Performance measurement systems, incentives, and the optimal allocation of responsibilities

Journal of Accounting and Economics 25 (1998) 321—347

Performance measurement systems, incentives, and the optimal allocation of responsibilities Thomas Hemmer* Graduate School of Business , University of Chicago, Chicago, IL 60637-1561, USA Received 1 May 1997; received in revised form 1 March 1998

Abstract I study the joint choice of responsibility assignment, performance measures, and rewards for a two-stage process where the quality of the initial stage work affects the required final stage effort. By assigning responsibilities to give the initial stage agent an incentive to sabotage the final stage, output is made informative about this agent’s attention to quality. I find conditions under which it is cost-effective to create and to contractually use such information. This analysis makes formal that the value of a performance measure is determined not simply by its congruity and precision but by its influence on the optimal organisational design.  1998 Elsevier Science B.V. All rights reserved. JEL classification: C70; D20; L23 Keywords: Contracting; Performance measurement; Organizational design; Push-pull; Complementarities

1. Introduction The need for new performance measures to complement the structure of the production process in order to motivate all tasks central to the success of a company has become a center of attention in managerial accounting textbooks. Much of the recent theoretical accounting literature addressing the use and value of multiple performance measures, however, has largely ignored complementarities between performance measures and organizational

* Tel.: 773 702 9359; fax: 773 702 0458; e-mail: [email protected] 0165-4101/98/$ — see front matter  1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 5 - 4 1 0 1 ( 9 8 ) 0 0 0 2 4 - X

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design. The typical setting analyzed is a single employee organization where the set of tasks is exogenous to the analysis. Key issues that have been addressed in this way are how to best design and utilize various performance measures as in Bushman and Indjejikian (1993a,b) and Hemmer (1996), and the value of introducing additional performance measures as in Feltham and Xie (1994). While relying on static, one-agent settings to study the best use of a given set of performance measures is of little concern; this approach is more troublesome when it comes to understanding the value of introducing additional performance measures. The are (at least) two reasons for this. First, in more interesting multi-person settings the optimal task and responsibility assignments in a given firm can easily change in response to a change in the set of available performance measures. Second, and central to this paper, the information carried by a given set of performance measures can also change in response to a reassignment of tasks or responsibilities among workers. That is, in a specific setting a performance measurement system cannot be used to encourage certain actions, this problem is potentially eliminated simply by changing the organization of the production process. The demand for and the value of additional performance measures in static settings thus has little to do with the demand for such measures in more realistic settings where all components of the organizational architecture are allowed to be chosen to complement each other. The purpose of this paper is to provide insights into the relation between the ability to measure performance and the optimal organization of production, how this relation affects other observable firm characteristics and, in particular, the demand for additional performance measures. To do this, I study a simple two-stage production process, where the tasks at the initial stage must be completed before the tasks at the final stage can be performed. Each stage requires the inputs of specialized agents which determine both the quality and the quantity of output. The objective of the owner is to maximize the value of his residual claim to the firm, by choosing the assignment of responsibilities in conjunction with the choice of an optimal performance evaluation and reward structure for the two agents. Two responsibility assignments compete for the title of optimal. One resembles a push system where the responsibility for initiating production is assigned to the agent performing the initial tasks (agent I) while the agent performing the final tasks (agent F) is simply responsible for keeping up with the  Brickley et al. (1997) use the term Organizational Architecture to represent the three issues which are also at the heart of the analysis in this paper: the choice of a performance evaluation system, a reward structure and an assignment of decision rights. Their text provides a detailed discussion of the need for making such choices jointly to ensure that the individual components complement each other. See also Milgrom and Roberts (1995) for a discussion of the role of complementarities in optimal organizational design.

