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Social Choice and Welfare

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28.03.2018 | Original Paper

Working time regulation, unequal lifetimes and fairness

verfasst von: Marie-Louise Leroux, Gregory Ponthiere

Erschienen in: Social Choice and Welfare | Ausgabe 3/2018

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Abstract

We examine the redistributive impact of working time regulations in an economy with unequal lifetimes. We first compare the laissez-faire equilibrium with the ex post egalitarian optimum, where the realized lifetime well-being of the worst off (usually the short-lived) is maximized, and show that, unlike the laissez-faire, this social optimum involves an increasing working time age profile and equalizes the realized lifetime well-being of the short-lived and the long-lived. We then examine whether working time regulations can compensate the short-lived. It is shown that uniform working time regulations cannot improve the situation of the short-lived with respect to the laissez-faire, and can only reduce well-being inequalities at the cost of making the short-lived worse off. However, age-specific regulations involving lower working time for the young and higher working time for the old make the short-lived better off, even though such regulations may not fully eradicate well-being inequalities.

Vorheriger Artikel Income inequality measurement: a fresh look at two old issues

Nächster Artikel Cost asymmetry and incomplete information in a volunteer’s dilemma experiment

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See Askenazy (2013) for a survey of these studies.

Holmlund and Pencavel (1988) and Friesen (2000) show that a reduction in the working time is associated with a significant rise in the hourly wage in countries such as Sweden, the Netherlands and Canada.

Christensen et al. (2006) emphasize that about 1/4–1/3 of longevity inequalities are due to the genetic background, over which individuals have little control.

For the sake of presentation, our results are here given only for the case of affluent economies (where productivity is sufficiently high so that the long-lived is better off than the short-lived). See the manuscript for the results concerning poor economies (where productivity is so low that the long-lived is necessarily worse off than the short-lived).

The reason why imposing a uniform working time age profile cannot increase consumption or well-being at the young age in comparison to the laissez-faire is that the intratemporal arbitrage between labor and consumption is already solved optimally at the laissez-faire.

The capacity of age-specific working time regulations to bring well-being equality is here limited by the upper bound on the labor supply of the surviving old.

We abstract here from the childhood period, which is not relevant for the issue at stake.

We abstract from the retirement decision. See Fleurbaey et al. (2016) on the selection of fair retirement age under fixed working time.

Throughout this paper, we assume, without loss of generality, that $w>\bar{c} $. This assumption allows us to avoid extreme cases that are irrelevant for the issue at stake.

Indeed, substituting for constant consumption and labor profiles into the intertemporal budget constraint yields:

$$\begin{aligned} c^{LF}(1+\pi )=\ell ^{LF}w(1+\pi ). \end{aligned}$$

Thus the life expectancy $1+\pi $ can be simplified from both sides, making the laissez-faire consumption independent from $\pi $. But given the “final equivalence of labor and utility”, if consumption is independent from $\pi $ , labor supply is also independent from $\pi $.

Note that, since per period utility is here constant along the lifecycle, it follows that the utility of a short-lived individual $U^{SL}$ is here exactly equal to the gain in lifetime utility when the agent survives to the next period (i.e. $U^{LL}-U^{SL}$). This equality is due to the conjunction of three assumptions: no pure time preferences, age-independent labor disutility and a perfect annuity market. This implies that, at the laissez-faire equilibrium, per period utility is the same at each period of life. We come back on this point later on in the manuscript.

In the Appendix we derive, under standard functional forms for $u(\cdot )$ and $v\left( \cdot \right) $, the threshold for the wage rate w beyond which the long-lived are better off than the short-lived.

Note that, in order to do justice to the idea of compensating the worst-off, one cannot, in the present context, rely on a utilitarian social welfare function, since, as we showed in Sect. 3, this social criterion legitimates the laissez-faire and the resulting inequalities in realized lifetime well-being between short-lived and long-lived individuals.

In particular, the fact that a prematurely dead person expected to have a long life does not seem to be a relevant piece of information to assess his lifetime well-being.

The underlying intuition goes as follows. At the ex post egalitarian optimum, consumption and working time profiles are chosen so as to maximize the well-being of the short-lived, whereas at the laissez-faire, consumption and working time profiles are chosen in such a way as to maximize a weighted sum of the well-being of the short-lived and the well-being at the old age. Given that the resource constraint is the same in the two optimization problems, the short-lived must be better off at the ex post egalitarian optimum than at the laissez-faire.

By “uniform” working time regulations, we mean regulations that consist in imposing flat working time profiles, i.e., a constant quantity of worked hours along the life cycle (i.e., $\bar{\ell }_{y}=\bar{\ell }_{o}=\bar{\ell }$ ). Non-uniform (age-specific) working time regulations are studied in Sect. 6.

It should be stressed here that $\bar{\ell }$ does not denote an upper bound for the number of hours worked, but the exact number of hours worked. This assumption simplifies the presentation of results, and is also close to real economies where individuals generally work full time, i.e. at the level of the uniform regulation.

Given that the policy instrument considered here (a uniform working time $ \bar{\ell }$) is extremely basic, one can regard this social planning problem as a kind of “third-best problem” (since this involves strong restrictions on available policy instruments).

Such a dilemma is a direct consequence of both consumption smoothing and the restriction put on the instruments, that is, it is imposed that $\bar{\ell }$ must be the same for all workers, independently of whether these are young or old.

One can regard the social planning problem of Sect. 6 as a “second-best problem” since the set of policy instruments $\left( \bar{\ell }_{y},\bar{\ell }_{o}\right) $ is here less constrained that in the problem of Sect. 5.

Note, however, that, contrary to what happens under uniform working time regulations (Sect. 5), consumption smoothing does not imply here that utility per period of life is constant along the life cycle, since labor time varies with the age.

The working time is expressed in hours per week. Note that the maximum working time equals 80 h per week, which corresponds to 5 days of 16 h of daily work (leaving only 8 h for sleep and daily activities).

This coincides with the corner solution $\ell _{o}^{*}=1$ in Sect. 4. As shown on Fig. 1, this corner solution arises for $\beta $ lower than 15. For $\beta >15$, there is an interior solution, corresponding to $\ell _{o}^{*}<1$ in the model.

If social recognition from labor matters a lot, and if this social recognition is only achieved for a sufficiently large working time, this would probably restrict the extent of optimal differentiation of working time between the young and the old.

Askenazy P (2013) Working time regulation in France from 1996 to 2012. Camb J Econ 37(2):323–347CrossRef

Becker G, Philipson T, Soares R (2005) The quantity and the quality of life and the evolution of world inequality. Am Econ Rev 95(1):277–291CrossRef

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Chemin M, Wasmer E (2009) 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. J Labor Econ 27(4):487–524CrossRef

Christensen K, Johnson T, Vaupel J (2006) The quest for genetic determinants of human longevity: challenges and insights. Nat Rev Genet 7:436–448CrossRef

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Fleurbaey M, Leroux ML, Pestieau P, Ponthiere G (2016) Fair retirement under risky lifetime. Int Econ Rev 57(1):177–210CrossRef

Fleurbaey M, Maniquet F (2004) Compensation and responsibility. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, 1st edn, vol 2, chapter 22, pp 507–604

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Titel: Working time regulation, unequal lifetimes and fairness
verfasst von: Marie-Louise Leroux
Gregory Ponthiere
Publikationsdatum: 28.03.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 3/2018
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-018-1123-7

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