Agency and Social Preferences
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1 Agency and Socal Preferences Danel Arce Economcs Program, GR 31 Unversty of Texas at Dallas 800 W, Campbell Rd. Rchardson, TX October 010 Abstract It s by now well-recognzed that the organzatonal behavor of agents reflects both market and socal consderatons. Indeed, the dea that agents have ntrnsc motvaton s ganng ground as a complementary approach to agency-theoretc solutons to the problem of moral hazard. We ntroduce and explore a nested representaton of altrustc, ethcal, moral, motvated, opportunstc, recprocal and socal dentty agent preferences. The result s a characterzaton of contract forms that facltates a rankng of agency costs across socal preference types. Moreover, we provde gudelnes for emprcal and expermental nvestgatons of socal preferences n prncpal-agent envronments.
2 1. Introducton It s by now well-recognzed that the behavor of agents reflects both market and socal consderatons. Indeed, recently there has been a prolferaton of analyses that explore the mplcatons of ntrnsc socal preferences n prncpal-agent models nvolvng moral hazard. Examples nclude ethcal agents versus altrusm (Casadesus-Masanell, 004), moral agents (Stevens and Thevaranjan 010), motvated agents (Besley and Ghatak, 005), recprocty (MacLeod, 007), and socal dentty (Akerlof and Kranton, 008). One ratonale for such nvestgatons s based on the dfference between predcted contract forms and/or level of effort and what s observed n practce or derved n the laboratory. Another ratonale s to explan the effect of ntrnsc motvaton on contract forms. For example, agents may experence ntrnsc utlty when the msson of the employer produces postve externaltes for socety. Industry or organzatonal culture may also reflect ntrnsc standards of behavor or norms of recprocty. Fnally, the dea that agents have socal preferences s complementary to the wthn-the-frm nature of the agency-theoretc approach to solvng moral hazard problems. In ths paper the nterconnectons between the alternatve socal preferences lsted above are llustrated wthn a unfyng framework so as to provde a rankng of agency costs across socal preference types. The relatonshp between these preferences has been somewhat obscured due to varatons n the underlyng model. By creatng a unfyng framework we are able to dentfy condtons under whch the aforementoned preferences consttute a nested set. Furthermore, several of the preferences are observatonally equvalent n terms of the agent s effort level and the ncentve component of the contract. What dfferentates these preferences are the fxed porton of the contract; the prncpal s resdual surplus; and the agent s utlty. Once the agency costs of socal preferences are dentfed, the way n whch socal preferences provde a complementary soluton to the problem of moral hazard can be better understood. The paper proceeds as follows. In the next secton we ntroduce a unfyng model of agents wth socal preferences. Ths also serves as a lterature revew. Agents are rsk neutral and select a contnuous level of effort that also corresponds to the probablty that the prncpal s good state/surplus s generated. Agents face a lmted lablty constrant so that the moral hazard problem remans. We dentfy the nested relatonshp between altrustc, ethcal, moral, motvated, opportunstc, recprocal and socal dentty preferences. In the followng secton we characterze the optmal contract for the unfyng model wth a bndng lmted lablty constrant and rank each socal preference type accordng to the agency costs assocated wth
3 ther correspondng contract and level of effort. In secton 4 two competng forms of a bndng partcpaton constrant are nstead consdered and t s shown that the market characterstc of the agent s outsde opton s crtcal for dfferentatng between dfferent types of socal preferences. Ths s brefly followed by a consderaton of the nteracton between rsk averson and socal preferences on contract forms. The concluson dscusses the mplcatons of these dfferences for contract desgn and expermental/emprcal tests of agent behavor.. A Unfyng Model Consder a model of moral hazard where both the prncpal (j) and agent () are rskneutral. The agent exerts effort e, whch s unobservable. Two potental states are determned by the agent s level of effort: hgh (S) and low (s), where S > s= 0. State S s generated wth probablty e [ 0,1] and s occurs wth probablty 1 e. The prncpal offers contract, (B, f), where B s the ncentve porton of the contract: the bonus when state S occurs; and f s the fxed porton of the contract. Agents are subject to a lmted lablty constrant; hence, the moral hazard problem s present under condtons of agent rsk neutralty. In ths way, we ntally examne the effect of socal preferences n the context of moral hazard ndependent of the ssue of rsk averson. We use a bonus contract rather than a lnear contract n order to rule out the potental for unbounded rsk takng by rsk-neutral agents under lmted lablty. DEFINITION: An agent wth socal preferences has the followng utlty functon: (1) U ( e, Bf ) = f + Be ½ e θ ( e* e) where: e* s the socal standard for effort; and θ s the pressure felt by agent to abde by the standard. By comparson, an opportunstc agent s preferences reflect only the monetary terms of the contract, f + Be, and the dsutlty of effort, preferences through the fnal term, θ ( e e) *. ½ e. Socal preferences augment opportunstc These preferences unte several strands of the lterature on socal preferences n agency. Frst, ths general form corresponds to agents wth ethcal or moral preferences (Casadesus- Masanell (004) and Stevens and Thevaranjan (010), respectvely). Whenθ > 0 the agent feels gulty f the standard s not met, and fθ < 0 the agent s unethcal/mmoral. Note that opportunstc agents exhbtθ = 0, thereby dstngushng opportunsm from unethcal behavor. In contrast to our analyss, both Casadesus-Masanell (hereafter, C-M) and Stevens and
