Leveraging Overtime Thresholds to Equalize Workload Distribution

How overtime cost multipliers and maximum legal working hours create economic pressure toward equal distribution of employment across the population.

Abstract

Most labor markets exhibit a paradox: some workers are overworked while others are underemployed or unemployed. This paper argues that overtime thresholds (the point at which extra hours cost employers a premium) and maximum legal working hours are not just worker protections - they are distribution mechanisms. When properly calibrated, they make it economically rational for employers to hire additional workers rather than overwork existing ones, pushing the system toward a more equal distribution of labor.

1. The problem: unequal workload distribution

In a simplified labor market with:

• N available workers
• W total hours of work to be done
• H_avg = W / N average hours per worker if work were equally distributed

The current reality is far from equal. The distribution of hours worked follows an uneven pattern. The table below is a stylized illustration - actual shares vary significantly by country, sector, and regulation. Countries with strong overtime laws (e.g., France) have a smaller overworked share; countries with weak enforcement (e.g., Japan, US) have a larger one.

Sources: OECD Employment Outlook (2023), Eurostat Labour Force Survey, ILO Working Time and Work Organisation reports. Ranges reflect variation across OECD countries.

Why does this happen? Hiring a new employee has high fixed costs (recruitment, training, benefits, onboarding). For an employer, it is often cheaper to pay overtime to an existing worker than to hire and onboard a new one - unless the overtime premium is high enough to offset those fixed costs.

2. The overtime threshold as a distribution lever

2.1 The employer's cost function

Let's define the employer's cost to get H total hours of work done:

• c = base hourly cost per worker (wage + benefits + overhead)
• T = overtime threshold (e.g., 35h or 40h per week)
• m = overtime multiplier (e.g., 1.25, 1.5, or 2.0)
• F = fixed cost per employee (recruitment, training, admin, workspace), amortized per period - if hiring costs €10,000 and average tenure is 3 years, then F ≈ €64/week

Note on amortization: Recruitment and training are one-time costs, not recurring. The model uses F amortized over expected employment duration so that the per-period comparison with overtime cost is fair. A high-turnover industry has a higher effective F per week than a low-turnover one, even with the same hiring costs.

Option A - Overwork existing workers:

For k workers each doing H/k hours, where H/k > T:

Cost_A = k × [c × T + c × m × (H/k - T) + F]
       = k × c × T + c × m × (H - kT) + k × F

Option B - Hire one more worker (k+1 workers, each doing H/(k+1) hours):

Assuming H/(k+1) ≤ T (the new hire brings everyone below the overtime threshold):

Cost_B = (k+1) × [c × H/(k+1) + F]
       = c × H + (k+1) × F

2.2 The tipping point

The employer hires an additional worker when Cost_B < Cost_A:

c × H + (k+1) × F < k × c × T + c × m × (H - kT) + k × F

Simplifying (let S = H/k - T, the overtime hours per current worker):

F < c × S × (m - 1)

This gives us the critical multiplier - the overtime rate at which hiring becomes cheaper than overworking:

m_critical = 1 + F / (c × S)
           = 1 + F / (c × (H/k - T))

Reading the formula: If amortized fixed cost F = €64/week and c = €20/hour, then at S = 5 overtime hours/worker: m_critical = 1 + 64/(20 × 5) = 1.64. Any multiplier above 1.64 makes hiring cheaper. At S = 10 hours: m_critical = 1.32 - less overtime is needed to trigger hiring when workers are more overloaded.

Key insight: The higher the overtime multiplier m, the fewer overtime hours an employer will tolerate before hiring. The overtime threshold T determines when this pressure kicks in. And the longer workers stay (lower amortized F), the easier it is to justify hiring.

2.3 Progressive overtime: increasing pressure

Some jurisdictions use progressive overtime rates that escalate with excess hours:

A progressive schedule creates increasing marginal cost for each additional overtime hour, making the cost curve convex. This means the employer hits the tipping point faster with each extra hour.

3. Maximum legal hours as a hard cap

While overtime multipliers create soft economic pressure, maximum legal working hours create a hard boundary:

3.1 The hard cap as a forcing function

Without a maximum, a high-enough wage premium could keep an employer using a single worker indefinitely. The legal maximum ensures that beyond a certain point, the employer has no choice but to distribute work:

If H_total > k × H_max → must hire at least ⌈H_total / H_max⌉ workers

This creates a minimum workforce size for any given amount of work, regardless of cost preferences.

