Citation 京都大学経済学部 Working Paper (1993), 21.

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1 Title Job design, delegation, and analysis coopea Autho(s) Itoh, Hideshi Citation 京都大学経済学部 Woking Pape (1993), 21 Issue Date URL Right Type Reseach Pape Textvesion autho Kyoto Univesity

2 WORKING NO. PAPER 21 / ~I I, ' I Design, Job Delegation, and Co opeation: I A Pincipal-Agent Analy sis by Hideshi Itoh., " Faculty of Kyoto y `1 Economics Univesity / ` i f.... n I ),,l J t_ f,, 1 _ 1, IN,I I",.i, I I` J, Faculty Kyoto Univesity, Kyoto, of Economics, 606 JAPAN a *~ f t. I 1 /. Y I f, /' 1

3 WORKING PAPER NO. 21 Job Design, Delegation, and Coopeation: A Pincipal-Agent Analysis by Hideshi Itoh Faculty of Economics Kyoto Univesity Octobe 1993

4 JOB DESIGN, A EEA93 DELEGATION AND COOPERATION Pincipal-Agent Analysis Abstact This pape analyzes how tasks ae assigned in oganizations. Tasks can be allocated vetically between a pincipal and an agent, o lateally among agents. The esulting oganizational job design detemines how many tasks ae delegated to agents, and how the agents' tasks ae divided among them. In the famewok of the standad pincipal-agent elationship with moal hazad, it is shown that (i) an incentive consideation causes the pincipal to goup a boad ange of tasks into an agent's job athe than hie multiple agents and make each of them specialize in just one task; and (ii) the pincipal may choose to delegate all the tasks in ode to mitigate a conflicting incentive poblem with agents.

5 Job design, delegation, and coopeation A pincipal-agent analysis* Hideshi Itoh Kyoto Univesity, Kyoto, Japan Octobe Intoduction One of the fist things an entepeneu must decide, upon foming a business oganization as an owne-manage by hiing subodinates, is how to allocate tasks among them. Thee ae two elevant questions. Fist, which of the tasks ae delegated to the subodinates and which ae left unde the entepeneu's contol? delegation of decision making in the oganization. The answe to this question detemines Second, how ae those tasks delegated to the subodinates to be divided among them? The answe detemines the division of labo among the subodinates. The issue of job design is impotant in inte-fim elationships as well. A manufactue and its pats supplies must specify thei functional oles: Do supplies only poduce pats following the dawings povided by the manufactue, o does the manufactue pemit the supplies themselves to design thei pats? Does the manufactue make each supplie specialize in a naow ange of components (e.g., poduce only seat cove) o make a supplie esponsible fo vaious components (e.g., poduce the entie seat)? It is an impotant step towad theoies of oganizational stuctues to undestand both vetical and lateal job stuctuing. This pape analyzes the job design poblem of the owne-manage o the manufactue in a simple pincipal-agent model with moal hazad. The _ paty who is a esidual claimant and is entitled to allocate tasks and design contactual tems is called a "pincipal." At the beginning, no paty possesses elevant infomation o expetise pivately. Theefoe, if the Coespondence to: Hideshi Itoh, Faculty of Economics, Kyoto Univesity, Sakyo-ku, Kyoto , Japan * Pape pesented fo the Eighth Annual Congess of th e Euopean Economic Association in Helsinki, August 1993, in the invited session "Contact theoy and economic oganization" chaied by J. Ceme. This eseach was suppoted by the Ministy of Education, Japan. 1