4 3 Thevaranjan (T-S) assume that agents are rsk averse. In T-S, the termθ(e* e) appends the agent s opportunstc preferences exactly as t appears n (1) and n C-M t s appears as θ(e* e). Our formulaton makes the contract for rsk-neutral agents consstent wth C-M s fndng that the ncentve porton of the optmal contract s ndependent of e* for agents that exhbt constant absolute rsk averson (CARA) shown below. Ths property holds when e* s set by the prncpal, and agents determne the pressure for adherence to ths standard( θ ). In T-S state S s not observable and the focus s nstead on the fxed component, f. Second, Akerlof and Kranton (008, herafter A-K) consder agents that have preferences for socal dentty correspondng to () ( ) U e, Bf = f + Be ½ e θ e* e, where θ > 0 s the effectve measure of dentty. These preferences are equvalent to the ethcal/moral preferences n (1) when e* > e. For example, f the prncpal sets e* at frst-best, then e* > e under moral hazard. Some tongue-n-cheek examples nclude the sports clché of askng players to gve 110% or those Deans who tell ther faculty that the percentage breakdown of research/teachng/servce for evaluaton or promoton s 50/50/0. Agents who see themselves as outsders relatve to prncpals are also lkely to set e such that e < e*. Ths equvalence should not be surprsng as ethcal/moral behavor s socally-determned and the occurrence of such behavor s often a functon of socal pressure( θ ) to adhere to the norm (e*). Consder a thrd case where e*= 0. The agent s utlty functon reduces to (3) ( ) ( ) U e, Bf = f + B+ θ e ½ e. Ths s precsely the utlty functon for motvated agents gven n Besley and Ghatak (005). Here,θ corresponds to the degree to whch agent ntrnscally values the good state when ts preferences algn wth the msson of prncpal j. Preferences and mssons are algned when = j, mplyngθ > 0; otherwse, θ = 0 (and agents act opportunstcally). Besley and Ghatak (hereafter, B-G) gve as examples the medcal and educaton ndustres, where prncpals and agents n nonproft organzatons wthn each ndustry may exhbt preferences for output that extend beyond proft consderatons to the nsttuton s contrbuton to socety; thereby explanng ntra-ndustry dfferences n contracts. A case n pont are tenured (full) economcs professors, who are known to publsh n top-ranked journals even though t s doubtful that the assocated effort can be explaned by the reward structure as t s understood to exst n many
5 4 unverstes and colleges. Our fourth example occurs when e* = 0 and θ = α S. The resultng preferences, (4) ( ) U e, Bf = f + Be ½ e + αes, are equvalent to Casadesus-Masanell s (004) verson of altrusm, where the agent s concerned about the gross surplus receved by the prncpal. Whenα > 0 agents exhbt altrusm towards prncpals andα < 0 mples that they are spteful. Obvously, opportunstc agents exhbtα = 0. Furthermore, rewrtng these preferences as ( ) ( ) U e, Bf = f + B+ α S e ½e reveals that f agent altrusm s msson-specfc then altrusm and motvaton concde when θ = α S. Fnally, MacLeod (007) consders the role of recprocty as a means for employng contract theory to explan socal preferences. Specfcally, he posts that otherwse opportunstc agents who are concerned wth recprocty face an ncentve compatblty constrant that reflects dsutlty from underperformance (a volaton of recprocty). Specfcally: (5) f + eb e { u + θ ( e e) } ½ max 0, *. The left-hand sde of (5) corresponds to the preferences for opportunstc agents. The rght-hand sde augments the opportunstc agent s outsde opton by a measure that captures underperformance. MacLeod s recprocty-based ncentve compatblty constrant s mathematcally equvalent to a partcpaton constrant for agents wth socal preferences. Ths s somewhat expected, as what can be obtaned by augmentng opportunstc preferences can be smlarly obtaned by subjectng those preferences to an equvalent constrant. The economc nterpretaton s qute dfferent; however, partcularly for agents wth socal preferences that face a bndng partcpaton constrant, as s shown n secton 4. OBSERVATION: these socal preferences are nested. The most general types of socal preferences are the ethcal, moral and socal dentty forms, where θ, e* > 0. These are referred to as norm-based preferences. Motvated agents reduce to the case whereθ > 0, e* = 0; and altrusm mples θ = αs,* e = 0. As all the preferences satsfyθ > 0, they reflect some form of MacLeod s (007) recprocty constrant for underperformance. To our knowledge ths observaton has not been made for ths collecton of preferences.
