Other regarding principal and moral hazard: the single agent case

Transcription

1 MPRA Munich Personal RePEc Archive Other regarding principal and moral hazard: the single agent case Swapnendu Baneree and Mainak Sarkar Jadavpur University, Jadavpur University. Novemer 24 Online at MPRA Paper No , posted 4. Novemer 24 5:5 UTC

2 OTHER-REGARDING PRINCIPAL AND MORAL HAZARD: THE SINGLE AGENT CASE Swapnendu Baneree Mainak Sarkar Department of Economics Jadavpur University, Kolkata-732 Astract: Using the classic moral hazard prolem with limited liaility we characterize the optimal incentive contracts when first an other-regarding principal interacts with a self-regarding agent. The optimal contract differs consideraly when the principal is inequity averse visa-vis the self-regarding case. Also the agent is generally weakly) etter-off under an inequity averse principal compared to a status seeking principal. Then we extend our analysis and characterize the optimal contracts when oth other-regarding principal and other-regarding agent interact. Keywords: Other regarding preferences, self regarding preferences, inequity-averse, status- seeking, optimal contract. JEL: D86, D63, M52. Corresponding Author. Department of Economics, Jadavpur University, Kolkata-732, INDIA. swapnendu@hotmail.com maidip@gmail.com

3 . Introduction: Standard economic theory, from its very inception, assumes that all economic participants are self-interested. This standard assumption, although is meaningful in many circumstances might not e true always. People are not always motivated y self-gain maximization; instead we often do care aout others and react in fair, altruistic ways. Unfair distriutions of wealth or consumption, relatively unequal payment structures do make us worried. From Guth, Schmitterger & Schwarze 982) and their famous experiment on ultimatum game to recent social experiments y Camerer 23), various experimental evidences have proved the existence of other-regarding preferences in ehavioural decision making. In fact relaxing the self-regarding hypothesis is crucial for contract theory since the aim is to design appropriate incentives, and therefore people s attitude towards other s welleing as well as his own welleing is crucial for incentive design. However, so far not much work has een done to see how classical contract-theoretic predictions change in the presence of other-regarding preferences. We in this paper try to analyze how participants interact in presence of interdependent other-regarding) preferences and how the conclusions otained deviate from the standard case of self-interested participants. Specifically we focus on the case where there is hidden action and an other-regarding principal interacts with first a self regarding agent and then an other-regarding agent. The agent is income constrained implying that a limited liaility constraint operates. We characterize the optimal contracts under various parametric cases and compare it with the standard self-regarding scenario. We see, first in the case of self-regarding agent, that the optimal contract differs consideraly when the principal is inequity averse. Also the agent is For a comprehensive survey of these experimental studies see Fehr and Schmidt 23). 2

4 generally weakly) etter-off under an inequity averse principal compared to a status seeking principal. Then we consider the case where an other-regarding principal interacts with an other-regarding agent. We characterize the optimal contracts and compare our results with Itoh 24). In Itoh 24) the principal was self regarding and there existed a unique optimal contract. Whereas, in our paper the principal is other regarding and we show that the same unique optimal contract exists for a status seeking principal and this doesn t necessarily hold for an inequity-averse principal. We also show that a status seeking principal is worse-off the more other regarding the agent is. An inequity-averse principal is also worse-off given that an additional condition holds. When the principal is ehind and therefore always inequity-averse, she would always prefer a status seeking agent. This entire analysis is carried out in a single principal-agent framework; multiple agent case is kept for future research. Examples of other-regarding principal can e an employer who is enevolent and cares aout the welfare and income distriution of the employee vis-a-vis his own. Other examples can e the concept of welfare capitalism where in some capitalist economies mainly in Europe) there was and still is) a practice of usinesses providing welfare services to their employees. There are also examples of employee s welfare cooperatives in Europe that took care of employee welfare in different dimensions 2. 2 Recent examples of companies that have practiced welfare capitalism include Kodak, Sears, and IBM which provides retirement enefits, health care, and employee profit-sharing, permanent employment, extensive security and fringe enefits among others See Gordon 994) for more). One interesting example from history can e Roert Owen, a utopian socialist of the early 9th century, who introduced one of the first private systems of philanthropic welfare for his workers at the cotton mills of New Lanark. He emarked on a scheme in New Harmony, Indiana to create a model cooperative, called the New Moral World. 3