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flow. The other resembles a pull system under which the responsibility for initiating production rests with the agent at the final stage while the initial stage agent is responsible for meeting the demand from the final stage. As I show, the key distinguishing feature between these two responsibility assignments is that the pull assignment provides a direct incentive for agent I to supply agent F with low quality units. The incentive for agent I to sabotage agent F is not present under the push assignment. Viewed in isolation, agent I’s incentive to sabotage production is clearly an undesirable feature that puts the pull assignment at a disadvantage. Taking a broader perspective reveals, however, that providing agent I with this undesirable incentive carries a potential reward. Specifically, agent I’s ability to influence agent F’s productivity makes the final output informative about the effort agent I puts into quality enhancement. This allows for the design of reward structures targeted at achieving superior product quality. Since the same information cannot be inferred from final output under the push assignment, it does not provide this opportunity. The choice between these two assignments is therefore dictated by the ability to design a cost effective monetary structure that takes advantage of the enriched information flow under the pull assignment to provide incentives for quality enhancement. The analysis in the paper leads to a number of empirically testable predictions. I show that since, under the pull assignment, firm performance is informative about both agents’ actions, it is optimal to tie the compensation of both agents to the overall performance of the firm. In contrast, having both agents share in the firm’s overall performance yields no benefits under the push assignment since firm performance (under this assignment) is informative only about the activities of agent F. Accordingly, arrangements that tie workers’ compensation to overall firm performance should be more prevalent in pull than push firms. These results also suggest that for firms that change from push to the pull responsibility assignment without also moving to a group-type reward structure, product quality and firm profitability will decrease rather than increase. On the other hand, firms that do make the appropriate adjustments to their reward structure should experience increases. I show that a necessary but not sufficient condition for the pull assignment to dominate is that the firm will optimally produce goods of higher quality and for  While comparison of the push and the pull assignments have only recently entered into managerial accounting texts, see, e.g., Horngren, et al. (1994) (p. 660) and Zimmerman (1997) (pp. 665—661), it has a long tradition in the operations literature, see e.g. Spearman and Zazanis (1992) for an overview. That literature typically focuses on the tradeoff between the benefits of low inventory holding cost and the ability to rapidly adjust to demand shocks (the pull), versus low risk of stock-outs and disruption of the information flow (the push). These comparisons ignore the incentives for individuals carrying out the production. Thus, the implications of such different manufacturing environments for the information provided by standard performance measures and, thus, for the need for additional performance measures remain largely unknown.

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workers to be more productive than if responsibilities were assigned according to the push approach. The gains in quality and productivity have to be sufficiently large before the pull assignment dominates. I also evaluate the implications of these two alternative responsibility assignments for the value of various forms of improvements of the production process. I find that, for the pull assignment, achieving higher levels of product quality requires enhancing the individual worker’s ability to influence the quality of the product. For the push assignment, in contrast, this has no effect on product quality. These results predict that pull firms dominate their push counterparts along the quality dimensions. Moreover, worker involvement in quality improvement programs is more prevalent in pull firms than in more traditional push firms. Finally, I provide insights into the value of introducing a supplementary measure of product quality. The main message is that the demand for an additional performance measure differs under the two responsibility assignments. Moreover, introducing an additional measure of performance can change the optimal responsibility assignment either from push to pull or vice-versa. As a result, analysis of the value of introducing new performance measures in static settings can lead to inappropriate conclusions. Since the pull assignment makes output informative about quality, the analysis predicts that the demand for additional measures in pull firms is tied to the randomness of volume. In contrast, in push firms the demand is tied to the level of quality attainable without the measure present. The rest of the paper is organized as follows. Section 2 outlines the setting and the formal model. Section 3 contains an analysis of optimal incentive design when responsibilities are assigned according to the push principle. In Section 4 the design of optimal incentives is analyzed when the firm uses the pull approach. The choice and the implications of the optimal assignment are addressed in Section 5. Section 6 provides insights into the value of adding an additional performance measure. A summary and discussion of the results is in Section 7.

