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Arguing about justice

 | 
Axel Gosseries
, 
Philippe Vanderborght

Cooperative justice and opportunity costs

Laurent de Briey

Résumé

Dans un article commun consacré à la justice linguistique, Ph. Van Parijs et moi-même avions essayé de définir un critère de justice coopérative permettant de déterminer une répartition des coûts de production d’un bien public entre des coopérants. Le critère proposé, soit une répartition des coûts proportionnels aux bénéfices retirés par chaque coopérant, ne prenait pas en considération les coûts d’opportunité. Après avoir montré cette non-prise en compte peut rendre la coopération inintéressante pour certains coopérants, le présent texte propose une révision de notre critère de justice coopérative intégrant les coûts d’opportunité.

Texte intégral

Introduction

1Some ten years ago, I published one of my first articles as Philippe co­author's. In 'Linguistic justice as cooperative justice' (de Briey & Van Parijs 2002; hereinafter BVP), we looked at the apportionment of the costs of creation of the public good represented by a common language. When Béa decides to learn the Al's language, Béa derives a benefit since she becomes able to communicate with Al. However, Al derives a benefit too without having made any effort. Would it not be fairer if he bore part of the costs of Béa's learning effort, by paying for some of her lessons for example? Would this also not be more efficient insofar as, in the absence of a contribution from Al, the cost borne by Béa might exceed the benefit she would derive from speaking the language of Al, but not the overall benefit that Al and Béa could derive from being able to communicate with one another? Could the non-contribution of Al in fact lead to a situation where both Al and Béa would be less satisfied than if they had cooperated?

2The article addressed this issue from the viewpoint of cooperative justice, that is to say where we regarded those participating in cooperation as being in equivalent initial situations, where as the correction of any inequalities prior to cooperation falls within the general framework of distributive justice. What we therefore endeavoured to do was to find a formula to apportion cooperation-related costs/benefits that does not alter the initial relative balance. The criterion of cooperative justice upheld in this article was the equalization of yields, on the premise that each cooperant should derive from the co-operation a benefit strictly proportionate to the share of the costs borne in it, i.e.:

3where:

  • b and B are the gross benefits derived respectively by the dominated (the one producing the common good) and the dominator,

  • c is the cost of production of the common good,

  • t is the subsidy paid by the dominator to the dominated (with 0 < t<c)

4The article reached an impasse, however, as to one point on which Philippe and I could not concur. This concerned opportunity costs, i.e. the benefit a cooperant could have derived had she/he devoted the resources invested in cooperation to another activity. In this brief text, I revert to that issue. I will (1) justify the need to factor-in the opportunity cost, (2) modify accordingly our criterion of cooperative justice in the case of cooperation between two agents, and (3) generalize this criterion of justice and apply it to the case of linguistic justice.

Why opportunity costs matter

5An anecdote similar to the one that Philippe and I relied upon in our joint paper (BVP: 8) serves to illustrate the importance of taking opportunity costs into account.

6Two professors, Axel and Yannick, move in together for the time it takes to complete a joint work in honour of an illustrious colleague. Yannick cannot stand seeing the slightest speck of dust and every day cleans the apartment they share. Axel, on the other hand, is quite happy with a more or less thorough clean-up once a week. Axel nevertheless derives a benefit from Yannick's efforts even though it is lesser than the one derived by Yannick himself. Let us set these benefits at, respectively, 2 and 6 for a cleaning cost of 1. It is then possible to apply the criterion of cooperative justice we proposed in our article and to ’even out’ the gross benefits/costs ratios of Axel and Yannick (see table 1 in the Appendix, lines i to viii).

7The application of our criterion leads Axel to bear part of the cleaning cost. Yet it would be possible for him to invest this contribution in another activity, like for example playing the French bagpipes which he loves but which Yannick could not care less about (Ex hypothesi, Yannick derives no benefit whatsoever from Axel's bagpipe playing). As the ’return’ on the costs he invests in the bagpipes is of 10/1, it is counter-productive for Axel to contribute to cooperation. The ’yield’ on his contribution to the cleaning is in fact lower than the one he obtains when he devotes himself to playing bagpipe. Consequently, the opportunity cost represented by his not being able to play the bagpipes versus the share of cleaning costs he bears is higher than the gross benefit he derives from this cleaning. The additional benefit he derives from cooperation is therefore negative (table 1, lines ix to xi). He thus finds himself in a less advantageous situation than if Yannick had devoted his time and energy to an activity from which he derives no benefit, e.g. phoning his family, which Yannick enjoys but which offers him a lower ’return’ or ’yield’ than cleaning the apartment, even when Axel makes no contribution to it (3/1 for 6/1, table 1, lines ix and iii).