6 5 3. Contracts for Agents wth Socal Preferences The benchmark for comparng contracts across agent types s the general form of agent preferences gven n (1). Furthermore, we make the followng assumpton n order to ensure an nteror soluton n dervng the agent s ncentve compatblty (IC) constrant: (6) S > θ S S+ θ ( ) ;, 0,1. Ths assumpton stems from the requrement that the frst-best soluton, whch maxmzes the sum of the agent s utlty and prncpal s payoff, must also be an nteror soluton. We address the ssue of contract feasblty/proftablty after determnng the optmal contract form. The agent s IC constrant s: (7) e= B+ θ. (IC) When the agent s preferences are observable to the prncpal, as s the case n all of the cted analyses, the prncpal maxmzes ts resdual surplus, Π j = ( S B) e f, subject to the agent s (IC), (PC), and lmted lablty (LL) constrants. 1 Gven (7), the prncpal s contractng problem s: max j ( )( θ ) B (8) ½ θ ( * ) Π = S B B+ f subject to f + Be e e e u (PC) (9) B+ f 0; f 0. (LL) In the remander of ths secton we assume that (LL) s the bndng constrant and address the alternatve n the followng secton. PROPOSITION 1: when the lmted lablty constrant bnds, the optmal contract s { } ( θ) θ ( θ) B= S /, f = max 0, u+ e* S+ /8 ; and the agent exerts effort e= ( S+ θ )/. Socal preferences ncrease the total surplus, Π + U, relatve to opportunstc preferences, but stll fall short of frst-best. Gven that e = S + θ s the frst-best level of effort j that maxmzes U +Π, the moral hazard problem remans as the agent s effort s less than frstbest. The ncentve component of compensaton, B, s a decreasng functon of the pressure to j 1 Alternatvely, one can rely on the presence of assortatve matchng (e.g., B-G). By assumng homogenety n the surplus, S; reservaton payoff, u = u > 0; and normalzng exstng wealth to zero we abstract from a formal matchng process.