6 pincipal could pefom all the tasks by heself, she would choose to do so, and the job design poblem would not be an issue. I instead assume that foming an oganization is inevitable: The pincipal must hie "agents" and allocate some of the tasks to them because, fo example, he attention is limited. In contast to the standad pincipal-agent elationship, howeve, the pincipal can choose to leave some of the activities unde he contol. This pape hence extends the analysis of job design among agents by Holmstom and Milgom (1991) and Itoh (1991, 1992) to include not only lateal but also vetical task assignment poblems-' The pape also studies implications of the use of aggegate pefomance measues fo the job design poblem. Each activity may not be measued sepaately, o even it can, diect obsevation of pefomance at each task is often subjective, and hence unlikely to be contactible. Howeve, some objective aggegate pefomance measues ae likely to be available. I hence assume that thee is a veifiable and "infomative" signal measuing joint pefomance in the oganization while pefomance at each task cannot be measued sepaately. In othe wods, the pincipal and the agents engage in team poduction. In the futue, the analysis in the cuent pape should be extended to incopoate subjective individual pefomance measues in a model of the thee-tie hieachy of pincipal-supeviso-agents. Since the focus of the pape is on the effects of objective aggegate pefomance measues, a model of the two-tie hieachy is used thoughout.' Two esults ae pesented in the famewok descibed above. Fist, when the pincipal delegates all the tasks to the agents, an incentive consideation causes he to goup a boad ange of tasks into an agent's job athe than hie multiple agents and make each of them specialize in just one task. In the model, the activities ae cost substitutes and hence when they can be pefectly obseved, specialization is bette. It is shown that when the activities,can.only be obseved impefectly, though team pefomance measues, the pincipal pefes non-specialization unde sufficiently small degees of cost substitutability. The notion that labo-foce specialization leads to efficiency, which has been well known in economics since Adam Smith, has been ecently challenged in pactice: In the best pefomance pojects in the wold automobile industy, task assignments among enginees tend to be boad both in 1 Riodan and Sappington (1987) analyze a.vetical task assignment poblem in an advese selection model. 2 Howeve, the qualitative esults of the pape continue to hold when contactible pefomance measues at each task ae available. See Itoh (1993) fo details.

7 beadth of activities and in ange of components (Clak and Fujimoto, -1991; Womack, et al., 1990); The high pefomance of Japanese manufactuing is often attibuted. to the capabilities of wokes who ae esponsible fo not only outine opeations but also unusual opeations such as those dealing with changes in poduct mix and labo mix, and with poblems due to machine beakdown and defective poducts (Koike, 1991). The pape. shows that such boad job stuctuing is desiable fom the incentive viewpoint even without technological complementaity among tasks. The second esult is that unde some conditions, the pincipal, when she must allocate some tasks to agents, chooses to delegate all the tasks in ode to mitigate a conflicting incentive poblem with the agents: Delegation is not a souce of incentive poblems but it can be an incentive device in addition to financial ewads. Such a mode of "complete delegation" is moe desiable as the aggegate pefomance is easie to measue o the agents have moe discetion about thei wok so as to be moe esponsive to incentives. The est of the pape is oganized as follows. The model is intoduced in Section 2. The esults ae pesented in Section 3. In Section 4, the possibility of task shaing among agents is discussed. Section 5 is concluding emaks. 2. The model The model is a simplified vesion of the one in Itoh (1993), which in tun utilizes the tactable linea agency model developed by Holmstom and Milgom (1987, 1991). A pincipal owns a poduction pocess that consists of two tasks t = 1, 2. Suppose that the benefit fom poduction is of the specific fom x = a1 + a2 + E whee at > 0 epesents unobsevable action (effot) at task t and c the eo tem. The pincipal and all the agents hied by the pincipal have identical infomation. All of them believe that c is Nomally distibuted with mean zeo and vaiance a2 > 0. Fo simplicity, I assume that x is the only available infomation fo contacting. This assumption can be dopped. Fo example, x and the actual benefit may be diffeent. A monitoing vaiable fo each task may be available and, though unlikely, may be contactible.3 In this pape, I focus on the exteme case in ode to highlight the effects of the use of team pefomance measues. 3 These cases ae analyzed in Itoh (1993).

