Regulation by Negotiation: the Private Bene t Bias · 2016-11-18 · Regulation by Negotiation: the...

Regulation by Negotiation: thePrivate Benefit Bias

Ariane Lambert−Mogiliansky∗ Pierre Picard†

An Article Submitted to

The B.E. Journals inTheoretical Economics

∗CERAS Ecole Nationale des Ponts eet Chaussees†University Paris X − Nanterre (THEMA)

Copyright c©2001 by the authors.

All rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem, or transmitted, in any form or by any means, electronic, mechanical, photocopying,recording, or otherwise, without the prior written permission of the publisher, bepress.

Regulation by Negotiation: the Private

Benefit Bias

Abstract

This paper analyses the role of non−pecuniary private benefits of managersin an incomplete contract approach to the regulation of utilities. Private ben-efits may take various forms: excessive job security, perks, empire buildingfeelings, overstaffingmodel describes the relationship between a government andthe manager of a firm which produces a public good, under private or publicownership. The firm’s production is characterized by its quantity and its flex-ibility, the latter corresponding to adaptability to changes in consumers’tastesor to new technologies. A larger output quantity entails larger private benefitsto the manager, while increasing flexibility runs counter to the managers’ pri-vate benefits. The manager decides upon non−verifiable investment in humanand non−human capital so as to facilitate an increase in the output quan-tity (capacity investment) or to improve the firm’s flexibility (investment inorganizational adaptability). We compare the effects of the ownership regimeon the manager’s incentives to invest and on the aggregate welfare. The pri-vate firm under−invests in capacity and organizational flexibility because thegovernment holds up a part of the gains through ex post renegotiation of themanager−government initial contract. Our analysis also highlights a fundamen-tal bias in the investment behavior of the state−owned firm: the manager ofsuch a firm only invests in capacity (he may even invest more than under pri-vate ownership) but he never invests in organizational adaptability. The modelshows that an increase in the government’s bargaining power exacerbates thehold up problem when the firm is privately owned, but that this result maybe reversed for capacity investment under public ownership. Finally, we showthat the superiority of private or public ownership depends simultaneously onthree factors: the bargaining powers of the manager and of the government,the degree of specificity of investments and the relative weight of quantity andflexibility concerns in the social welfare.

1 IntroductionA common argument in favor of privatization of public utilities is that state-owned regulated firms tend to resist changes that hurt their employees. Inother words, private ownership is likely to be more favorable to flexibility.Privately owned enterprises are more responsive to changes in consumers’tastes and technologies that require organizational adaptability. Conversely,at least during some periods of history, success of nationalized firms has beenmore convincing in activities where top priority was given to the growth ofproductive capacity. More generally, the records of state owned firms is mostconvincing where their development could go hand in hand with extensiveprivate benefits granted to its workers1.This paper analyzes the role of private benefits in contexts where theymay

either put a brake on firms’ flexibility or stimulate investment in capacity.It shows that indeed there is a remarkable distinction in the role played bynon-pecuniary private benefits (job security, empire building feelings, perks,overstaffing...) depending on whether the regulated firm is under publicownership or its assets are privately owned.In the following analysis, the fact that private benefits may play differ-

ent roles according to the ownership regime will arise as a consequence ofthe incompleteness of the regulatory contract. In an hypothetical world ofcomplete contracts with benevolent regulators, ownership would play no role.The regulator could mimic the market by offering a comprehensive incentivescheme to the firm.2 Some degree of incompleteness in regulatory contractsis thus necessary for asset ownership to matter at all. The recent works ofHart and Moore (1999) and Segal (1999) provide a foundation for contractincompleteness which emphasizes the role of ex-post renegotiations (ratherthan that of the inability to, ex-ante, describe the actions, an argument chal-lenged by Maskin and Tirole (1999)). The infeasibility of a commitment notto renegotiate ex post, makes the nul (incomplete) contract optimal whenthe environment is rich enough. There exists also plenty of evidence of in-completeness in the contractual arrangements between regulatory bodies and

1Railroad transportation and electricity production in France during the sixties andthe seventies are good examples of such a situation.

2This is true when assset ownership is the sole distinction between the two regulatoryregimes, in particular when there is no difference in the regulator’s information about thefirm depending on who owns the assets.

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1Lambert-Mogiliansky and Picard: Regulation by Negotiation

Produced by The Berkeley Electronic Press, 2002

private or public firms in the regulation of utilities in Western countries3. Aconcomitant characteristic feature of utilities regulation is the role played byex post negotiations whether the regulated firm is private or public. Regu-lation through negotiations is a reality as soon as one approaches concreteissues.Contrary to several theoretical contributions to the privatization debate

in terms of incomplete contracts which have emphasized the role of infor-mational asymmetries - in particular Laffont and Tirole (1991) and Schmidt(1996)4-, we will not appeal to informational specificities of public and pri-vate governance structures. Instead, the focus will be on incentive issuesrelated to ex post negotiation.5 In this respect, our analysis is closely re-lated to an article by Hart, Shleifer and Vishny (1997).They investigate theefficiency of the government’s in-house provision of services (such as the op-erations of prisons, hospitals or schools) compared to contracting out with aprivate company. They emphasize a multi-task issue related to the lack ofcompetition: private firms have too strong incentives in cost reduction andtoo weak incentives in quality improvement. In contrast, here the questionat issue is how employees’ non-pecuniary private benefits affect the outcomeof regulation.A second important distinction with the Hart, Shleifer and Vishny paper

is more technical: it is related to the way we define the default options.More specifically, what happens in case of negotiation failure when the firm ispublic? Hart, Shleifer and Vishny assume that, in such a case, the managerof a public firm can be replaced but then the government only realizes afraction of the value of the investment. In our model, the manager cannot bereplaced as long as he complies with the initial contract. The government who

3See for instance Armstrong, Cowan and Vickers (1994), Einhorn (1994), and Helm(1994) on regulation of utilities in the UK.

4Laffont and Tirole’s (1991) main argument is related to the costs of agency in a multi-principal framework. They assume better congruence between managerial and ownershipgoals in the privatized regime. But the manager in the private firm has two masters(shareholders and the regulator) which generates conflicts and reduces incentives. Sim-ilarly, Schmidt’s (1996) argument is essentially informational. He views privatization asa commitment device to credibly harden the budget constraint. The key to credibility isthat the government has less information about the private firm than about the publicone.

5In particular we do not assume that the regulator is better informed only becausethe firm is in public ownership. In facts, empirical evidence shows that public firms (forinstance, EDF or SNCF in France) are not seldom quite successful in effectively concealinginformation e.g., by providing huge amounts of untractable data. In contrast, the EnglishOfwat(Office of Water regulation) has been successful in imposing an accountability andreporting standard to the private water companies. This information is extensively usedin yardstick competition.

