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Competition and Incentives with Motivated Agents

By TIMOTHY BESLEY AND MAITREESH GHATAK*

A unifying theme in the literature on organizations such as public bureaucraciesand private nonprofits is the importance of mission, as opposed to profit, as anorganizational goal. Such mission-oriented organizations are frequently staffed bymotivated agents who subscribe to the mission. This paper studies incentives in suchcontexts and emphasizes the role of matching the mission preferences of principalsand agents in increasing organizational efficiency. Matching economizes on theneed for high-powered incentives. It can also, however, entrench bureaucraticconservatism and resistance to innovations. The framework developed in this paperis applied to school competition, incentives in the public sector and in privatenonprofits, and the interdependence of incentives and productivity between theprivate for-profit sector and the mission-oriented sector through occupationalchoice. (JEL D23, D73, H41, L31)

The late twentieth century witnessed a his-toric high in the march of market capitalism,with unbridled optimism in the role of the profitmotive in promoting welfare in the productionof private goods. Moreover, this generated abroad consensus on the optimal organization ofprivate good production through privatelyowned competitive firms. When it comes to theprovision of collective goods, no such consen-sus has emerged.1 Debates about the relativemerits of public and private provision stilldominate.

This paper suggests a contracting approach tothe provision of collective goods. It focuses ontwo key issues: how to structure incentives, and

the role of competition between providers. Atits heart is the idea that organizations that pro-vide collective goods cohere around a mission.2

Thus production of collective goods can beviewed as mission-oriented.

Our approach cuts across the traditionalpublic-private divide. Not all activities withinthe public sector are mission-oriented. For ex-ample, in some countries, governments own carplants. While this is part of the public sector, theoptimal organization design issues here are nodifferent from those faced by General Motors orFord. Not all private sector activity is profit-oriented. Universities, whether public or pri-vate, have many goals at variance with profitmaximization. Our examples will draw fromboth the public and the private sectors.

The missions pursued in the provision ofcollective goods come from the underlying mo-tivations of the individuals (principals andagents) who work in the mission-oriented sec-tor. Workers are typically motivated agents, i.e.,agents who pursue goals because they perceiveintrinsic benefits from doing so. There are manyexamples—doctors who are committed to sav-ing lives, researchers to advancing knowledge,judges to promoting justice, and soldiers to de-fending their country in battle. Viewing workers

* Besley: London School of Economics, HoughtonStreet, London WC2A 2AE (e-mail: [email protected]);Ghatak: London School of Economics, Houghton Street,London WC2A 2AE (e-mail: [email protected]). Theauthors would like to thank numerous seminar participantsas well as Daron Acemoglu, Alberto Alesina, MadhavAney, Ben Bernanke, Michela Cella, Leonardo Felli, JulianLe Grand, Caroline Hoxby, Rocco Machiavello, MegMeyer, Hannes Mueller, Andrei Shleifer, Daniel Sturm,Steve Tadelis, Jean Tirole, and two anonymous referees forhelpful comments. Financial support from the Economicand Social Research Council through research grant RES-000-23-0717 is gratefully acknowledged.

1 We use the term “collective good” as opposed to thestricter notion of a “public good.” Collective goods in thissense also include merit goods. This label also includes agood like education to which there is a commitment tocollective provision, even though the returns are mainlyprivate.

2 See, for example, James Q. Wilson (1989) on publicbureaucracies and Robert M. Sheehan (1996) on nonprofits.Jean Tirole (1994) is the first paper to explore the implica-tions of these ideas for incentive theory.

616

as mission-oriented makes sense when the out-put of the mission-oriented sector is thought ofas producing collective goods. The benefits andcosts generated by mission-oriented productionorganizations are not fully reflected in the mar-ket price. In addition, donating our incomeearned in the market to an organization thatpursues a mission that we care about is likely tobe an imperfect substitute for joining and work-ing in it. This could be due to the presence ofagency costs or because individuals care notonly about the levels of these collective goods,but also about their personal involvement intheir production (i.e., a “warm glow”).

It is well known from the labor literature oncompensating differentials that employmentchoices and wages depend on taste differences(Sherwin Rosen, 1986). This paper exploreshow these economize on the need for explicitmonetary incentives while accentuating the im-portance of nonpecuniary aspects of organiza-tion design in increasing effort. Thus, missionchoice can affect the productivity of the orga-nization. For example, a school curriculum ormethod of discipline that is agreed to by theentire teaching faculty can raise schoolproductivity.

Mission preferences typically differ, how-ever, between motivated agents. Doctors mayhave different views about the right way to treatill patients, and teachers may prefer to teachdifferent curriculums. This suggests a role fororganizational diversity in promoting alterna-tive missions and competition between organi-zations in attracting motivated agents whosemission preferences best fit with one another.We show that there is a direct link between suchsorting and an organization’s productivity.

The insights from the approach have applica-tions to a wide variety of organizations includ-ing schools, hospitals, universities, and armies.In this paper we abstract from the question ofpublic versus private ownership.3 The primi-tives are the production technology, the moti-vations of the actors, and the competitiveenvironment. We also abstract (for the mostpart) from issues of financing.

We benchmark the behavior of the mission-oriented part of the economy against a profit-

oriented sector where standard economicassumptions are made—profit seeking and nononpecuniary agent motivation. This is impor-tant for two reasons. First, we get a precisecontrast between the incentive structures ofprofit-oriented and mission-oriented production.Second, the analysis casts light on how changesin private sector productivity affect optimalincentive schemes operating in the mission-oriented sector. This has implications for de-bates about how pay-setting in public sectorbureaucracies responds to the private sector.

Our approach yields useful insights into on-going debates about the organization of themission-oriented sector of the economy. Forexample, it offers new observations on the roleof competition in enhancing productivity inschools. More generally, it suggests that one ofthe main virtues of private nonprofit activity isthat it can generate a variety of different mis-sions which improve productivity by matchingmanagers and workers who have similar mis-sion preferences. An analogous argument canbe made in support of decentralization of publicservices. On the flip side, however, public bu-reaucracies, whose policies can be imposed bypoliticians, may easily become demotivated inthe event of a regime change. Also, whilematching on mission preferences is potentiallyproductivity enhancing, it also leads to conser-vatism and can raise the cost of organizationalchange.

This paper contributes to an emerging litera-ture which studies incentive issues outside ofthe standard private goods model.4 One strandputs weight on the multitasking aspects of non-profit and government production along thelines of Bengt Holmstrom and Paul Milgrom(1991). Another emphasizes the career concernaspects of bureaucracies (Mathias Dewatripontet al., 1999; Alberto Alesina and Guido Tabel-lini, 2004). These two areas are brought to-gether in Daron Acemoglu et al. (2003).However, these all work with standard motiva-tional assumptions. This paper shares in com-mon with George Akerlof and Rachel Kranton(2005), Roland Benabou and Tirole (2003),Josse Delfgaauw and Robert Dur (2004), Avi-nash Dixit (2001), Patrick Francois (2000),Kevin Murdock (2002), Canice Prendergast

3 See Besley and Ghatak (2001) on the question ofoptimal ownership in the context of public goods. 4 See Dixit (2002) for a survey of this literature.

617VOL. 95 NO. 3 BESLEY AND GHATAK: COMPETITION AND INCENTIVES WITH MOTIVATED AGENTS

(2001), and Paul Seabright (2003) the notionthat nonpecuniary aspects of motivation mat-ter.5 In common with Vincent Crawford andJoel Sobel (1982) and Philippe Aghion and Ti-role (1997), our approach emphasizes how non-congruence in organizational objectives canplay a role in incentive design. We explore,however, the role of matching principals andagents—selection rather than incentives—as away to overcome this.6

The remainder of the paper is organized asfollows. In Section I, we lay out the basic modeland study optimal contracts and the matching ofprincipals and agents. Section II explores appli-cations of the model, and Section III concludes.

I. The Model

A. The Environment

A “firm” consists of a risk-neutral principaland a risk-neutral agent. The principal needs theagent to carry out a project. The project’s out-come (which can be interpreted as quality) canbe high or low: YH � 1 (“high” or “success”)and YL � 0 (“low” or “failure”). The probabilityof the high outcome is the effort supplied by theagent, e, at a cost c(e) � e2/2. Effort is unob-servable and hence noncontractible. We assumethat the agent has no wealth and so cannot put ina performance bond. Thus, a limited-liabilityconstraint operates, which implies that the agenthas to be given a minimum consumption levelof w� � 0 every period, irrespective of perfor-mance. Because of the limited-liability con-straint, the moral hazard problem has bite. Thisis the only departure from the first-best in ourmodel.

We assume that each principal has sufficientwealth so as not to face any binding wealthconstraints, and that the principal and agenteach can obtain an autarchy payoff of zero.

