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

The no-shirking wage floor

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Back-loaded pay as a bond

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Prize spreads: effort and sabotage

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies