The economics of envy

JOURNAL OF

ELSEVIER

Journal of Economic Behavior and Organization Vol. 26 (1995) 311-336

EconomicBeha~ & Organ~afion

The economics of envy Vai-Lam Mui Department of Econoraics, University of South California, Los Angeles, CA 90089-0253, USA Received 8 December 1992; revised 28 August 1994

Abstract Equity theory in psychology, observed responses to reform in socialist countries, and studies in the field of organizational behaviour all suggest that envy can play an important role in economic behaviour. This paper incorporates envy into the standard economic choice framework. The model provides a natural extension of the theory of equity in psychology. It is used to analyze how agents' innovating, retaliating, sabotaging, and sharing behaviour are jointly determined by legal institutions and agents' propensities for envy. Implications for the economics of organization and the reform of socialist economies are discussed. Keywords: Envy; Innovation; Retaliation; Sabotage; Sharing; Legal institutions JEL classification: A12; D00; D23; D62; K42; O31; P21 (T)he blind, burning envy of your neighbour's success.., has become the most powerful brake on the ideas and practice of perestroika. Until we at least damp down this envy, the success of perestroika will always be in jeopardy.... -(Nikolai Shmelyov, an advisor to the former Soviet government. Quoted in Smith 1990, p. 205)

1. Introduction Although the normative significance of envy has been discussed in welfare economics (Baumol, 1987, Foley, 1967, Varian, 1974), the behavioral implications of envy have not received much attention in the economics literature. Some notable exceptions exist. Banerjee (1990) presents an equilibrium model of envy and shows how progressive income taxation can be used to correct the distortions created by envy. Brennan (1973) shows how envy and malice can motivate 0167-2681/95/$09.50 © 1995 Elsevier Science B.V. All fights reserved SSDI 0167-2681(94)00079-4

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non-altruistic individuals to support redistribution programs because the individuals value reduced consumption by the rich. Brenner (1987) presents evidence to show that individuals care about their relative economic statuses, and demonstrates that such concern may lead to risk-taking behaviour. Elster (1991) observes that people may abstain from becoming superior to others so as to avoid provoking their envy. Kirchsteiger (1995) incorporates envy into the standard bargaining model to explain findings in ultimatum game experiments. In this paper, I explore the role of envy in provoking sabotage or retaliation against others using the economists' traditional rational choice framework, taking into account the costs of such actions. A major difference between the current paper and previous research on envy is that I explicitly consider how legal institutions affect agents' innovating, retaliating, and sabotaging behaviour. The expanded decision model provides a means for analysing the interactions among people's propensities for envy, the nature of the innovation opportunities, and legal institutions. The model thus yields a natural "economic" extension of the theory of equity in social psychology. I assume that people compare their economic well-being with others', and that if an innovator introduces an innovation that improves his relative economic status, those who lag behind (the followers) experience envy. The analysis of the strategic interactions between the follower and the innovator yields some interesting results concerning retaliation, sabotage, and innovation. For example, it is natural to conjecture that an increase in the legal authority's propensity to punish retaliation and sabotage will always increase the incidence of innovation. This conjecture turns out to be incorrect; I show that it can reduce the incidence of innovation. Moreover, while an increase in the authority's propensity to punish retaliation will always make it more costly for an envious agent to inflict retaliation on others, I show that there exist conditions under which an envious agent will actually support an "appropriate" increase in this propensity. I also present empirical evidence to show that as a way to reduce the threat of envious retaliation, an innovator may engage in voluntary sharing. I demonstrate that in general, voluntary sharing is not sufficient to fully mitigate the problems of envy. I conclude the paper by discussing possible ways to extend the model to study issues pertinent to institutional design and collective action.

2. The significance of envy That envy plays an important role in social and economic life has been emphasized by many anthropologists and sociologists (Bailey, 1971, Schoeck, 1966). Foster (1967), for example, provides accounts of different envy-reducing social customs in the village of Tzintzuntzan. One example is the attitude towards pregnancy. The villagers consider children highly desirable. If a woman is pregnant, it is a cause for celebration, but the family will keep the pregnancy a

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secret as long as possible. According to Foster, this is because a baby is considered to be a " g o o d " for the family and the mother will suffer from others' envy. Even after the pregnancy becomes publicly known, there are still attempts to avoid reminding others that the woman is pregnant. As noted in the quote of Shmelyov at the head of the paper, envy poses a significant constraint on socialist economic reforms. William and Jane Taubman (1989) observe that to many Soviet people, socialism "seems to amount to social envy, the insistence that 'my neighbour not live better that I do', even if the prospect of doing so prompts him to produce more for us both." (p.143) Drawing on the experiences of the Eastern European countries, Brenner (1990) emphasizes the importance of reforms in legal institutions to mitigate the problem of envy. Smith (1990) observes that the Soviet press is full of stories about owners of cooperative restaurants or other small service shops being attacked by others who resent their successes. He concludes that this hostility toward those who moved ahead may "freeze the vast majority into the immobility of conforming to the group", and will discourage the emergence of the new entrepreneurs (p.202). This same concern is echoed in other socialist countries. In China, peasants enjoy greater economic autonomy with the new "responsibility system". While the state still retains ownership of land, it often delegates the right to use the land to peasants by signing long term contracts with them. Specialized households (zhuan ye hu) which have taken advantage of these opportunities often found themselves the subjects of hostility, and even attack, from their fellow villagers (Nee, 1989). From January to June 1984, the Peoples Daily (Renmin Ribao) - the official Communist Party newspaper, ran a column titled, " H o w to view those peasants that became rich first?" Government officials repeatedly emphasized that "it is ideologically correct for some of the citizens to become rich first," and that " t o get rich is glorious" (Renmin Ribao, Mar. 22, 1984, p.5, Apr. 16, 1984, p.2, June 3, 1984, p.5). The importance of economic innovation was emphasized. The column also revealed a strong sentiment in the countryside that "some people have gone too far in getting rich" (Renmin Ribao, Apr. 16, 1984, p.2). The following case is typical. Tan Anji is a peasant in Hubei province. In 1982, he was one of the richest persons in the village (with an annual income of 9000 yuan). However, as soon as he got rich, misfortunes followed. In January 1983, the timber for his new house was stolen. Later, half the vegetables in his field were stolen. In March, his pregnant cow was stabbed to death. In May, two of his goats - and in June some of his hens - were poisoned. He cancelled the fish farming project he had started when people commented that it was an "unreliable" business. He commented: " I dare not work too hard to get rich again." (Renmin Ribao, Apr. 15, 1984, p.2). Some behaviour, which looks like envious retaliation, like theft, may instead be simply a way of taking the wealth of the owners. But such explanations do not fit all the facts. For example, why was Tan Anji's property destroyed rather than