5 Quite a few recent papers have dealt with the matter of incorporating other regarding or social) preferences into contract theory 3. One of the earlier papers that talked aout other regarding preferences and moral hazard is the paper y Itoh 24). The paper focused mainly on the interaction etween a self-regarding principal and an other-regarding agent and showed that the principal is in general worse-off the more other-regarding the agent is. Although Itoh 24) riefly mention other-regarding principal, he doesn t analyze the other-regarding principal self-interested agent case in detail, and this paper attempts to fill that gap and show that interesting non-trivial outcomes occur in such a structure. Englmaier and Wamach 2) 4 address optimal incentive contracts with inequity-averse agents and show that the optimal structure of the contracts does get altered. But they don t focus on other-regarding principal. Dur and Glazer 28) use a principal-agent model to study profit-maximizing contracts when a worker envies his employer. They show that envy tightens the worker's participation constraint and calls for higher pay and/or a softer effort requirement. This paper is also an example where the agent is other-regarding whereas the principal is self-regarding whereas we focus exclusively on the case where the principal is other regarding 5. The rest of the paper is organized as follows: In section 2 we examine the enchmark self-interested principal-agent case. In section 3 we analyze the interaction etween otherregarding principal and self-regarding agent. In section 4 we analyze the case where oth 3 For a survey on this topic see Englmaier 25). 4 They focus on continuum of outcomes whereas we focus on discrete outcomes. 5 Other papers like Englmaier and Leider 28) incorporate reciprocal preferences into a moral hazard framework and derive properties of the optimal contract and implications for organizational structure. Also Hart and Moore 998) incorporate social preferences into a contracting prolem ut that was done in an incomplete contracting framework. 4

6 the principal and the agent are other-regarding. Section 5 provides concluding remarks and throws some light on future works. 2. The self-interested enchmark: We riefly analyze how players react in a standard principal-agent framework where oth parties are assumed to e self-interested in nature. We assume oth the principal and agent to e risk-neutral. The principal hires an agent for engaging in a proect, where the agent can choose either high or low effort denoted y e and e respectively where e > e Effort is unoservale and hence non-verifiale. Cost to the agent for implementing effort e is d and for e. The proect can either succeed or fail. The proect returns in case of success and in case of failure which are verifiale 7. In case the agent puts e i the proect succeeds with proaility p i, i =, and it is assumed that > p > p. Denote > 6. p = p p. We assume that the value of is sufficiently high such that the principal optimally implements high effort over low effort. We maintain this assumption throughout the paper. Assumption : is sufficiently high such that it is optimal for the principal to elicit high effort from the agent i.e. p > pd / p holds. The timing of the game is as follows: the principal offers a wage contract { w, w } where the agent is paid w in case of success and w if the proect fails given w, =,, which implies that a limited liaility LL) constraint operates and therefore the 6 Our intuition goes through even with continuum of effort choices. 7 Without loss of generality we focus on a - outcome. 5

7 agent cannot e paid a negative amount 8. The agent then can either accept or reect the contract. If reected, the game ends and the agent receives his outside option u which is assumed to e 9. The proect outcome is then realized and wages are paid accordingly. The payoff functions of the self-interested principal and the agent are U P = w and U A = w d respectively where and d are the proect returns and effort costs in the th state respectively, = success, failure. Similar to Itoh 24) we assume that the principal wants to implement e over e. Therefore the principal will maximize p p w + p ) ] suect to the participation constraint [ w p w + w d, the incentive compatiility constraint w p d and the limited liaility constraints w ; =,, where w = w w. One optimal first-est contract when effort is oservale is d / p, ). One can easily check that this first est doesn t satisfy the incentive compatiility constraint and therefore no first est is implementale when effort is non-verifiale. The optimum wage contract, under non-verifiaility, is stated elow: Claim: The optimal unique wage contract is given y w * = d / p, w * ). No firstest wage contract can e implemented. = The participation constraint will not ind at the optimum and the agent gets a rent equal to p d / p. With this preamle we go over to our analysis of other-regarding principal and self regarding agent. 8 This implies that the set of feasile contracts are given y w w ) w, ) 6 { satisfies LL } C =., w 9 The implication is that at the optimum the participation constraint will not ind. One can extend the analysis to u > without changing the qualitative aspect of the paper much. In fact there is a continuum of first est contracts.