8 A contact specifies payments to agents and a task allocation mode. The pincipal cannot pefom both tasks by heself, and hence she must hie at least one agent to allocate tasks. The pincipal has fou feasible task, allocation modes. (i) Patial delegation: The pincipal delegates task 1 (o task 2) to an agent and pefoms task 2 (task 1, espectively) by heself. (ii) Non-specialized complete delegation: The pincipal delegates both tasks to an agent. (iii) Specialized complete delegation: The pincipal hies two agents called agent 1 and agent 2 and delegates task t to agent t (t = 1, 2). Let w(x) be the payments to the agent unde patial delegation o non-specialized complete delegation, and wt(x) be the payments to agent t unde specialized complete delegation. The paty who is assigned a task incus pivate cost. When the agent pefoms both tasks unde non-specialized complete delegation, his cost is C(a1,.a2 ). Unde the othe modes, the paty who pefoms task 1 (task 2) beas cost C1(a1) C(a1, 0) (espectively C2(a2) :_ C(0, a2 )).4 To obtain explicit solutions, I assume that the cost function is quadatic and of the fom C(al, a2) = 2ca2 + 2cat + bca1a2 whee c > 0 and b E [07 1]. Paamete b epesents a degee of cost substitutability between two tasks. When b = 0, two tasks ae independent in the sense that the choice of a1 does not affect that of a2 even unde non-specialization. When b > 0, inceasing effot at task 1 aises the maginal cost of effot at task 2. When b = 1, two activities ae pefect substitutes, and the cost depends only on the total effot a1 + a2. Note that two tasks ae symmetic in the cost function fo all b since C1(a) = C2 (a) = 2ca2. Two modes of patial delegation ae thus indiffeent, and I only conside the patial delegation mode in which the agent pefoms task 1.5 Let d E { p, n, s } epesent a task allocation mode: d = p implies patial delegation, d = n non-specialized complete delegation, and d = s specialized complete delegation. The pincipal is isk neutal. Thee is a pool of agents who ae isk avese with pefeences epesented by the exponential utility function: When an agent's income (payment eceived minus cost of action) is I, his utility is - exp{-i} whee > 0 is the coefficient of absolute isk avesion. The pincipal selects agents with identical coefficient of absolute isk avesion 4 I am assuming that task shaing is impossible, because, fo example, each task equies use of a machine that cannot be opeated by both agents at the same time. See Section 4 fo discussion on task shaing. 5 See Itoh (1993) fo the analysis of asymmetic cases.

9 and identical poductivity, and thei esevation wages ae assumed to be zeo. I assume that the payment schemes take the linea fom w(x) = ax`' + -y unde mode d E { p, n }, and wt (X) = atx + yt fo t = 1, 2 unde d = s.6 Given a task allocation mode, the pincipal chooses the shae paametes a o (a1, a2) to maximize the cetainty equivalent of joint suplus subject to incentive compatibility constaints.7 The cetainty equivalent of joint suplus is given as follows: al + a2 - Ci (a1)- C2 (a2)- 2 a2a2 unde d = p; a1 + a2 - C(a1, a2) - 2 at a2 unde d = n; a1 + a2 - C, (a,) - C2 (a2)- 2 a2a2-2 a2a2 unde d = s. The incentive compatibility constaints ae given as follows: Unde d = p, a - Ci (a1) = 0 fo the agent and (1 - a) - C' (a2) = 0 fo the pincipal; Unde d = n, a - Ca, (a,, a2) a - Cat (a1, a2) = 0; And unde d = s, a1 - C1(a1) = 0 and a2 - C2 (a2) = 0. 0 and Let a* be the optimal shae paamete unde mode d. Note that because of symmety, the optimal shae ates fo agent 1 and fo agent 2 ae equal unde the specialized delegation mode. The compaison among task allocation modes is based on the cetainty equivalent of joint suplus unde (d, a*): If (d, a*) yields highe joint suplus than (d', a*,), then the pincipal pefes to choose the fome than the latte. The optimal task allocation mode is d such that the joint suplus is the highest unde (d, a* ). 3. The esults I stat with the analysis of division of labo between agents. Suppose that the pincipal delegates both tasks. The question is whethe she assigns one agent to both tasks o hies two agents each of which pefoms a distinct task. The optimal shae ates unde d = n. and d = s ae calculated as * 2 1 an 2 + (1 + S)a2c and as = 1 + a2c* 6 See Itoh (1993) fo a justification of this assumption. It is possible to show that the model pesented hee is egaded as a educed fom of a dynamic model as in Holmstom and Milgom (1987), in which optimal incentives ae povided with linea contacts. The fixed components y and (71,72) simply play a ole of suplus tansfe between the pincipal and the agents. 5