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stolen? Surely, some of the acts of retaliation in the countryside are motivated by envy. The problem of envy does not only arise in the context of socialist economic reform. The phenomena of social comparison and relative deprivation, and their importance in organization life, have long been important topics of research by sociologists and social psychologists (Olson et al., 1986). In his analysis of the importance of equity considerations in social life, Homans (1974) argues that in any human group, the relative status of a member of a group is determined by his contribution to the group, as perceived by other members. Naturally, the greater a member's contribution, the greater his standing. Using the theory of equity in social psychology (Adams 1963), Homans argues that without changes in his contribution to the organization, attempts by a member to change his relative status are usually met with hostility by other group members. This is because such attempts violate the member's notion of what constitutes an equitable hierarchy of statuses in the organization. To illustrate his argument, Homans elaborates Whyte's pioneering field study of gang behaviour in Street Corner Society (Whyte, 1943). This work provides a detailed account of the behaviour of a street gang. One of the frequent activities of the gang was bowling. Doc was the leader of the group. Alec, another member, had low status. Alec considered himself to be a good bowler and once boasted to another member, Long John, that given the way he was bowling, he could defeat all other members of the gang. Long John dismissed Alec's challenge by asserting that " y o u think you could beat us, but, under pressure, you die!" (Whyte 1943, p.19). When Doc arranged a formal bowling tournament between all members, Alec made it known to other members that " h e intended to show the boys something." In the tournament, he took the lead in the first four frames, but, frustrated by verbal attacks of other members, his performance deteriorated rapidly. He finished last. Later, Long John commented that he "just wanted to be sure that Alec didn't win" since "that wouldn't have been right." Moreover, when asked by Whyte what he would have done if Alec and Dodge (another member of the gang) did win the game, Doc commented that " i f they had won, there would have been a lot of noise. Plenty of arguments. We would have called it lucky - things like that. We would have tried to get them in another match and then ruin them. We would have to put them in their places." (Whyte 1943, p.21, emphasis added). In economics, status considerations are also featured prominently in the earlier works of Veblen (1934) and Dusenberry (1949). More recently, Frank (1985) develops a model that shows bow people's concerns for their relative positions in the income hierarchy of an organization can lead to wage compression. Bolton (1991) presents a bargaining model in which a bargainer's utility depends both on his income from the settlement and its ratio to that of his opponent. This essay focuses on the fact that when a person introduces any changes (what I refer to as innovations) that improve his relative status, those whose relative status are

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affected adversely by such changes (the followers) will suffer from envy toward the innovator. I study how the follower's incentive to engage in sabotage and retaliation, as well as the innovator's incentive to innovate, are affected by the nature of the innovation and the legal authority's propensity to punish retaliation and sabotage. Suppose that two agents are engaging in independent production activities. Each agent is endowed with one unit of labour, which can be used to produce income y. I assume that the agents do not derive any utility from leisure. The economic utility of agent i is given by a function Vi(Yi). This assumption, together with the assumption below on how an agent compares his opportunity set to the other's, implies that each agent will always devote all of his labour endowment to production. I assume that limy, .~ oVi'(Yi ) --- oo,V/' > 0, V/" < 0 To simplify exposition, I assume that agent i's production function is fi(Li) = YiLi, 0 < L i < 1. Then Y/=f/(1) is the maximum output of agent i. The production functions are assumed to be common knowledge. I further assume that given the two production possibility sets, agent i will compare Y~ to Yj. If I12 > I11, 1 will perceive 2 as having a better opportunity set than him. 1 will then suffer from envy. I also assume that when 111 > I12, 1 will not derive any psychological satisfaction from being economically better off than 2. 1 Let E I ( Y 2 / Y 1) be l ' s envy of 2 given the observed incomes of the two agents. El(.) is l ' s propensity for envy. Envy enters negatively into a persons utility function. I assume that

EI~Y1 ]

(1) > 0 , if Y2111> 1

This formalization of envy can be viewed as an application of the theory of equity in psychology proposed by Adams (1963), which has been used by some economists to study the employment relationship (Akedof and Yellen 1990, Garner, 1986, I.evine, 1991). According to this theory, a social relationship is equitable from a persons point of view if Outcome of Person 1

Outcome of Person 2

Input of Person 1

Input of Person 2

(2)

In my model, the outcomes are the agent's maximum outputs and the inputs are

1For a discussionof the implicationsof relaxingthis assumption, see Mui (1992).

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the maximum labour inputs. The economic environment is equitable if and only if El//1 = y2//1.2

This theory of equity further predicts that when I:1 < Y2, 1 perceives that he is in an unfavourable position in an inequitable relationship, and may take actions either to increase 1:1 (if possible) or to decrease Y2 so as to restore equity. One way to achieve the latter is to retaliate against 2. This implication is consistent with the evidence discussed above. When a person observes that the innovator in his neighbourhood has successfully introduced an economic innovation (setting up a cooperative restaurant, growing a new kind of crop) and has moved ahead, this change in relative economic status will cause him to suffer from envy. In order to get even, he may inflict different kinds of punishment on the innovator (perhaps attacking the innovator's restaurant, or even physically assaulting him). I will refer to such punishments as post-innovation retaliation. Let R 1 be the level of retaliation 1 inflicts on 2. R 1 is normalized in a way so that one unit of retaliation requires one unit of labour. Thus, 0 _ 0, F~' < 0, FI(1) < 1. That is, there are diminishing returns in punishing the other person. Since FI(R 1) < 1, if Y1 < Y2, EI(Y2/Y1)( 1 - FI(RI)) will always be positive. Although retaliation against 2 does reduce l's suffering from envy, it will not completely offset l ' s suffering from envy. Thus, being economically worse off than others will always decrease a person's utility. Note that if FI(R 1) = 0, 1 does not regard retaliation as a legitimate way of getting even. Regardless of the costs of inflicting retaliation upon others, such a person will not engage in retaliation. One problem with the equity theory is that it does not explain how the environment in which agents interact affects the equilibrium level of retaliation. It is important to recognize that it is often costly for an agent to retaliate against others. One component of these costs is the opportunity cost of actual resources a person incurs in retaliating against others (money spent to buy the poison used to kill the livestock of the neighbour, etc.). If 1 chooses to inflict R1 units of

2 The theory of equity maintains that the "values" of the outcomes as well as of the inputs are

subjective. In the above formulation, I take the outcome to be the maximum output and input to be the maximum labour of each person. I also assume that the subjective values of all of these variables coincide with the objective values. Thus, the relationship is equitable if and only if 1:1/1 = Y2/1, i.e., Y1 = 1:2. The simplifying assumptions imply that the preference for equity is reduced to a preference for equality. The model can be adapted to allow for the notion of equity more generally. Suppose that 1 perceives 2 to be more competent than he is, so that 1 considers a situation to be equitable so long as 2's income is not "too much" higher than his. This can easily be incorporated in the model by assuming that l ' s subjective value of 2's maximum input is k > 1. Equation (1) can then be rewritten as EI(Y2//1:1) = 0 if Y2//Y1 < k, EI(Y2//Y1) > 0, E~ > E i > 0, if Y2//Y1 > k. Adaptation of equation (1) for the case of k < 1 is straightforward.

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retaliation on 2, the labour time left for production activities will be (1 - R 1) and 1 will only get an economic utility V1(Y1(1- R1)). When the retaliation is in the form of illegal activities, for example, burning the crops of one's neighbour or physically assaulting one's co-worker, the cost of retaliation will include the expected punishment that a person may receive. Assume that all retaliation takes the form of illegal activities 3 and are subject to punishment by the authority if detected. Following Becker (1968), let P(3') be the probability of apprehension and TI(R 1, Y) be the punishment inflicted on 1 if 1 is convicted for having committed a retaliation of the level R r The parameter Y measures the resources the government devoted in detecting and punishing retaliation. 3' will be referred to as the authority's propensity to punish retaliation. An increase in 3' implies that both the total and the marginal expected punishment for retaliation will increase. To simplify notation, let CI(R1, 3")= P(3")TI(R 1, 3") be the expected punishment (in utility terms)l expects to suffer when his chosen level

acl(R1,3')

of retaliation against 2 is R 1. I assume that C1(0 , 3") = 0 and limsl _~0

OR1

= 0. Moreover, for all R 1 positive, the following conditions hold. 0C1(R1,3') 0R1

02C~(R1,3") > 0,

0R12

02C1(Rt,3") > 0,

0Rlib/

0C~(R1,3') > 0,

03'

> 0

(3) Finally, let GI(R 2) be the disutility that 1 suffers from 2's retaliation. I will assume that GI(0) = 0, G'~ > 0, G~ > 0. In sum, the utility function for agent 1 is

UI( Y1,Y2,R1,R2) = VI(YI(1- R1) ) - EI( ~ ) ( 1 - FI( R1) ) - C1(R1,3") - GI(R2)

(4)

The utility function of agent 2 has an analogous expression.

3. The model I assume that the agents have inherited the " s a m e " technologies Yi = ~Lr This implies that the incomes of the two agents will be Y1 = Y2 ffi Y and there is no envy in the society initially. In the context of socialist economic reforms, this is a stylized representation of the fact that in the pre-reform era, the agents were 3 This assumption simplifiesthe exposition and can be relaxed without affecting the results of the analysis. One can instead assumethat there exists a range of retaliation(say, for any R1 between0 and Sl ) that does not involveany illegal activities and the only costs of choosing an R1 in this range is the opportunity costs of the foregoneincome.

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" m o r e or less equal." Now suppose that once reform policies are put in place, one of the agents devises an innovation that gives him the option of choosing a better technolog_y Yi = aLi, with Y < a. If he adopts the innovation, his income will be Y~= a > Y. This innovation may come from the new knowledge that he obtains through interactions with the outside world, or it may reflect the fact that economic reform has allowed him more freedom to utilize his talent and knowledge. I restrict my attention to the class of innovations that will also benefit the other agent economically. This benefit may come from the follower imitating the innovation, or through some kind of spill-over effect that would enable the follower to improve his technology. Thus, if a peasant entrepreneur establishes a profitable rural enterprise, it may not only increase his own income, but may also make better jobs available to the other agent. I will assume that agent 1 is the innovator while agent 2 is the follower. If 1 adopts an innovation that increases l ' s income to a > Y, the spill-over effect from l ' s innovation will enable 2 to employ a new technology Y2 = aaL2. The parameter ot captures how much the innovation benefits the follower relative to the innovator. I will focus on innovation opportunities with 0 < a < 1, so that the benefit to the innovator exceeds (or equals) that to the follower. Such an innovation is said to have a normal spill-over effect. 4 The innovation opportunity available to the agents is described as (a, aa). Note that 2's choice set is dependent on whether 1 adopts the innovation. I assume that all information in the model is common knowledge to the agents. The timing of events in the model can be summarized by the following time line:

1

Agent 1 chooses his technology

[

Agent 2 chooses his technology

i i

4, Emotions are generated

i i

4, Retaliation takes place

[

Payoffs are realized

Since each agent knows the utility function of the other agent, he can perfectly anticipate the other agent's emotional reaction to any changes in the economic environment. Given this structure, subgame-perfect equilibrium is the natural solution concept for the model. In this case, 1 maximizes his utility by solving Max V I ( Y I ( 1 - R a ) ) - E a ( Y 2 ( Y ' ) rleff,a} Y1

](1-Fa[RI(Y1,Y2(Y1))] ) ]

- C1[ R,(Y1,Y2( Y1)),T] - GI[ R2(Y1,Y2( I"1))]

(5)

4An innovation is said to have a strong spill-over effect ira > 1, so that the benefit from the innovation to the innovator is less than that to the follower. See footnote 6 below on h o w the potential innovator's propensity for envy may discourage him from adopting an innovation that has a strong spill-over effect.

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s.t.

R1 - C I ( R I , T ) - GI(R2(Y1,Y2) )

RE(YI'Y2) • argmaxVE(Y2(1 - R 2 ) ) - E 2

(6)

~2 (1 - F 2 ( R 2 ) )

R2

- C 2 ( R 2 , T ) - GE(RI(YI,Y2) )

r2(rl) •

v2(r2(1 -R2)) -E2

(7)

(1 - F2(R2(YI,Y )))

Y2

-- C2( R2( YI ,Y~),T ) -- a2( gl( gl ,r~) )

(8)

Denote the equilibrium by (YI*, Y2*, R~', R~ ). I assume that ff Yj > Y~, then holding Yj constant, i's utility is increasing in Yv This implies that given an innovation with a normal spill-over effect, if 1 adopts the innovation, 2's best response will be Y2(a)= aa. This is due to the fact that since Y < ~ a < a, in equilibrium, 1 will never be envious of 2, henceR 1 -- 0. ff 1 adopts the innovation, compared to any Y2 < aa, aa gives 2 a higher level of economic utility and also a lower level of psychological disutility. Let R 2 (a, ~a) be the solution to (7) for (Y1, Y2 (II1)) -- (a, ~a). 5 To simplify notation, define H 1 (Y1, Y2) --- UI(Yp Y2, R1 (Y1, Y2), R2 (I11, Y2))

-VI(YI(1-R1))-E1

( ~11 Y2 )(I - FI(RI(Y1,Y2))

- CI(RI(I"1,Y2) ,3') - G I ( R 2 ( r l , r 2 ) )

(9)

Then, by adopting the innovation, 1 increases his utility by the amount Hi(a, eta) - H i (Y, Y). It will be assumed that if i is indifferent between innovating or not, he will innovate. I get the following result. Observation. Consider an innovation (a, txa) with a normal spill-over effect. (i) If l ' s economic gain from innovation is sufficiently high so that it can more than offset the threat of 2's envious retaliation, 1 will adopt the innovation. That is, //1 (d, ~ a ) -- /-/1 (Y, Y) = [Vl(a) - GI(R2(a, aa))] - VI(Y) _> 0 =* YI* = a, Y2* = aa, RI* = 0, R~ = R2(a, ota) > 0. (ii) If l ' s economic gain from innovation is not sufficient to offset the threat of 2's envious retaliation, 1 will maintain the s Note that given the assumptions on V/, Fi(Ri) and Ci(R~, T), for II1 > Y2, V2(Y2(1- R2))E2(Y1/Y2)( 1- F2(R2))-C2(R2, T) is strictly concave in R 2. Thus, from (6) and (7), RI(Y1, Y2) = 0, and R2(Y1, Y2) > 0 are both uniquely defined.

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original technology. Thus, there will be neither innovation nor observed incidents of retaliation. That is, Vl(a)

-

VI(Y) < G l ( R 2 ( a , a a ) )

~ ]11" = ]"2* = Y, R1 = R 2 = 0.