2. The model Consider the activities of two agents working in sequence, one an expert sander the other an expert painter, sanding and painting an unfinished wooden chair. Each agent can choose how much to supply of (at least) two different kinds of inputs: volume related ‘speed’ and quality promoting ‘attention’. Due to the sequential nature of the production process, the results of the agents’  Painting a chair prior to sanding it makes little (if any) sense. However, the model can easily be adapted to represent a setting where the agents work simultaneously on different parts to be assembled at some later stage and where the care taken by one agent affects the efforts of the other agent.

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decisions are not independent. First, while either one of the agents can always choose to work faster, if the other agent does not follow, the faster agent will eventually be forced to wait. Second, the smoothness of each chair likely affects the ability of the paint to bond as well as the ease by which it can be painted. Thus, the attention paid by agent I affects both the quality of the final product and the productivity of agent F. The model I use to formalize this setting is closely related to Hemmer’s (1995) two-stage sequential extension of the linear multi-task principal—agent model originally developed by Holmstro¨m and Milgrom (1987, 1991). Thus, I invoke the following assumptions. First, to abstract from issues pertaining to inventory policy I assume that the facility is operated according to the ‘just-in-time’ principle. Accordingly, the number of units finished at the final stage, i.e., the final output of the facility, always equals the number of units produced of the intermediate product. Moreover, over any period of time the output of the facility is determined by the ‘least active’ of the two stages (as well as random events). Letting a and a denote the level of effort directed at increas' $ ing speed by the agent working at the initial and the final production stages, respectively. Then, the stochastic production volume, t, for the facility is assumed to be determined as

t"min[u a ; u a ]#e, ' ' $ $

(1)

where u , a , u , a 31 , and e&N(0,p). p is strictly positive and finite. The ' ' $ $ > parameters u and determine the productivity of speed-enhancing effort at the  initial and the final stages, respectively and depend on factors such as the sophistication of the production technology which is utilized and the individual

 No matter how large a buffer inventory is available, as long as its bounded, the volume of the final output is, in the end, determined by the slowest of the two stages. If agent F works ‘too fast’ he will eventually have to wait for agent I. On the other hand, if agent F does not work ‘fast enough’, agent I is eventually forced to wait for agent F to finish the chairs piling up between the work stations. See also Goldratt and Cox (1986) (Chapter 13).  Most of the differences between the basic model presented in this section and that of Hemmer (1995), such as the form of the production and personal cost functions are mainly cosmetic and introduced with the exclusive intent of streamlining notation and to produce the insights in the most parsimonious way possible. The only substantive difference is that in Hemmer (1995) tasks can be reassigned and even shared between the two agents while here the owner is unable to pursue such strategies since the expertise needed for executing the tasks at the initial (final) stage is assumed to be specific to agent I (F).  This assumption of ‘no buffer inventory’ is made merely as a matter of convenience. First, as discussed in footnote 4, even if buffers are available a faster agent will eventually have to wait for a slower one. Moreover,in this model it is actually optimal not to allow any inventory to accumulate between the two stages.

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skills of the agents. The noise term e captures the random relation between these efforts and realized output. With the structure of Eq. (1), when one agent works slower than the other, the harder working agent is forced to wait. The time the faster agent will spend waiting is positively related to t,u a !u a . (2) ' ' $ $ A positive t here implies that agent I has worked faster than needed for producing the current output, t, since by Eq. (1), the (expected) output is then determined by the slower working agent F. Conversely, if t is negative agent F is the agent who was worked unnecessarily fast. Thus, t reflects that a sequential environment allows the agents to make inferences about their relative efforts. In order to simplify the analysis as much as possible I assume that t, the measure of the time spent waiting by agents, is publicly observable. It is important to note, however, that t does not reveal anything to the principal about either agent’s total effort. This information must still be obtained from t. The quality of the intermediate (and final) product is represented by the parameter q31>. Values of q approaching zero reflect a low level of product quality, while higher values of q imply higher quality. Two factors are assumed to influence the choice of product quality: the nature of the production technology employed and the quality enhancing effort of agent I. To capture these factors, I assume that q31> is a level of quality provided ‘for free’ in that the production technology allows agent I to choose any level of quality q4q without having to exert costly quality enhancing effort. Such efforts are, however, required to enhance quality beyond the q-level. I assume that the  highest level of quality agent I can achieve is given by q"max[q;ja ], (3)  O and, thus, the level of effort required to achieve some level of quality is given by



q/j, for q'q, a"  O 0, otherwise,

(3)