10 Fix paametes (c,, 01" ). When b = 1 (two activities ae pefect substitutes), one has an = as. This does not imply that the optimal effots ae equal unde two modes, howeve. Unde non-specialization, the total effot satisfies an = c(ai + a2) while unde specialization, fo each task t, as = cat. It is theefoe clea that d = s attains highe joint suplus than d = n. Next suppose b = 0. Then an > as. By the incentive compatibility constaints, the effots chosen by the agent unde contact (n, as) ae equal to the optimal effots unde (s, as ). Howeve, the joint suplus is highe unde the fome contact because of the additional isk pemium tem unde d = s. The joint suplus is hence highe unde (n, an) than unde (s, as ) when b = 0. The optimal value of joint suplus unde d n is deceasing in b since an is deceasing in b and the joint suplus is inceasing in a. Since unde d = s the optimal value of joint suplus is independent of b, I have shown the following poposition. Poposition 1. Fix paametes (c, ) 012 ). Then thee exists b E (0, 1) such that fo all. b < b, the pincipal pefes non-specialized complete delegation to specialized complete delegation. The impotant insight fom this esult is that an incentive poblem causes the pincipal to assign an agent to a boad ange of tasks. If actions wee publicly obsevable, the pincipal would neve choose to assign an agent to both tasks fo all b > 0. Howeve, when actions ae unobsevable, fo all values of c,, and o.2, non-specialization attains highe suplus fo sufficiently small degees of cost substitutability. The advantage in technology will be taded off against the incentive consideation. Note that no technological complementaity is assumed hee since b > 0. Next conside the optimality of delegating both tasks. The optimal shae ate unde patial delegation is given by ap Q2c* It is always smalle than an and as. The undelying logic is evident fom the incentive compatibility constaints. Unde patial delegation, thee is a conflicting inteest between the pincipal and the agent. Once the payment scheme has been set, both the pincipal and the agent must be given incentives, and inceasing the agent's shae educes the pincipal's motivation. Such a conflict disappeas once both tasks ae allocated to agents. Howeve, delegating moe tasks accompany moe esponsibility. Compaing the joint suplus unde 6

11 thee modes leads to the following esult.8 Poposition 2. Fo all b E [0,1], if c,, and.2 ae sufficiently small, a complete delegation mode, whethe specialized o non-specialized, is pefeed to patial delegation. The poposition shows that thee is a case whee the pincipal pefes delegating both tasks to agents, in ode to mitigate the conflicting incentive poblem. Othe than monetay ewads, delegation of tasks can be an additional incentive device. Howeve, complete delegation has its own cost. Agents ae given moe esponsibility and hence must incu moe isk. The impotant paametes that affect the optimal task allocation ae a2 and c. Vaiance 012 epesents the difficulty of measuing joint pefomance. If a2 - * 0, both modes of complete delegation can attain the fist best since the optimal shae ate appoaches to one, while the conflicting inteest between the pincipal and the agent pevents the oganization with patial delegation fom achieving the fist best (ap --> 2 ). On the othe hand, if the team pefomance is had to measue,: complete delegation is costly in tems of isk shaing, and hence keeping a task unde the pincipal's contol attains highe joint suplus. Paamete c is the slope of the maginal cost of effot when pefoming just one task. This paamete has an impotant intepetation. The invese c-1 epesents the esponsiveness of effot, to incentives at each task unde patial delegation o specialized complete delegation: Fom the incentive compatibility constaints, unde patial delegation (delegating task 1), aa1 /oa aa2 /O(1 - a) = c-1, and unde specialized delegation, aal /Oa1 = N2 /49a2 = c-1. The effot. esponsiveness is a little diffeent unde non-specialized complete delegation, and is,given by aa1 /, ea. = 49a2/0a,= [(1 + b)c]-1. Unde eithe mode, the shae paamete is inceasing in c-1: Stonge incentives ae povided as agents ae moe able to espond, to them. And the effot esponsiveness could be contolled. Fo example, as Holmstom and Milgom (199.1) analyze, poviding moe feedom to agents by allowing thei "pivate activities", can incease the agents' esponsiveness and wok as an incentive instument. Moe geneally, the pincipal could invest in wok conditions to educe the maginal cost of effot: the cost function could be C(a1, a2, a3) with Ca3 < 0 and Cata3 < 0 fo t = 1, 2 whee a3 is the level of investment. Theefoe, the poposition implies that when the pincipal can aise the agents.' discetion about thei wok o impove thei wok conditions, moe delegation of tasks and s The deivation of the esult is. staightfowad and not instuctive, and thus omitted. 7