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owns the residual control rights can however decide for another (additional)use of the assets. It must then compensate the manager for the eventualadditional verifiable costs these modifications of the basic good bring forth;in other words the manager is ensured to receive a salary. The private benefitbias follows as a distinguishing feature of public management, because of theconjunction of two features of the regulatory contract: incompleteness andguaranteed salary. The intuition is that the guaranteed salary protects thefirm’s manager from full expropriation (in case of negotiation failure), itsecures that private benefits are unalienable. Similar results (e.g., excessemployment) have been obtained by Shleifer and Vishny (1994). However,in their model the politicians directly care for high employment in regulatedfirms while our government is benevolent: he maximizes social welfare.We hope that our approach provides a sensible explanation for some his-

torical and cross-country distinctions in preferences about the public or pri-vate ownership of utilities. In particular, publicly owned regulated firms canbe more efficient than private ones in periods of extensive growth of the in-dustry and in countries with a command and control approach to regulationwhere the government has a strong bargaining power. Examples are pro-vided by railway and electricity industry in France during the sixties andseventies. In contrast, the regulated private firm is likely to be more efficientin periods of intensive, quality oriented, growth such as in today’s telecomindustry. Furthermore, regulated private firms perform generally better ineconomies where the bargaining power of the government and of the firmare more balanced such as the Anglo-American ones. The intuition is thatthe gains from congruence between the government’s and the employees’ ob-jectives (in periods of extensive growth) can be exploited to a larger extentwhen the firm is public, because incentives are driven by private benefits. Incontrast, the costs of non-congruence (when more flexibility is needed) canbe mitigated by private ownership insofar as privately owned assets can beredeployed to new activities in case of negotiation failure between the firmand the government.The remaining of the paper is organized as follows. The general setting

is presented in Section 2. Section 3 characterizes the outcome of the nego-tiations between the regulated firm and the government. Section 4 analysesthe firm’s investment policy and presents our main results. Illustrations ofthe results and concluding comments are offered in Section 5. The proofs aregathered in an appendix.

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2 The Setting

2.1 Basic assumptions

The model describes the relationship between two agents : the manager of afirm and the government. The firm produces a pure public good defined by(y, f) ∈ R+2 . The main distinction between y and f is that a larger y entailslarger non-pecuniary private benefits for the manager, while it is the contraryfor f : increasing f would reduce the manager’s nonpecuniary benefits. Wewill interpret y as a quantitative measure of the output and f as consumer-oriented quality or flexibility in the organization of production. The managerlikes increasing the output -in its quantitative dimension- because produc-ing more increases job security or because it flatters the manager’s empirebuilding feelings. On the contrary, turning the firm’s organization towardsconsumers’ tastes requires a better adaptability on the part of the manager.It may require an increase of flexibility in terms of working hours or locationthat typically runs counter to the manager’s nonpecuniary benefits. In whatfollows, keeping in mind this interpretation, we will refer to y and f respec-tively as to the output quantity and to flexibility in the firm’s organization.However, other interpretations of y and f are possible as soon as increasesin y and f are related respectively to higher or lower nonpecuniary benefitsfor the firm’s manager.The output is a pure public good that cannot be marketed.6 Production

requires the manager’s human capital as well as non-human capital. Underpublic (private) ownership, non-human capital is owned by the government(the manager). The manager’s services can be contracted upon in a com-petitive market, but the government-manager contracts are incomplete. Themanager and the government write a contract that specifies some character-istics of the goods or services to be supplied. These aspects of the allocationcorrespond to a “basic good” in Hart’s (1995) and Hart-Shleifer-Vishny’s(1997) terminology. The basic good is defined by a description ( in terms ofquantity and flexibility) of the output provided by the firm or by similar firmsin the past periods. Since this description is unambiguous, the basic good canbe contracted upon. Increasing capacity or flexibility beyond the basic goodis possible but not contractible. More precisely, we may decompose (y, f ) as

y = y0 + y1

f = f0 + f1

6Under some conditions our results carry over with only slight modifications to situa-tions where the firm has also market revenues.

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where (y0, f0) correspond to the characteristics of the basic good (in termsof quantity and flexibility). For notational simplicity we let (y0, f0) = (0, 0).(y1, f1) correspond to variations in quantity and flexibility that cannot be

contracted upon, because they are embodied in specific management deci-sions depending on so many contingencies that it would be too costly to makethem explicit in the contract. Since (y0, f0) = (0, 0), we have (y, f) = (y1, f1).The (y1, f1) components of the allocation is chosen as the outcome of a

bargaining between the government and the manager once the state of natureis known. In case of negotiation failure, (y1, f1) is chosen by the agent whoowns the non-human assets - the government or the manager -.This agenthas the residual right, i.e. the rights to choose the part of the allocation notincluded in the contract.The contract also specifies the price w0, the net monetary transfer ( in

excess of compensation for monetary costs) to be paid by the government tothe manager when the latter provides the basic good. Under private own-ership, w0 is the price received by the manager who acts as an independentcontractor. Under public ownership, w0 is the wage received by the manageras an employee of the government. Beside the monetary payoff, the managerearns private benefits which are non-pecuniary and non-verifiable.After the contract is signed, the manager decides upon non-verifiable in-

vestments. These investments increase the consumer surplus associated withthe quantity and the flexibility of the firm’s output. They are specific tothe government-manager relationship. Using them outside this particular bi-lateral relationship would entail an efficiency loss -i.e. it would lead to alower government-manager surplus. Some investments make an increase inthe output quantity easier and other investments improve the flexibility inthe adaptation of the output to the consumers’ preferences: we call themrespectively investment in capacity and investment in organizational adapt-ability.Let us consider the private and public ownership cases in turn in order to

describe the dynamics of contractual relationships between the governmentand the manager. Under private ownership, the model is standard. Afterthe contract is signed and the investments are made, the manager and thegovernment learn about new contingencies that may call for modifications ofthe original contract. Unless the contract is renegotiated, the manager willonly supply the basic good : indeed, in our model (see below), any departurefrom this agreement would be unprofitable insofar as the government wouldnot pay for such a change in the absence of agreement. Renegotiations musttherefore lead to the government paying a price larger than w0, while themanager commits to produce a “modified good”, i.e. an allocation (y, f )that has been modified to take relevant contingencies into account. In what

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follows, for notational simplicity, the various contingencies that may occurare not explicitly described and the expectation operator associated withthe distribution of the states of the world is deleted. In the absence ofrenegotiation, the manager only provides the basic good. He then receives theprice w0 from the government and he may use assets outside the relationshipwith the government. As above indicated, he then incurs an efficiency lossbecause of the relation specificity of investments.Under public ownership, the government owns the residual control rights

over the non-human assets. The initial contract can be renegotiated and, insuch a case, the manager commits on producing a modified good and thegovernment increases the manager’s wages. In the absence of renegotiation,the government uses its assets to implement modifications in the allocationunder the constraint that the manager is secured the contracted wage. In con-trast with Hart, Shleifer and Vishny (1997), we assume that the governmentcannot fire the manager in case of negotiation failure when the latter fulfillshis initial contractual obligations. This captures the fact that public employ-ees generally enjoy a solid job security so that the threat of firing cannot beused as a credible threat. Next, we assume that the private benefits asso-ciated with the management of a public firm is so large that the managerwould never choose to quit provided that the government secures his wage.Imposing a decision on a reluctant manager entails a fixed cost. This costcaptures the expenditures related to preparing and following up the imple-mentation of decisions. A key assumption in the model is that this directmonitoring of the firm’s activity makes the firm’s costs, associated with theimposed decisions, verifiable. So in particular the government can committo compensate them i.e. to guarantee the manager’s monetary wage. So in asituation of renegotiation failure, the manager receives a monetary net pay-off equal to w0 and enjoys (puts up with) the nonpecuniary private benefitsassociated with the imposed allocation.