 Using a normal distribution introduces the potential for negative production. However, as demonstrated in Hemmer (1996), volume could be modeled as the product of an agent’s effort and a log-normal noise term. Taking ¸N of volume then results in a measure with the exact same characteristics as t. This interpretation of t implies that the optimal contract is actually concave in volume.  The final stage is likely also to have direct implications for the quality of the final product. However, unlike agent I’s quality enhancement efforts, agents F’s quality enhancing activities will not have any implications for the execution of agent I’s tasks. I therefore simplify the model by assuming that only agent I is in a position to influence product quality. This simplification has no bearing on the results.  Since agent I can supply upto q for free, any level of q4q has a natural interpretation as ‘sabotage’.  

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where a 31> and j31> are the level of attention paid to given unit of the O intermediate product by agent I and the productivity of such effort, respectively. I assume that agent I’s choice of q, or equivalently a , is observable only to agent O I. Furthermore, that no separate measures of product quality are available. Since the choice of q determines the attention agent I must pay to each unit, the total quality enhancing effort, a , which agent I must exert is proportional to O v and thus determined as a "va . (4) O O Because the quality of the units produced by agent I has consequences for execution of the final activity by agent F, the final stage productivity parameter u in Eq. (1) should be function of q. I assume that w is simply increasing $ $ linearly in q such that: u "cq, (5) $ where c is a positive productivity parameter. Again, I assume that agent F cannot observe agent I’s choice of q. During the production process, agent I can draw an inference about q since he knows both a and c in Eq. (1). Due to $ the presence of the e-term, however, this inference is not perfect. The choice agent I makes about quality could also have implications for the product’s market price. For simplicity and with little loss of generality, however, I assume that the price is a constant and that the per-unit selling price minus variable unit costs (other than labor) is one. Finally, each agent’s utility function is assumed to be given by º(¼, a , a , a )"e\P5\!, (6) ' O $ where ¼ denotes individual wealth, r is the coefficient of absolute risk aversion and C denotes an agent’s personal cost of supplying productive inputs. As in Holmstro¨m and Milgrom (1987, 1991), this analysis relies on sharing rules that are linear in the available performance measures. I denote the payment to agent I (F) as s (s ). Both agents have (identical) alternative employment opportuni' $ ties such that each agent requires a minimum (expected) utility level, º,!e\P(h), in order to accept employment. Also, to facilitate the derivation of closed form results, I represent the personal cost to an agent of a given activity by c(a )"a/2, H H

(7)

 In practice, various noisy measures providing contractible information about product quality may well be available. Section 6 is dedicated to the demand and value of making such a measure available.

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and assume that an agent’s total cost of engaging in a given number of activities is additively separable in the personal cost of engaging in the individual activities as specified by Eq. (7). Given the focus of this paper, the problems facing the principal in this setting are twofold. First, he is faced with the usual task of designing the contracts with the agent. Second, before he does this, the principal must also specify the interaction (i.e. the rules of the game being played) between the two agents. The sequence of events and activities underlying this analysis is summarized in Fig. 1.

3. The push assignment In this section the incentive problem facing the principal is analyzed assuming that the (supply) push responsibility assignment is used for the production process outlined in Section 2 and summarized in Fig. 1. As discussed in Section 1, a push assignment provides agent I with the responsibility to make as many units of the intermediate product as possible and ‘push’ these units on to the final stage. Agent F is simply made responsible for finishing these units on a timely basis so that agent I does not have to wait. In other words, under the push assignment agent I must commit himself to a level of a without considering agent F’s choice of a , ' $ while agent F can condition his choice of a on agent I’s choice of a . Thus with $ ' respect to a and a , the push assignment makes agent I the Stackelberg leader ' $ and agent F the follower in the game played between the two agents. Because the responsibility of agent F is dictated by the result of agent I’s efforts, the optimal contract for agent F is very simple. Agent F can be persuaded to fulfill his responsibilities through an arrangement specifying a flat wage which will cover all of agent F’s costs (including those of foregone opportunities) if and only if agent F works fast enough so that agent I never has to wait. Otherwise, agent F will be paid nothing. The prospect of being paid nothing will keep agent F working and since such an arrangement in equilibrium provides agent F with risk-free compensation, it is the lowest-cost contract that will make agent F implement the desired action. The discussion is formalized as observation 1.