12 moe intense incentives ae likely to follow. 4. Task ovelap and coopeation In the pevious analysis, it has been assumed that task ovelap is not feasible: If two agents ae hied, each of them specializes in a diffeent task and does not exet effot to the othe task. Howeve, it is often obseved that a goup of tasks is assigned to a goup of wokes and they coopeate at each task within the goup. Is thee a meit of task ovelap and coopeation? The possibility of task shaing has been studied unde the assumption that pefomance at each task is measued sepaately. Holmstom and Milgom (1991) show that it is neve optimal fo two agents to be jointly esponsible fo any task when thee is a continuum of tasks and they ae pefect substitutes. Itoh (1991) shows that thee ae cases in which joint esponsibility 'i s optimal. His sufficient condition is not satisfied if activities ae pefect substitutes in the cost function. Howeve, when aggegate pefomance measues ae used fo contacting, task shaing is optimal even if tasks ae "almost" pefect substitutes. To see this, suppose that a is so high that specialized complete delegation is optimal. Let ai be the optimal effot by agent 1 at task 1, that satisfies the incentive compatibility constaint as - ca* = 0. Now suppose that agent 1 can exet effot to task 2 as well. Let h1 be agent 1's effot at task 2. Suppose that technology is of the specific linea fom x = a1 + a2 + h1 + E. Fix as and conside a pai of (a1, h1) that satisfies the new incentive compatibility constaints: as (a1, h1) = 0 and as -- Chi (a1, h1) = 0. The solution satisfies a1 + h1 = 2[(1 + S)c]-1 as > ai fo b < 1. Thus by allowing task shaing, highe joint suplus can be attained. This esult follows because the shae paamete fo team pefomance aleady povides an incentive fo an agent to exet effot to the othe agent's task: Thee is no fixed cost to povide incentives fo new activities in contast to the case whee the benefit fom each task is measued sepaately as in Holmstom and Milgom (1991) and Itoh (1991). The analysis of task shaing and coopeation is moe inteesting when the pincipal has an altenative incentive scheme that pomotes "competition" via use of elative pefomance evaluation. When pefomance at each task can be measued sepaately and thee is a systematic uncetainty so that individual measues ae positively coelated, elative pefomance evaluation is valuable. Howeve, since elative pefomance evaluation povides each agent with an 8

13 incentive to educe the othes' pefomance, it is essential.to peclude task shaing- (Lazea, :1989). Which is bette, peventing task ovelap and using elative pefomance evaluation, o allowing task shaing and using joint esponsibility? This question has been analyzed in Itoh (1992): Coopeation should be pomoted if the coelation coefficient is sufficiently small. An extension of the model in this pape also leads to, a cicumstance in which elative pefomance is used in the optimal contact. Suppose that thee ae thee tasks t = 1, 2, 3 and two team pefomance measues x1 and x2, which ae given by x1 = a1 + a3 + Ei and x2 = a2 + a3 + E2. The Nomal noise tems c1 and E2 ae assumed, to be stochastically independent. Tasks 1 and 2 ae "local" in the sense that each of them affects just one pefomance measue while task 3 is "global" in that both measues ae affected by action at task.3. Fo example, task 1 and task 2 ae sales activities at teitoies 1 and 2, espectively, and x1 and x2 ae actual sales at those teitoies. Task 3 is advetising activities that affect the sales at both egionṣ Suppose that agent A is assigned task 1, agent B task 2, and the pincipal pefoms task 3. The agents' compensations ae given by the linea schemes WA(x1,x2) = a1x1 + a2x2 + ao and WB(x1, X2) = /31x1 + /32x2 +,30- This is the situation analyzed by Camichael (1983). As he shows in his model, hee the optimal shae ates satisfy a1 > 0, a2 < 0, /3i < 0, )3 > 0, I ai) > (a2 ~, and 1,Q2 1 >. `l /3i 1 To see this., note that the incentive compatibility constaints ae given by a1 - C{ (a1) = 0, 02,- C2 (a2) = 0, and {1- a1 - ~1) + ( 1 - a2.- /32)- C3 (a3) = 0 whee Ct(at) is the pivate cost. of effot at, task t. The fist two equations ae the incentive compatibility -constaints fo the agents, the last one fo, the pincipal who is assigned task 3. To povide incentives fo the agents,. a1 > 0 and /32 > 0 must. hold. This educes the pincipal's incentive at task 3. Howeve, since _a2. and /31 come into the last equation only, they ae utilized to aise the pincipal's incentive, and hence they ae negative at the optimum. Despite the stochastic independence between x1 and x2, the agents ae ewaded based on not only the absolute pefomance xt but also by "elative pefomance" x1- X2. And again it is bette fo the pincipal to estict task shaing between the agents. Howeve, the pincipal may benefit by delegating task 3 to the agents and motivating task shaing via assignment of joint esponsibility, that is, at > 0 and /3t > 0 fo t = 1, 2. Since the exact mode of delegation in this setting is had to specify (e.g., How do the agents detemine action at task 3? How ae they going to shae the cost of effot?) and the analysis is complicated, I only suggest the