3.2 Combined effect

The overtime multiplier and legal maximum work together as a two-stage mechanism:

1. Stage 1 (soft): Overtime costs make additional hiring economically attractive
2. Stage 2 (hard): Legal maximums make additional hiring legally required

              Cost per hour
                  ▲
                  │            ╱ Hard cap
            ×2.0  │          ╱  (illegal)
                  │        ╱
            ×1.5  │      ╱
                  │    ╱
            ×1.25 │  ╱
                  │╱
            ×1.0  │─────────
                  └──────────────────► Hours/worker
                  0    T    T+8  T+16  H_max

4. Modeling the equilibrium

4.1 Optimal workforce size

For a firm with total work demand W hours per week, the optimal number of workers k* minimizes total cost:

k* = argmin_k [ k × F + c × min(W/k, T) × k + c × m × max(W/k - T, 0) × k ]
     subject to: W/k ≤ H_max

As m increases, k* increases - the firm hires more workers, each working fewer hours.

As H_max decreases, k* increases - the firm is forced to spread work across more people.

4.2 Population-level distribution

At the macroeconomic level, if all firms face the same overtime rules, the aggregate effect is a compression of the hours distribution:

• Variance of hours worked decreases
• Mean hours per employed worker decreases
• Employment rate increases (assuming demand for work remains constant - see §5.5 for when this doesn't hold)

Under the simplifying assumptions that all labor is substitutable and total work demand W is fixed, the Gini coefficient of hours worked approaches zero as:

• m → ∞ (overtime becomes prohibitively expensive)
• H_max → H_avg (maximum approaches the average)

4.3 The ideal convergence (theoretical limit)

In the theoretical limit, if T = H_avg, m is sufficiently high, and all workers are interchangeable:

Every worker works exactly W/N hours
Gini coefficient of hours = 0
Employment rate = 100% (of those seeking work)

This is the equal distribution equilibrium - achieved not by mandate, but by economic incentive.

Important caveat: This limit is unreachable in practice. Not all work is divisible (a 12-hour surgery cannot be split into two 6-hour surgeries without risk), not all workers are substitutable (§5.2), and total demand is not fixed (§5.5). The model shows the direction of the effect and the levers available, not a reachable end state. The practical goal is reducing the Gini coefficient, not eliminating it.

5. Practical considerations and trade-offs

5.1 Fixed costs resist distribution

The main counterforce is fixed per-employee cost F. If F is high relative to overtime costs, employers tolerate significant overtime before hiring. Policies that reduce F amplify the distribution effect:

• Simplified hiring/firing procedures
• Shared benefit pools (universal healthcare vs. employer-provided)
• Reduced administrative burden per employee
• Co-working spaces reducing per-worker facility costs

5.2 Skill specificity

Not all work is interchangeable. If a task requires a rare skill, the employer cannot simply "hire another worker." This creates inelastic demand for specific workers, reducing the distribution effect.

Mitigation: Investment in education and training widens the pool of qualified workers, making labor more substitutable and the distribution mechanism more effective.

5.3 The informal economy escape valve

If overtime regulations are too aggressive, work may shift to the informal economy where no rules apply. The optimal policy finds the multiplier that maximizes formal employment distribution without pushing work underground.

5.4 Demand elasticity: W is not fixed

The model assumes total work demand W stays constant as overtime becomes expensive. In practice, firms facing higher labor costs may:

• Automate tasks that were previously done by overtime workers
• Offshore work to jurisdictions with weaker overtime regulation
• Reduce output by cutting product lines or services
• Increase prices, reducing consumer demand, which in turn reduces W

This is the central empirical debate around France's 35-hour week (loi Aubry, 1998–2000). Proponents point to net job creation; critics argue that GDP growth slowed and firms absorbed costs through wage moderation rather than new hiring.

The redistribution effect of overtime policy depends on how elastic labor demand is. In sectors with low substitutability (healthcare, education), demand is inelastic and the mechanism works well. In sectors exposed to international competition (manufacturing, tech), demand is elastic and work may simply leave the jurisdiction.

Implication for calibration: Overtime thresholds and multipliers should be set with awareness of sectoral elasticity. A blanket policy may work for domestic services but harm export-oriented industries. Sector-specific thresholds or transition periods may be necessary.