 In Eq. (4) a is related to the production volume. Unlike for risk, there is no clear theoritical O guidance on agent’s attitudes towards variations in workload. While some agents may prefer a predictable work-load, other may be averse to monotony and prefer a work environment in which periods of relatively hard work interchange with periods of relative relaxation. To eliminate any confounding effect on results introduced by such attitudes, it is assumed that whenever effort is uncertain, an agent simply considers the expected effort. Given the structure of this model, adding uncertainty to a yields little but clutter. O  All proofs are provided in Appendix A.

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Fig. 1. The events and various stages of the contracting and production process.

Observation 1. Let superscript h on a variable reflect the equilibrium value for the variable when responsibilities are assigned as a push system. Also let X ,u, and X ,u. Then, under the push assignment, the optimal incen' ' $ $ tive contract for agent F is



0#(X /XF )(aF)/2, if t40 ' $ ' S (t,t)" $ 0, otherwise. Under the push assignment, t provides a direct measure of whether agent F meets his contractual obligations. Since agent I is responsible for initiating the  To streamline notation I use an upper case Greek letter to represent the lower case equivalent squared.

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production, there is no such direct measure available on which to discipline agent I. Instead a piece-rate contract is needed here to ensure that agent I supplies the desired (second-best) level of productive inputs. Ideally, the incentive arrangement for the initial stage would provide agent I with separate incentives for a and a . Again, no contemporaneous measure of product quality ' O is available for contracting here. Thus, the only measure the principal can use to influence agent I’s actions is production volume, t. Observation 2 summarizes the implication for product quality. Observation 2. Under the push assignment agent I will supply product quality qF"q.  In other words, the push assignment provides agent I with no incentive to enhance product quality beyond the technology-dictated level q. Thus, uF "cq. $ Since, on the other hand, it does not give him any incentive for sabotage either, a benevolent agent will choose qF"qN .  provides him with an incentive never to Given that agent F’s optimal contract make agent I wait, the incentive problem related to agent I’s supply of volume enhancing effort, a , is now easily solved for the push assignment. Lemma ' 1 details the solution. ¸emma 1. Let R,rp, where r is the agent’s coefficient of absolute risk aversion and p is the variance of the random noise in output. ¹hen, for the push assignment, optimal incentive contract for agent I is given by SF(t)"BF#bFt , ' ' $ ' where bF"[1#X /XF #R/X ]\, and BF is a constant the magnitude of which ' ' $ ' ' is determined to ensure that agent I’s overall compensation satisfies his minimum utility requirement. The strength of the optimal incentive pressure provided to agent I under a push assignment, as measured by bF, has intuitive properties in line with ' optimal incentives in non-sequential models: The monitoring problem is reflected by the last term in the bracket. As the ability to monitor deteriorates (i.e., p and, thus, R increases), the strength of incentives given to the agent will decrease while the agency costs will increase.

 I rely on the standard assumption of benevolence meaning that an agent, when personally indifferent, will always make choices that are best for the principal.  For issues pertaining to the optimality of the linear contracts, see Holmstro¨m and Milgrom (1987, 1991).