8 3. Other regarding principal and self regarding agent: From various experimental evidences, starting from the ultimatum game, it has een shown that the principal is not always motivated y self-interest see Forsythe et al., 994). The principal might act other-regarding either ecause she is fair-minded, or she anticipates that otherwise, the unequal distriution of payoff might hurt the agent and thus he might retaliate and hurt the principal. Or, put simply, a principal can e enevolent and therefore might care aout the welleing of the agent vis-à-vis his own payoff. As already mentioned in the introduction, the concepts of welfare capitalism and the employee s welfare cooperatives in Europe stand testimony to the existence of other-regardingness in employer s preferences. In this section, we will focus on the prolem of a single otherregarding principal interacting with a self-interested agent. We will try and characterize the optimal contracts in this framework. The maor departure of this model from the enchmark one is that the utility function of the principal is not only a function of her own material payoff ut also of the agent s material payoff. We work with a modified version of a piecewise linear utility function due to Fehr and Schmidt 999) and Neilson and Stowe 23). The function captures a roader class of other-regarding preferences viz. inequityaversion and status-seeking as will e explained shortly. All the other asic assumptions are kept same as the enchmark case. Following Fehr and Schmidt 999) and Neilson and Stowe 23) we can write the utility function of the principal as For more on other regarding preferences and different approaches see Itoh 24). 7

9 U P = w w f π f 2w 2w ); ); when when w w w w Principal ahead) Principal ehind) πρ 2 ) The first part of the principal s utility function corresponds to the case where principal s net payoff when the proect succeeds) exceeds that of the agent s i.e. w > w which implies w < / 2. The second part corresponds to the case where principal is ehind i.e. w < w implying w > / 2. In case of failure, since = and w = limited liaility inds as we will see), the question of principal or agent eing ahead doesn t arise. The parameter π >, a constant, captures the extent to which the principal cares aout the agent s material payoff. If π = we get ack the standard self-regarding case. ρ, another constant, captures situations where the principal is either inequity averse or status seeking. If ρ <, the principal prefers to increase the difference in payoffs when he is ahead, i.e. the principal is status seeking 3. If ρ >, the principal s utility is decreasing in the difference in payoffs etween the principal and the agent and therefore the principal is said to e inequity averse, even if he is ahead. When the principal is ehind then he is always inequity averse. Along with this we make the standard assumptions that f ) = and f z) > for z >. The oective of the principal is to maximize her own expected utility, suect to the agent participating in the proect and putting in high effort. Now, as efore, even here the implicit assumption we make is that the principal wants to implement high effort over low 4. 2 Itoh 24) also works with the same function. Here we take the agents payoff to e his wage. One can alternatively specify agent s payoff net of his effort cost, i.e. w d and it is straightforward to extend our analysis in this direction. 3 This terminology is due to Neilson and Stowe 23). 4 Which implies that the following condition holds: p 2 ) ) pw pπρ f w p pπρ f, i.e. the principal s payoff from implementing high effort exceeds that from implementing low effort. 8

10 Since the agent is self-interested the principal needs to satisfy the standard incentive compatiility constraint pw d and the participation constraint pw d of the agent in order to make the agent put in high effort and also accept the contract. Therefore at the optimum the principal has to offer w d / p in case of success. It is easy to check that the participation constraint will e satisfied and not ind 5. Now given this, two possile cases might arise and are descried elow: i) Case : / 2 > d / p Straightforward oservation suggests that the principal will not offer w > / 2 as it would mean that the principal will e ehind the agent and thus the inequity-averse nature of the principal would lower her enefit further down. Hence, it is not optimal to have w > / 2. Therefore, this is the case where w will optimally lie somewhere etween d p / and / 2 and the principal will always e ahead at the optimum. Therefore, given inding limited liaility implying w, the prolem of the principal in this case can e formulated as: = Maximize = p w πρ f 2 )] Suect to U P [ w a) ) p w d Participation constraint) pw d Incentive compatiility constraint) We now state our first proposition: 5 This is a consequence of the assumption that the outside option of agent is. 9

11 Proposition : a). w = d / p, w ) is the unique optimal contract if the principal is status-seeking in = nature ρ < ). ). w = / 2, w ) will e the unique optimal contract if the principal is inequity-averse = ρ > ) and if 2πρ f ' 2w ) > holds. c). If ρ > & 2πρ f ' 2w ) = for some w [ d / p, / 2] then w, ) is an optimal contract. However if f.) is linear and 2πρ f ' 2w ) = w [ d / p, / 2] then any contract { d / p, / 2], w } Proof: w will e optimal. [ = a). The expected enefit to the principal when high effort is implemented is U P = p[ w πρ f 2w )] Hence, w = p + 2 p πρ f ' 2w ) = p [2πρ f ' 2w ) ] if ρ <. Thus, U P / < w = d / p and it is unique. Therefore w = d / p, w = ) is the unique optimal contract if the principal is status-seeking. The agent gets a positive net expected payoff equal to p d / p and the principal gets p[ d / p πρ f 2d / p)] which is certainly positive for ρ <. ). Since U P w = p [2πρ f ' 2w ) ], if 2πρ f ' 2w ) > then / w > / for ρ >. Therefore w * = / 2 and it is unique implying that w = / 2, w ) = U P would e the optimal contract iff 2πρ f ' 2w ) >. Note that in this case the loss from inequality is zero and the principal s payoff is p / 2 whereas the agent gets p / 2 d >, since / 2 > d / p.