2.2 The Model

The main notations Let us first define the objective of each agent. The

government’s payoff is denoted by UG . It is the difference between theconsumers’ surplus and the transfer to the firm. It is written as

UG = v1 (y, i) + v2(f, e)− t (1)

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where v1 (y, i) and v2(f, e) denote the two components of the consumers’ sur-plus which are respectively associated with quantity and flexibility in thefirm’s output. t is a monetary transfer to the firm which covers its monetaryproduction costs and the payment to the manager. The consumers’ surplusdepends on the output (y, f ) and also on a two-dimension investment of thefirm denoted by (i, e) ∈ R+2 . The investments i and e correspond to the effortlevels made by the manager in order to adapt the firm’s supply to the con-sumers’ tastes and requirements, as well as to new technologies. These arenon-verifiable investment which cannot be contracted upon. i is an invest-ment in capacity while e is an investment in organizational adaptability. Weassume v01i > 0, v

01y > 0, v

001y2 ≤ 0, v001iy > 0, v02e > 0, v02f > 0, v002f2 ≤ 0, v002ey > 0.

In particular, the assumptions on the sign of the cross derivative of v1 (re-spect. v2) mean that an additional investment in capacity (respect. organi-zational adaptability ) makes it more valuable in terms of consumers’ surplusto increase the output (respect. the flexibility).The payoff of the manager is denoted by UM . It is written as

UM = w + µ1(y)− µ2(f )− [ψ1(i) + ψ2(e)] (2)

where

w = manager’s monetary income

µ1(y)− µ2(f) = non-pecuniary private benefits

ψ1(i) + ψ2(e) = investment cost

We assume that the manager is ex ante willing to participate if UM ≥ 0.The functions ψ1 (i) and ψ2 (e) capture the non-verifiable private cost of theinvestment. They are such that ψ0k(.) ≥ 0,ψ00k (.) ≥ 0,ψk(0) = 0,ψ0k (0) =0,ψ0k(∞) =∞ for k = 1 and 2. ψ1 (i)+ψ2 (e) include the costs of organizingproduction with new technologies, adapting the promotion system to muta-tions, developing a consumer oriented corporate culture etc... . The functionµ1(y) − µ2(f ) corresponds to the difference between non-pecuniary quasi-rents and non-pecuniary costs of the manager : status, perks, independencein decision-making, empire building feelings, etc.... We assume µ01(.) > 0,µ001(.) < 0 and µ

02(.) > 0, µ

002(.) > 0. Hence, investing in capacity increases the

manager’s private benefits whereas investment in organizational adaptabilityreduces the private benefits.Let c1(y) + c2(f ) denote the monetary production cost, including market

wages paid to workers who may be hired by the manager on labor spotmarkets, with c0k(.) > 0 and c00k(.) > 0 for k = 1 and 2. The firm has nomarket revenue. Hence

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w = t− [c1(y) + c2(f)]

For notational simplicity, we assume µk(0) = ck(0) = vk(0, .) = 0 fork = 1 and 2. Hence, w0 denotes the transfer paid to the manager when thebasic good is provided (since c1(0) = c2(0) = 0).

Timing The timing of the manager-government relationship is as follows :

1) The government proposes a contract to the manager as a take it orleave it offer. This contract specifies that the basic good (y0, f0) = (0, 0)should be supplied by the manager and that a transfer t = w0 will be paidby the government.2) The manager either refuses the government’s proposal and the game

ends, or he accepts it.3) The manager chooses i and e.4) The manager and the government learn about the relevant contingen-

cies.5) The government and the manager negotiate about (y1, f1, t) = (y, f, t) .6) If they reach an agreement, they proceed to implement it. If the

negotiation fails, a non-cooperative game is played.

Hence, the government contracts the provision of the basic good on acompetitive market, in which the managers’ reservation utility is normalizedat UM = 0. After the investments have been made, the manager and thegovernment are locked in a bilateral relationship. A renegotiation of the ini-tial contract may then take place, with specific bargaining powers for thegovernment and for the manager.

The basic features of the game played in case of negotiation failure arethe following. Firstly, the agent who owns the non-human assets chooses theoutput combination (y1, f1) = (y, f) because he has the residual rights on theuse of these assets. This means in particular that, under public ownership,the government may impose an increase in quantity or flexibility beyond thebasic good, provided that w0 is paid to the manager. In such circumstances,the government directly monitors the decisions of the firm which allows itto verify the variation in costs induced by its orders and thus to commit onpaying the wage w07. Secondly, whatever the property rights, the manager

7Apart from this particular case where the government monitors the decision of thefirm, costs are not verifiable which prevents the parties to contract on them.

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may choose to stay or to quit. Let us describe this non-cooperative gamewith more details.Under private ownership, if the manager stays, he can choose the output

(y, f), because he owns the non-human assets and his payoff is given by

UM = t− [c1(y) + c2(f)] + µ1(y)− µ2(f )− [ψ1(i) + ψ2(e)].

If he quits, only the basic good is provided to the government but the man-ager can use his human and non-human assets outside the relationship withthe government which will provide him some positive pecuniary and non-pecuniary benefits. These benefits will be denoted by K1(i) + K2(e), withK 01 ≥ 0 and K 0

2 ≥ 0. The manager’s payoff is thenUM = t+K1(i) +K2(e)− [ψ1(i) + ψ2(e)]

Since the government will not pay more than the contractual transfer t = w0whether the manager stays or quits (because no agreement has been reached),it is a dominant strategy for the manager to quit if

µ01(0) < c01(0) (3)

since in that case we have

µ1(y)− c1(y) < K1(i) +K2(e) for all y, i, e (4)

Condition (4) means that the manager of the private firm has no incentivesto produce more (of y and f ) than the basic good unless he gets additionalmonetary rewards. In what follows, we assume that (3) holds.Under public ownership, in case of negotiation failure, the output (y, f )

is decided upon by the government. The manager may decide to stay or toquit (after having provided the basic good). We denote by u∗ the variationin the manager’s surplus if he quits8 We assume

u∗ < −µ2 (f) ≤ 0 for all f (5)

which ensures that under public ownership the manager’s ex post partici-pation constraint is not binding (see below) : whatever the non-pecuniaryprivate costs that correspond to the (imposed) allocation, the manager ofthe public firm does not want to quit. Here also, a dominant strategy forthe government is to pay the contractual wage w0 and nothing more to the

8Contrary to the private ownership case, this variation in the manager’s surplus doesnot depend on his investments i and e, since they are incorporated in the non-humanassets owned by the government

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manager. This is possible because costs are supposed to be verifiable whenthe government monitors the public firm’s activity. In any case (whether themanager stays or quit), the government incurs a fixed reorganization costP which represents the costs of preparing and implementing any imposeddecision (y, f) 6= (0, 0)9.Hence, under our assumptions, in case of negotiation failure, the manager

of the private firm quits and he uses his assets outside the relationship withthe government. Under public ownership, the manager stays and he receivesthe nonpecuniary benefits in addition to the contractual wage.