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The relative productivity term X /XF in the denominator for bF reflects that ' $ ' here, unlike in a single agent setting, any unit produced by agent I must receive finishing effort by agent F. If XF is very large relative to X little effort is needed $ ' to finish the units produced by agent I and the cost of this final activity can be ignored. For smaller values of X finishing is more costly and it is therefore less F$ desirable to encourage production of intermediate units. This leads to lower incentives for agent I. The relative productivity term ) /X has some interest' F$ ing implications for the optimal incentive pressure in sequential settings. Lemma 2 provides the specifics. ¸emma 2 *bF ' ]0 for X /XF ^R/X , ' $ ' *u ' *bF *bF ''0, ''0, (ii) *c *q  Following Lemma 2(i), increased productivity of a does not unambiguously ' lead to stronger incentives for agent I as would be the case in a single-agent setting. Only for suffeciently low levels of u this will be the case. If u is high ' ' relative to u , it is not worthwhile for the principal to use improvements in u to $ ' further lever-up the incentives simply because it is too expensive to have the relatively unproductive agent F finish the extra units that agent I is expected to produce. Instead, when u is already high, the principal prefers to use further ' improvements in u to reduce agent I’s costly exposure to incentive-related risk, ' which is the undesired effect of bF. Thus, while in a single agent setting improved ' signal-to-noise always lead to stronger incentives, the opposite occurs in this setting where output is the result of multiple agents’ sequential activities if the productivity of the initial-stage agent is sufficiently high relative to the productivity of the agent assigned to the final stage. In contrast to the ambiguous effect of improved productivity of the other agent, agent F, will always result in increased incentives for agent I under the push assignment. The link here is straight forward. An improvement in agent F’s productivity makes it less costly to have agent F finish a given number of units made in the initial stage. This makes it attractive for the units produced by agent I will also lead to higher equilibrium production, since an increase in q improves agent F’s productivity which, as reported in lemma 2(ii), leads to stronger incentives for agent I. (i)

4. The pull assignment In this section, I analyze the incentive problem when responsibilities are assigned using the pull approach. Under a pull assignment, agent F determines

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production volume. That is, the assignment for agent F is to finish as many units of the intermediate product as possible thereby, via his demand, to ‘pull’ units of the intermediate product out of the initial stage. The responsibility assigned agent I is to ensure that agent F never needs to wait for units. Thus, under the pull system agent F must commit himself to a level of a on agent F’s choice of ' a . Accordingly one way to summarize the difference between this and the push $ assignment is that, ignoring again agent F’s choice of quality, the push assignment makes agent F the Stackelberg leader and agent I the Stackelberg follower. Since this assignment is exactly the reverse of that in the previous section it is tempting to think of these two alternative decision right assignments as being simply mirror images. Then, under the pull assignment agent I should be disciplined through a forcing arrangement just as agent F is under the push (Observation 1). Such an arrangement would specify a flat wage to cover all of agent I’s costs (including opportunity costs) if and only if agent F does not have to wait for units. Disciplining agent I via this type of an arrangement exposes only agent F to incentive related risk. However, when the pull assignment is used this forcing arrangement will leave agent I with quite undesirable incentives to guide his choice of quality, q. Observation 3 provides the details. Observation 3. Suppose that responsibilities are assigned according to the pull approach and that agent I is compensated with a flat wage to cover his cost of expected effort as well as his opportunity costs iff t50. Then agent I sabotages the production by choosing qJ"0. The intuition behind Observation 3 follows. Under this assignment agent F is given control over (expected) production volume. Yet, while agent I is not assigned direct control of production volume he is in indirect control here. Specifically, via his choice of quality he can affect the speed by which agent F can produce. The lower the quality agent I supplies, the fewer the units that will be finished for a given level of finishing effort a . Consequently, the lower the $ quality the fewer the units of the intermediate product agent I will have to supply. This contrasts with the push assignment where agent I controls both expected volume and quality, and therefore derives no benefits from sabotaging agent F. It is important to realize here that Observation 3 does not imply that using pull results in inferior quality. Rather, Observation 3 is a cornerstone for understanding the role of responsibility assignment in providing the principal with contractible information about product quality. As shown in the following, it is the very incentive to sabotage agent F that makes output informative about I’s choice of q. To be more specific, expected production volume under the pull assignment is determined jointly by agent I’s choice of q and agent F’s choice of a . Consequently, production volume generated by the pull assignment is also $ informative (in the Holmstro¨m (1979) sense) about both q and a , while under the $