8Equalizing the gross benefits/costs ratios without taking account of opportunity costs thus means imposing on Axel a contribution such that he will agree to bear it only under duress. Now this is precisely the objection we used in our article to refute the criterion proposed by Pool: an egalitarian apportionment of costs among the various cooperants (BVP: 16-7). Since at that time we deemed this objection sufficient to disqualify the Pool criterion, I must admit today that it does impose a change to our own criterion of cooperative justice.

9Fortunately, the importance of Axel’s opportunity cost does not mean that it is not collectively advantageous to contribute to the cost of cleaning. In fact, although the additional benefit derived by Axel from cooperation – i.e. the net benefit minus the opportunity cost – is negative, the total additional benefit derived from cooperation is indeed positive (table 1, line xi). This means that it must be possible to define a criterion of cooperative justice under which a level of transfers can be determined so that cooperation is at the same time efficient, fair and free.

Factoring opportunity costs into the justice criterion

10If I recall rightly, what Philippe and I disagreed on was precisely how we should integrate opportunity costs. In his view, it was a cost like any other that we could thus consider as being factored in to the overall costs. It seemed to me, on the other hand, that the opportunity cost was not… a cost, but a benefit that one waivered. As I saw it, the real benefit of cooperation is not the benefit that one person derives from the good produced by cooperation, but the additional benefit that this good inputs in relation to the benefit it would have derived from an alternative investment. Mathematically, the issue is whether, in our formula, the opportunity cost is to be added to the denominator or subtracted from the numerator.

11I therefore propose to adapt our criterion of justice and to consider that what is to be equalized is the ratio between, on the one hand, the gross benefits derived from cooperation minus the opportunity cost and, on the other hand, the cost of the contribution to cooperation. In a simple situation where two agents cooperate and where only one initially bears the total cost of production of the common good, as in the case of cleaning the apartment, or when Béa learns the language of Al, this is equivalent to:

12where

  • b and B are the gross benefits derived respectively by the dominated and the dominator,

  • o and O are the rates of returns/yields of the alternative activity to cooperation for, respectively, the dominated and the dominator,

  • c is the cost of production of the common good,

  • t is the subsidy paid by the dominator to the dominated (with 0 < t<c)

13It is to be noted that formula (2) can also be expressed as follows:

14This means that equalizing for each cooperating agent the ratio between, on the one hand, the difference between the gross benefits of cooperation and the opportunity cost and, on the other hand, the cost of contributing to cooperation is tantamount to equalizing for each cooperant the difference between the ’output’ of cooperation and that of the alternative activity. Consequently, if o and O are equal – in other words if the output of the alternative activities is identical for all agents – we are back to the formula (1) and a transfer amount identical to the one obtained by not factoring-in the opportunity cost.

15It is now possible to apply this new criterion to the situation of cooperation between Axel and Yannick. The amount of subsidies received by Yannick is henceforth only of 1/7. The output of cooperation is now 14 for Axel and 7 for Yannick, which for the one and the other represents an increase of 4 in relation to the rates of return/yield of the alternative activity (respectively 10 and 3). They thus both derive an additional benefit from cooperation which is perfectly proportionate to the importance of their contribution, i.e. respectively of 4/7 and of 24/7 for contributions of 1/7 and of 6/7. This gives them an additional benefit on contributions ratio of 4 (table 1, lines xii to xix). It is interesting to note that the sum of the additional benefits of cooperation is higher when the subsidy is of 1/7 rather than of 1/4 (table 1, lines xi and xix). The revision of our criterion of justice therefore guarantees that cooperation is not only equitable but also efficient.

Generalization and application to linguistic justice

16The thus amended criterion of justice can of course be generalized to any number of communities comprising N members as follows:

17or

18where

  • i, j, k… is a agent taking part in cooperation, who has specific characteristics,

  • N is the number of agents presenting the same characteristics,

  • B are the gross benefits derived from cooperation for each agent i,

  • O is the return/yield of the alternative activity to cooperation for each agent i,

  • c is the cost of production of the common good,

  • t is the subsidy received by one agent i (with 0 < t<c).

19It is now possible to apply this formula to the issue of linguistic justice. I shall be looking at two of the situations addressed in our initial article. First, Al, An and Béa are learning Esperanto (BVP: 27-8). Second, three communities comprising respectively 20, 10 and 1 member(s) and where the two smallest communities are learning the dominant language (BVP: 28-31). I am taking up the principle present in the initial article whereby the gross benefit derived from cooperation by one person corresponds to the number of its potential new interlocutors.