The mapping from effort to outcome is thesame for all projects. We also assume that

agents are identical in their ability to work onany type of project. Projects differ exclusivelyin terms of their missions. A “mission” consistsof attributes of a project that make some prin-cipals and agents value its success over andabove any monetary income they receive in theprocess. This could be based on what the orga-nization does (charitable versus commercial),how they do it (environment-friendly or not),who the principal is (kind and caring versusstrict profit-maximizer) and so on. Allowingagents to have preferences over their work en-vironment follows a long tradition in labor eco-nomics (see, for example, Rosen, 1986).

In our basic model, missions are exogenouslygiven attributes of a project associated with aparticular principal. In Section I C, we examineconsequences of endogenizing mission choice.

There are three types of principals andagents, labelled i � {0, 1, 2} and j � {0, 1, 2}.The types of principals and agents are perfectlyobservable. If the project is successful, a prin-cipal of type i receives a payoff of �i � 0. Allprincipals receive 0 if a project is unsuccessful.Principals of type 0 have the same preferencesas in the standard principal-agent model, i.e., �0is entirely monetary. However �1 and �2 mayhave a nonpecuniary component. To focus ex-clusively on horizontal aspects of matching be-tween principals and agents, we assume that�1 � �2 � �.7

Some agents care about the mission of theorganization for which they work. Formally thisimplies that the payoff of such agents dependson their own type, and the type of the principalfor whom they work. Like principals, all agentsare assumed to receive 0 if the project fails,irrespective of with whom they are matched.Agents of type 0 have standard pecuniaryincentives—their utility depends positively onmoney and negatively on effort. Since they aremotivated solely by money, they do not careintrinsically about which organization theywork for. In contrast, an agent of type 1 (type 2)receives a nonpecuniary benefit of �� from

5 Some of these ideas consider the possibility that intrin-sic motivation can be affected by the use of explicit incen-tives (see also Richard Titmuss, 1970, and Bruno S. Frey,1997). We treat the level of intrinsic motivation as given.

6 See Daniel Ackerberg and Maristella Botticini (2002),Kaniska Dam and David Perez-Castrillo (2001), andEdward P. Lazear (2000) for approaches to principal agentproblems where sorting is important.

7 We use the term horizontal matching to describe asituation where there is no difference in the productivity oforganizations when principals and agents are efficientlymatched. The standard vertical matching model looks atsituations where some principals and agents are more pro-ductive regardless of whom they match with. We will brieflyreturn to the implications of vertical sorting in Section II B.

618 THE AMERICAN ECONOMIC REVIEW JUNE 2005

project success if he works for a principal oftype 1 (type 2), and � if matched with a princi-pal of type 2 (type 1), where �� 0.8

The payoff of an agent of type j who ismatched with a principal of type i when theproject succeeds can therefore be summarizedas:

�ij � �0 i � 0 and/or j � 0� i � �1, 2�, j � �1, 2�, i � j�� i � �1, 2�, j � �1, 2�, i � j.

We will refer to the parameter �ij as agentmotivation and agents of type 1 and 2 as moti-vated agents. We will refer to the economy asbeing divided into a mission-oriented sector(i.e., i � 1, 2) and a profit-oriented sector (i.e.,i � 0).

We make

ASSUMPTION 1:

max��0 , � � �� 1.

This ensures that there is an interior solution foreffort in all possible principal-agent matches.

The analysis of the model is in three steps.We first solve for the optimal contract for anexogenously given match of a principal of typei and an agent of type j. Contracts betweenprincipals and agents have two components: afixed wage wij , which is paid regardless of theproject outcome, and a bonus bij , which theagent receives if the outcome is YH. Initially, wetake the agent’s reservation payoff u� j � 0 to beexogenously given. Second, we consider theextension to endogenous missions which makes�ij endogenous. Third, we study matching ofprincipals and agents where the reservation pay-offs are endogenously determined.

B. Optimal Contracts

As a benchmark, consider the first-best casewhere effort is contractible. This will result in

effort being chosen to maximize the jointpayoff of the principal and the agent. Thiseffort level will depend on agent motivationand hence the principal-agent match. Thecontract offered to the agent, however, playsno allocative role in this case.9 Thus, whilematching may raise efficiency, it has no im-plications for incentives in the first best. It isstraightforward to calculate that the first-besteffort level in a principal-agent pair where theprincipal is type i and the agent is type j is�i � �ij . The expected joint surplus in thiscase is 1⁄2 (�i � �ij)

2.10

In the second best, effort is not contractible.The principal’s optimal contracting problem un-der moral hazard solves:

(1) max�bij ,wij�

u ijp � ��i � bij�eij � wij

subject to:

(a) The limited-liability constraint requiringthat the agent be left with at least w� :

(2) bij � wij � w� , wij � w� ;

(b) The participation constraint of the agentthat:

(3) uija � eij �bij � �ij � � wij �

12

eij2 � u� j ;

(c) The incentive-compatibility constraint, whichstipulates that the effort level maximizes theagent’s private payoff given (bij , wij):

eij � arg maxeij�0,1

�eij�bij � �ij� � wij �12

eij2�.

We will restrict attention to the range ofreservation payoffs for the agent in which theprincipal earns a nonnegative payoff. Theincentive-compatibility constraint can be sim-plified to:

8 These payoffs are contractible, unlike in Oliver D.Hart and Holmstrom (2002), where noncontractibility ofprivate benefits plays an important role. Also, these areindependent of monetary incentives, which is contrary tothe assumption in the behavioral economics literature(see Frey, 1997).

9 Any values of bij and wij such that the agent gets at leastw� in all states of the world, and his expected payoff is atleast u� j, will work.

10 The Pareto-frontier is a straight line with slope equalto minus one and intercepts on both axes equal to the jointsurplus.


(4) eij � bij � �ij

as long as eij � [0, 1].11

Let v� ij be the value of the reservation payoffof an agent of type j, such that a principal oftype i makes zero expected profits under anoptimal contract. Also, due to the presence oflimited liability, the participation constraint ofthe agent may not bind if the reservation payoffis very low. Let vij denote the value of thereservation payoff such that for u� j � v ij , theagent’s participation constraint binds. In the Ap-pendix we show that v�ij and v ij are positive realnumbers under our assumptions, and v ij � v�ij.

12

A further assumption is needed to guaranteethe existence of optimal contracts under moralhazard. In particular, the payoff from projectsuccess to the principal and/or the agent must behigh enough to offset the agency costs due tomoral hazard, and must ensure both parties re-ceive nonnegative payoffs. The following as-sumption provides a sufficient condition for thisto be true for any principal-agent match:

ASSUMPTION 2:

14

min��0 , ��2 � w� 0.

The following proposition characterizes theoptimal contract. All proofs are presented in theAppendix.

PROPOSITION 1: Suppose Assumptions 1 and2 hold. An optimal contract (b*ij , w*ij) between aprincipal of type i and an agent of type j givena reservation payoff u� j � [0, v� ij] exists, and hasthe following features:

(a) The fixed wage is set at the subsistencelevel, i.e., w*ij � w� ;

(b) The bonus payment is characterized by

b*ij � �max�0,�i � �ij

2 � if u� j � 0, v ij

�2�u� j � w� � � �ij if u� j � v ij , v� ij;

(c) The optimal effort level solves: e*ij � b*ij � �ij.

The first part of the proposition shows thatthe fixed wage payment is set as low as possi-ble. Other than the agent’s minimum consump-tion constraint, the agent is risk neutral and doesnot care about the spread between his income inthe two states. Hence, the principal will want tomake the fixed wage as small as possible.

The second part characterizes the optimalbonus payment and the third part characterizesoptimal effort, which follows directly from theincentive-compatibility constraint. Limited lia-bility implies that the principal cannot inducethe first-best level of effort in the presence ofmoral hazard.13 In choosing b the principalfaces a trade-off between providing incentivesto the agent (setting b higher) and transferringsurplus from the agent to himself (setting blower). Accordingly, the reservation payoff ofthe agent plays an important role in determiningb, and the higher the reservation payoff, thehigher is b.

Another important parameter is the motiva-tion of the agent. For the same level of b, anagent with greater motivation will supply highereffort. From the principal’s point of view, b is acostly instrument of eliciting effort. Since agentmotivation is a perfect substitute for b, moti-vated agents receive lower incentive pay at theoptimum. The various possibilities can be clas-sified in three cases that depend on the value ofthe reservation payoff, and whether the agentvalues project success more than the principal:

Case 1: If the agent is more motivated than theprincipal and the outside option is low, thenb*ij � 0, i.e., there should optimally be no in-centive pay.