3 Negotiations

We proceed by backward induction. We shall first analyze negotiations giventhat the investments i and e are sunk. We start by characterizing the statusquo payoffs that prevail in case of negotiation failure. These default payoffscorrespond to the dominant strategies of the manager and of the governmentin the non-cooperative game that has just been described.

3.1 The default payoffs

Assume first that private ownership prevails. Then, in case of negotiationfailure, the basic good is supplied, the transfer t = w0 is paid and the in-vestments are used by the manager outside the firm-government relationship,i.e. the manager chooses to quit after having provided the basic good. Thedefault payoffs of the government and of the manager are then respectivelywritten as

UGp = −w0 (6)

UMp = K1 (i) +K2(e) + w0 − [ψ1(i) + ψ2(e)] (7)

Under the public ownership regime, a negotiation failure leads to the gov-ernment simply imposing its most preferred allocation y, f, t −at additionalcost P if (y, f) 6= (0, 0)− under the constraint that the manager receives atleast w0, i.e.

t ≥ w0 + c1(y) + c2(f )It will be optimal for the government to choose (y, f) 6= (0, 0) if P is nottoo large (see below for the definition of the upper bound of P ). Assume

9More realistically, we could assume that the reorganization cost continuously dependon (y, f)

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that this is actually the case. The most preferred allocation corresponds toan output quantity by (i) and to a flexibility bf (e) . Hence, the government’sdefault payoff is

UGn =bΩ1(i) + bΩ2(e)− w0 − P (8)

if the manager stays or

UGn =bΩ1(0) + bΩ2(0)−w0 − P

if the manager quits10, where

bΩ1(i) = v1 (by (i) , i)− c1(by (i)) (9)

bΩ2(e) = v2( bf (e) , e)− c2( bf (e)) (10)

where by (i) , bf (e) maximizev1 (y, i) + v2(f, e)− [c1(y) + c2(f )]

with respect to (y, f) i.e. by(i) and bf(e) are such thatv01y (by, i) = c01(by) (11)

v02f(bf , e) = c02( bf ) (12)

which implies by0(i) > 0 and bf 0(e) > 0. Indeed, choosing by (i) , bf(e) and payingt = c1(by (i)) + c2( bf(e)) + w0 to the manager is a dominant strategy of thegovernment. If the manager stays, his default payoff is then

UMn = w0 + µ1(by (i))− µ2( bf (e))− [ψ1(i) + ψ2(e)]. (13)

If the manager quits (after providing the basic good and receiving his con-tractual wages w0) , his payoff would be

UMn = u∗ + w0 − [ψ1(i) + ψ2(e)] (14)

10We here assume that the gains from investment are cancelled if the manager quits.We could assume that a fraction of the gains from investment are preserved if the managerof the state-owned firm quits in which case we would have

UGn = bΩ1(λ1i) + bΩ2(λ2e)− w0 − Pwhen the manager quits, where λ1 and λ2 are the proportions of investments which arepreserved with 0 < λ1 < 1 and 0 < λ2 < 1 . This is in fact an unimportant aspect of ourmodelling since, under public ownership, staying is a dominant strategy of the manager.

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Condition (5) implise that staying is a dominant strategy of the manager.If the government chooses (y, f) = (0, 0), no reorganization cost would

be incurred and the government default payoff would be UGn = −w0. Hencechoosing (y, f) = ( by(i), bf(e)) 6= (0, 0) is an optimal strategy of the govern-ment if

P ≤ bΩ1(i) + bΩ2(e) (15)

which provides an upper bound on the size of P . In what follows we assumethat (15) holds for all i, e11.Note that by condition (3) the manager wouldprefer to deliver y = 0, f = 0 when no agreement is reached.

3.2 Equilibrium allocation

We assume that the negotiation between the manager and the governmentleads to the Nash bargaining solution. Hence given w0, i and e , the outcomeof the negotiation is obtained by maximizing³

UM − UM´1−α ³

UG − UG´α

(16)

with respect to y, f and t, where α and 1−α are respectively the government’sand the manager’s bargaining powers12. UM and UG are the default payoffs:they are given by (6)-(7) if the firm is private or by (8)-(13) if it is public.At the Nash solution, y, f maximize the aggregate surplus

UM+UG = v1 (y, i)+v2 (f, e)+µ1 (y)−µ2 (f)−c1 (y)−c2(f)−ψ1 (i)−ψ2 (e)

which gives y = y∗(i) and f = f∗(e) with

c01 (y∗) = v01y (y

∗, i) + µ01 (y∗) (17)

c02 (f∗) = v02f (f

∗, e) + µ02 (f∗) (18)

Note that y∗0(i) > 0, f ∗0(e) > 0 and also that

y∗(i) > by(i) for all i11See footnote 13 for the consequences of deleting inequality (15)12The parameter α captures features of the institutional context in which regulation

operates independently of the ownership regime. Indeed, more often than not, regulationis operated in a complex of institutions that are a bequest from the past. One exampleof such an institutional context is provided by the Common Law tradition in Anglo-American countries. This context secures for regulatory bodies a larger independencefrom the political power than in a country like France. In France, public interventionismand the command and control approach to regulation are inherited from the so-calledColbertian tradition.

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f ∗(e) < bf (e) for all e.Let

Ω∗1(i) = v1 (y∗(i), i)− c1 (y∗(i)) , (19)

Ω∗2 (e) = v2 (f∗(e), e)− c2(f ∗(e)), (20)

µ∗1(i) = µ1 (y∗ (i)) , (21)

µ∗2(e) = µ2 (f∗ (e)) , (22)

At equilibrium, we have

UM + UG = W∗1 (i) +W

∗2 (e)

where

W ∗1 (i) = Ω∗1(i) + µ

∗1(i)− ψ1(i),

W ∗2 (e) = Ω∗2 (e)− µ∗2(e)− ψ2(e).