12 c). For ρ >, B P / w = if 2πρ f ' 2w ) =. If f.) is linear and 2πρ f ' 2w ) = holds for all w then any w [ d / p, / 2] will e optimal. But if f.) is non-linear then 2πρ f ' 2w ) = holds for any specific value of w and that w [ d / p, / 2] will e optimal. QED The intuition of the first part is simple. Since the principal is status seeking, he enoys eing ahead and therefore he will optimally offer a wage in case of success) that is as low as possile and ust satisfies the incentive compatiility constraint. Therefore the principal will optimally offer w = d / p and also gets the agent to put in high effort and accept the contract. The agent gets a positive net expected payoff equal to p d / p since the participation constraint doesn t ind at the optimum. In the second case two opposite effects are at play. First the direct effect of paying more to the agent reduces the utility of the principal. But the principal also suffers a utility loss from inequity. Therefore increasing w towards / 2 reduces inequity and therefore leads to an increase in the principal s utility. If the marginal utility gain due to reduced inequity is sufficiently high i.e. 2πρ f ' 2w ) > then second effect will dominate and therefore the principal will optimally offer w = / 2 if the proect succeeds. But if the first effect dominates then it is optimal for the principal to offer a low enough wage to minimize the loss due to increased wage payment and therefore, w = d / p will e optimal. Finally, if the first effect is exactly outweighed y the second effect then the principal s expected utility remains unchanged with respect to changes in w and any w [ d / p, / 2] will e optimal if f.) is linear. However if f.) is non-linear then 2πρ f ' 2w ) = can hold only for a specific value of w and therefore that w will e the optimal wage in case of success. Therefore it is evident that the optimal contract is

13 sensitive to whether the principal is inequity-averse or status-seeking. Except for the situation where 2πρ f ' 2w ) =, the optimal contracts are ang-ang in nature and are unique. But amidst all these, what happens to the agent s payoff? The next proposition states the result: Proposition 2: The agent is weakly) etter-off under an inequity-averse principal than a status seeking principal. Proof: p w d > p d p d = p d / p w d / p, / 2] since / 2 > d / p. Equality / > holds for w = d / p. Therefore, the result. QED Case 2: / 2 < d / p This is the case where the principal is certainly ehind the agent when the proect succeeds. Again, for the tractaility of solution, we assume that is sufficiently high such that it is optimal for the principal to offer a contract and elicit high effort from the agent. The principal is always inequity-averse when he is ehind. Similar to the previous case, at the optimum, the limited liaility will ind and therefore given that the principal wants to elicit high effort the principal s prolem ecomes Maximize U P = p[ w π f 2w )] Suect to a) p w d Participation constraint ) pw d Incentive compatiility constraint 2

14 Since the principal wants to elicit high effort from the agent he cannot offer a success wage which is less than d / P and since he is inequity averse it is optimum for the principal to offer ust w = d / P and ensure that the agent accepts the contract 6. Therefore, w = d / P, w ) will e the unique optimal contract. One final case we consider is = when / 2 = d / P. It seems ovious that the optimal wage offer then would e w = / 2 = d / P, w ). = 3.. Alternative Specification: We have so far assumed that the principal compares his income w to the agent s w. But since the principal knows that the agent incurs a private cost of implementing high effort, he might compare his net payoff w to the net earning w d of the agent in case of high effort. In case of low effort the agent doesn t incur any cost of effort. Thus under this alternate specification the new other-regarding utility function of the principal can e written as: U P = w w πρ f πf 2w 2w + d ) d ) i i when when w w w w d d i i principal principal ahead ehind ) ) where d i = d for e = e and d i = for e = e. Similar to the earlier case the principal is ahead when the proect succeeds) if w > w d holds implying w < + d) / 2. The second part corresponds to the case where principal is ehind i.e. w < w d implying w > + ) / 2. We re-emphasize our assumption that the value of is such that at the d optimum the agent only elicits high effort, therefore we need not worry aout the situation 6 This can also e seen from the fact that B P / w = [ p 2πP f '2w )] < when w / 2 and therefore optimal success wage will e w = d / P. 3

