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To allot or not to allot public services? An incomplete contract approach


Using an incomplete contract framework, we analyze the consequences of allotment in public procurement. Allotment aims at dividing a public service into several lots that can be awarded to different operators. This increases the number of bidders during the competitive tendering, as well as it reduces the size of the service managed by each operator. We model the impacts of allotment both on price and quality of public services provided under public procurement. When the quality of services depends on non-contractible efforts made by the operators during the execution of the contract, our results show that (1) the operators have higher incentives to make non-contractible efforts when there is no allotment, and that (2) allotment does not maximize the joint payoffs of the public and private parties (i.e. the total surplus), but mainly benefits public authorities representing the users of the service.

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  1. Source: World Bank


  3. This directive states that “in view of the diversity of public works contracts, contracting authorities should be able to make provision for contracts for the design and execution of work to be awarded either separately or jointly”. The transcription of this directive in the European national legislations has been progressively made (through the legislative decree no. 163 of April 2006 in Italy, the 2006 new Public Procurement Act (BVergG 2006) in Austria, the German Ordinance on the Award of Public Contracts (Vergabeverordnung - VgV) revised in 2009, the Law 30/2007 in Spain, and the Article 10 of the new French Code des Marchés publics in 2006).



  6. Decision of the Conseil d’Etat, July 23rd 2010 Région Réunion no. 338367.

  7. See Notice no. 138-229700, notice published in the British Official journal for public procurement, on July 21st, 2011. Other examples about different European countries can be found in the supplement to the Official Journal of the European Union (Tender electronic daily: The question of allotment is also at stake in the on-going reform for train liberalization in Europe: regional public authorities wonder whether they will award all their train lines to a same operator, or whether they should propose a call for tenders per lot of lines (Leveque (2007)).

  8. This assumption can also be found in Hart et al. (1997) and Bennett and Iossa (2006).

  9. More broadly, the impact of the number of bidders during a competitive tendering on the final price paid by the public authorities has already been widely documented in the economic literature. A competition effect is expected thanks to a higher number of candidates during the competitive tendering (Gomez-Lobo and Szymanski 2001; Brannman et al. 1987). Yet, a large number of candidates can also increase the price, because of the winner’s curse effect (Milgrom 1989; Hong and Shum 2002), or because of ex post opportunistic renegotiations (Guasch 2004). We will discuss these effects in Sect. 5.

  10. Very few countries in Europe have the possibility to contract-out towards public agencies. Then, we only focus in this paper on contracting-out towards private firms.

  11. Source:




  15. La restauration des usagers du service public scolaire ou à caractère social en Alsace, Cour des Comptes, Annual Public Report, February 2006.

  16. We implicitly consider that the public authority has already made her decision to use public procurement, and now has to decide whether to allot the service or not. This allows us to compare the two types of public procurement, i.e. with and without allotment, which is the goal of this model. However, beyond public procurement, other options are also available for the public authority, such as in-house provision of services, or other types of contractual public-private partnerships. See Hart et al. (1997) for a comparison between in-house provision and privatization of public services in an incomplete contract framework, and Hoppe and Schmitz (2010) for a study of the different types of public-private partnerships.

  17. We interchangeably call e and i “investment” or “effort”.

  18. Assuming that the cost-reducing innovations could be inefficient (producing more adverse effects than social benefits) or that the qualitative innovations produce more costs than benefits would not change our results. See footnote 23.

  19. These assumptions can also be found in Hart et al. (1997) and Bennett and Iossa (2006). The allocation of the control rights to the public authority plays here a critical role: it determines the default payoff of the operator by making the agreement of the public authority indispensable.

  20. We could also assume that the private operator is irreplaceable because the cost to find another operator (during the execution of the contract) to implement the innovation would be too high as regards to the cost to deal with the current operator, so that the public authority cannot get rid of the private operator until the end of the contract.

  21. We did not discuss here the source of the bargaining power. The bargaining powers of the parties can be different because the parties’ degree of impatience on the outcome of the bargaining is different. Since it is time consuming to negotiate, and time is valuable to the parties, a player’s bargaining power is higher the less impatient he is relative to the other negotiator. For a discussion on the determinants of bargaining powers, see Muthoo (1999). Moreover, we assume that σ does not depend on the number of components the operator manages: a higher number of components may lead to increase the bargaining power of the private operator. But the public authority can also threat not to renew the contract on all these components, and this threat is all the stronger as the number of components contracted out is high.

  22. We call “payoff” the final gain UG for the public authority and UM for the manager, and “surplus” the sum of these payoffs, S = UG + UM.