5.5 Part-time proliferation

If overtime is very expensive, the rational employer response isn't only "hire full-time workers" - it can also be "hire part-time workers below the threshold T." This creates a risk of:

• Workers with insufficient hours to earn a living wage
• Fragmented schedules across multiple employers
• Loss of benefits tied to full-time status
• A precarious underclass that is technically "employed" but worse off than before

This failure mode was observed in some sectors after France's 35-hour reform, particularly in retail and hospitality. The distribution of hours improved on paper (lower Gini) while the distribution of income worsened.

Mitigation: Minimum contract hour guarantees, pro-rata benefits for part-time workers, and penalties for excessive use of short-hour contracts. These are listed in §7.5 as complementary measures, but they are arguably a prerequisite for the overtime mechanism to produce genuine equity rather than statistical redistribution.

5.6 Productivity effects

Shorter individual hours can increase per-hour productivity (reduced fatigue, better focus), partially offsetting the fixed-cost increase of more workers. Studies from Sweden's 6-hour workday experiments and France's 35-hour week suggest productivity per hour rises when total hours fall - though total output per worker decreases.

6. The overtime tax: a self-funding redistribution mechanism

The overtime multiplier makes overwork expensive for the employer, but the premium goes to the worker - it doesn't directly fund the system that supports those who have no work. A dedicated overtime tax closes this loop.

6.1 The mechanism

Introduce a tax t on every overtime hour, paid by the employer on top of the overtime wage, and earmarked exclusively for unemployment benefits:

Overtime tax per hour = c × t    (where t is the tax rate, e.g. 0.10–0.25)

The employer's total cost for one overtime hour becomes:

Cost_overtime_hour = c × m + c × t = c × (m + t)

This tax revenue flows directly into the unemployment insurance fund:

Revenue = t × c × O_total

Where O_total is the total overtime hours worked across the economy.

6.2 The self-balancing property

This creates a negative feedback loop - a system that corrects itself:

More overtime → more tax revenue → more funding for unemployment benefits
                                 → more support for retraining/hiring
                                 → more workers available
                                 → less overtime needed
                                 → less tax revenue needed
                                 → equilibrium

The mechanism is self-balancing because:

1. When unemployment is high: There is political and economic pressure to increase overtime taxes. This makes overtime more expensive, pushing employers to hire from the unemployed pool instead. The tax revenue funds training and benefits for the transition.

2. When unemployment is low: Less overtime tax revenue is collected (because there's less overtime), but less is needed (because fewer people need benefits). The system naturally scales down.

3. At equilibrium: Overtime is minimal, the tax collects little, and little is needed - work is already well-distributed.

6.3 Compared to general taxation

Traditional unemployment benefits are funded from general income tax or payroll contributions. Percentage-based payroll taxes are neutral between one worker doing 40 hours and two workers doing 20 hours each (same total wage, same total tax). However, fixed per-employee contributions - social security minimums, mandatory insurance, administrative registration - do penalize headcount. The more workers on the payroll, the higher the total fixed contribution, regardless of hours.

An overtime-specific tax targets this differently:

The overtime tax aligns the funding mechanism with the policy goal: the behavior you want to reduce (overtime) directly funds the outcome you want to achieve (employing the unemployed). It also partially offsets the fixed per-employee costs that resist redistribution (§5.1) - the overtime tax revenue can subsidize hiring costs, reducing effective F.

6.4 Calibrating the tax rate

The tax rate t should be set so that the total overtime tax revenue covers the unemployment benefit expenditure:

t × c × O_total ≥ U × B

Where:

• U = number of unemployed receiving benefits
• B = average benefit per unemployed person
• O_total = total overtime hours in the economy

Solving for t:

t ≥ (U × B) / (c × O_total)

The boundary problem: As the system succeeds and overtime drops toward zero, O_total → 0 in the denominator. If any unemployment remains (U > 0), the required tax rate explodes toward infinity. This is not a failure of the concept but a signal that the overtime tax alone cannot fund unemployment benefits when overtime is nearly eliminated.

In practice, this means:

1. The overtime tax works as a transitional funding mechanism - effective when there is significant overtime to tax, which is precisely when the redistribution is most needed.
2. A floor mechanism is necessary: Below a minimum O_total, residual unemployment benefits should be funded from general revenue or a flat minimum employer contribution. The overtime tax supplements, not replaces, the baseline safety net.
3. The tax rate should have a cap (e.g., t_max = 0.30) to prevent distortionary spikes during economic shocks that temporarily reduce overtime while increasing unemployment.