This observation is a formal statement of the assertion reviewed in section 2, namely, that the threat of others' envious retaliation can deter a person from adopting an innovation. 6 3.1. Legal institutions, socialist economic reform, and the economics of organization

I now analyze how a change in y, the authority's propensity to punish retaliation, affects the equilibrium outcome. From (7), for Y1 > Y2, R2 (¥1, Y2) is determined by the first order condition 7 F~(RE) = Y2V~(Y2(1 - R E ) ) +

Ez

OR 2

(10)

At the optimum, the marginal reduction of disutility from envy due to retaliation equals the marginal cost of retaliation, where the marginal cost of retaliation consists of both the opportunity of foregone income and the expected punishment by the authority. Given that V2 and F z are concave and C 2 is convex in R2, the second order condition is satisfied. Differentiating this first order condition with respect to T, yields

02C2(Rz,T) dR 2 dy

0REOT

=

|'l|[V\F, ,

02C2 < 0

(11)

v2 J 2 + This result of dR z (Y1, Y2)/d'Y < 0 can be given a comparative institutional interpretation. It says that holding the pattern of income distribution and the agents' propensities for envy constant, a deterioration in the efficacy of the legal institutions in protecting the agents from retaliation will increase the follower's

6 Suppose that the innovation has a strong spill-over effect instead of a normal spill-over effect. That is, the innovation opportunity is (a, ~ a ) with a < a a s o that the innovation benefits the follower more than it does the innovator. In this case, if Y2(a)= ~ a and l ' s economic gain from adopting the innovation is not sufficient to compensate for the increase in his suffering from envy, 1 will not adopt the innovation. This provides an example in which a potential innovators own propensity for envy discourages him from adopting the innovation. 7 The possibility of corner solutions are ruled out by the assumption that limy2~ 0 V2(Y2)f°v, limR2 ~ 0 F2(R2) =oo, and limR2 ~ 0 ~C2(R2, 'Y)/~R2 = 0.

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incentive to retaliate against the innovator. In countries undergoing economic reform, rural residents, unlike their urban counterparts, often do not have easy access to formal legal protection. The result implies that for the same relative increase in his income, an innovator in a rural area is more likely to suffer from envious retaliation than an innovator in an urban area. Since overt retaliation in the form of physical assault or trespass on others' properties is severely punished in societies with well- established legal institutions, it is very costly for an envious person to retaliate against others. Hence, people do not need to worry about the possibility that their neighbours may inflict severe retaliation on them. However, the derived result can also explain why a person who has just "moved ahead" in the organization he belongs to may need to worry about the potential threat of envious retaliation even in such a society. The envious person could provide false and unfavourable information to the envied person's superior regarding the person's performance and conduct. Or he can refuse to cooperate with the envied person so as to prevent him from performing well in the organization. Since most of these actions do not constitute any kind of criminal offense, they can only be punished by the organization itself. Moreover, they are inherently difficult to detect and this puts a natural limit on the organization's ability to deter them. Since the most severe punishment that an organization can impose on a member is to " f i r e " the member, this sets a natural upper bound on the level of expected punishment an organization can impose on its members. This implies that the more costly it is for a potential innovator to "exit" from an organization, the more likely that others' envious retaliation will discourage him from adopting the innovation. This would apply, for example, to cases in which the innovator derives a significant rent from his job, or if the "organization" is a relationship that is highly valuable to him emotionally. I now shift my attention to the agents' preferences regarding how severely the authority should punish retaliation. In deciding whether to innovate, 1 anticipates that if he innovates, he will suffer from post-innovation retaliation by 2. It is obvious that when the prevailing legal institutions do not impose a strong enough penalty against retaliation, the threat of envious retaliation by 2 can deter 1 from innovating. Slightly less obvious is the fact that if the innovation has a significant spill-over effect so that 2's economic gain from the innovation can more than offset his disutility from envy, 2 will actually prefer 1 to adopt the innovation. This requires that, for given 3~ a V2( aa(1 - R2(a, a a ) ) )

-

V2(Y ) > E2( ~ a )(1 - F2[ R 2 ( a , a a ) ] ) + C2[RE(a,aa),3, ]

(12)

It is perfectly possible that for certain innovation opportunities and some classes of preferences, both inequality (12) and the condition V l ( a ) - GI(R2(a,

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aa)) < VI(Y), would hold simultaneously. In this case, even though 2 will suffer from envy after l ' s innovation, he still prefers 1 to adopt the innovation. However, since 2 cannot credibly commit not to inflict a high (to be exact R 2 (a, aa)) level of retaliation upon 1, 1 will choose not to innovate. Thus, 2's propensity for envious retaliation not only hurts 1 but also discourages 1 from adopting an innovation that will increase 2's utility. 8 Proposition 1 and its corollary establish that in this case, 2 will support "appropriate" increases in the authority's propensity to punish retaliation, although such an increase will always increase 2's costs of using retaliation to " g e t even." Defining 7 * (a, a a ) -- 3, * to be the level of the authority's propensity to punish retaliation such that 1 is indifferent between innovating or not innovating, i.e., 3" * is such that I11(a, a a ) - HI(Y, Y ) = 0. Recall that if 1 is indifferent between innovating or not, he will innovate. Since d[ Hi(a, a a ) - HI(Y, Y ) ] / d 3 ' = - G 1 dR2(a, aa)/d3" > 0, it follows that 1 will innovate if and only if 3' _> 3' *. Proposition 1. I f V2 (aa(1 - R 2 (a, a t ) ) ) - V2(~') > E2(a / aa)(1 - F2[R2(a, aa)]) + C2[R2(a, aa), 3" *], then there exists ~,> 3/* such that any increase in the governments propensity to punish retaliation from 3" < 7 * to 31~ (3" *, ~,) will increase the utilities of both 1 and 2. Proof. See the appendix. The idea behind proposition 1 can be illustrated with a simple diagram. In Fig. 1, I draw each agents' equilibrium payoff as a function of 3'. l ' s payoff is represented by the smooth curve ABC. This curve is horizontal at the range of 7 < 3' *. In this range, there will be no innovation and l ' s payoff will be the constant HI(Y, Y) -- VI(Y). At point B where 3' = 3" *, agent 1 is just indifferent between innovating or not. For 3' > 3' *, ABC is upward sloping because lll(a, aa, 3')is increasing in 3'. 2's payoff is represented by the curve DEGF. D E G F is also horizontal at the range of 3, < 3" *. In this rang_e, there will be no innovation and 2's payoff will be the constant II2(Y, Y ) = Ve(Y). At point G where 3' = 3'*, there is a discrete jump in 2's payoff. This is due to the fact that 2's economic gain due to the spill-over effect is so significant that it will more than offset 2's disutility from envy. Since 1-12 (a, aa, 3") is decreasing in 3' for 3' > 3' *, D E G F is downward sloping in this range. Suppose that the current level of 3' is smaller than 3' *. As revealed by the diagram, so long as one chooses a 3' sufficiently close to 3' *, say any point to the left of ~, any increase of 3' from the status quo to 3' ~ (3" *, "~) will increase the utilities of both agents.

s In his recent book, Frank presents interesting findings in biology, psychology and sociology to support the argument that in some cases, emotions may be as important as material payoffs (Frank, 1988). He further shows that if emotional reaction is an integral part of ones personality, then possession of certain sentiments (for example, honesty) may actually help one to make credible commitments and will increase one's payoffs. My result here can be regarded as a woeful corollary of Frank's proposition.