The equilibrium payoffs are

U ∗G = α[W ∗1 (i) +W

∗2 (e)− (UG + UM)] + UG (23)

U∗M = (1− α) [W ∗1 (i) +W

∗2 (e)− (UG + UM)] + UM . (24)

The gains from negotiation are W ∗1 (i) +W

∗2 (e) − (UG + UM ). (23)-(24)

mean that they are split in proportions α, 1−α between the government andthe manager.The equilibrium aggregate surplus W ∗

1 (i) +W∗2 (e) is supposed to be con-

cave with respect to(i, e). Using the envelope theorem shows that it is maxi-mized at i = i∗ and e = e∗ such that

ψ01 (i∗) = v01i (y

∗ (i∗) , i∗) . (25)

ψ02 (e∗) = v02e (f

∗ (e∗) , e∗) (26)

Finally, we will also assume

0 ≤ K 01 (i) < v

01i (y

∗ (i) , i) for all i, (27)

and0 ≤ K 0

2 (e) < v02e (f

∗ (e) , e) for all e. (28)

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This simply states the relation specificity of investment in capacity or flexi-bility, i.e. the marginal value of the investment in the best alternative use isless than its marginal social value within the relationship between the man-ager and the government. Intuition suggests that investment in capacity isprobably more specific than investment in organizational adaptability. Thisis particularly the case when the former includes aspects of site specificity(for instance when the issue is the production of a local public good). Hence,we will devote special attention to the case where investment in capacity istotally specific, i.e. K 0

1 (i) = 0.

4 The firm’s investment policy

4.1 The private ownership regime

Under private ownership, after substituting UG = UGp and UM = UMp in(23), the government’s equilibrium payoff is written as

U∗Gp = α[Ω∗1(i) + Ω∗2(e) + µ∗1(i)− µ∗2(e)]− [K1(i) +K2(e)]− w0

Similarly, the manager’s payoff is

U∗Mp = (1− α) [Ω∗1(i) + Ω∗2(e) + µ∗1(i)− µ∗2(e)]− [K1(i) +K2(e)]

+w0 +K1(i) +K2(e)− [ψ1 (i) + ψ2 (e)]

Let ip, ep be the manager’s optimal investments. ip, ep maximize U ∗Mp

with respect to i, e ≥ 0 which implies[αK 0

1 (ip) + (1− α) v01i (y∗ (ip) , ip)]− ψ01 (ip) ≤ 0

= 0 if ip > 0(29)

and

[αK 02 (ep) + (1− α) v02e (f

∗ (ep) , ep)]− ψ02 (ep) ≤ 0

= 0 if ep > 0.(30)

We assume that U ∗Mpis concave with respect to i and e. Hence (29) and

(30) fully characterize the investment levels under private ownership.

14

14

Given the manager’s participation constraint UM ≥ 0, the optimal trans-fer decided upon by the government is such that U∗Mp

= 0, which gives

w0 = ψ1 (ip)+ψ2 (ep)−(1− α) [Ω∗1(ip)+Ω∗2(ep)+µ

∗1(ip)−µ∗2(ep)]−α[K1 (ip)+K2(ep)].

The government’s payoff is thus

U ∗Gp = W∗1 (ip) +W

∗2 (ep). (31)

4.2 The public ownership regime

The government’s payoff from negotiation with a state-owned firm is

U∗Gn = α[Ω∗1(i) + Ω∗2(e) + µ∗1(i)− µ∗2(e)]− [bΩ1(i) + bΩ2(e) + bµ1 (i)− bµ2 (e)− P ]

+bΩ1(i) + bΩ2(e)−w0 − P,where bµ1 (i) = µ1(by (i)) and bµ2 (e) = µ2( bf (e)). Let in be the investment levelchosen by the firm in the public ownership regime: in maximizes

U∗Mn= (1− α) [Ω∗1(i)+Ω∗2(e)+µ∗1(i)−µ∗2(e)]−[bΩ1(i)+bΩ2(e)+bµ1 (i)−bµ2 (e)−P ]

+bµ1 (i)− bµ2 (e) + w0 − [ψ1 (i) + ψ2 (e)]

We assume that U∗Mnis concave in (i, e). Maximizing U ∗Mn

with respectto i ≥ 0 and e ≥ 0 yields the following first-order optimality conditions

αbµ01 (in) + (1− α) [v01i (y∗ (in) , in)] −v01i (by (in) , in)]

−ψ01 (in) ≤ 0

= 0 if in > 0

(32)

and

−αbµ02 (en) + (1− α) [v02e (f∗ (en) , en) −v02e( bf (en) , en)]

−ψ02 (en) ≤ 0

= 0 if en > 0

(33)

Given the manager’s participation constraint UM ≥ 0, the optimal wagechosen by the government is such that U∗Mn = 0, which gives

w0 = (1− α)[bΩ1(in) + bΩ2(en)− (Ω∗1(in) + Ω∗2(en) + µ∗1(in)− µ∗2(en))]

+ψ1(in) + ψ2(en)− α[bµ1 (in)− bµ2 (en)]− (1− α)P

15



Hence, the government’s payoff is

U∗Gn =W∗1 (in) +W

∗2 (en) (34)

Conditions (29)-(30) and (32)-(33) establish that, at equilibrium, themarginal benefit of investment for the firm is equal to its marginal cost ψ01 (i)or ψ02 (e) when the investment level is strictly positive. However, the defi-nitions of the marginal benefit of investment strongly differ depending onwhether the firm is private or public. The marginal benefit of a private firm-i.e. the terms in square brackets in (29) and (30)- is a weighted sum of theincreases in the surplus inside and outside the firm-government relationshipassociated with a unit increase in investment. When the firm is state-owned,the marginal benefits of investments in capacity or organizational adaptabil-ity -i.e. the terms in curly brackets in (32) and (33)- are written as a weightedsum of the marginal non-pecuniary benefits in the imposed solution bµ01(in)or −bµ02(en) and of the difference between the marginal consumers’ surplusassociated with a unit increase in investment, respectively in the equilibriumallocation and in the imposed allocation. In what follows, this difference iscalled the incremental marginal surplus.(31) and (34) show that the government’s optimal payoff is equal to the

aggregate surplus. Obviously, this comes from the fact that the governmentcontracts with the manager on a take or leave it basis, which allows thegovernment to extract the whole surplus.

These results allow us to characterize the investment behavior of the firm.Let us consider the private and public ownership regimes in turn.

Proposition 1 The investment behavior of a private firm is such that:

0 < ip < i∗ and 0 < ep < e

∗ if α > 0

ip = i∗ and ep = e∗ if α = 0

Proposition 1 states that the private firm under-invests except whenα > 0, because the government holds up a part of the benefits of its in-vestments through ex post negotiation. The only case where the investmentlevel of the private firm coincide with the socially optimal level is when thegovernment has no bargaining power (α = 0), in which case there is no issueof expropriation through negotiation.

16

16

Proposition 2 The investment behavior of a state-owned firm is such that13

i) in > 0 and en = 0;ii) in > ip if and only if αK 0

1(in) < αbµ01(in)− (1− α)v01i(by(in), in);iii) in > i∗ if and only if αbµ01(i∗)− (1− α)v01i(by(i∗), i∗) > αψ01(i

∗).

Corollary 1 Suppose K1(i) is replaced by θK1(i), where θ > 0. Then for θsufficiently small, there exists α ∈ (0, 1) such that in > ip whenever α > α.