15 where the agent might put in low effort. All other assumptions of the previous section are kept intact. Is it still optimum for the principal to offer zero wage in case of failure? To understand that note the sutle difference of this case with the earlier one. If the principal offers zero wage in case of failure the agent s net payoff now is d whereas the principal s payoff is zero. Therefore the principal is always ahead when the proect fails assuming that he pays zero in case of failure. Now a status seeking principal will enoy this inequity and therefore he will optimally pay w =. But a sufficiently inequity averse principal might not like this and therefore might optimally offer a positive wage in case of failure to minimize inequity and consequently offer a even higher w so that the incentive compatiility is satisfied. Therefore whether or not limited liaility inds will e conditional and the following lemma states a sufficient condition for limited liaility to ind at the optimum: Lemma : The principal will optimally offer w if 2 πρ f ' d 2 w ) < w Proof: To fix ideas suppose the principal is ahead if the proect succeeds. Now, given w the principal will choose that w that will maximize his expected payoff = p [ w πρ f 2w + d)] + p ) w πρf d w ) U P = 2 if w = p )[2 f ' d 2w ) ] / < >. Put differently U P πρ w then w.the principal can > = therefore optimally reduce w such that the incentive compatiility constraint is satisfied. Again if the principal is ehind if the proect succeeds then the principal is inequity averse in case of success. Therefore the expected payoff function of the principal will e U P w f d ) = p [ π πρ w w f 2w d)] + p) 2. It is always the case that U P / w = p[ 2π f '2w d) ] <. Therefore reducing w always enefits 4

16 the principal and therefore if 2πρ f ' d 2w ) < w holds then it is again optimum for the principal to set w = and reduce w such that the incentive compatiility inds. QED Note that the aove condition is automatically satisfied if the principal is status seeking, i.e. if ρ <. For the tractaility of solutions, for the time eing we will assume that the aove condition holds and therefore at the optimum limited liaility inds. Assumption 2: 2πρ f ' d 2w ) <, w holds. > Given assumption 2 we have w. Now we characterize the optimal contracts given that = > assumption 2 holds. Internalizing this the oective of the principal is to maximize her expected utility suect to the participation constraint p w d and the incentive compatiility constraint pw d. Similar to the previous situation we will consider the following two situations: if + d ) 2 > d / p / then similar to the previous case the principal will not offer w > + ) / 2 as it would mean that the principal will e ehind d the agent and thus the inequity-averse nature of the principal would lower her enefit further down. Hence, it is not optimal to have w > + ) / 2. Therefore, this is the case where w will optimally lie somewhere etween d d / p and + d) / 2 and the principal will always e ahead at the optimum. Therefore, given assumption 2 implying w, the prolem for the principal is to maximize = U P πρf )) = p[ w πρ f 2w + d)] + p) d suect to the participation constraint and the incentive compatiility constraint. Since y assumption 2 we know that 2 πρ f '.) < holds then the unique optimal solution will e w = d / p, w ). On the = other hand if + d ) 2 < d / p /, the wage offer w can t e anything less than d / p to 5

17 satisfy the incentive compatiility constraint. Since, principal is always ehind in this case, again the unique optimal wage offer will e w = d / p, w ). Therefore we get Proposition 3: = If the effort cost is considered, given assumption 2, w = d / p, w ) is the unique = optimal contract irrespective of whether the principal is status-seeking or inequity averse. But if assumption 2 doesn t hold the principal will optimally offer a positive w such that the inequity from eing ahead is minimized. Therefore if the optimal failure wage is set at w = / 2 then the resultant utility loss from inequity when the proect fails goes to zero. d Again we can consider the two previous su-cases. If + d ) 2 > d / p and given that 2 f '.) > /, given w = / 2 d πρ holds the optimal success wage is set at = )/ 2 d w + and one can check that the incentive compatiility is satisfied if / 2 > d / p. Again if + d ) 2 < d / p / then the only contract that satisfy the incentive compatiility constraint is w = d / p, w ). Therefore = Claim 2: πρ and + d )/ 2 > d / p holds, then w = + d )/ 2, w = / 2) If 2 f '.) > will e the d unique optimal contract. The limited liaility will not ind in this case. Otherwise w = d / p, w ) is optimal and the limited liaility will ind at the optimum. = 6