6.5 Political viability

This approach has a clear narrative advantage: the practice of overwork is funding the support for those who have no work. It reframes overtime not as a personal choice but as a systemic cost - one that the employer should bear and that society should redirect.

It also avoids the classic objection to unemployment benefits ("why should I pay for people who don't work?") by tying the funding specifically to the practice that creates the imbalance.

Tax incidence caveat: The employer pays the tax, but may pass the cost through in three ways: (1) lower base wages for workers, (2) higher prices for consumers, or (3) reduced profits for shareholders. The actual incidence depends on the relative bargaining power of each group and the elasticity of demand for the firm's output. In sectors with strong unions and inelastic demand (utilities, healthcare), employers absorb more. In competitive sectors with elastic demand (retail, gig economy), workers and consumers bear more. A full analysis of incidence is beyond this paper's scope, but policymakers should monitor whether base wages decline after implementation - if they do, the tax is effectively being paid by the workers it is meant to protect.

7. Policy recommendations

Based on this framework, the following calibration maximizes workload distribution:

7.1 Overtime threshold (T)

Set T at or slightly below the target average hours:

T ≤ W_national / N_workforce

This ensures that any firm requiring above-average hours per worker immediately faces overtime costs.

7.2 Overtime multiplier (m)

Use a progressive schedule calibrated to fixed costs:

m₁ = 1 + F / (c × band₁)    for first overtime band
m₂ = m₁ × 1.5               for second band
m₃ = m₂ × 1.5               for third band

Where band is the width of each overtime tier (e.g., 5 hours). This ensures that by the second or third band, hiring is always cheaper.

7.3 Maximum hours (H_max)

Set a hard cap that limits the damage when economic incentives fail:

H_max = T + sum(bands)

Typically T + 10h to T + 15h - enough flexibility for genuine peaks, tight enough to prevent structural overwork.

7.4 Overtime tax rate (t)

Set the earmarked overtime tax so that revenue covers unemployment expenditure (see §6.4):

t = min(t_max, (U × B) / (c × O_total))

Where t_max is a regulatory cap (e.g., 0.25–0.30). Below a minimum overtime volume, fund residual unemployment from general revenue. Review annually and reduce as distribution improves.

7.5 Complementary measures

8. Conclusion

Overtime thresholds and maximum working hours are more than individual protections - they are macroeconomic distribution tools. The overtime multiplier creates a cost gradient that makes equal distribution the economically rational choice, while the legal maximum provides a hard floor on workforce size.

The path to equal workload distribution is not to mandate how much each person works, but to make the cost structure favor spreading work across more people. By calibrating four parameters - threshold (T), multiplier (m), maximum (H_max), and overtime tax (t) - policymakers can tune the labor market toward a more equal equilibrium where fewer people are overworked and fewer are left without work.

The overtime tax completes the circuit: the very practice that creates unemployment - overworking some while excluding others - directly funds the support system for those excluded. The mechanism is self-balancing: as work distributes more evenly, overtime shrinks, the tax collects less, and less is needed.

The math is clear: when overtime is expensive enough, maximums are tight enough, and the cost of overwork funds the alternative, the cheapest option for every employer is to hire more people and work each of them less. Individual self-interest, channeled through the right cost structure, produces collective equity.

References and further reading

• Cahuc, P. & Zylberberg, A. - Labor Economics (MIT Press) - theoretical foundations of labor demand and overtime
• Cette, G., Chang, S. & Konte, M. - "The decreasing returns of working time" (2011) - productivity and hours worked
• EU Working Time Directive 2003/88/EC - legal framework for maximum hours in Europe
• Crépon, B. & Kramarz, F. - "Employed 40 hours or not employed 39: Lessons from the 1982 mandatory reduction of the workweek" - natural experiment on France's hours reduction
• Pencavel, J. - "The Productivity of Working Hours" (2014) - Stanford study on diminishing returns of long hours
• Hunt, J. - "Has Work-Sharing Worked in Germany?" (1999) - Kurzarbeit and employment effects
• Chemin, M. & Wasmer, E. - "Using Alsace-Moselle Local Laws to Build a Difference-in-Differences Estimation Strategy of the Employment Effects of the 35-Hour Workweek Regulation in France" (2009) - demand elasticity and employment effects
• OECD Employment Outlook (2023) - cross-country data on hours worked distribution
• Eurostat Labour Force Survey - EU working hours statistics by country and sector
• Hamermesh, D. - Labor Demand (Princeton University Press) - theory of labor demand elasticity and substitution