11 This will be the case under the optimal contract. Thebonus payment bij will never optimally set to be greater than orequal to the principal’s payoff from success �i because thenthe principal will be receiving a negative expected payoff.Therefore, by Assumption 1, eij � 1. Also, it is never optimalto offer a negative bonus to the agent. The limited-liabilityconstraint requires that bij � wij � w� and so is feasible only ifwij � w� . But by increasing bij and decreasing wij while keepingthe agent’s utility constant, effort will go up and the principalwould be better off. Therefore, eij � 0.

12 We also show that v� ij is less than the joint surplusunder the first-best, which is what one would expect in thepresence of agency costs.

13 Making the agent a full residual claimant (i.e., bij ��i) will elicit the first-best effort level, but the principal’sexpected profits will be negative, making this an unattrac-tive option for him.


Case 2: If the principal is more motivated thanthe agent and the outside option is low, then

b*ij �12

��i � �ij �.

In this case, the principal sets incentive payequal to half the difference in the principal’sand agent’s valuation of the project.

Case 3: If the outside option is high then

b*ij � �2�u� j � w� � � �ij .

The optimal incentive pay, in this case, is setby the outside market with a discount depend-ing in size on the agent’s motivation.

The third part of the proposition characterizesoptimal effort, which depends on the sum of theagent’s motivation and the bonus payment. Inthe first case, the principal relies solely on agentmotivation, while in the second and third cases,additional incentives in the form of bonus pay-ments are provided. In Case 3, the effort level isentirely determined by the outside option.

We now offer three corollaries of this prop-osition, which are useful in understanding itsimplications for incentive design. The first de-scribes what happens in the profit-orientedsector:

COROLLARY 1: In the profit-oriented sector(i � 0), the optimal contract is characterized bythe following:

(a) The fixed wage is set at the subsistencelevel, i.e., w*0j � w� ( j � 0, 1, 2);

(b) The bonus payment is characterized by

b*0j � ��0

2if u� j � 0, v 0j

� 2�u� j � w� � if u� j � v 0j , v�0j

for j � 0, 1, 2;(c) The optimal effort level solves: e*0j � b*0j

( j � 0, 1, 2).

This follows directly from the fact that �0j �0 for j � 0, 1, 2. Notice that Case 1 above is nolonger a possibility—the agent in the profit-oriented sector must always be offered incentivepay to put in effort.

The next two corollaries regard the mission-oriented sector and illustrate the importance ofmatching principals and agents.

COROLLARY 2: Suppose that u�0 � u�1 � u�2.Then, in the mission-oriented sector (i � 1, 2),effort is higher and the bonus payment lower ifthe agent’s type is the same as that of theprincipal.

To see this, observe from part (b) of Prop-osition 1 that the bonus paid to the agent isdecreasing in his motivation, and is zero ifthe agent is at least as motivated as the prin-cipal. Moreover, the bonus is higher if i dif-fers from j. The observation that effort ishigher combines parts (b) and (c) of Proposi-tion 1. Hence, organizations with “well-matched” principals and agents will havehigher levels of productivity, other things be-ing the same (in particular, assuming thatreservation payoffs of agents are the same forall types).

COROLLARY 3: Suppose that u�0 � u�1 � u�2.Then, in the mission-oriented sector (i � 1, 2)bonus payments and effort are negatively cor-related in a cross section of organizations.

This follows directly from Corollary 2.Thus, holding constant the reservation pay-offs of agents (u� j), productivity (i.e., optimaleffort) and incentive pay will be (weakly)negatively correlated across organizations.This result, which appears surprising at firstglance, is capturing a pure selection effect.Holding the characteristics of the principalsand the agent constant, greater incentive paydoes lead to higher effort and higher produc-tivity, as in the standard principal-agentmodel. However, the heterogeneity among or-ganizations in the mission-oriented sector isdriven partly by the preferences of the agents,which affect both effort and incentivepayments.

These two corollaries are useful in demon-strating the costs of poor matching of princi-pals and agents in a world where there aremotivated agents. In Section I D, we showhow endogenous matching of principal-agentpairs and endogenous determination of theagents’ reservation payoffs can increaseefficiency.


C. Endogenous Motivation

In this section, we discuss how our frame-work can be extended to make the motivation ofagents endogenous by allowing the principal topick the mission of the organization.14 Supposethat both the principal and the agent in themission-oriented sector care about the mission.Let the mission be denoted by x, which is a realnumber in the unit interval X � [0, 1]. For thesake of concreteness, x could be a school cur-riculum with 0 denoting secular education and 1denoting a high degree of religious orientation.Let the nonpecuniary benefits of the principaland the agent conditional on project success beaffected by the mission choice. Formally, letgi(x) and hj(x) denote the payoff of a principalof type i and an agent of type j (i � 1, 2 and j �1, 2) when the mission choice is x � X. Thebasic model can be thought of as a case in whichthe mission is not contractible and is picked bythe principal after he hires an agent. In this case

x*i � arg maxx�X

�gi�x��,

which is independent of the agent’s type.15

If the mission choice is contractible, how-ever, then it might be optimal for the principalto use the mission choice to incentivize theagent, either by picking a “compromise” mis-sion somewhere between the principal’s andagent’s preferred outcomes or even picking theagent’s preferred mission. A full treatment ofthis is beyond the scope of this paper. However,to illustrate the issues involved, we provide asimple example. Consider Case 2 of Proposi-tion 1. Suppose that gi(x) � P � 1⁄2 (x � i)

2

and hj(x) � A � 1⁄2 (x � j)2 where i � X and

j � X are the “ideal” missions of principals oftype i and agents of type j, and P � A. Recallthat in this case, the agent is given a bonuspayment of 1⁄2 (�i � �ij) and the optimal effortlevel is e*ij � 1⁄2 (�i � �ij). The principal’sexpected payoff in this case is e*ij(�i � b*ij) � w�� 1⁄4 (�ij � �i)

2 � w� . The optimal mission, ifcontractible, will therefore solve:

x*ij � arg maxx�X

14�gi�x� � hj�x��2.

It is straightforward to show that the optimalmission choice is given by x*ij � (j � i)/2.16

This compromise mission increases �ij rela-tive to the case where the principal picks hisideal mission of i. Thus compromising on themission will reduce the need for incentive pay,i.e., b*ij will be lower. However, overall effort(and hence the productivity of the organization)will be greater. This illustrates how, absent per-fect matching, mission choice can be manipu-lated to raise agent motivation and is asubstitute for financial motivation.

We assume that full contractibility or non-contractibility of the mission are the two ex-treme cases. In reality, mission choice is likelyto be subject to incentive problems and a keyaspect of organization design aims to influencemission choice. In ongoing work, we study howchoosing nonprofit status or giving agents dis-cretion in mission-setting could be viewed asmechanisms through which a principal precom-mits not to choose missions that may be viewednegatively by agents. Although the mission can“bridge the gap” between the principal andagent, it is no substitute for having them agreeon the mission in the first place. In the nextsection, we explore how this comes aboutthrough matching.

D. Competition

A key feature of our model is that the types ofprincipals and agents affect organizational effi-

14 Endogenous motivation or mission preference couldbe the result of “socialization” of agents by principals (seeAkerlof and Kranton, 2005).

15 Thus, �� hj(x*j), � � hj(x*

i) for i � 1, 2, j � 1, 2, andi j.

16 Without loss of generality, suppose i � j. Observethat a value of x that exceeds i or is less than j will neverbe chosen since it is dominated by choosing x � i or x �j. The problem in this case is to choose x to maximize1⁄4 (gi(x) � hj(x))2 subject to the constraint gi(x) � hj

(x) (which is one of the conditions that characterizes case 2of Proposition 1). Notice that gi(x) � hj(x) is a concavefunction which attains its global maximum at (i � j)/2.The first derivative of (gi(x) � hj(x))2 is 2(gi(x) � hj(x))(dgi(x)/dx � dhj(x)/dx). The unique critical point of1⁄4 (gi(x) � hj(x))2 is therefore (i � j)/2. Notice that thederivative is strictly positive for all x � [j, (i � j )/2)and strictly negative for all x � ((i � j)/2, i]. Therefore,the function (gi(x) � hj(x))2 and affine transformations of itare pseudo-concave, and so the function attains a globalmaximum at x � (i � j)/2 (see Carl P. Simon andLawrence Blume, 1994, pp. 527–28). As P � A, the con-straint gi(x) � h j (x) is satisfied at x � (i � j )/2.


ciency. In this section, we consider what hap-pens when the different sectors compete foragents reverting to the case where the mission isexogenous.17 We study this without modelingthe competitive process explicitly, focusing in-stead on the implications of stable matching.We look for allocations of principals and agentsthat are immune to a deviation in which anyprincipal and agent can negotiate a contract thatmakes both of them strictly better off. Were thisnot the case, we would expect rematching tooccur.