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push assignment volume is informative about a only. This in turn allows the ' principal to contractually elicit products with quality exceeding the base level, q, something that cannot be achieved with the push assignment. The choice of an optimal assignment, then, is dictated by which of the two effects, the incentive effect or the information effect, dominates. The enhanced information flow under the pull assignment can be exploited by the principal to provide contractual incentives to agent I for increasing product quality. Thus, in return for providing an undesirable incentive for agent I, the pull assignment of responsibilities offers a unique means for the principal to influence agent I’s choice of quality. The way to take advantage of this is to provide agent I (as well as agent F) with a contract that is increasing in volume. Lemma 3 details the optimal volume-based incentive arrangement for both agents. ¸emma 3. If the manufacturing process is organized following the pull approach, agent I and agent F’s respective wages are optimally determined as S (v,t)"BJ #bJ v, ' ' ' S (v)"BJ #bJ v, $ $ $ where



h#(a#a)#bJ (bJ R!vN ), for t50,  ' O ' ' BJ " ' !bJ v, otherwise, ' BJ "h#a#bJ (bJ R!vN ), $  $ $ $ bJ "[1#XJ /X #R/XJ #RXJ /XJ #A]\, $ $ ' $ $ ' bJ "bJ ;[XJ /X #2XJ Q/K], ' $ $ ' D XJ 4Q 4¼ A, $ Q#R # , K X K '







and



Q,

q for q'q,  0 otherwise.

Note here that the purpose of applying bJ to volume in the contract with ' agent I under a pull assignment is not to elicit more of the effort agent I direct towards completing another unit. This would be wasteful since agent I should only produce what agent F demands, which is already ensured by the forcing arrangement. Instead, the purpose of the volume-based incentive for agent I is to elicit units of higher quality. Higher quality units are more easily finished by

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agent production without having to supply more effort. Of course, increased volume carries a direct monetary reward for agent I when bJ exceeds zero. ' By Lemma 3 bJ is positive and q is increasing in bJ . Thus, if the principal wants ' ' to secure a higher level of q he will incur an added cost, since an increase in the weight placed on volume in the contract with agent I increases the cost of sub-optimal risk sharing. However, the important message of Lemma 3 is that by incurring this cost the pull assignment allows the principal to implement any level of q by appropriately choosing bJ . Also, from the expression in Lemma 3 it ' is apparent that agent I’s response to the incentive parameter bJ depends on the ' expected production as determined by uJ a . The higher the expected through$ $ put, the stronger are the incentives provided to agent I. Of course, the expected throughput is determined jointly by agent F’s equilibrium effort choice and uJ , $ both of which will depend on the level of q the principal decides to implement via the choice of incentives for agent I. More interestingly, the structure of bJ is conceptually the same and, thus, from ' an empirical perspective not any different from bF. Stated differently, while the ' purpose of bF and bJ is completely different (bF is used to enhance volume, bJ to ' ' ' ' enhance quality), the directional change in bF for a change in the underlying ' parameter values is the same as for bJ . Thus, it is not feasible to infer of the type ' incentives provided to a given agent from the observed correlation between pay and performance in this sequential setting without referencing the structure of the organization in which the agent works.

5. Choice of an optimal assignment In this Section 1 compare directly the responsibility assignment detailed in the preceding sections. This comparison provides insights into the forces that dictate the choice of an assignment and is used to generate testable predictions about differences between organizations that rely on the push and the pull approach to responsibility assignment. Justification for this comparison is provided by the following observation. Proposition 1. For the model outlined in Section 2, the optimal assignment of responsibilities is either the push outlined in Section 3 or the pull outlined in Section 4. Whether the push or the pull assignment is optimal for the setting in this paper depends on the effect on the total certainty equivalent, ¹CE; for a given technology and a specific pair of agents, which approach (when used optimally) will yield the highest total certainty equivalent? Lemma 4 provides the foundation for answering this question.