20Tables 2 and 3 (see Appendix) correspond to the first of these situations according to whether or not opportunity costs are taken into account. Learning the dominant language would have a cost of 1 for Béa, while Esperanto represents only a cost of ½. Béa then manages to convince Al and An to also learn Esperanto and undertakes to pay them a subsidy so that this cooperation is equitable. If the return/yield ratio of the alternative activity of Al and An is of 11/9 and of 2 for Béa, the amount of subsidies Al and An should receive will be of 1/14 for each of them, which represents for Béa a tax of 1/7 on top of her cost of learning Esperanto. The output of cooperation is of 7/3 for Al and An and of 28/9 for Béa. If she thus has a higher ’return’ than Al and An, it is because the return/yield ratio of her alternative activity is higher than that of Al and An. The difference between the output of cooperation and that of the alternative activity of each agent is, however, perfectly equal and amounts to 10/9. Our revised criterion of justice is thus satisfied. Al and An will consequently each derive from cooperation a net benefit of 4/7, while the net benefit of Béa will be of 19/14. Finally, if we subtract opportunity costs from the gross benefits, which amount to 11/21 for both Al and An and to 9/7 for Béa, we obtain the additional benefits of cooperation in relation to the benefits that could have been produced had the agents devoted their contribution to their respective alternative activity. This additional benefit is of 10/21 for Al and An and of 5/7 for Béa, which is perfectly proportionate to the level of their contributions.

21Table 4 (see Appendix) shows what occurs if our revised criterion of justice is applied to the case of three linguistic communities. I kept all parameters of the initial article (BVP: 29) while factoring-in opportunity costs for the members of A, B and C of, respectively, 9, 8 and 3. Our revised criterion of justice imposes/requires that each member of A contributes to the learning of their language by those of B by paying a subsidy of 11/15 (i.e.

220.733 for 0.79 without taking opportunity costs into account). Here each member of B receives a subsidy of 3/2 (for 1.51 without taking opportunity costs into account). The real change concerns the member of C who must henceforth also contribute to financing the subsidy received by the members of B to the amount of 1/3 (while he was initially receiving a subsidy of 0.7). Our revised criterion of justice is nevertheless respected as these amounts allow each cooperant to derive from the cooperation – after subtraction of the opportunity cost her/his participation in it represents – a benefit perfectly proportionate to her/his contribution.

Conclusion

23Taking opportunity costs into account is essential in order to ensure that the criterion of cooperative justice be at the same time respectful of equity, freedom and efficiency. Opportunity costs are, however, not as much costs comparable to the time and various resources that a cooperant invests in cooperation as a benefit she/he waivers. This is why opportunity costs must not be added to these other costs, but rather subtracted from the benefit(s) derived from cooperation. This leads me to propose a revision whereby the costs of cooperation must be shared in proportion to the additional benefits that each cooperant derives from cooperation in relation to the benefits she/he would have had by investing in an alternative activity.

24In the example in table 4, it may appear counter-intuitive that member C should pay a subsidy in addition to the effort of learning she/he is also bearing. This is, however, a consequence of the greater benefit she/he derives from cooperation and of her/his lower opportunity cost. The fact of belonging to the smallest community is particularly crucial. She/he is clearly (thus) penalized by having had the misfortune of being born into this community. However, as already pointed out in our initial article this is a component that is prior to cooperation. If this is regarded as a source of injustice, it is up to distributive justice to remedy it.

Bibliographie

References

DE BRIEY, L., & VAN PARIJS, Ph. (2002), 'La justice linguistique comme justice coopérative', Revue de philosophie économique, 5: 5-37.

Annexes

Appendix

Table 1: Implications of taking opportunity costs into account

Table 1: Implications of taking opportunity costs into account

Table 2: Situation of Al, An and Béa in case of learning of Esperanto integrating opportunity costs

Table 2: Situation of Al, An and Béa in case of learning of Esperanto integrating opportunity costs

Table 3: Situation of Al, An and Béa in case of learning of Esperanto without integrating opportunity costs

Table 3: Situation of Al, An and Béa in case of learning of Esperanto without integrating opportunity costs

Table 4: Situation of A, B, and C in case of learning of the language of A by B and C integrating opportunity costs

Table 4: Situation of A, B, and C in case of learning of the language of A by B and C integrating opportunity costs

Table des illustrations

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Auteur

Laurent de Briey (PhD in philosophy, Louvain & MA in Economics) is Assistant Professor at the University of Namur (FUNDP). His research focuses especially on moral and political philosophy. He has notably published Le conflit des paradigmes (ULB, 2006) and Le sens du politique (Mardaga, 2009). He is also director of Cepess (the research centre of the Belgian political party CDH), actively involved in the current negotiations aimed at reforming Belgian fiscal federalism.

© Presses universitaires de Louvain, 2011

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