First, we need to introduce some additionalnotation. Let Ap � {p0, p1, p2} denote the setof types of principals and let Aa � {a0, a1, a2}denote the set of types of agents. FollowingAlvin E. Roth and Marilda Sotomayor (1989),the matching process can be summarized by aone-to-one matching function � : Ap � Aa3Ap � Aa such that (a) �(pi) � Aa � {pi} forall pi � Ap; (b) �(aj) � Ap � {aj} for all aj �Aa; and (c) �(pi) � aj if and only if �(aj) � pifor all (pi, aj) � Ap � Aa. A principal (agent)is unmatched if �(pi) � pi (�(aj) � aj). Thisfunction simply assigns each principal (agent)to at most one agent (principal) and allows forthe possibility that a principal (agent) remainsunmatched, in which case he is described as“matched to himself.”

Let nip and nj

a denote the number of principalsof type i and the number of agents of type j inthe population. We assume that n1

a � n1p and

n2a � n2

p to simplify the analysis. However, thepopulation of principals and agents of type 0need not be balanced—we consider both unem-ployment, i.e., n0

a � n0p, and full employment,

i.e., n0a � n0

p. We assume that a person on the“long-side” of the market gets none of the sur-plus which pins down the equilibrium reserva-tion payoff of all types of agents.18

From the analysis in the previous section, fora given value of u� j, we can uniquely character-ize the optimal contract between a principal oftype i and an agent of type j. We begin byshowing that any stable matching must haveagents matched with principals of the sametype. This is stated as:

PROPOSITION 2: Consider a matching � andassociated optimal contracts (w*ij , b*ij) for i � 0,1, 2 and j � 0, 1, 2. Then this matching is stableonly if �(pi) � ai for i � 0, 1, 2.

This result says that all stable matches musthave principals and agents matched assorta-tively. This argument is a consequence of thefact that, for any fixed set of reservation pay-offs, an assortatively matched principal agentpair can always generate more surplus than onewhere the principal and agent are of differenttypes.19

This result allows us to focus on assortativematching. The next two results characterize thecontracts and the optimal effort levels in twocases—full-employment and unemployment inthe profit-oriented sector.

In the full employment case, principals com-pete for scarce agents with the latter capturingall of the surplus. This sets a floor on the payoffthat a motivated agent can be paid. Whether theparticipation constraint is binding now dependson how �0 compares with �ij and �. Let

� � max�� , �� .

We assume that when the mission-oriented andprofit-oriented sectors compete for agents, thenmission-oriented production is viable:

ASSUMPTION 3:

�� 0 .

The following proposition characterizes theoptimal contracts and optimal effort levelsunder the stable matching in the full-employment case:

PROPOSITION 3: Suppose that n0a � n0

p ( fullemployment in the profit-oriented sector). Thenthe following matching � is stable: �(aj) � pjfor j � 0, 1, 2 and the associated optimalcontracts have the following features:

17 It would be straightforward to extend the model toincorporate matching with endogenous missions.

18 For the case n0a � n0

p there is a range of possible valuesof the reservation payoff.

19 This requires a nonstandard matching argument be-cause of our focus on horizontal sorting. Recent results onassortative matching in nontransferable utility environmentsby Patrick Legros and Andrew F. Newman (2003) cannot beapplied in our setting.


(a) The fixed wage is set at the subsistencelevel, i.e., w*jj � w� for j � 0, 1, 2;

(b) The bonus payment in the mission-orientedsector is:

b*11 � b*22 �12

max��, �0 � ��02 � 4w� � � ��

and the bonus payment in the profit-oriented sector is:

b*00 ��0 � ��0

2 � 4w�

2;

(c) The optimal effort level solves: e*jj � b*jj �� for j � 1, 2 and e*00 � b*00.

The proposition illustrates how competitionand incentives interact. There are two effects.First, there is a matching effect. This reduces thedegree of heterogeneity in contracts observed inthe mission-oriented sector relative to the casewhere principals and agents are non-assortativelymatched. This also raises organizational pro-ductivity, which follows using the logic of Cor-ollary 2 given assortative matching. If theparticipation constraint is not binding, then thisis achieved with concomitant reductions in in-centive pay.20 In our setup, all agents in themission-oriented sector receive the same incen-tive payment in equilibrium and are equallyproductive.

Second, there is an outside option effect.Competition among principals pins down theequilibrium value of the outside option. Withfull employment in the profit-oriented sector,the expected payoff of profit-oriented principalsis driven to zero, with agents capturing all thesurplus from profit-oriented production. Thereservation utility of a motivated agent is set bywhat he could obtain by switching to the profit-oriented sector. A sufficiently productive profit-oriented sector (�0 � ��0

2 � 4w � �) leads toa binding participation constraint and a mission-oriented sector that uses more incentive pay. Thusthe outside option effect can also raise productiv-ity, but by increasing incentive pay of agents.

Proposition 3 also gives a sense of whenincentives will be less high-powered in mission-oriented production with motivated agents.Even if the participation constraint binds, thelevel of incentive pay in the mission-orientedsector is less than in the private sector by anamount �� . Without the participation constraintbinding, incentive pay in the mission-orientedsector is zero if �� , which also implies thatincentives are more high powered in the profit-oriented sector.21

We now consider what happens if there isunemployment in the profit-oriented sector andprofit-oriented principals are able to extract allthe surplus from this agent (at least in so far asthe limited-liability constraint permits). Thesupply price of motivated agents is now deter-mined by their unemployment payoff. The fol-lowing proposition characterizes this case:

PROPOSITION 4: Suppose that n0a � n0

p (un-employment in the profit-oriented sector). Thenthe following matching � is stable: �(aj) � pjfor j � 0, 1, 2 and the associated optimalcontracts have the following features:

(a) The fixed wage is set at the subsistencelevel, i.e., w*jj � w� for j � 0, 1, 2;

(b) The bonus payment in the mission-orientedsector is:

b*11 � b*22 ��

2� ��

and the bonus payment in the profit-oriented sector is:

b*00 ��0

2;

(c) The optimal effort level solves: e*jj � b*jj �� for j � 1, 2 and e*00 � b*00.

The effect of competition on incentives nowacts purely through the matching effect. Thepresence of unemployment unhinges incentivesin the mission-oriented and profit-oriented sec-tors of the economy since the only outside op-

20 Matching can improve productivity even under thefirst-best. The analysis of the second-best offers insights onthe effect of matching on the pattern of incentive pay.

21 It is possible to have more high-powered incentives inthe mission-oriented sector, but only if the participationconstraint is not binding, and � is high relative to �0 and �� .


tion is being unemployed. Principals earnpositive profits, and employed agents in bothsectors earn a rent relative to the unemployed inthis case.

Contrasting the results in Proposition 1 withthose in Propositions 3 and 4 yields interestinginsights into the role of competition in themission-oriented sector, and its role in changingthe pattern of incentive pay and in improvingproductivity. The results in this subsection cor-respond to an idealized situation of frictionlessmatching. They provide a benchmark for whatcan be achieved in a decentralized economy andhow matching can raise productivity and affectthe structure of incentive pay.

II. Applications

The benchmark for our analysis is the casewhere principals and agents are matched andallocated by endogenously determined reserva-tion payoffs, as illustrated in Section I D. Evenin a world of motivated agents, however, theremay be frictions that prevent this idealized out-come from being attained. These comprise suchnatural frictions as search costs and asymmetricinformation. There may also be “artificial” fric-tions due to government policies. A number ofgovernment policies in recent years have leanedtoward reducing these artificial barriers to acompetitive, decentralized system of collectiveservice provision.22 These may involve reformswithin the public sector or initiatives to fostergreater involvement of the nonprofit sector inservice provision. The model developed here iswell placed to think through the implications ofsuch developments.

In this section, we discuss three main con-texts in which the ideas apply. We begin with adiscussion of nonprofit organizations. We thendiscuss how the provision of education inschools might fit the model. Finally, we discusspublic bureaucracies.

A. Nonprofit Organizations

The notion of a mission-oriented organiza-tion staffed by motivated agents correspondswell to many accounts of nonprofit organiza-

tions. The model emphasizes why those whocare about a particular cause are likely to end upas employees in mission-oriented nonprofits.This finds support in Burton A. Weisbrod(1988), who observes, “Non-profit organiza-tions may act differently from private firms notonly because of the constraint on distributingprofit but also, perhaps, because the motivationsand goals of managers and directors ... differ. Ifsome non-profits attract managers whose goalsare different from those managers in the propri-etary sector, the two types of organizations willbehave differently” (page 31). He also observes,“Managers will ... sort themselves, each gravi-tating to the types of organizations that he or shefinds least restrictive—most compatible withhis or her personal preferences” (page 32).23

Weisbrod also cites persuasive evidence tosupport the idea that such sorting is important inpractice in the nonprofit sector. The notion of amission-oriented organization is, however,somewhat more far-reaching than that of a non-profit. For example, such sorting can be veryimportant in such “socially responsible” for-profit firms as the Body Shop.24

How exactly nonprofit status facilitatesgreater sorting on missions raises interestingissues. If the organization can contract over themission up front, as in Section I C, then itshould make no difference whether there is aformal nonprofit constitution. Thus, as arguedby Edward Glaeser and Andrei Shleifer (2001),adopting nonprofit status must have its roots incontracting imperfections. This would be rele-vant if the principal has some incentive to actopportunistically ex post in a way that divertsthe mission from what the agent would like.This would make it difficult to recruit motivatedagents or “demotivate” those already in the or-ganization to the extent that opportunism is notanticipated. The possibility of such “missiondrift” would also speak in favor of havinga board of trustees that will safeguard the

22 These are sometimes known as quasi-market reforms(see, for example, Julian Le Grand and Will Bartlett, 1993).

23 See Glaeser (2002) for a model of nonprofits whereworkers and managers of nonprofits have something likeour mission-preferences, i.e., caring directly about the out-put of the firm.