7 adhere to the standard, θ ; but s ndependent of the socal standard, e*. The condtons on fxed component, f, are derved by solvng for the optmal varable component, B, and nsertng t nto the PC. The fxed component s an ncreasng functon of e*. 6 COROLLARY 1: For specfc agent types the optmal contract s characterzed as follows. () The opportunstc (O) agent contract (θ=0) s B O = S/, f O = u. Opportunstc agents exert effort e O = S/. The agent s utlty and prncpal s payoff are U O = u + S /8 and Π O = S /4 u. () Norm-based agents receve the optmal contract( B, f ) characterzed n proposton 1 and behave accordngly. Furthermore, U = f + (S+θ) /8 θe*, Π=(S+θ) /4 f. () Motvated (M) agents who are matched wth msson-algned prncpals ( = j) receve contract B M = (S θ)/, f M = max{0, u (S+θ) /8}. They exert effort e M = (S+θ)/. Furthermore, U M = f M + (S+θ) /8, Π M = (S+θ) /4 f M. If prncpals and agents are not well matched ( j), then the opportunstc contract prevals. (v) Altrustc (A) agents (θ=αs, e*=0) receve contract f A = max{0, u ((1+α)S) /8}, B A = (1 α)s/, and exert effort e A = (1+α)S/. U A = f A +((1+α)S) /8, Π A = ((1+α)S) /4 f A. Proposton 1 and ts assocated corollary have several novel mplcatons. Frst, normbased agents and motvated agents exert the same level of effort. Second, these agents accept the same ncentve porton of the contract, B = B M < B O. Thrd, what dfferentates these agents s the fxed porton of the contract. Norm-based agents potentally receve a larger fxed component, f f M, as f s an ncreasng functon of the ethcal standard, e*. Fourth, the ncentve porton of the norm-based contract (B) s not a functon of the ethcal standard and s lower than that for opportunstc agents. Note that n some sense ths s expected, as socal preferences are a lnear functon of e*, but ths allows us to be consstent wth C-M s fndng that CARA utlty functons that are augmented by ethcal preferences also lead to an ncentve component of the contract that s ndependent of e*. The consstent fndng s that t s not the socal standard, e*, that matters but the way n whch socal consderatons are ntrnscally valued n the payoff functon through the term θ. Consequently, ntrnsc consderatons (θ) reduce the varable porton of the contract and rase the fxed component; thereby reducng the opportunty cost of socally-motvated behavor. Ffth, B = B M and f f M mply that prncpals (weakly) prefer to be matched wth
8 7 motvated rather than norm-based agents (Π M Π). In other words; msson algnment s more effectve for prncpals than s specfyng an ethcal standard of behavor. At the same tme, even when f, f M > 0 profts are hgher as compared to employng opportunstc agents. Sxth, f the fxed porton s present then prncpals must have suffcent captal on hand to employ normbased agents; otherwse, they face a bndng lqudty constrant. Hence, t s n the nterest of standard-specfyng prncpals to express a standard, e*, that s n keepng wth ther lqudty constrant. Moreover, f the prncpal s lqudty constrant tghtens wth competton (due to a decrease n S), then ethcal standards and market competton are nversely related. From proposton 1, f s nversely related to S and postvely related to e*. Hence, when the frm faces a bndng lqudty constrant, f S decreases due to competton then e* must decrease as well. { } Fnally, the contracts are proftable when ( S+ θ) > u+ θe ( S+ θ) /4 max 0, * /8. Lqudty ssues asde, for gven values of S and θ there are values of e* for whch t s not proftable to employ norm-based agents but t s proftable to employ motvated agents. In other words, the effcency cost of moral hazard s greater when agents exhbt norm-based preferences than when they are motvated. Moreover, the effcency costs of moral hazard are lower for motvated agents than for opportunstc agents. Of course, msson dentty may not be feasble for all prncpals. Prncpals who must nstead focus on ethcs/morals/socal dentty should keep ther standards n check. 4. Market consderatons Thus far market consderatons have entered nto our analyss through the way n whch competton n the product market nfluences the magntude of S. If labor market condtons affect the contractual relatonshp between prncpal and agent then the effects of a bndng partcpaton constrant must be consdered. Yet because ths process s not as straghtforward as t may seem, we reproduce the PC for the purposes of the dscusson and analyss below. (8) ½ θ ( * ) f + Be e e e u (PC) Wth the excepton of MacLeod (007) the agency approach to socal preferences operatonalzes the partcpaton constrant as t s gven above. When ths constrant s rewrtten: (10) f + Be ½e u + θ(e* e), t s suggestve that agents wth socal preference have an outsde alternatve that exceeds that for opportunstc agents, u. If the reservaton payoff s market-determned ths need not be the case.