18 4. Both Other Regarding Principal and Agent: We now examine the situation where oth the principal and the agent are other regarding and oth the principal and the agent cares aout each other s material payoffs. The principal s other regarding utility function is given y ) as in section 3. The primitives of the agent s possile effort choices and the associated costs and other assumptions remain the same as in the enchmark model i.e. section 2). In addition to this, following Itoh 24), we assume that the agent also has the following utility structure: U A = w w d d i i αγ v2w αv ); 2w ); when w when w w < w Agent ahead) Agent ehind) 2) where α > captures the extent to which the agent cares aout the principal s material payoff. Whenα =, we get ack the standard self-regarding case. The constant γ captures situations where the agent is inequity averse or status seeking. Ifγ <, the agent is status seeking 7 whereas when γ > the agent is inequity averse. Also when the agent is ehind then he is always inequity averse. We retain the standard assumptions that v ) = and v z) > for z >. Therefore in essence the modeling of other-regardingness of the agent is similar to that of the principal following Nelson and Stowe 23)). Once again to simplify our analysis we start with the assumption that w. Later we = will show that at the optimum the limited liaility will indeed ind. Now given the current specification the agent doesn t suffer from inequity when the proect fails, following Itoh 24), the incentive compatiility constraint of the agent can e written as follows: w αγ v 2w ) d / p if w > / 2 ICa) 7 This terminology is due to Neilson and Stowe 23). 7

19 w α v 2w ) d / p if w / 2 IC) where ICa) and IC) are the incentive compatiility of the agent when he is ahead and ehind respectively. Lemma 2 Itoh 24)): A necessary condition for a contract to satisfy IC) is / 2 d / p. The proof of the aove lemma is given in Itoh 24). The logic is simple, the left hand side of IC) is increasing in w. Therefore at least one contract satisfying IC) will exist if the IC) is satisfied at w = / 2. Putting w = / 2 in IC) we get the required condition. Now, one can define ~w such that w~ α v 2w ) = d / p 3) It is straightforward to show that w~ / 2 if / 2 d / p holds. We focus on the following two su-cases. Case : / 2 d / p This is the case where the principal is weakly) ahead of the agent since w / 2. We can therefore state the next result which is in essence similar to what has een stated in Itoh 24) and this holds when the principal is status seeking i.e. ρ <. Proposition 4: If / 2 d / p holds then w ~, ) in the unique optimal contract for a status seeking principal if oth > 2πρ f ' z) and > 2αγv' z) holds z >. Proof: We complete the proof in several steps. ~ Step : First we will show that w, ) is a candidate optimal contract. Since, ) found y satisfying IC) with equality it will suffice to show that, ) w ~ is w ~ satisfies the participation constraint. Since y definition w ~ α v 2 w ~ ) = d / p d / p it is proved 8

20 ~ that w, ) satisfies the participation constraint. Therefore, ) contract. Step 2: Now to show the uniqueness of, ) Suppose, ), w ) w ~ is a candidate optimal w ~ we go y the method of contradiction. w ~ is not the optimal contract and there exists another optimal contract w such that w. We will show that if > 2πρ f ' z ) z >, it must e that > w < / 2 since w >. To do that first we show that if the principal is status seeking then an optimal contract, w ) w with 2 w > / and w > is not a possiility. But if a contract like that existed then the principal would have een ehind under oth success and failure states under ) p w, w and therefore the following must hold: [ w π f 2w ) ] + p )[ w πf 2w )] > p [ w~ πρ f 2 ~ )] w ~ p [ w w + f w ) πf 2w ) ] > p )[ w + πf 2w )] πρ 2 ~ since w > which in turn implies that w~ w > π f 2w ) πρ f 2 ~ ). It is ovious that w π f 2w ) πρ f 2 w ~ ) for ρ < and therefore w ~ w. Since w ~ < / 2, > w > is never a possiility. So a contract ) / 2 ruled out 8. The other possiility is a contract ) > > w, w such that w > / 2 and w > is w, w such that w / 2 and w >. We will show that it must e the case that w ~ > w. Now given w / 2, the principal is weakly) ahead when the proect succeeds and ehind when the proect fails and therefore the principal s expected payoff under ) w, w is given as 8 Also note that if w ~ > w then oth 2w ) and 2w ~ ) can t e positive and since the function f z) is defined for z > the analysis ecomes mathematically inconsistent. 9