24 On the Web site of the Body Shop, their “values” aredescribed as follows: “We consider testing products oringredients on animals to be morally and scientifically in-defensible”; and “We believe that a business has the respon-sibility to protect the environment in which it operates,locally and globally” (see http://www.thebodyshop.com/).


mission. It also shows the importance of havinga motivated principal, i.e., someone who is ded-icated to the mission, running theorganization.25

Empirical studies suggest that in industrieswhere both for-profits and nonprofits are in op-eration, such as hospitals, the former sectormakes significantly higher use of performance-based bonus compensation relative to base sal-ary for managers (Jeffrey P. Ballou andWeisbrod, 2003; Richard J. Arnould et al.,2000). It is recognized in the literature thatmanagers may care about the outputs producedby the hospital or the patient. Researchers areunable, however, to explain this empirical find-ing. In the words of Ballou and Weisbrod(2003), “While the compensating differentialsmay explain why levels of compensation differacross organizational forms, it does not explainthe differentials in the use of strong relative toweak incentives.” Our framework provides asimple explanation for this finding.

In addition, Arnould et al. (2000) find that thespread of managed care in the United States,which increases market competition, has in-duced significant changes in the behavior ofnonprofit hospitals. In particular, they find thatthe relationship between economic performanceand top managerial pay in nonprofit hospitalsstrengthens with increases in HMO penetration.In terms of our model, this can be explained asthe effect of an increase in the profitability ofthe for-profit sector (�0) which tightens theparticipation constraints of the managers.

Our framework also underlines the value ofdiversity in the nonprofit sector, provided thereis a variety of views on the way in whichcollective goods should be produced (as repre-sented by the mission preferences). Weisbrod(1988) emphasizes this role of nonprofit orga-nizations in achieving diversity. For example,he observes that nonprofits likely play a moreimportant role in situations where there isgreater underlying diversity in preferences forcollective goods. He contrasts the United Statesand Japan, suggesting that greater cultural het-erogeneity is partly responsible for the greaterimportance of nonprofit activity in the United

States. Our analysis of the role of competition insorting principals and agents on mission prefer-ences underpins the role of diversity in achiev-ing efficiency. Better matched organizations canresult in higher effort and output. Hence, diver-sity is good not only for the standard reason,namely, consumers get more choice, but also inenhancing productive efficiency.

Nonprofit organizations rely on heteroge-neous sources of finance—a mixture of privatedonors, government grants, and endowments.The analysis so far has abstracted from suchissues by assuming that the principal has asource of wealth. Hence, the analysis best fitsorganizations that are endowment-rich. Butgiven the importance of external finance inpractice, it is interesting to think through theimplications of introducing a third group ofactors—donors—who contribute to the organi-zation.26 We would expect donors, like agents,to pick organizations on the basis of the mis-sions they pursue. When such matching is per-fect, the existence of outside financiers raises nonew issues.

The more interesting case arises when donorshave mission preferences that differ from thoseof any matched principal-agent pair in the econ-omy. They can then seek to influence organiza-tions by offering a donation that is conditionalon changing the mission of the organization.But our analysis suggests that externally en-forced mission changes come at a cost, since theagent (and possibly the principal) will becomedemotivated and the organization will becomeless productive.27 This leads us to conjecturethat endowment finance will generally be asso-ciated with higher levels of productivity in thenonprofit sector.

The role of the donor can also give someinsight into the difference between public andprivate finance. In publicly funded organiza-tions, the government plays the role of a donor.It can use this role to influence mission choice.We would expect its mission preferences to bedetermined either by electoral concerns or con-stitutional restrictions (e.g., maintaining a neu-tral stance with respect to religious issues). Thegovernment may be able to provide financial

25 This suggests that promotion of insiders may be im-portant in such organizations as a way of preserving themission.

26 See Glaeser (2002) for a related attempt to considerthe role of donors in the governance of nonprofits.

27 Formally, both �i and �ii will be lower.


support to some private organizations, but if itdoes so, it might distort their missions towardits preferred style of provision. In so doing, itcan reduce productivity, since agents will beless motivated as a consequence. Indeed, whenU.S. President George W. Bush announced thepolicy of federal support for faith-based pro-grams in 2001, some conservatives expressedconcern that involvement with the governmentwill undermine the independence of churches,and this might have a demoralizing effect.28

Thus, we would expect government-funded or-ganizations, on average, to be less efficient thanthose privately financed through endowments.However, whether they are more or less produc-tive than those funded by private donations isless clear, given the earlier discussion.

B. Education Providers

Education providers are a key example ofmotivated agents, regardless of whether pub-licly or privately owned. The approach devel-oped here provides some useful insights into therole of competition and incentives in improvingschool performance.29 Moreover, the modelworks equally well when thinking about pub-licly and privately owned schools without in-voking the implausible assumption that thelatter are profit-maximizing.

Some schooling policies, specifically thoserestricting diversity in mission choice, haveserved to prevent the kind of decentralized out-come studied in Propositions 3 and 4. However,recent policies to encourage entry and compe-tition between schools may allow schools to

emerge with more distinctive missions. For ex-ample, in the United Kingdom, Prime MinisterTony Blair has been emphasizing the impor-tance of diversity in his education policy. In theUnited States, initiatives to encourage charterschools are based on the idea of creating schoolsthat cater to community needs. The competitiveoutcome that we characterize can be thought ofas the outcome from an idealized system ofdecentralized schooling in which schools com-pete by picking different missions and attractingteachers who are most motivated to teach ac-cording to those missions.

To think through these issues formally, con-sider the model of mission choice introduced inSection I C. For simplicity, we will focus on theallocation of a balanced population of teachers(agents) to schools taking the outside option inthe profit-oriented sector as given. In this con-text, a mission could be a curriculum or amethod of teaching.

At one extreme is a centralized world whereschools are forced to adopt homogeneous mis-sions as a matter of government policy. Supposethat this mission is x � (1 � 2)/2, which isset between the preferred missions of the twotypes of principals and agents. Even if princi-pals and agents match on the basis of missionpreferences, there is no improvement in schoolproductivity, as principals’ and agents’ payoffsdepend on x, which is fixed exogenously.

Now suppose that the government offersschools the freedom to set their own missions. Itcould do so by allowing new schools to enter orby allowing existing schools to change theirmissions and to compete for teachers on thebasis of their mission preferences. Applying thelogic of Proposition 2, we now have schoolswith missions 1 and 2 , with principals andagents matched on the basis of their missionpreferences.

The model predicts that this form of compe-tition will yield increases in school productivityin all schools—all agents and principals willhave higher levels of motivation than whenmissions are homogeneous.30 Thus, theoreti-cally at least, school competition of this form is“a rising tide that lifts all boats,” to use Hoxby’s

28 See “Leap of Faith” by Jacob Weisberg, February 1,2001, Slate (http://www.slate.msn.com).

29 As Caroline M. Hoxby (2003) points out, while theempirical literature suggests that there are productivity dif-ferences across schools and that competition may affectthese, there has been relatively little theoretical work ondeterminants of school productivity. Hoxby (1999) is a keyexception. She models the impact of competition in a modelwhere there are rents in the market for schools, and arguesthat a Tiebout-like mechanism may increase school produc-tivity. Other approaches to the issue, such as Dennis Eppleand Richard Romano (2002), have emphasized peer-groupeffects (i.e., school quality depends on the quality of themean student) but as far as “supply side” factors are con-cerned they assume that some schools are more productivethan others for exogenous reasons. Akerlof and Kranton(2002) provide important insights into the economics ofeducation using ideas from sociology.

30 This result holds true whether or not the outside optionbinds, as long as it remains fixed exogenously by the profit-oriented sector and is the same for all motivated agents.


(2002) phrase. The model also provides an al-ternative explanation for why some schools(such as Catholic schools) can be more produc-tive by attracting teachers whose mission pref-erences are closely aligned with those of theschool management.