Proposition 2-i establishes the existence of a bias in the investment policyof a public firm: the manager of such a firm only invests in capacity, he neverinvests in organizational adaptability. To understand the logic of this result,let us come back to the two determinants of investment of a state-owned firm:the incremental marginal surplus and the marginal non-pecuniary benefits.We know that y∗(i) > by(i) and f∗(e) < bf(e) , i.e. in the imposed solution thequantity is insufficient and the flexibility is excessive, by comparison with thesocially efficient allocation. Consequently, the incremental marginal surplusis positive when investment is in terms of capacity and it is negative wheninvestment is in term of flexibility. We also have by0(i) > 0 and bf 0(e) > 0.Hence, a larger investment in capacity leads to a larger output quantity in theimposed solution and thus to larger non-pecuniary benefits for the manager.Conversely, increasing investment in organizational adaptability provides abetter flexibility in the imposed solution and thus lower private benefits. Weconclude that, under public ownership, the two determinants of the man-ager’s investment go in the same direction: they induce positive marginalprofits when investment is in terms of capacity and negative marginal profitswhen investment is in terms of organizational adaptability. This explains theresult in Proposition 2-i.Proposition 2-ii and Corollary 1 show that investment in capacity may be

larger when the firm is public than when it is private. This is particularly thecase when the investment in capacity is highly specific and the bargainingpower of the firm is low. In that case the private firm strongly under-investsbecause the hold-up of its profits is particularly high and capacity investmentof the public firm may exceed the one of the private firm.

13When (15) does not hold at equilibrium, we have by(i) = 0 and bf(e) = 0. Comparing(29) and (32) then shows that ip > in in that case. In other words, when it is too costly tothe government to impose a change in the output vector, the public manager’s equilibriuminvestment is smaller than that of the private manager.

17



In particular, when in > ip , then µ∗1(in) + µ∗2(en) > µ∗1(ip) + µ

∗2(ep) =

µ∗1(ip). Hence, when capacity investment is higher in the public firm than inthe private firm, the manager of the public firm obtains larger non-pecuniarybenefits than the manager of the private firm. Two reasons cumulate here:investment in capacity induces positive non-pecuniary benefits and the man-ager of the public firm do not incur the non-pecuniary costs of organizationaladaptability investments.Proposition2-iii shows that a state-owned firm may even invest more than

what would be socially efficient: we would then have in > i∗. Since i∗ andthe bµ1(i) function do not depend on α, the inequality in Proposition 2-iii issatisfied if bµ0(i∗) > ψ0(i∗) and α is large enough.

Proposition 3 i) Under private ownership, the investments in capacity andin organizational adaptability and the government’s payoff are decreasing with

respect to the government’s bargaining power, i.e.∂ip∂α

< 0 ,∂ep∂α

< 0 and

∂U∗Gp∂α

< 0. The first-best optimum is reached at α = 0.

ii) Under public ownership, a sufficient condition for investment in ca-pacity to be increasing with respect to the government’s bargaining power, i.e.∂in∂α

> 0, is v0001iy2 ≤ 0 and v0001y3 − c000 ≤ 0. In such a case, we have∂U∗Gn∂α

> 0

if in < i∗.

An increase in the government’s bargaining power exacerbates the hold-up problem, which discourages the firm from investing in specific assets.Hence, as indicated in Proposition 3-i, optimally under private ownershipthe whole bargaining power should be given to the manager. Proposition3-ii shows that, for capacity investment, this result may be reversed underpublic ownership. This may at first sight appear paradoxical. Although theissue of expropriation is more serious the larger the government’s bargainingpower, the firm has stronger incentives to invest! The reason is that, whenthe government’s bargaining power increases, the manager cares more abouthis private benefits in the imposed solution which incites him to invest incapacity. As regards investment in organizational flexibility, we know that itis entirely neglected by the manager of the state-owned firm, whatever thedistribution of bargaining powers. Hence, in the public ownership regime, thegovernment payoff varies in the same direction as the capacity investment.The intuition of Proposition 3-ii is the following. Equation (24) shows thatthe equilibrium payoff of the manager gets closer to his default payoff whenthe government’s bargaining power increases. Furthermore, under public

18

18

ownership, the default payoff of the manager is equal to the sum of the con-tractual wages w0 and of the private benefits, less investment costs -see(13)-.Hence, the manager’s investment behavior is more and more affected by pri-vate benefits when the government’s bargaining power is increasing, whichstimulates capacity investment. More precisely, we know from (32) that in astate-owned firm, the marginal benefits of capacity investment is a weightedsum of the marginal private benefits (with weight α) and of the incrementalmarginal surplus (with weight 1 − α). As above mentioned, the marginalprivate benefit and the incremental marginal surplus are both positive forcapacity investment. Under the conditions given in Proposition 3-ii, themarginal private benefit is larger than the incremental marginal surplus, sothat an increase in α leads to an increase in the marginal benefits of capacityinvestment, which exerts a positive effect on capacity investment.

Proposition 4 Suppose that the functions v1 (y, i) , µ1(y), c1 (y) and ψ1(i)are respectively replaced by σv1 (y, i) , σµ1(y), σc1 (y) and σψ1(i) and thatthe functions v2(f, e), µ2 (f) , c2(f) and ψ2(e) are respectively replaced by(1−σ)v2(f, e), (1−σ)µ2 (f), (1−σ)c2(f) and (1−σ)ψ2(e),where 0 < σ < 1.Suppose also that K1(i) is replaced by θ1σK1(i) and K2(e) is replaced byθ2(1− σ)K2(e) where 0 < θ1 < 1 and 0 < θ2 < 1.Let

i0 = arg maxK1(i)− ψ1(i), i ≥ 0i1 = arg maxbµ1(i)− ψ1(i), i ≥ 0

Assume that i0 < i1 < i∗ . Assume also v0001iy2 ≤ 0 and v0001y3 − c000 ≤ 0.Then, there exists α(σ, θ1, θ2) in (0, 1), decreasing in σ and increasing in θ1and θ2, such that ip > in and U∗Gp > U∗Gn if α < α(σ, θ1, θ2) and ip < inand U ∗Gp < U∗Gn if α > α(σ, θ1, θ2). If i1 < i0 , then U ∗Gp > U∗Gn for allα, σ, θ1, θ2.

Proposition 4 shows that the superiority of private or public ownershipdepends simultaneously on three factors: the bargaining powers of the man-ager and of the government, the degree of specificity of investments andthe relative weight of quantity and flexibility concerns in the social welfare.Note that i0 and i1 in Proposition 4 respectively denote the equilibrium in-vestments in capacity under private and public ownership when α = θ1 = 1.If i0 < i1 < i∗, then public ownership dominates private ownership whenα = θ1 = 1 and when renegotiation of the government-manager contractis only about the quantitative dimension of the output (i.e. σ = 1). By

19



continuity, still when σ = 1,there exists α less than one, such that publicownership is superior to private ownership if α < α < 1. When σ decreases,then the relative weight of the flexibility dimension in the social welfareincreases which makes a case for private ownership. Consequently, when σis less than one, the threshold value α(σ, θ1, θ2) over which public ownershipis superior to private ownership is decreasing with σ. Likewise α(σ, θ1, θ2) isincreasing in θ1 and θ2 because a less specific investment in capacity favorsprivate ownership. When i1 < i0, private ownership is always superior topublic ownership. The definition of i0 and i1 shows that public ownershipmay possibly be superior to private ownership only if capacity investmentsare highly specific (as for instance in the case of site specificity) and if suchinvestment bring large positive private benefits to the firm’s manager in theimposed solution.