9 8 A vable alternatve s that all agents face the same outsde opton the alternatve gven for opportunstc agents (u) because f an agent wth socal preferences rejects a contract that recognzes ther socal preferences, ther next best alternatve may not be a prncpal that specfes a standard of effort, e*, or shares the msson of the agent. The relevant PC therefore becomes: (11) f + Be ½e u. (PC ) Ths form of the partcpaton constran s consstent wth workers wth socal preferences who do not expect that outsde job opportuntes at other frms wll result n commensurate ntrnsc benefts. That s, there s somethng ntrnsc and specfc to ther transacton wthn the frm that s unlkely to be reproduced elsewhere (e.g., through unemployment benefts). We consder the case of each bndng partcpaton constrant n turn. PROPOSITION : f the ntrnsc partcpaton constrant n (8) bnds, the optmal contract s f = 0, B = ( u+ θe* ) θ; and e= ( u+θe ) *. It s no longer the case that the level of effort s dentcal across socal preferences. Norm-based agents exert more effort than ther motvated counterparts and they are pad a hgher bonus. Ths bonus s not smply reduced by θ, as occurs for motvated agents. Instead, the bonus s an ncreasng functon of the effort standard. COROLLARY : a comparson of contracts across each agent type facng a bndng ntrnsc partcpaton constrant reveals: () Motvated agents receve a lower bonus than opportunstc agents, B M < B O. () Norm-based agents receve a larger bonus than motvated agents, B > B M. ()The relatonshp between the bonus for norm-based and opportunstc agents s ambguous and depends on the standard for effort. (v) These contracts are proftable when S ( u θe ) > + * θ. Once agan, there are values of e* for whch t s not proftable to employ norm-based agents but t s proftable to employ motvated agents. Gven that U = u when the PC bnds, msson algnment s agan second best. Lmted lablty, B > 0, holds; otherwse, the partcpaton constrant s volated.
10 PROPOSITION 3: f the non-ntrnsc partcpaton constrant n (11) bnds, the optmal 9 contract s f = 0, B u θ = + ; and e= u+ θ + θ. Ths proposton yelds the novel observaton that the potental for agents wth socal preferences to be pad less than opportunstc agents s purely a functon of the assumpton that socal preferences mply a hgher reservaton utlty than would be otherwse assocated wth opportunstc agents. If all agents have the same outsde opton, then agents wth socal preferences are unambguously pad more; they exert more effort; and ther agency costs may be hgher. Moreover, there s no observable dfference between norm-based and motvated agents. By contrast, when the lmted lablty constrant s bndng the composton of pay s dfferent between opportunstc agents and those wth socal preferences as the fxed component of pay comes nto play as compensaton for a reduced ncentve component of pay. Furthermore, the fxed component of pay dfferentates norm-based agents from motvated ones. 5. Rsk averson In ths secton we brefly consder the nteracton between socal preferences and rsk averson. Ths s accomplshed by ntroducng a rsk averson parameter, (1 r), r [0,1], that nteracts wth the state-contnent porton of the agent s utlty functon à la Dow (004) and Carln and Gervas (009); where r = 0 mples rsk neutralty and r = 1 for nfnte rsk averson. The preferences for norm-based versus motvated agents are U(e, Bf) = f + (1 r)be ½e θ(e* e) and U M (e, Bf) = f + (1 r)(b+θ)e ½e, respectvely. These preferences are no longer nested, as U U M when e* = 0. Agan, both preferences reduce to the opportunstc case when θ = 0. The assocated IC constrants are: (1) e = (1 r)b + θ and e M = (1 r)(b+θ) (IC r ) It s no longer the case that norm-based and motvated agents exert the same level of effort for a gven contract. In partcular, a norm-based agent s effort s bounded away from zero as ts level of rsk averson ncreases whereas a motvated agent s effort s not smlarly bounded. Ths s because the rsky outcome, S, must occur for the motvated agent to receve the ntrnsc beneft, θ. The prncpal selects B j to maxmze Π j = (S B j )e f j subject to the LL and, by assumpton, a non-ntrnsc partcpaton constrant: f + (1 r)be ½e u.