14 possibility and leave igoous analysis fo futue eseach. Note that delegating the global task to agents may be optimal because the pincipal can contol the agents' choice though team pefomance measues. If the ole of the global task is to educe the cost of effot (e.g., impoving wok conditions), delegation is neve optimal. To see this, modify technology to x1 = a1 + E1 and x2 = a2 + E2. The ole of task 3 is to educe the costs of effot at tasks 1 and 2: The cost functions ae witten as C1(a1, a3), C2(a2, a3), and C3(a3), and satisfy act/aa3 < 0, a2ct/(aataa3) < 0, and C3 > 0 fo t = 1, 2. Suppose that the agents, when assigned task 3, select a3 to maximize the cetainty equivalent of thei joint suplus, that is, to minimize C, (a,, a3) + C2(a2, a3) + C3(a3). It is then neve optimal to delegate task 3 to the agents, since thei choice of a3 ignoes the effects of a3 on the incentive compatibility constaints. The pincipal has no way to contol thei choice of action at task Conclusion Job design is an impotant decision fo oganizations. It detemines division of labo and delegation patten of decision making. This pape analyzed those two aspects of job design simultaneously, and showed that impotant insights ae obtained fom incentive consideations: thee is an incentive eason fo gouping a boad ange of tasks into an agent's job, and delegation of all the tasks to a subodinate may be adopted as an incentive instument. The pape focused on the use of veifiable and infomative team pefomance measues. Intoducing subjective measues fo each activity into the model by extending to a theetie hieachy is one diection fo futue eseach. The pape also adopted the "complete contacting" appoach: Decision making authoity was assumed to be a well specified notion, witten into a contact though task assignment. Howeve, delegated authoity is often vague in scope and entitlement: Who has authoity about what? The analysis of delegated authoity in an "incomplete contacting" famewok will be impotant, and hopefully the cuent pape offes a useful benchmak. 10

15 Refeences Camichael, L., 1983, The agent-agents poblem: payment by elative pefomance, Jounal of Labo Economics 1, Clak, K. B. and T. Fujimoto, 1991, Poduct development pefomance: stategy, oganization, and management in the wold auto industy (HBS Pess, Boston). Holmstom, B. and P. Milgom, 1987, Aggegation and lineaity in the povision of intetempoal incentives, Econometica 55, Holmstom, B. and P. Milgom, 1991, Multitask pincipal-agent analyses: incentive contacts, asset owneship and job design, Jounal of Law, Economics, and Oganization 7 (special issue), Itoh, H., 1991, Incentives to help in multi-agent situations, Econometica 59, Itoh, H., 1992, Coopeation in hieachical oganizations: an incentive pespective L aw, Economics, and Oganization 8, , Jounal of Itoh, H., 1993, Job design and incentives in hieachies with team poduction, Mimeo. (Kyoto Univesity, Kyoto, Japan). Koike, K., 1991, Leaning and incentive systems in Japanese industy, Mimeo. (Hosei Univesity, Tokyo, Japan). Lazea, E. P., 1989, Pay equality and industial politics, Jounal of Political Economy 97, Riodan, M. H. and D. E. M. Sappington, 1987, Infomation, incentives, and oganizational mode, Quately Jounal of Economics 102, Womack, J. P., D. T. Jones and D. Roos, 1990, The machine that changed the wold (Rawson Associates, New Yok). 11