The general point is that a decentralizedschooling system where missions are developedat the school level will tend to be more produc-tive (as measured in our model by equilibriumeffort) than a centralized one in which a uniformmission is imposed on schools by govern-ment.31 This is true regardless of whether weare talking about public or private schools.32

Allowing more competition through missionchoice reallocates teachers across schools andimproves efficiency while reducing the need forincentive pay. Thus, our approach shows thatcompetition between schools can have effectson productivity without creating a need for in-centive pay.33

A general concern with school competition isthat sorting leads to inequality. This would hap-pen in our model if there were vertical ratherthat horizontal differentiation between the prin-cipals and agents. Specifically, suppose that

some agents have high �, no matter what prin-cipal they are matched with, and that someprincipals have high �, regardless of the agentthey match with. In this case, it is possible toshow that, in a stable matching, high � agentswill be matched with high � principals.34 Ap-plied to schools, this predicts segregation ofschools by quality.35 However, centralizingmission choice is not a solution to this problemunless certain kinds of mission preferences andlevels of motivation happen to be correlated.Rather, the solution will lie in creating incen-tives for highly motivated teachers to work withless motivated principals.

C. Incentives in Public Sector Bureaucracies

Our model can also cast light on more generalissues in the design of incentives in public bu-reaucracies. Disquiet about traditional modes ofbureaucratic organization has led to a variety ofpolicy initiatives to improve public sector pro-ductivity. The so-called New Public Manage-ment emphasizes the need to incentivize publicbureaucracies and to empower consumers ofpublic services.36 Relatedly, David Osborne andTed Gaebler (1993) describe a new model ofpublic administration emphasizing the scope fordynamism and entrepreneurship in the publicsector. Our framework suggests an intellectualunderpinning for these approaches. By focus-ing, however, on mission orientation, which isalso a central theme of Wilson (1989), we em-phasize the fundamental differences betweenincentive issues in the public sector and thosethat arise in standard private organizations.

The results developed here give some insightinto how to offer incentives for bureaucratswhen there is a competitive labor market. Ourframework implies that public sector incentivesare likely to be more low powered because itspecializes in mission-oriented production. Ittherefore complements existing explanations,

31 The approach offered here is distinct from existingtheoretical links competition and productivity in the contextof schools. For example, yardstick competition has beenused extensively in the United Kingdom where “leaguetables” are used to compare school performance. Whethersuch competition is welfare improving in the context ofschools is moot since the theoretical case for yardstickcomparisons is suspect when the incentives in organizationsare vague or implicit, as in the case of schools (see, forexample, Dewatripont et al., 1999). Another possible para-digm for welfare-improving school competition rests on thepossibility that it can increase the threat of liquidation witha positive effect on teacher effort (Klaus M. Schmidt, 1997).This possibility could easily be incorporated into our modelas a force that increases the cost to the agent (in this case ateacher) of the outcome where the output is YL.

32 Arguably our model offers an excessively rosy view ofcompetition. Missions may be driven by ideological, reli-gious, or political concerns, some of which may not con-tribute to the social good. With horizontally differentiatedschools, society could also end up being fragmented, mak-ing it more difficult to solve collective action problems. Ina more realistic world of multidimensional missions, theissue for school policy will be which aspect of the missionto decentralize.

33 This holds if the outside option is fixed. However, ifschool competition raises the outside options of teachers,then it could lead to more use of incentive pay. For a reviewof recent debates about incentive pay for teachers, see EricA. Hanushek (2002).

34 This is the more standard result from the matchingliterature. Since we have nontransferable utility (due tolimited liability), we can use the insights from Legros andNewman (2003).

35 This differs from the standard model of school segre-gation based on peer group effects in production. See, forexample, Epple and Romano (2002).

36 See Michael Barzelay (2001) for backgrounddiscussion.


based on multitasking and multiple principals,of why we would expect public sector incen-tives to be lower powered than private sectorincentives (Dixit, 2002). It provides a particu-larly clean demonstration of this, as the produc-tion technology is assumed to be identical in allsectors.

In a public bureaucracy, we might think ofthe principal’s type being chosen by an electoralprocess. The productivity of the bureaucracywill change endogenously if there is a change inthe mission due to the principal being replaced,unless there is immediate “rematching.” Thisprovides a possible underpinning for the diffi-culty in reorganizing public sector bureaucra-cies and a decline in morale during the processof transition. Over time, as the matching processadjusts to the new mission, this effect can beundone, and so we might expect the short- andlong-run responses to change to be rather dif-ferent. As Wilson (1989, p. 64) remarks, in thecontext of resistance to change in bureaucraciesby incumbent employees, “... one strategy forchanging an organization is to induce it to re-cruit a professional cadre whose values are con-genial to those desiring the change.” Thissuggests a potentially efficiency-enhancing rolefor politicized bureaucracies where the agentschange with changes in political preferences.

The approach also gives some insight intohow changes in private sector productivity ne-cessitate changes in public sector incentives.Consider, as a benchmark, the competitive out-come in Proposition 3. Changes in productivitythat affect both sectors in the same way willhave a neutral effect. However, unbalanced pro-ductivity changes that affect one sector mayhave implications only for optimal contracts. Tosee this, consider an exogenous increase in �0.In a situation of full employment as described inProposition 3, even if public employees initiallyreceive a rent above their outside option, theparticipation constraint will eventually bind.The model predicts that this will lead to greateruse of high-powered incentives in the publicsector.37

Putting together insights from Propositions 3

and 4, we can shed some light on why thearguments of the New Public Management topromote incentives in the public sector becamepopular, as they did in countries like New Zea-land and the United Kingdom in the 1980s.There were two components. First, the UnitedKingdom experienced a fall in motivationamong principals and agents in the public sectorunder Prime Minister Margaret Thatcher due toher efforts to change the mission of public sec-tor bureaucracies. Since this was done in thetime of high unemployment, as Proposition 4predicts, there was little consequence for publicsector incentives. However, in the 1990s, therewas a return to full employment and a rise inprivate sector wages—raising �0 in terms of ourmodel. This, as Proposition 4 predicts, causedthe public sector to consider schemes thatmimic private sector incentives.

The model can also cast light on anothercomponent of the New Public Management—attempts to empower beneficiaries of publicprograms. Examples include attempts to involveparents in the decision-making process ofschools, and patients in that of the public healthsystem. This is based on the view that publicorganizations work better when members oftheir client groups get representation and canhelp shape the mission of the organization. Themodel developed here suggests that this workswell, provided that teachers and parents sharesimilar education goals. Otherwise, attempts byparents to intervene will simply increase mis-sion conflict, which can reduce the efficiency oforganizations.

One key issue that frequently arises in dis-cussions of incentives in bureaucracies is cor-ruption. By attenuating the property rights ofthe principal, corruption can motivate the agentand may have superficial similarities with ourmodel here. But there are two key differences:corruption is purely pecuniary and it is not“value creating.”38 The insights developed here

37 In the unemployment case described in Proposition 4,private sector productivity does not affect public sectorproductivity. Hence, we would expect issues concerning theinteraction between public and private pay to arise predom-inantly in tight labor markets.

38 Our framework can capture the differences formally ifwe suppose that �i � Bi � R and �ij � �R where R is theamount that an agent of type j “steals” from a principal oftype i. (The cost of stealing is parametrized by � 1.)Assuming for simplicity that the agent’s outside option iszero, the optimal contract (applying Proposition 1) is now:

�b*ij , w*ij � � �Bi � �1 � ��R

2, w� � .


are quite distinct from incentive problems dueto corruption.

A common complaint about public bureau-cracies is that they are conservative and resistinnovation.39 Our model can make sense of thisidea. In a profit-oriented organization, anychange that increases the principal’s payoff, �0 ,will be adopted. However, in a mission-orientedorganization, the preferences of the agent needalso be taken into account. Consider, for thesake of illustration, Case 2 of Proposition 2. Theprincipal’s expected payoff in this instance ise*ij(�i � b*ij) � w� � 1⁄4 (�ij � �i)

2 � w� . Since amission-oriented organization will innovateonly if �i � �ij is larger, it is optimal for theprincipal to factor in the effect that it has on themotivation of the agent. If innovations reduce�ij , they might be resisted even if �i is higher. Ifwe think of �i as predominantly a financialpayoff, then innovations that pass standard fi-nancial criteria for being worthwhile (raising�i) may be resisted in mission-oriented sectorsof the economy. Since much of the drive forefficiency in the public sector uses financialaccounting measures, this could explain whypublic bureaucracies are often seen as conser-vative and resistant to change.

III. Concluding Remarks

The aim of this paper has been to explorecompetition and incentives in mission-orientedproduction. These ideas are relevant in discus-sion of organizations where agents have somenonpecuniary interest in the organization’s suc-cess. Key examples are nonprofits, public bu-reaucracies, and education providers. Withmotivated agents, there is less need for incen-tive pay. There is also a premium on matchingof mission preferences.