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C

v, (~)

l's payoff

I I I I

G

rL~(a, ~a, ¢)

v~ I

2'sp~off

I I I I I

¥ Fig. 1.

Corollary. (Using the legal institutions as a means to achieve credible commitment for the control of emotional reactions). Suppose V2( ~ a ) ( 1 - R 2 ( a , o t a ) ) )

--

V2(Y ) > E 2( ~ a ) ( 1 - / 7 2 [ R 2 ( a , o l a ) ] )

+

1,

and the current level of T chosen by the authority is 3' < 3' * so that there is no innovation. Then both the follower and the innovator will support changes in government policies that increase the government's propensity to punish retaliation from 3' < Y * to 3' ~ (Y *, ~'). This corollary highlights the interactions among the agents' propensities for envy, the nature of the innovation opportunity, and the legal institutions. Since the innovation has a significant spill-over effect, 2 will actually prefer 1 to adopt the innovation. However, 1 will not innovate unless 2 can credibly commit 9 not to impose "too much" retaliation against 1. Given that 2 has a propensity for envy that cannot be changed at will, there is no way for 2 to achieve this kind of credible commitment if the status quo of the legal institution was to remain unchanged. Although an increase in the authodty's propensity to punish retaliation 9 For an early discussion of the notion of credible commitment, see Schelling (1960). Thaler and Shefrin (1981) presents an interesting application to the problem of self-control, while Williamson (1983) demonstratgs how contracting parties can use "hostages" to achieve credible commitments.

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will always increase 2's costs to use retaliation as a means to "get even", 2 will now still support "appropriate" increases in the authority's propensity to punish retaliation. Such a change from the status quo would enable 2 to credibly commit not to inflict a high level of retaliation upon 1 which would in turn induce 1 to adopt the innovation. Note that although both 1 and 2 would support any increase of 3, from 3' < 3' * to 3"~ (3' *, ~/), they have conflicting preferences regarding the magnitudes of such increases. 1 would prefer an increase in 3' as large as possible while 2 would prefer a small increase. In fact, the most preferred change for 2 is an increase in 3' from the status quo to 3' *. If the reverse of inequality (12) holds, any increase in 3' that increases l's utility would decrease 2's utility and would not be supported by 2.

3.2. The level of aggregate innovation Using this model, we can also analyze whether the threat of the follower's envious retaliation will always decrease the aggregate level of innovation. Let (YI*, Y2*) be the equilibrium levels of income for the two agents. The aggregate level of innovation can be defined as YI*+ Y2*-2Y. If there is only one innovation process available, the threat of envious retaliation will never increase the aggregate level of innovation. However, suppose that there are now two innovation processes available in the economy. These two innovation processes are represented by (a, aa), (b, fib) with Y < aa < a, ~" < [3b < b. If 1 adopts the innovation (a, aa), l's income will be a, and 2 will then be able to choose I"2 from {Y, aa}. The same interpretation holds for (b, [3b). Assume that Y < b < a, so that from l ' s perspective, the innovation process (a, aa) is economically superior to the innovation process (b, [3b). In the absence of 2's propensity for envy, 1 will adopt the innovation (a, aa). I also assume that aa < fib, namely, the innovation process that is economically superior from l ' s perspective has a much weaker spill- over effect (or much more difficult for 2 to imitate).

Proposition 2. (Envy and the aggregate level of innovation). If b + [3b > a + a a, that is, due to its larger spill-over effect, the innovation (b, [3b), though is economically inferior to (a, aa) for 1, implies a higher aggregate level of innovation. (ii) V l ( b ) - GI(R2(b, [3b)) > Max[V1(~9, V l ( a ) - GI(R 2 (a, aa))]. That is, although 1 "s economic gain will be lower if he adopts the innovation (b, [3b) instead of (a, t~a), he will still prefer to adopt the former innovation because he will suffer a lower level of retaliation from 2. Then, the equilibrium outcome will be Y1* = b, Y2* = fib. That is, the potential threat of envious retaliation will actually increase the aggregate level of innovation. While 2's propensity for envy does discourage 1 from adopting an innovation that increases income inequality "too much", this mechanism now actually (i)

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increases the aggregate level of innovation. 10 This result also suggests that if the authority's objective is to maximize the aggregate level of innovation in the society, it may not always be desirable for the authority to choose a high level of since this may encourage 1 to adopt the innovation that has a smaller spill-over effect. 3.3. Envy and pre-innovation sabotage Besides post-innovation retaliation, an envious person can also engage in pre-innovation sabotage to prevent the innovator from succeeding in innovating. For example, when it is known that someone in the village is planning to establish a new factory in the village, villagers may lobby the local bureaucrats to veto the plan. A really envious person could set the factory site on fire after it is built but before it becomes operational. Analogously, if a member of an organization comes up with a new project that is profitable for the organization, other members of the organization may have the incentive to convince the decision makers in the organization that it is a bad idea. Envious members of the organization can prevent the potential innovator from improving his status using this kind of sabotage. Let S 2 denote the level of sabotage 2 inflicts on 1 after 2 learns that an innovation (a, ota) with a a < a is available to 1. I again assume that one unit of sabotage requires one unit of labour. The probability that 2 can successfully prevent 1 from adopting the innovation is _Q(S2), with Q(0) = 0, Q' > 0, Q" < 0. Assume that Vl(a) - GI(R2(a, aa)) > VI(Y) so that in the absence of 2's act of sabotage, 1 will adopt the innovation. It will also be assumed that V 2 ( Y ) > V2 ( a a ( 1 - R2) ) - E 2 ( a / a a ) ( 1 F2(R2) ) - C2(R2, "y). That is, 2's economic benefit from the spill-over effect of l ' s innovation is not sufficient to offset 2's disutility from envy. Hence, 2 will inflict sabotage on 1. Let D2($2, 'y) be 2's expected punishment for sabotaging on 1. I assume that D2(0 , ' y ) = 0, liras2 _, 0 0D2($2, ]/)/0S2-~ O. Moreover, for all S 2 positive, the following conditions hold. -

002(52 ,~t)

as2

0202 (52 ,~t) >0,

as~

OO2(S2 ,-y) >0,

~

0202(52 ,~) >0,

0s2~

>0 (13)

When the spill-over effect from the innovation is not large enough, 2 will have the incentive to inflict sabotage on 1. 2's optimal choice of R 2 and S 2 can be solved by backward induction.

10In this example, the aggregate level of innovations is measured by the ex post increase in the aggregate income. When either introducing or adopting an innovation involvesuncertainty and ex ante investment, a m o r e natural measure of aggregate innovation should be the aggregate level o f e x a n t e investment in innovation activities. A result akin to proposition2 can still be obtained with regard t o stochastic innovations.

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If 1 indeed adopts the innovation, 2's optimal choice of

MaxU (a, .)