21 p [ w πρ f 2w )] + p )[ w πf 2 )]. Again y assumption ) w optimal and this implies that the following holds: p [ w πρ f 2w )] + p )[ w πf 2w )] > p [ w~ πρ f 2 ~ )] w which in turn implies that p [ w~ w + f 2 w ~ ) πρ f 2w )] > p )[ w + πf 2w )] > w, w is πρ since w. p w~ w πρ f 2 w ~ f w to hold we need Now for [ + ) πρ 2 )] > [ w~ + πρ f 2 w ~ )] > [ w + πρ f 2 )] to hold. Put differently if [ w f 2 )] w > w +πρ is an increasing function of w i.e. if > 2πρ f '.) holds then certainly the previous inequality holds which implies that w ~ > w and therefore w < / 2 holds. So if another optimal contract, w ) w such that w > exists then it must e that w < ~w. Note that the condition > 2πρ f ' z) is always true for a status seeking principal. The final step shows that if 2αγv' z) > then no contract, w ) w such that w can e optimal. Step 3: Now, given w < / 2 and we will follow Itoh 24) to complete the proof. Since ) w, w satisfies the incentive compatiility constraint we get > Comining 4) and 3) we get w w α v 2w ) + αγ v2w ) d / p 4) + αγ v 2w ) ~ 2 ) 2 ~ ) / 2 ) 2 ~ w + α v w αv w w + w p + α v w αv w ) 5) Similar to Itoh 24), after re-arranging terms we get w + αγ v2w ) αv 2w ) αv 2 ~ ) 6) / p w 2

22 Since w ~ > w, the right hand side of 6) is positive. Thus, if the left hand side is nonpositive, ) w, w does not satisfy the incentive compatiility constraint, which is a contradiction. > 2αγv' z) ensures that the left hand side is non-positive and therefore ) w, w such that > optimal contract. QED w cannot e an optimal contract. Therefore, ) w ~ is the unique A pathological case arises when the principal is in-equity averse, that is ρ > ) and it is not certain that π f 2w ) πρ f 2 w ~ ). But if the principal is moderately in-equity > averse in the sense that ρ is not very high such that π f 2w ) πρ f 2 w ~ ) holds then our previous result will follow 9. > For the rest of our analysis we assume that oth > 2πρ f ' z) and > 2αγv' z) holds z > and we maintain this as an assumption. Assumption 3: Both > 2πρ f ' z) and > 2αγv' z) holds z >. What happens to the principal s expected utility when the agent ecomes more otherregarding? The next result sheds some light on this: Proposition 5: A status seeking principal is worse-off the more other regarding the agent is. An inequity averse principal is also worse-off if 2 πρ f z) < holds. Proof: Note that the principal s optimal expected utility in this case will e * U P = p w~ πρ f 2 w ~ )]. Therefore [ α w~ + πρ 2 ~ w 2 f w ) α α * U ~ P = p 9 But if π f 2w ) 2 ~ πρ f w ) < then there might e a case where there might exist a contract w, w ) such that w ~ < w with w > / 2 and w > holds. This arises due to the fact that if the principal is w ~,. Therefore it is technically possile w to make the principal relatively etter-off vis-à- strongly in-equity averse then the loss from inequity is more under ) for another contract w, w ) such that w > / 2 and > vis ~, ) 2 w. But if the principal is not sufficiently inequity averse when ahead then this pathological case can e ruled out.

23 w~ α = [ 2 πρ f 2 w ~ ) ] w~ v 2w ) = d / p. Now from 3) ~w is defined such that α. Let ) = α 2w ) α ) f α = v ~ 2w ) < f α w~ v and therefore for w ~ < / 2. To maintain equality 3) ~w has to increase and w~ therefore > α. Now if < U P * ρ, then < α unamiguously. Again if ρ > then * U P α < iff 2 πρ f z) < holds. QED To explain the aove proposition, note that the agent is always ehind and therefore is inequity averse in this situation. So the greater the α, more wage will have to e paid to the agent to make up for the agent s welfare loss due to inequity. Now a status seeking principal will hate this increased wage payment and therefore will e unamiguously worse-off the more other regarding the agent. On the contrary a, inequity-averse principal might like this increased wage payment since this will lead to reduced inequity and if the positive in-equity effect dominates the negative wage effect then the inequity-averse principal will e etter-off dealing with a more other-regarding agent. Put differently the inequity-averse principal will not prefer a more other fair-minded agent if the negative wage effect dominates the positive in-equity effect. The condition 2 πρ f z) < ensures that the negative wage effect dominates the positive in-equity effect. Case 2: / 2 < d / p We now riefly consider the case where / 2 < d / p holds and therefore IC) cannot e satisfied and thus the principal has to choose a contract ), 22 w such that w > / 2 to satisfy