20

20

5 Illustrations and concluding comments

The effects of private benefits on managers’ incentives has been widely em-phasized in the literature on corporate governance. Indeed, one of the mostpopular ways to model the basic moral hazard problem in corporate gov-ernance uses the concept of private benefit enjoyed by insiders (cf. Tirole(2001)). Although this is not usual, it should not be astonishing to alsofocus the analysis of ownership and control of public utilities on private ben-efits. Among the many different examples of private benefits of controllinga public utility, we may name a few: empire building feelings, private inter-est for a particular activity(e.g., a new technology development project), jobsecurity, opportunities to hire friends and relatives, convenient overstaffing,lack of internal conflict, channeling money to affiliated entities, unmotivatedexpenses, etc...The approach and results of this paper may be usefully illustrated by

some examples. SNCF (the French railroad monopoly) provides a good ex-ample of how deeply insiders’ private benefits may affect the management ofa public utility. According to the Fondation Saint Simon (1997), a Frenchthink tank on the efficiency of public administrative bodies, SNCF is charac-terized by a corporate culture which neglects the economic indicators in favorof a system relying on technical and budgetary performances. As a result,financial responsibility is weak and we are in a situation of a soft budget con-straint. This culture also systematically favored new investment as opposedto reorganization of the work force, successfully resisting to most attemptsto structural changes. Insiders have also succeed in acquiring and defendingvery significant privileges in terms of working conditions, overstaffing andretirement legislations.As an illustration of possible interactions between managers’ private ben-

efits and non-contractible investments, let us consider two examples.The first one is related to security enhancing organizational changes and

innovations. We here may think about developing a corporate culture sup-porting personal responsibility for safety, or emphasizing safety aspects inthe elaboration of new projects and in R&D activities. Such concerns areparticularly important in risky activities such as nuclear energy but also forpublic transportation. When such investments are intensive, rene-gotiation should lead to an increase in safety standards. Likewise, in publictransportation, safety is often used as an argument to resist cuts in the laborforce and to implement innovative projects. This suggests that a concern forsafety is congruent with the employee’s interest, i.e. it is connected withpositive private benefits. In such a case, our model predicts that public own-

21



ership may be efficient because the government can exploit this congruenceto achieve a high level of welfare. It turns out that some of the sectors thatare still strongly resisting against privatisation are sectors where safety ishighly valued. In France, examples are precisely railroad transportation andelectricity production14.The second type of investment is related to flexibility enhancing organi-

zational changes and innovations. Non-contractible investments may includeadapting the organizational structure to enable a quick response to changesin consumer demand, for instance by preparing for an out-sourcing of someactivities or, more generally, for a restructuring of the firm’s activities amongsites or product lines. It may also include developing a strategy to get ridof “older” less flexible workers. Out-sourcing or restructuring often meansunemployment or at best reduced job security if the old employees can keeptheir employment in the new structure. In such a case, a concern for flexibilitywould not be congruent with employee’s private interests. Our theory thenpredicts that public ownership is inefficient. The telecom industry providesa good example of this situation. It witnesses quick developments that ne-cessitates a high degree of flexibility to respond to technological innovations,and it has been extensively privatized in Europe most successfully.Our theoretical approach has been developed in terms of incomplete con-

tracts. The model we have presented shows that, at equilibrium, the privatebenefits play a different role in the determination of incentives to invest. Un-der public ownership, the investment incentives are strongly affected by thenon-pecuniary private benefits obtained by the firm’s employees within therelationship with the government. Under private ownership, the incentivesto undertake non-contractible investment are affected by pecuniary and non-pecuniary benefits obtained outside the relationship and the driving forcebehind investment is the ability of the firm to redeploy its assets to otheruses in case of negotiation failure (i.e. the specificity of its investments).This distinction yields interesting implications for the relative perfor-

mances of the two regulatory regimes depending on the technological andthe institutional context. If the firm’s investment is connected with positivemarginal private benefits for the employees such as a decision to expand theactivity and if the investment is significantly specific, public ownership mayyield a higher payoff to the government. This suggests that the technological

14Of course, safety is also a major concern for many other sectors (such as airlines andthe chemical industry) which are private in France. However such branches of industryare highly competitive, with a worldwide market place, contrary to utilities like railroadtransportation and (still to a large extent) electricity. The fact that firms operate incompetitive markets may explain by itself for numerous reasons that a private ownershipregime emerged as the most efficient one.

22

22

state of a regulated industry is of crucial importance when the issue of priva-tization is discussed. Historically, most public utilities have gone through aperiod of extensive development and they are today in a phase of consumer-oriented intensive growth. This is, for instance, the case of the Europeanelectricity and telecom industry. The previous results gives a rationale forwhy the electricity industry in France may have been kept in public owner-ship under the sixties and the seventies in countries like France, during thebuilding up of the nuclear power plants, while its privatization is discussedtoday.The relative efficiency of the ownership structure also depends on the

institutional context in so far as it determines the regulator’s effective bar-gaining power. Our model predicts that private ownership dominates publicownership when the government’s bargaining power is not too large. In prac-tice, this should be related to the ability of the government to credibly com-mit not to abuse its power. In contrast, when the regulator is interventionist,public ownership may be preferable. This provides us with a non-ideologicalargument for explaining cross-country distinctions in the regulation of publicutilities. While the technological and informational contexts are essentiallythe same, the Anglo-American countries have typically been ahead of the pri-vatization wave. Our analysis suggests that the gains of privatization weremore important in these countries than in continental Europe.

23



A P P E N D I X

Proof of Proposition 1

The results follow from equations (25) to (30) and from the fact that U ∗Mp

is concave with respect to i and e.


(i) We have bµ01 (i) = µ01(by (i))by0 (i) > 0Furthermore v001iy > 0 and y

∗(i) > by(i) givev01i (y

∗ (i) , i)− v01i (by (i) , i) > 0Assume in = 0. We then have

αbµ01 (0) + (1− α) [v01i (y∗ (0) , 0) −v01i (by (0) , 0)]− ψ01 (0)

= αbµ01 (0) + (1− α) [v01i (y∗ (0) , 0) −v01i (by (0) , 0)] > 0

which contradicts (32). Hence in > 0.We have bµ02 (e) = µ02( bf (e)) bf 0 (e) > 0

Furthermore v002ef > 0 and f∗(e) < bf(e) give

v02e (f∗ (e) , e)− v02e

³ bf (e) , e´ > 0Hence the left-hand side in (33) is negative which gives en = 0.

(ii) We know from (29) that in > ip if and only if

αK 01 (in) + (1− α) v01i (y

∗ (in) , in)− ψ01 (in) < 0

Using in > 0 and (32) gives

ψ01 (in) = αbµ01 (in) + (1− α) [v01i (y∗ (in) , in)− v01i (by (in) , in)]

Consequently, in > ip if and only if

αK 01 (in)− αbµ01 (in) + (1− α)v01i (by (in) , in) < 0

hence the result.