=

l

-

-

)

-

(a)

R2

is determined by

- C2(R2,Y ) - Oa(SE,Y )

(14)

Moreover, 2 chooses the level of sabotage by solving

Ms2axQ(S2)V2(Y(1 -

$2)) + (1 - Q(S 2)){ 112(aa(1 - S 2 - RE))

-E2(-~a)(1-F2(R2))-C2(R2,Y))-D2(S2,Y

)

(15)

The first order conditions are

dII2(a'aa) dR2

a

aaV~(ota(l_S2_R2))+E2(__~a)Fi(R2 ) aC2(R2,T)

OR2

=0

(16)

- Q( S2)Iqz~(Y(1- S2) ) -(1-O(S2))aaV~(aa(1-SE-R2) )

0D2($2 ,Y) 8S2 =0

(17)

(17) says that 2 has the incentive to inflict sabotage on I because such activities decrease the probability that 1 can succeed in adopting an innovation which will reduce his welfare. At the optimum, the marginal benefit of sabotage (the first term in the right hand side of (17)) equals the marginal cost of sabotage, where the marginal cost consists of both the opportunity cost of foregone income and the expected punishment. 11

11 The second order conditions require that d2II2(a, a a ) / d R 2 = o t 2 a 2 V ~ ( o t a ( 1 - S 2 - R 2 ) ) + E 2 ( a / a a ) F [ ( R 2 ) - O2C2(R2, y ) / S R 2 < O, d 2 E U 2 / d S 2 = Q"(S2XV2tY(1 - S2))-[V2(ota(1 - S 2 RE))-- E 2 ( a / a a ) ( 1 - F2(R2) ) - C2(R 2, y ) ] ) + Q(S2)t'2V~(Y(1 - $2)) + (1 - Q(S2))a2a2V~(ota(1 S 2 -- R 2 ) ) - 0 2 D 2 ( $ 2 , "y)//OS2 + 2Qr(S2)[otaV~(ota(1 - - S 2 - R 2 ) ) - ~r~(y(1 - $2))] < 0. By assumption, V~' < 0, F~ < 0, and 82C2/SR 2 > 0, thus, d2H2 ~ d R 2 < 0. Since V~' and ~ are both negative while 82D2/8S 2 is positive, the only term that can possibly be positive in the R.H.S. of the second equation is 2 ~ ( S 2 ) [ a a V ~ ( a a ( 1 - S 2 - R 2 ) ) - Y V ~ Y ( 1 - $2))]. It will be assumed that this term is smaller than the absolute values of the other terms so that d 2 E U 2 / d S 2 < 0. Additional assumptions are also needed to ensure that the Hessian matrix is negative definite.

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These conditions can be used to further study how changes in y affect the equilibrium. While it is natural to conjecture that an increase in the authority's propensity to punish retaliation and sabotage will increase the incidence of innovation, it turns out that this may not always be the case. In particular, it is possible that an increase in the punishment for retaliation and sabotage can actually increase the equilibrium level of sabotage. This will in turn increase the probability that the innovation opportunity will be "destroyed" by the follower and thus cause a reduction in the incidence of innovation. To see why such perverse result can arise, d e f i n e A - d 2 H 2 ( a , a a ) / d R 2, =- d 2 E U 2 / d S 2. Assume that A/~ - (1 - Q ( S E ) ) a 4ag[v~( a a ( 1 - S 2 - RE))] 2 0. Differentiate the first order conditions w.r.t. % I get

dR 2 + a2a2V~'(aa(l -S 2 -R2)) A---~7 (1 -

Q(S2))( a2a2V~'( a a ( 1 0202($2 ,Y)

-

-

Sz -

dS2 = 02C2(R2,'Y)

(18)

dR 2 . dS2 R2)))-~-~ + A~-~

~C2( R2 ,~/) Q'(S2)

as2a~/

(19)

ov

One can rewrite (19) as

dS 2 1 [ a2D2(SE,Y) _ _ = -= × [ dy A aS2/b/

aC2(RE,y ) Q'(S2)

ib/

- (1 - Q ( S 2 ) ) ( ot 2a2V~ ' ( a a ( 1 - S 2 - R 2 ) ) ) ~

(20)

Using Cramers rule, I get

dR2

Aa2c2(R2'v) t)g2a'Y

dy

[a2D2(S2,'Y) ~2a2V;(.a(1-s2-R2))[ ~ Q'(SO0C2(_~2,~/) ) A,~ - ( 1 - Q(S2))a4a4[V~'(aa(1 - S 2 - R2))] 2 (21)

dS2 d--~-=

AI~~°2D2 -Q

'

oc: ~

o2c2

fS2)-'~-}-fl-QfS2))°t2a2V:z'(aa(1-S2R2))~R2a,y

A/~ - ( 1 - Q(S2))a4a4[V~'(aa(1 - S 2 R2))] 2 -

-

(22)

In general, the signs of d R 2 / d ~ and dS2/d]/ are indeterminate. 12 More importantly, this comparative static exercise reveals that it is possible that while an

12 However, it can be shown that dR2/d'y > 0 is not consistent with dS2//d T > 0. That is, an increase in cannot possibly lead to a simultaneous increase in both sabotage and retaliation.

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increase in y indeed reduces the level of retaliation, such an increase in y may actually increase the level of sabotage in equilibrium. Proposition 3. Suppose that starting from an initial equilibrium, a small increase in y does reduce the equilibrium level of retaliation, that is, dR e / d y < O. Then dg2/d'y > 0 if and only if O2D2(S2, y) / OS20"y< Q'(S2) 0C2(R2, "y) / OT + d R 2 / dY (1 - Q(S2))a2a2Vj ' (aa(1 - S 2 - R2)). That is, if the feedback effects on S 2 due to an increase in the expected punishment for post-innovation retaliation is more significant than the direct effect due to an increase in the expected punishment for pre-innovation sabotage, then an increase in y may actually increase S 2. Hence, an increase in y can actually reduce the probability that the innovation will be adopted in the society. The intuition for this result can be clarified by separating the effects of an increase in the punishment against sabotage form that of an increase in the punishment against retaliation. An increase in y has three effects on 2's incentive to inflict sabotage on 1. First, it increases 2's marginal cost of inflicting sabotage on others. This effect reduces 2's incentive to inflict sabotage on 1 (that is, 02D2($2, 'y)//0S20Y > 0). However, with an increase in y, it becomes more costly for 2 to use post-innovation retaliation against 1 as a means of "getting even." This implies that 2's utility decreases by a larger amount if 1 succeeds in innovating (this effect is captured by the term Q'(S2) 0C2(R2, y ) / 0 y > 0) and 2 has a stronger incentive to inflict sabotage on 1. Moreover, if an increase in y indeed succeeds in reducing R2, given that there is diminishing marginal utility in income, such a decrease in R 2 reduces the opportunity costs of sabotage. It is possible that these two "feedback effects" on S 2 due to the increase in the punishment for retaliation are more than sufficient to offset the direct effect on S 2 caused by an increase in the punishment for sabotage. In this case, an increase in the authority's propensity to punish retaliation and sabotage will actually increase the equilibrium level of sabotage. 13 This result suggests that if the objective of the government is to encourage innovation, even setting aside the fact that increasing y is costly, it may not always be desirable to increase its propensity to punish retaliation and sabotage.