24 ICa). The principal is always ehind in this situation and therefore inequity averse. The agent can e either inequity-averse or status seeking. To fix ideas define w * such that the following holds: w α v2w * ) = d / p 4) * γ g α w and we get * v w Define ) = α γ 2 * ) w * > / 2 if γ > we get α ) g α = γv 2w * ) < α ) g α = γv w * ) 2. Since for and therefore to maintain equality w * 4) w * should increase given > 2αγv' z) assumption3). Therefore we get >. The α * principal s expected utility is given y = p w * π f 2w * )] and it is U P [ immediate that the principal is worse off given an increase in w * since * U P = p[ 2 π f 2w * ) ] <. Therefore if the agent is inequity averse then a more w * other-regarding agent makes the inequity averse) principal worse-off. But if γ < we get w * < α * U and since P < w * which implies that a more status seeking agent makes the inequity averse) principal etter-off. We can state the aove finding succinctly: Proposition 6: If / 2 < d / p holds then the principal is inequity averse and would always prefer a status seeking agent. An inequity-averse principal will never enefit from a more inequity-averse fair-minded) agent. This is due to the fact that the principal is already ehind in this case and if the agent is inequity averse the agent hates eing ahead. Therefore if the agent ecomes more inequity-averse he has to e compensated more y an increased wage. This will hurt the 23

25 already ehind inequity averse principal more. On the contrary the principal will enefit from a more status-seeking agent. Since in this case the principal is ehind the agent and the agent eing status seeking enoys eing ahead. Now if the agent ecomes more status seeking the principal can optimally reduce his payment and still get to elicit high effort from the agent. Put differently now it is possile for the principal to implement high effort from the agent at a lower cost. This in turn makes the principal less-ehind and therefore the inequity-averse principal will enefit from a more status seeking agent. 5. Conclusion: This paper analyzes optimal contracts when an other-regarding principal interacts separately with a self-regarding and other-regarding agent that hitherto has een left untouched in the literature. We showed that when an other-regarding principal interacts with a self-regarding agent the optimal contract differs consideraly when the principal is inequity averse compared to the self-regarding case. Put differently when the principal is status seeking we get ack the self regarding result whereas when the principal is inequity averse the optimal success wage is consideraly higher than the self regarding case. Then we considered the case of an other-regarding principal interacting with an other-regarding agent and we show that the a unique optimal contract similar to Itoh 24) exists ut if the principle is status seeking, otherwise not. We also show that a status seeking principal is worse-off the more other regarding the agent is. An inequity-averse principal can also worse-off under certain parametric configurations. Finally when the principal is ehind and therefore always inequity-averse, she would always prefer a status seeking agent. One limitation of our paper is that we in this paper consider a single principal agent interaction whereas one can conceive of a situation where an other-regarding principal is interacting with more than one 24

26 agents. Therefore a natural extension of this paper is to consider a multi-agent framework ut one has to e careful while defining other-regardingness of the principal in the multiagent framework. 25

27 References: Camerer, C. F., 23. Behavioral Game Theory. Princeton, NJ: Princeton University Press. Dur, R., Glazer, A., 28. Optimal incentive contracts when workers envy their osses. Journal of Law Economics and Organization. 24 ), Englmaier, F., 25. A survey on moral hazard, contracts, and social preferences. In: Agarwal, B., Vercelli, A. Eds.), Psychology, Rationality and Economic Behaviour: Challenging Standard Assumptions. Palgrave-MacMillan, Hampshire, UK, Englmaier, F., Leider, S., 28. Contractual and organizational structure with reciprocal agents. CESifo Working Paper 245. Englmaier, F., Wamach, F., 2. Optimal incentive contracts under inequity aversion. Games and Economic Behaviour Fehr, E., Schmidt, K. M., 999. A Theory of Fairness, Competition and Cooperation. Quarterly Journal of Economics. August, 43), Fehr, E., Schmidt, K. M., 23. Theories of Fairness and Reciprocity: Evidence and Economic Applications. In: Dewatripont, M., Hansen, L. P., Turnovsky, S. J. Eds), Advances in Economics and Econometrics: Theory and Applications, Eighth World Congress, Vol. I. Camridge: Camridge University Press,

28 Forsythe, R., Horowitz, J. L., Savin, N. E., Sefton, M Fairness in Simple Bargaining Experiments. Games and Economic Behaviour. Vol. 6, pp Gordon, C., 994. New Deals: Business, Laor, and Politics in America, Camridge, U.K.: Camridge University Press. Guth, W., Schmitterger, R, Schwarze, B., 982. An Experimental Analysis of Ultimatum Bargaining, Journal of Economic Behavior and Organization, 3, Hart, O., Moore, J., 28. Contracts as reference points. Quarterly Journal of Economics. 23 ), 48. Itoh, H., 24. Moral Hazard and Other-Regarding Preferences. Japanese Economic Review. Vol 55, No., Neilson, W. S., Stowe, J., 23. Incentive Pay for Other-Regarding Workers. mimeo. 27