Much remains to be done to understand theissues better. It is particularly important to un-derstand how the existence of motivated agentsaffects the choice of organizational form. Theanalysis also cries out for a more completetreatment of the sources of motivation and thepossibility that motivation is crowded in or outby actions that the principal can take.40

In this paper, we have maintained a sharpdistinction between mission-oriented and profit-oriented sectors. However, private firms fre-quently adopt missions. In future work, it wouldbe interesting to develop the content of missionchoice in more detail and to understand howmission choice interacts with governance of or-ganizations and market pressures.

APPENDIX

To prove Proposition 1, we proceed by prov-ing several useful lemmas. Substituting for eijusing the incentive-compatibility constraint, wecan rewrite the optimal contracting problem inSection I B as:

max�bij ,wij�

u ijp � ��i � bij��bij � �ij� � wij

subject to the limited-liability and participationconstraints:

wij � w�

uija �

12

�bij � �ij �2 � wij � u� j .

This modified optimization problem involvestwo choice variables, bij and wij , and two con-straints, the limited-liability constraint and theparticipation constraint. The objective functionu ij

p is concave and the constraints are convex.Now we are ready to prove:

LEMMA 1: Under an optimal incentive con-tract, at least one of the participation and thelimited-liability constraints will bind.

PROOF:Suppose both constraints do not bind. As the

participation constraint does not bind, the prin-

The corresponding effort level is

e*ij � b*ij � �R �Bi � �1 � ��R

2.

So long as � � 1, both the principal and agent are worseoff because of corruption. Also, the productivity of theorganization is decreasing in R in this case.

39 The ensuing argument could equally be applied toreligious organizations, advocacy groups, and nongovern-mental organizations, which are often accused of being rigidin their views and approaches.

40 Frey (1997), Benabou and Tirole (2003), and Ak-erlof and Kranton (2003) make important progress in thisdirection.


cipal can simply maximize his payoff with re-spect to bij , which yields

bij � max��i � �ij

2, 0�

and the corresponding effort level is

eij � bij � �ij � max��i � �ij

2, �ij�.

Since the participation constraint is not binding,and by assumption wij � w� , the principal canreduce wij by a small amount without violatingeither of these constraints. This will not affecteij , and yet will increase his profits. This is acontradiction and so the principal will reducewij until either the limited-liability constraint orthe participation constraint binds.

LEMMA 2: Under an optimal incentive contractif the limited-liability constraint does not bind,then (a) eij is at the first-best level; and (b) theprincipal’s expected payoff is strictly negative.

PROOF:We prove the equivalent statement, namely,

if eij is not at the first-best level then the limited-liability constraint must bind. As b �i, effortcannot exceed the first-best level. The remain-ing possibility is that eij is less than the first-bestlevel. Suppose this is the case, i.e., eij � bij ��ij � �i � �ij. We claim that in this case thelimited-liability constraint must bind. Supposeit does not bind. That is, we have an optimalcontract (bij

0, wij0) such that bij

0 � �i and wij0 � w� .

Suppose we reduce wij0 by � and increase bij

0 byan amount such that the agent’s expected payoffis unchanged. Since the agent chooses effort tomaximize his own payoff, we can use the en-velope theorem to ignore the effects of changesin wij and bij on his payoff via eij. Then duij

a �eij dbij � dwij � 0. The effect of these changeson principal’s payoff is duij

p � deij(�i � bij) �(eij dbij � dwij). The second term is zero byconstruction and the first term is positive and sothe principal is better off. This is a contradic-tion. This proves the first part of the lemma.Next we show that if the limited-liability con-straint does not bind, then the principal’s ex-pected payoff is strictly negative. From the firstpart of this lemma, if the limited-liability con-

straint does not bind, then eij � �i � �ij. Fromthe incentive-compatibility constraint, this im-plies bij � �i. Since wij � w� (the limited-liability constraint does not bind) and w� � 0,this immediately implies that the principal’sexpected payoff uij

p � �wij � 0.

LEMMA 3: Suppose Assumption 2 holds. Thenv� ij is a strictly positive real number that doesnot exceed Sij.

PROOF:By Lemma 2, if the principal’s expected pay-

off is nonnegative, then the limited-liabilityconstraint must bind. Therefore, wij � w� . Giventhe modified version of the optimal contractingproblem stated at the beginning of this section,the only remaining variable to solve for is bij.The agents payoff is increasing in bij. Thereforewe can solve for bij from the equation (�i �bij)(bij � �ij) � w� � 0 (the principal’s expectedpayoff is equal to 0). Being a quadratic equationit has two roots, but the higher one is the rele-vant one since the agent’s payoff is increasingin bij. This is:

bij ��i � �ij � ��i � �ij �

2 � 4w�

2.

Substituting this into the agent’s payoff func-tion, we get

v� ij �1

2 ��ij � �i � ��ij � �i �2 � 4w�

2 � 2

� w� .

By Assumption 2, (�ij � �i)2 � 4w� � 0 for

all i � 0, 1, 2 and all j � 0, 1, 2. Therefore,v� ij is a real number. It is strictly positive as�i � 0 and �ij � 0. Also, as w� � 0, v� ij Sij(the equality holds if w� � 0).

LEMMA 4: Suppose Assumption 2 holds. Thenv ij lies in the real interval (0, v� ij).

PROOF:Suppose the participation constraint does not

bind. By Lemma 1, the limited-liability con-straint binds and

bij � max��i � �ij

2, 0�.


The agent’s payoff is 1⁄2 (b*ij � �ij)2 � w� �

1⁄8 (�ij � max{�i, �ij})2 � w� . This is a positivereal number as �i � 0 and �ij � 0. There aretwo cases, depending on whether �i is greaterthan or less than �ij. In the former case it is clearupon inspection that vij � v� ij. In the latter case,we need to show that �ij � �i �(�(�ij � �i)

2 � 4w� )/2 � �ij. Upon simplifica-tion this condition is equivalent to �i�ij � w� � 0.By Assumption 2, 1⁄4 �i

2 � w� � 0. In the presentcase, by assumption �ij � �i. Therefore �i�ij ��i

2 � 1⁄4 �i2 and so this condition holds given

Assumption 2.

PROOF OF PROPOSITION 1:Now we are ready to characterize the opti-

mal contract and prove its existence. ByLemma 1 and Lemma 2, the only relevantcases are the following: (a) the limited-liability constraint binds but the participationconstraint does not bind; and (b) both theparticipation constraint and the limited-liability constraint bind. From the proof ofLemma 4, the former case can be usefullysplit into two separate cases depending onwhether �i is greater than or less than �ij.This means there are three cases to study:

Case 1: The participation constraint does notbind and �ij � �i. We have already estab-lished in the proof of Lemma 1 that in thiscase the limited-liability constraint will bindand that:

b*ij � max��i � �ij

2, 0� � 0

w*ij � w�

e*ij � b*ij � �ij � �ij .

From Lemma 4, the agent’s payoff is 1⁄2 �ij2 � w� .

Since the participation constraint does not bindby assumption in this case, the following mustbe true:

12

�ij2 u� j � w� .

The principal’s payoff is

�b*ij � �ij ��i � b*ij � � w� � �ij�i � w� .

Case 2: The participation constraint does notbind and �ij �i. In this case:

b*ij � max��i � �ij

2, 0� �

�i � �ij

2

w*ij � w�

e*ij � b*ij � �ij ��i � �ij

2.

The agent’s payoff is 1⁄8 (�i � �ij)2 � w� in this

case. Since the participation constraint does notbind by assumption in this case, the followingmust be true:

18

��i � �ij �2 u� j � w� .

The principal’s payoff is

�b*ij � �ij ��i � b*ij � � w� �14

��i � �ij �2 � w� .

Case 3: The participation constraint and thelimited-liability constraint bind. These con-straints then uniquely pin down the two choicevariables for the principal. In particular, we get

w*ij � w�

b*ij � �2�u� j � w� � � �ij .

Using these and the incentive-compatibilityconstraint, we get

e*ij � b*ij � �ij � �2�u� j � w� �.

As b*ij �i , e*ij � �2(u� j � w� ) �i � �ij.Therefore, u� j � w� 1⁄2 (�i � �ij)

2. Noticethat in this case b*ij � 0 as that is equivalentto u� j � w� � 1⁄2 �ij

2 and this must be truebecause otherwise the participation constraintwould not bind. The payoff of the agent inthis case is, by assumption,

uija � u� j .

The principal’s payoff is:

uijp � �2�u� j � w� ��i � �ij � �2�u� j � w� �� w� .