4. S h a r i n g

The discussion so far has excluded the possibility of side payments between the agents. Yet one way to cope with the threat of envious retaliation may be to have the innovator share part of his new wealth with those who lag behind. With such voluntary redistribution, it may be possible for the innovator to innovate and then 13This is analogousto the result in Holmstromand Milgrom(1991) that, in a multi-taskprincipal-agent relationship, increasingperformanceincentives for one task may cause effortto be allocatedaway from others.

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carefully choose a transfer scheme to reduce others' envious retaliation while still making himself better off than without innovation. Indeed, there is evidence that this kind of sharing does exist. Foster (1967, chapter 7) reports on a custom in Tzintzuntzan that dictates that a person who has acquired some new possession admired by others give others something. He explicitly interprets this as an effort to reduce envy. In discussing the emergence of private cooperatives in the Soviet Union, Smith reports that while in 1989, these cooperatives have paid the state 1.6 billion ruble in taxes, they made charitable contributions worth 226 million rabies in the same year (Smith 1990, p.287). Such sharing behaviour is also widely observed in China in many regions (Renmin Ribao, Feb. 5, 1984, Apr. 5, 1984, p. 2, Apr. 15, 1984, p.2). In a study of peasant entrepreneurship in Yunan province, Liang (1984) reports that it is common to fmd specialized households making substantial contributions to local public goods such as irrigation facilities, public schools, and public nursing centres. Liang also observes that envy and hostility toward peasant entrepreneurs are also widely observed in the area. The peasant entrepreneurs are keenly aware of others' envy towards them. Most of them emphasize that the fact that they shared their wealth with other peasants proves they care not only about getting rich themselves, but they also want to help others get rich. Hence, other peasants should not be hostile towards them. It seems reasonable to conclude that at least some of these sharing activities are motivated by the effort to reduce the threat of envious retaliation. 14 With the possibility of voluntary sharing, the timing of events in this model can be summarized as follows: I I Sabotage takes place

t

Agent 1 chooses his technology

I

Agent 2 chooses his technology

I I

I I

I I

Voluntary transfer takes place

Emotions are generated

Retaliation takes place

l

Payoffs are realized

Suppose that it is costless for an agent to receive gifts from others. Let t I be the amount of voluntary transfer that 1 gives to 2. 2's utility after the agents have chosen their technologies (Y1, I12) can be written as H2(Y1,Y2) = V2(Y2(1 - $ 2 - R 2 )

+tl)

- C2(R2,T) - D2(S2,T)

-E 2

Y l - t l' ](1-F2(R2)) Y2+t 1" (23)

14 These observations suggest that, in the presence of envy, even if the innovator does not have a genuine altruistic concern for the follower, he may still engage in sharing strategically so as to reduce the threat of envious retaliation from the follower. The current model implies that if agents in the community have the propensities for envy, they will retaliate against those who have moved ahead of themselves. But, after they themselves have moved ahead, they will engage in some kind of "altruistic" behaviours strategically. An interesting line of future research will be to incorporate both envy and genuine altruism into the model.

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For any I12 ~ {Y, aa}, let ti(a , ]12) be the optimal transfer that agent i will give to the other agent if the incomes of 1 and 2 are a and Y2, respectively. Since I am interested in subgame perfect equilibria, define YE(a) to be 2's best response to a subject to the condition that Y2 ~ {~',aa}. It is obvious that Y2(a)= cta. Let ti(a , cta) be the optimal transfer that agent i chooses to give the other agent in the post-innovation subgame. Since a a < a, it can immediately be observed that tl(a, a a ) > 0 while t2(a, a a ) = 0. Define t 1 - tl(a , ola). I get Proposition 4. (The efficacy of sharing in mitigating sabotage and retaliation) (i) For the innovation opportunity (a, aa) , with voluntary sharing, Iil* = a can always be supported as the equilibrium. (ii) Supposing that the innovation opportunity (a, aa) only has a small spill-over effect, so that, in the absence of sharing, 2 will be made worse off by l ' s innovation and will choose to inflict sabotage on 1. Then it is possible that even with the possibility of voluntary sharing, 2 will still choose to inflict sabotage on 1 so as to prevent 1 from succeedin_g in innovating. In particular, if Vl(a - t; ) - GI(R2(a - t; , o~a + tT )) > Vt(Y) and

a(1-

+ t; ) - E: a - t ;

)(l_Fz(R2(a_ti,ota+ti)))

- C 2 ( R 2 ( a - tl* ,ola + tl* ),~/) < V2(Y), then S 2 = 0. Proof. (i) If (a, aa)Vl(a) - GI(R2(a , aa)) >_ VI(Y) , then can be supported as an equilibrium outcome even in the absence of sharing. I f V i ( a ) - G I ( R E ( a , aa)) < VI(Y), in the absence of sharing, 1 will not adopt the innovation. Then, if sharing is possible, since Y < a a < a, the strategy of adopting the innovation and then choosing a level of transfer equal to t 1 = (a - a a ) / 2 will give agent 1 a payoff Vl(a + a a ) / 2 ) > VI(Y). Hence, 1 will always do strictly better by adopting the innovation than not adopting the innovation. That (ii) is true is obvious. [] (ii) explains why voluntary sharing may not always be effective in eliminating the problem of sabotage. Since 2 knows that if 1 succeeds in innovating, 1 will only give a transfer to him that is optimal from l's perspective. It is possible that this transfer to 2 will not be high enough to reduce 2's disutility from envy to the "acceptable" level. In this circumstance, it will still be optimal for 2 to inflict sabotage on 1. This result also suggests that as a way to reduce 2's incentive to do that, 1 may have the incentive to pre-commit to an arrangement that gives 2 some influence in choosing t 1, the post-innovation transfer. Although (i) suggests that voluntary sharing can fully mitigate the threat of envious retaliation, this result only holds when we restrict our attention to the special case of "non-stochastic" innovation. In a more general model with stochastic innovation, in which an innovator needs to invest resources in innovation and with a positive probability may fail in innovating, this result no longer

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holds. 15 With stochastic innovation, conditional on 1 succeeding in innovating, 2's retaliation will decrease l ' s utility. Thus, 1 will have the incentive to give a voluntary transfer to 2 so as to reduce 2's retaliation. Since 1 will not capture the full return on his investment in innovative activity, this constitutes an incentive to restrict investment. Thus, the sharing mechanism cannot fully mitigate the threat of others' envious retaliation. So far, it has been assumed that agents are always willing to accept gifts from others. However, if there are psychological and sociological costs involved in accepting gifts (Bailey 1971), the efficacy of voluntary sharing in mitigating the problems of envy will be further undermined. Moreover, if agents are not indifferent between receiving gifts from others and receiving transfers from the government, the model suggests that indirect transfers among the agents, mediated by government taxation policy (or by other third parties), dominates voluntary sharing in supporting innovation. It is useful to compare and contrast the result regarding voluntary sharing in this model with Becker's work on altruism and envy in the family (Becker, 1981). In Becker's model, there is an altruistic parent who will make transfers to all of her children. Becker shows that in the presence of an altruistic parent, even if a child, say, Tom, is envious of his sister, he will not take actions to reduce his sister's income if such an action reduces her income more than it increases his own income. The reason is that if Tom takes such an action, it will induce the altruistic parent to increase her contribution to T o m ' s sister and reduce her contribution to Tom. In equilibrium, this will make Tom worse off. Hence, Tom will not adopt such an action. That is, the existence of an altruistic third party (the parent) helps to mitigate the problem of envy among the children. However, as Becker himself has observed, envy in a family will have far more damaging consequences if "not disciplined by the effective altruism of some members" (Becker 1981, p.185). In my model, there is no such third party. In this setting, voluntary sharing by the innovator to the follower cannot completely mitigate the problem of retaliation and sabotage.