24

24

(iii) We know from (32) that in > i∗ if and only if

αbµ01 (i∗) + (1− α) [v01i (y∗ (i∗) , i∗)] −v01i (by (i∗) , i∗)]

−ψ01 (i∗) > 0

Using (25) allows us to rewrite this condition as

αbµ01(i∗)− (1− α)v01i(by(i∗), i∗)− αψ01(i∗) > 0

hence the result.

Proof of Corollary 1

Proposition 2-ii shows that in > ip if and only if

α[bµ01 (in) + v01i (by (in) , in)− θK 01(in)] > v

01i (by (in) , in) (35)

Observe that in does not depend on θ.Assume

θ <bµ01 (in)K 01(in)

Then (35) is satisfied if and only if α > bα, withbα = v01i (by (in) , in)

v01i (by (in) , in) + bµ01 (in)− θK 01(in)

∈ (0, 1)


(i) Using (29) and the concavity of U∗Mpwith respect to i shows that

∂ip/∂α and K 01 (ip) − v01i (y∗ (ip) , ip) have the same sign. Using (27) then

shows that ∂ip/∂α < 0. One can show similarly that ∂ep/∂α < 0.(31) then gives

∂U∗Gp∂α

= W ∗01 (ip)

∂ip∂α

+W ∗02 (ep)

∂ep∂α

with W ∗01 (ip) > 0 and W ∗0

2 (ep) > 0 when α > 0 because 0 < ip < i∗ and0 < ep < e

∗ in that case and W ∗1 (ip),W

∗2 (ep) are concave functions. Hence

∂U∗Gp∂α

< 0

25



When α = 0, we have ip = i∗ , ep = e∗ and

U ∗Gp =W∗1 (i

∗) +W ∗2 (e

∗)

which shows that the aggregate surplus is maximized in such a case.(ii) Using (32) and the concavity of U ∗Mn with respect to i shows that

∂ip/∂α and

A = bµ01 (in)− [v01i (y∗ (in) , in)− v01i (by (in) , in)]have the same sign. Equation (11) allows us to write

by0(i) = v001yi(by(i), i)c001(by(i))− v001y2(by(i), i)

which gives

bµ01 (in) = µ01(by (in))by0 (in) = µ01(by (in))v001yi(by(in), in)c001(by(in))− v001y2(by(in), in) (36)

Furthermore,

v01i (y∗ (in) , in)− v01i (by (in) , in)

= v001iy (θy∗ (in) + (1− θ)by (in) , in) [y∗ (in)− by (in)] (37)

for some θ in (0, 1).Assume v0001iy2 ≤ 0. Using y∗ (in) > by (in) gives

v001iy (θy∗ (in) + (1− θ)by (in) , in) ≤ v001iy (by (in) , in) (38)

hence, using (36), (37) and (38) allows us to write

A ≥ v001iy (by (in) , in) [ µ01(by (in))c001(by(in)) − v001y2(by(in), in) − y∗ (in) + by (in)] (39)

Assume also v0001y3−c000 ≤ 0, which means that c0(y)−v01y(y, i) is a (weakly)convex function of y.We obtain

[c00(by(in))− v001y2(by(in), in)][y∗ (in)− by (in)]≤ [c0(y∗(in))− v01y(y∗(in), in)]− [c0(by(in))− v01y(by(in), in)] (40)

= µ01(y∗ (in))

(39) and (40) imply

A ≥ v001iy (by (in) , in) [y∗ (in)− by (in)]µ01(by (in)) − µ01(y∗ (in))µ01(y∗ (in))

26

26

by(in) < y∗(in) and µ001 < 0 then give µ01(by (in)) > µ01(y∗ (in)) and thus A >

0,which completes the proof.


Let ip(α, θ1), ep(α, θ2), in(α) and en(α) be the equilibrium investment strate-gies, respectively under private and public ownership.. We have in(1) = i1

and ip(1, 1) = i0 and

∂ip∂α

< 0 ,∂ip∂θ1

> 0 ,∂ep∂α

< 0 ,∂ep∂θ2

> 0 ,∂in∂α

> 0 , en(α) = 0

We may write U∗Gp as a function of α, σ, θ1 and θ2 :

U∗Gp(α, σ, θ1, θ2) = σW ∗1 (ip(α, θ1)) + (1− σ)W ∗

2 (ep(α, θ2))

with∂U∗Gp∂α

= σW ∗01

∂ip∂α

+ (1− σ)W ∗02

∂ep∂α

< 0 (41)

∂U ∗Gp∂θ1

= σW ∗01

∂ip∂θ1

> 0 (42)

∂U∗Gp∂θ2

= (1− σ)W ∗02

∂ep∂θ2

> 0 (43)

Likewise we may write U∗Gn as a function of α and σ :

U∗Gn(α, σ) = σW ∗1 (in(α)) + (1− σ)W ∗

2 (0)

Using in(1) = i1 < i∗ gives

∂U∗Gn∂α

= σW ∗01

∂in∂α

> 0 (44)

We also have

U∗Gp(0, σ, θ1, θ2) > U∗Gn(0, σ) for all σ, θ1, θ2 (45)

and

U∗Gp(1, σ, θ1, θ2) = σW ∗1 (i

0) + (1− σ)W ∗2 (ep(0, θ2))

< σW ∗1 (i

1) + (1− σ)W ∗2 (0)

because i0 < i1 < i∗. Using in(1) = i1 gives

U∗Gp(1, σ, θ1, θ2) < U∗Gn(1, σ) for all σ, θ1, θ2 (46)

27



(41), (44), (45) and (46) show that there exists bα(σ, θ1, θ2) in (0, 1) suchthat

U∗Gp(bα, σ, θ1, θ2) = U∗Gn(bα, σ)which implies U∗Gp > U

∗Gn if α < bα(σ, θ1, θ2) and U∗Gp < U∗Gn if α > bα(σ, θ1, θ2).

We also have ip(bα, θ1) < in(bα) and ep(bα, θ2) > 0. (42) and (43) imply∂bα∂θ1

> 0 and∂bα∂θ2

> 0

Furthermore∂ bα∂σ

=

∂U∗Gp∂σ− ∂U∗Gn

∂σ∂U∗

Gn

∂α− ∂U∗

Gp

∂α

< 0

because∂U ∗Gn∂α

> 0∂U∗Gp∂α

< 0

and∂U∗Gp∂σ− ∂U∗Gn

∂σ= W ∗

1 (ip(bα, θ1))−W ∗1 (in(bα))

−[W ∗2 (ep(bα, θ2))−W ∗

2 (0)] < 0

28

28

References

[1] Armstrong M., S. Cowan et J. Vickers (1994), Regulatory Reform - Eco-nomic Analysis and British Experience, MIT Press, Cambridge.

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[12] Tirole Jean (2001) “Corporate Governance”, Econometrica, Vol 69, N1,January 2001, 1-35

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