  23. Let us notice that in case innovations would be inefficient such that c′(e) − b′(e) < 0 or β′(i) < 0 then no innovation would be implemented. Then, assuming that the innovations could be inefficient would not change our results, since they would not be implemented. Indeed, the net effect of these efforts would be negative, and there would be no room for renegotiation between the parties. The public authority that would support the largest part of the negative impact of these investments would veto their implementation. Another case happens when c′(e) − b′(e) > 0 but b′(e) < 0, i.e. the effort e reduces cost and increases quality. With such an effort, no sharing of the gains could occur during the renegotiation. The reason is that the public authority cannot credibly impose a sharing of the gains, because her threat to veto the implementation of an investment that creates a benefit for her is not credible. Such a veto would lead to a zero payoff for her, while she can get −Lb(e) > 0 if the investment is implemented. As a consequence, because she cannot credibly threat to refuse the investment, it is implemented without any sharing of the gains. The private operator would get L(c(e)) from his effort e, so that his incentive would be Lc′(e) = 1. The public authority would get a gain −Lb(e) > 0. The incentive of the private operator would be still higher under non-allotment than allotment, as when b(e) > 0.

  24. The innovation can only be applied on the components managed by the private operator and cannot be implemented on the components managed by the other operator. This is explained by the fact that the human capital of the manager making the effort e or i is indispensable to the implementation of the innovations resulting from these efforts. Moreover, the operator who discovered the innovations cannot be asked by the public authority to implement these innovations on the lots he is not responsible for.

  25. We make the simplifying assumption that components are not interconnected so that there is no network externalities between the components that could increase the effect of the non-contractible investments, if the service was not allotted. However, such (positive) externalities would strengthen our results by giving additional incentives for the operator to invest. On the contrary, by dividing the service into lots, the operators could not expect such externalities, and would have fewer incentives to invest.

  26. They can anticipate the efforts e and i even if they cannot contract on them (See Hart 2003; Hoppe et al. 2011).

  27. Let us also add that some other studies report that an increase in the number of bidders could also lead to higher prices because of the winner’s curse effect (Hong and Shum 2002). This effect mainly appears in common value auctions, i.e. a situation where the actual value of the item for sale is the same for everyone but bidders have different private information about what that value is. The winner tends to be the bidder with the most overly optimistic information concerning the service or object’s value. When a bidder bids only as regards to his private information, this would lead to negative expected profits. Consequently, in equilibrium, we should expect a rational bidder to internalize the winner’s curse problem by bidding less aggressively (Milgrom 1989). Compte (2004) shows that such effect can persist in pure private-value auctions. However, in our model, since the cost to perform the service is observable by all the parties, there is no possibility of winner’s curse effect. Then, an increase in the number of bidders should only lead to a competition effect, i.e. a decrease in prices (as it has been empirically shown in the case of the London bus transport Amaral et al. 2012).

  28. This paradox is that it usually takes a large number of firms to ensure that prices equal marginal costs, while the competition (in prices) between only two firms should theoretically be sufficient to charge a price equal to the marginal cost. For the theoretical approaches of the Bertrand Paradox, see Cabon Dhersin and Drouhin (2010), Vives (2001), Spulber (1995), Kreps and Scheinkman (1983) and Edgeworth (1925).

  29. The higher competitive pressure caused by an increasing number of bidders is also explained in the economic literature in theoretical models assuming private information on the costs of bidders. See McAfee and MacMillan (1987) or Milgrom (1989).

  30. A solution could be to choose the solution that maximizes the total surplus, and then implement redistributive policies. However, this implies to rely on an efficient tax system, and the effect of redistribution could be anticipated by the operators, thus lowering their efforts to innovate.

  31. Let us note that the public interest is a fundamental notion of public law, but few has been written on the economics of public interest and on the economics of public law. See Rose-Ackerman (1994) for a contribution to the economic analysis of public law.

  32. The public interest as the interest of the people as a whole mainly refers to the “general will" as described by Rousseau (1762).

  33. Recent references on mergers of municipalities are Hirota and Yunoue (2011), Di Porto et al. (2011) and Frère et al. (2011).


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We wish to thank Patrick Schmitz and Eva Hoppe for helpful discusssions at an earlier stage of this work. We also thank Louis-Roch Burgard, Eshien Chong, Antonio Estache, Frédéric Marty, Paola Valbonesi, and seminar participants at the 2011 ISNIE Conference at Stanford University, and the 2011 JMA Conference in Sousse, Tunisia. We are solely responsible for any remaining errors.

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Correspondence to Claudine Desrieux.

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de Brux, J., Desrieux, C. To allot or not to allot public services? An incomplete contract approach. Eur J Law Econ 37, 455–476 (2014).

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  • Public procurement
  • Allotment
  • Incomplete contracts
  • Public services

JEL Classification

  • L33
  • L22
  • L24
  • L11
  • K12