5. Discussion The above analysis has focused on how agents' propensities for envy may substantially complicate their strategic interactions related to innovation. A natural

15Extending the model to allow for the possibilityof stochastic innovation also enables us to study how changes in ~, affectsthe follower's decision regarding how to allocateresourcesbetween investing in the emulation of the innovator's innovation or retaliating against the innovator. These issues are discussed in Mui (1992).

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direction for future research is to generalize the model to a multiple-agent setting. This generalization will allow us to study how a community may engage in some form of collective action to ensure that an innovator shares the result of his innovation in a way desired by the community. Such collective action may take the form of formal legislation, informal social customs, or even blatant violence. One would also want to know whether the presence of envy will magnify or mitigate the free-rider problem that the community may experience in orchestrating this kind of collective action. Moreover, since an innovator can choose his gift to each agent in the community strategically, it will be useful to find out whether such strategic behaviour on the part of the innovator can undermine the efficacy of collective action against him by others. Another direction for future research is to study the problem of optimal government policy in the presence of envy. The current essay focuses on how changes in the authority's propensity to punish retaliation and sabotage affect the equilibrium behaviour of the agents. A natural extension would be to introduce an explicit objective function of the government and study how the government can design legal institutions to maximize its objective in the presence of envy. One can think of the problem of institutional design in the presence of envy as a study of the problem of externalities. Since the degree of the spill-over effect plays an important role in determining the equilibrium, besides punishing retaliation and sabotage (that is, taxing these activities), the government can also consider the alternative of subsidizing activities that increase the spill-over effects of innovations. It will be useful to study the problem of optimal institutional design in such an enriched environment. With slight reinterpretation, the model developed above generates some interesting implications for the study of organizational design. It implies that in choosing a reward for an individual who has made a substantial contribution to an organization, a promotion is n o t equivalent to a bonus that increases the person's future discounted income by the same amount. The idea is that an individual who has made a significant innovation is likely to suffer from retaliation by the envious members in his work group, or - perhaps more importantly - by his superiors. In this case, promotion may reduce the ability of these envious members to retaliate against the innovator and will thus be considered to be a preferred arrangement by him. Similarly, a person who has made a substantial innovation may be relocated to another division even though such a relocation may involve economic losses for both the organization and the individual. Moreover, the "feedback effects" identified in proposition 3 imply that an increase in central management's propensity to punish retaliation and sabotage may actually increase the members incentives to inflict sabotage on potential innovators. This would decrease the probability that a potential innovator will succeed in innovating. Finally, the sharing model provides a rationale for why organizations often require their members to share

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tions by seminar participants at UC, Berkeley, USC, the 1993 WEA meeting at Lake Tahoe, and the 1993 SITE Summer Workshop at Stanford University. All errors are exclusively my responsibility.

Appendix

Proof of proposition 1 By definition, for any y < y *, l ' s equilibrium payoff will be Hi(Y, Y ) = VI(Y). That is, there will be no innovation. For any y > y *, l ' s equilibrium payoff will be lll(a, aa) > Hi(Y, Y). To emphasize the fact that for y > y *, the agents' equilibrium payoffs will vary with the parameter y, I will rewrite agent i's payoff as Hi(a, aa, y). When y < y *, 2's equilibrium payoff will be H2(Y, Y) = V2(Y). At y = y*, 2's equilibrium payoff will be II2(a, aa, y * ) = V2( e t a ( 1 - R2( a , a a ) ) ) - E2( a / a a X 1 - F 2 [ _ R 2 ( a ,

ota)]) - C2[ R2( a , ota), y * ] .

By assumption, Fl2(a, aa, y * ) > II2(Y, Y). That is, at y = y * , there is a discrete jump in 2's payoff. For y > y *, 1 will adopt the innovation and 2's payoff will thus be II2(a, aa, y). By the envelop theorem, dH2(a, aa, y ) / d y = 0C2(R 2, y ) / 0 y < 0 so that 2's payoff is decreasing y in the range of y > y *. Since 2's payoff is continuous in y except at y = y *, by continuity, there exists ~ > 0 such that for all y ~ (y *, y + ~), H2(a, aa, y) > FI2(Y, Y). Choose {, = y* + e. By construction, Fl2(a, aa, y) > FI2(Y, Y) for y ~ (y *, ~/). Since ~/> y *, by definition of y * and the fact that IIl(a, aa, y) is increasing in y, Hi(Y, Y) for y ~ (y *, ~).

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credit for their innovations with co-workers and superiors, and gives an equilibrium explanation for wage compression. 16 To better illuminate these considerations, consider a modified version of Tirole's model of a three-tier hierarchy (Tirole, 1986). Suppose the principal hires a supervisor and an agent to engage in innovative activities. Compared to the principal, both the supervisor and the agent have better information concerning the profitabilities of different innovation opportunities. The supervisor is entrusted with the authority to choose which innovation process he and the agent will work on. Assume that the expected profit of each innovation opportunity depends on the efforts exerted by the agent and the supervisor, as well as some stochastic disturbances. Incorporating envy into this standard model poses additional problems for organizational design. For example, the potential threat of envious retaliation from the other person may discourage both the supervisor and the agent from exerting " t o o much" effort in innovative activity. Moreover, the superior's propensity for envy may induce him to veto a profitable innovation process proposed by his subordinate if the proposal will enable his subordinate to substantially improve his relative status within the organization. While the existence of moral hazard problems suggests that the principal has the incentive to rely on the supervisor to monitor the agent's behaviour (or vice versa), the principal now needs to take into account that, with envy in operation, both the supervisor and the agent have an incentive to file false reports as means to retaliate against the other person. This set of issues warrants careful analysis and I leave them as subjects for future research.

Acknowledgements This paper is based in part on essay one of my dissertation. I am grateful to George Akerlof for invaluable help and encouragement. I also thank Nick Argyres, Kenneth Arrow, Abhijit Banerjee, Pranab Bardhan, Reuven Brenner, Ralph Chami, Richard Day, Eddie Dekel-Tabak, Joe Farrell, Jim Fearon, Steve Goldman, Gillian Hadfield, Eric Jones, Theodore Keeler, Timur Kuran, David Levine, Andy Neumeyer, Peter Rosendorff, Julie Schaffner, Brian Wright, an anonymous referee, and especially Duncan Foley, Matthew Rabin, and Oliver Williamson for helpful comments and conversations. I have also benefitted from helpful sugges-

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