From the proof of Lemma 3, this is equal tozero if u� j � v� ij. Therefore, so long as u� j v� ij , uij

p � 0.Finally, we must check that the optimal con-

tract exists. The principal’s expected payoffwhen u� j � 0 and �ij � �i is �ij�i � w� . ByAssumption 2 this is positive for i � 1, 2 andj � 1, 2. The principal’s expected payoff whenu� j � 0 and �ij � �i is 1⁄4 (�i � �ij)

2 � w� . ByAssumption 2 this is positive. In both cases theagent receives a strictly positive expected pay-off even though u� j � 0. In the first case, theagent’s expected payoff is 1⁄2 �ij

2 � w� and in thesecond case it is 1⁄8 (�i � �ij)

2 � w� , which arestrictly positive real numbers by Lemma 4. Onthe other extreme, if the principal’s expectedpayoff is set to zero, the agent’s expected payoffunder the optimal contract is v� ij , which is astrictly positive real number by Lemma 3. Forall u� j � vij , the participation constraint bindsand the principal’s expected payoff is a contin-uous and decreasing function of u� j, and so anoptimal contract exists for all u� j � [0, v� ij].

PROOF OF PROPOSITION 2:Let zj be the reservation payoff of an agent of

type j ( j � 0, 1, 2). Then from the proof ofProposition 1 the expected payoff of a principalof type i (i � 0, 1, 2) when matched with anagent of type j ( j � 0, 1, 2) is given by:

�*ij � zj � � ��i�ij � w�for �i � �ij

and zj � w� �1

2�ij

2

��i � �ij�2

4� w�

for �i � �ij

and zj � w� �1

8��i � �ij�

2

�2�zj � w� ��i � �ij � �2�zj � w� �� w�

for1

8��i � �ij�

2 zj � w� v� ija.

From the proof of Proposition 1, �*ij(zj) is(weakly) decreasing in zj for all i � 0, 1, 2 andall j � 0, 1, 2. First consider principals in themission-oriented sector. As �1 � �2 � �, forany given value of z0 � z1 � z2 � z, �*ii(z) ��*ij(z) for i � 1, 2, for j � 0, 1, 2, and i j.Next consider principals in the profit-orientedsector. For any given value of z0 � z1 � z2 � z,

�*00(z) � �*01(z) � �*02(z). We now demon-strate that all stable matches must beassortative.

Suppose that there is a stable nonassorta-tive match with reservation payoffs ( z0, z1,z2). Since n1

a � n1p and n2

a � n2p, there must be

at least one match involving a principal oftype i (i � 1, 2) and an agent of type j i( j � 0, 1, 2). We show that this leads to acontradiction.

Of the various possibilities, we can eliminateimmediately the one where a principal of type i(i � 1, 2) is matched with an agent of type j i ( j � 0, 1, 2) and, correspondingly, an agent oftype i is unmatched. Such an agent receives theautarchy payoff of 0 and so a principal of typei (i � 1, 2) cannot possibly prefer to hire anagent of type j i as �*ii(0) � �*ij(zj) for all i �1, 2, for all j i, and zj � 0. Given this, thereare three types of nonassortative matches thatwe need to consider.

First, a principal of type i (i � 1, 2) ismatched with an agent of type 0 and, corre-spondingly, an agent of type i is matched witha principal of type 0. Stability implies a prin-cipal of type i would not wish to bid away anagent of type i from a principal of type 0. Thisimplies �*i0( z0) � �*ii( zi) which in turn im-plies that zi � z0 as �*ii( z0) � �*i0( z0).Similarly, the fact that a principal of type 0prefers to hire an agent of type i (i � 1, 2)over an agent of type 0 implies that �*0i( zi) ��*00( z0), which in turn implies z0 � zi. Butthat is a contradiction.

Second, a principal of type 1 is matched withan agent of type 2 and, correspondingly, anagent of type 1 is matched with a principal oftype 2. By stability a principal of type 1 wouldnot wish to bid away an agent of type 1 from aprincipal of type 2. This implies �*12(z2) ��*11(z1), which in turn implies that z1 � z2 since�*11(z2) � �*12(z2). Similarly, the fact that atype 2 principal does not want to bid away atype 2 agent implies that �*21(z1) � �*22(z2).But by a similar argument this implies that z2 �z1. This is a contradiction.

Third, a principal of type i (i � 1, 2) ismatched with an agent of type 0, an agent oftype i is matched with a principal of type j i( j � 1, 2), and an agent of type j is matchedwith a principal of type 0. Repeating the argu-ments used above, the fact that a principal oftype i (i � 1, 2) prefers an agent of type 0 to an


agent of type i implies zi � z0. Similarly, as aprincipal of type j i ( j � 1, 2) prefers an agentof type i to an agent of type j implies zj � zi.Together, these two inequalities imply zj � z0.However, the fact that a principal of type 0(weakly) prefers to hire an agent of type j to anagent of type 0 implies z0 � zj, which is acontradiction.

Therefore there is no stable nonassortativematch.

PROOF OF PROPOSITION 3:By Proposition 2, we can restrict attention on

assortative matches. Since n0p � n0

a, there areunemployed profit-oriented principals. There-fore, all employed principals in the profit-oriented sector must be earning zero profits. Thestated contracts are optimal according to Prop-osition 1 relative to a common reservation pay-off for all types of agents of:

u �18

��0 � ��02 � 4w� �2 � w� .

This is the payoff that an agent of any typewho is matched with a principal of type 0receives when the principal’s expected payoffis zero and can be obtained by setting i � 0 inthe expression for v� ij in the proof of Lem-ma 3. Accordingly, this is the relevant reser-vation payoff of all agents under full employ-ment. We proceed to prove that the proposedassortative matching is stable.

All employed principals in the profit-oriented sector are earning zero profits. Theycannot therefore attract away an unmotivatedagent from another profit-oriented principalwithout earning a negative profit. Hence thematching within the unmotivated sector isstable.

An agent of type j ( j � 1, 2) receives a payoffof v j

a � max{1⁄8 �2 � w� , u} � v a. Since this isthe same for both types of motivated agents, and�*ii (z) � �*ij (z) for i � 1, 2 and for all j � 0, 1,2, the proposed matching is stable within themission-oriented sector.

Finally, we show that matching between theprofit-oriented and mission-oriented sectors isstable.

Let us define the following function to sim-plify notation:

g�x1, x2� � �2�x1 � w� ��x2 � �2�x1 � w� �� w� .

This gives the payoff of a principal under anoptimal contract when the participation con-straint is binding, the reservation payoff of theagent is x1, and the joint payoff of the principaland the agent from success is x2 (e.g., if theprincipal is type i and the agent is type j thenx2 � �i � �ij).

First we show that a principal of type 0 willnot be better off hiring an agent of type 1 or 2by offering him a payoff of at least v a comparedto what he earns under the proposed match withan unmotivated agent. Currently such a princi-pal earns an expected payoff of 0. If he hires anagent of type j ( j � 1, 2) the participationconstraint will bind since 1⁄8 (� � ��)2 � w� �1⁄8 �0

2 � w� for i � 1, 2 (by Assumption 3). Thereare two cases to be considered. First, va � u.Then the maximum payoff that a principal oftype 0 can earn from an agent of type j ( j � 1, 2)is g(v a, �0) � g(u, �0) as v a � u. But byconstruction g(u, �) � 0 in the full-employmentcase and so such a move is not attractive. Sim-ilarly, if va � u, the maximum payoff that aprincipal of type 0 can earn from an agent oftype j ( j � 1, 2) is g(u, �0), which is the samethat he earns in his current match.

Next we show that a principal of type i (i �1, 2) will not find it profitable to attract anunmotivated agent who earns u. A principal oftype i (i � 1, 2) can earn at most g(u, �) fromsuch a move, which is strictly less than g(u, � ��) (what he was earning before), in case theparticipation constraint was binding. Now let usconsider the possibility that the participationconstraint was not binding. Notice that g(u,�) � 1⁄2 (�0 � ��0

2 � 4w� ){� � 1⁄2 (�0 ��0

2 � 4w� )} � w� 1⁄4 �2 � w� (since theexpression 1⁄2 y(a � 1⁄2 y) is maximized at y �a). As the participation constraint was not bind-ing by assumption in this case, the principal wasearning either �� w� (if �� ) or (� ��)2/4 � w� (if �� ). In the former case, as �� , �� w� � 1⁄4 �2 � w� . In the latter case,1⁄4 �2 � w� (� � ��)2/4 � w� for all �� 0, � �0. Thus, the proposed matching is stable asclaimed.

PROOF OF PROPOSITION 4:The stated contracts are optimal contract ac-

cording to Proposition 1 and Corollary 1, rela-tive to a common reservation payoff of zero.This is what we would expect as n0

p � n0a and so


there are unemployed agents. The rest of theproof is similar to that of Proposition 3 and ishence omitted.

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