11 10 PROPOSITION 4: under condtons of rsk averson, r (0, 1], the optmal contracts and effort levels for norm-based and motvated agents are, respectvely: () () (1 rs ) θ (1 rs ) + θ (1 rs ) 3θ B = ; e= ; f = max 0, u e ; (1 r) 4 and S θ S+ θ S 3θ BM = ; em = (1 r) ; fm = max 0, u (1 r) em. 4 Norm-based agents are agan offered less ncentve pay than motvated agents, B < B M, and exert more effort, e > e M. Moreover, B s decreasng n the norm-based agent s rsk averson whereas B M s ndependent of the motvated agent s rsk averson. In partcular, the nteractve term, Β/( θ r) < 0, s ndcatve that for norm-based agents, rsk-averson further decreases the ncentve component of pay; just as t typcally does for opportunstc agents. By contrast, because a motvated agent s ntrnsc component of utlty s subject to the same rsk as the ncentve component of pay, only the motvated agent s effort reflects the agent s degree of rsk averson, as t drectly translates nto the probablty that B and θ are receved. In ths way, motvaton offsets rsk averson when t comes to ncentve pay. Fnally, f f M as the fxed component of pay must compensate for a lower ncentve component of pay n order for a normbased agent to be wllng to partcpate. 6. Concluson Once t s recognzed that agents evaluate ther relatonshp wth an organzaton n terms of both monetary and ntrnsc benefts, compensaton schemes must be judcously talored so that the ncentve component of pay recognzes how socal consderatons augment the source of ncongruence between prncpal and agent. In addton, the fxed component of pay must allow for suffcent lattude for agents to act accordng to ther socal preferences. In partcular, we nvestgate the mplcatons of altrustc, ethcal, moral, motvated, opportunstc, recprocal and socal dentty preferences wthn a prncpal-agent framework. What these preferences have n common s that ther socal component s expressed wth reference to how the agent s acton s ntrnscally vewed relatve to a socal standard of behavor or outcome, rather than wth respect to the welfare of other agents. When moral hazard s due to an agent s lmted lablty, t s shown that a nested representaton of these socal preferences s possble. Wthn ths context ncentve pay s defned by the pressure agents feel to adhere to a norm, or the addtonal beneft
12 11 they receve from the knowledge that the organzaton benefts socety. Yet ncentve pay does not dstngush the agent types ths s accomplshed through the fxed component of pay. For example, ethcal agents requre a larger fxed component of pay so that ethcal actons that reduce ncentve-based pay are recognzed n the form of fxed pay. In the end t s the composton of the ncentve structure that matters for accommodatng socal preferences. In general, prncpals can rely on agents wth socal preferences to exert more effort than opportunstc agents, but whether they are pad more or less than ther opportunstc counterparts depends upon whether agents have outsde optons that are consstent wth ther socal preferences. In ths respect we provde the novel result that what always matters s the ntensty of the ntrnsc motvaton (θ) rather than the standard of behavor (e*). For ths reason organzatons that produce postve externaltes for socety are at a contractual advantage relatve to those who set targets for ndvdual performance and rely on group pressure to meet the standard. Indeed, the ntensty of ntrnsc preferences has the potental to offset an agent s rsk averson when the agent s preferences algn wth the prncpal s socetal msson. By contrast, norm-based agents must be compensated to the degree that ther actons fall short of the standard. Fnally, ths study has mplcatons for behavoral/expermental nvestgatons of socal preferences and agency. Our results on the nested relaton of agent s socal preferences under lmted lablty translate nto the expermental settng partcularly well; as lmted lablty s also consstent wth the realty of the vast majorty of agency experments, n whch subjects do not leave the laboratory wth losses. Ths s because there are both prvacy and credblty ssues assocated wth makng subjects pay for the losses ncurred durng an experment. Wthn ths context, our results suggest an expermental desgn that allows for treatments n whch the expresson of a prncpal s msson s contrasted wth a prncpal that suggests a standard for effort. These then lead to dfferences n the fxed component of pay, but not the varable component of pay or the agents effort. Furthermore, the hgher the standard for effort the larger the fxed component becomes.
13 1 References Akerloff, George A. and Rachel E. Kranton 008. Identty, Supervson, and Work Groups. Amercan Economc Revew, Papers & Proceedngs, 98() Besley, Tmothy and Matreesh Ghatak 005. Competton and Incentves wth Motvated Agents. Amercan Economc Revew, 95(3) Carln, Bruce I., and Smon Gervas Work Ethc, Employment Contracts, and Frm Value. Journal of Fnance 64: Casadesus-Masanell, Ramon 004. Trust n Agency. Journal of Economcs & Management Strategy, 13(3) Dow, James Is Lqudty Self-Fulfllng? Journal of Busness 77: MacLeod, Bentley 007. Can Contract Theory Explan Socal Preferences? Amercan Economc Revew, Papers & Proceedngs, 97() Stevens, Douglas E. and Alex Thevaranjan 010. A Moral Soluton to the Moral Hazard Problem. Accountng, Organzatons and Socety, 35(1)
Price and Quantity Competition Revisited. Abstract
rce and uantty Competton Revsted X. Henry Wang Unversty of Mssour - Columba Abstract By enlargng the parameter space orgnally consdered by Sngh and Vves (984 to allow for a wder range of cost asymmetry,
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