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¸emma 4. For the push assignment, the maximum total certainty equivalent achievable is ¹CEF"X ;[2[1#X /XF #R/X ]]\. ' ' $ ' For the pull assignment, the maximum total certainty equivalent achievable is ¹CEJ"X ;[2[1X /XJ #R/X #RX /(XJ )#AX /XJ ]\. ' $ ' ' $ ' ' $ ¹CEJ differs structurally from ¹CEF by the two additional risk-terms in the denominator. The presence of these additional terms reflects that risk that must be placed on agent I to elicit quality-enhancing effort from him under the pull assignment. For q4q the AX /XJ -term, equals zero. The value of the ' $  RX /(XJ )-term therefore reflects the risk that must be placed on agent I to ' $ counter his pull-specific incentive to sabotage agent F. The cost associated with placing this additional risk on agent I under the pull assignment therefore can be thought of as the direct cost of making v informative about a . The A-term in the O expression for ¹CEJ instead reflects the additional costs of adverse risk sharing of providing agent I with incentives to produce intermediate units with quality exceeding q. Proposition 2 establishes qJ'q as a necessary condition for the pull  to be preferred to the push assignment.  Proposition 2. A necessary condition for the pull to dominate the push assignment is that qJ, the optimally chosen product quality conditional on the pull assignment being used, is strictly higher than qF, the optimally chosen product quality conditional on the push assignment being used. Formally: ¹CEJ'¹CEF only if qJ'qF ("q).  The message of Proposition 2 is that since achieving any level of quality is much more costly under the pull than under the push, one only wants to consider the pull assignment under circumstances where incurring this extra cost is compensated by a higher level of product quality. That is, achieving higher quality is a necessary requirement for the pull assignment to be a viable alternative to the (traditional) push. Proposition 2 does not, however, guarantee that a pull assignment can ever be the preferred approach to organizing a given production line. Proposition 3 shows that one cannot rule out either of the two responsibility assignments ex ante, and outlines conditions under which the principal prefers the pull assignment as well as conditions under which the push assignment is preferred. Proposition 3 (i) Fix +x , c, k, R,. Then, there exists a strictly positive value of q, denoted qL , ' such that for q(qL , it is optimal to use the pull assignment while for q'qL , push  q"qL the two assignments are economically equivalent.  is optimal. For 

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(ii) Fix +u , c q, R,. Then, there exists a strictly positive value of j, denoted jK , '  K , it is optimal to use the push assignments while for j'jK , pull such that for j(j is optimal. For j"jK the two assignment are economically equivalent. While part (i) of Proposition 3 seems to run counter to Proposition 1, the discrepancy is easily reconciled. Following Proposition 2 the pull can only dominate if qJ is higher than q ("qF). If q is very low (as an extreme case   consider q"0), it is fairly cheap to provide agent I with a volume-based  incentive to produce units with quality in excess of q. As q increases, however, so   does the cost of providing agent I with a compensation-based incentive to counter the pull-specific incentive for sabotage and give him an incentive to deliver quality in excess of q. Part (ii) of Proposition 3 reemphasizes this intuition. Recall (from Eq. (3)) that j is the productivity of agent I’s qualityenhancing effort. Thus for high values of j it does not require much effort for agent I to improve quality beyond the q-level. Accordingly, overcoming the cost  of the adverse incentive of the pull assignment is decreasing in j. Propositions 2 and 3 both address pre-existing conditions that make a particular responsibility assignment optimal. Some implications for difference in observed firm characteristics are highlighted in Proposition 4. Proposition 4. Consider two firms, H and ¸, identical in every way except that: (a) for firm H, q& is marginally higher than qL while for firm ¸, q* is marginally  lower than qL , or  (b) for firm H, j& is marginally lower than jK while for firm ¸, j* is marginally higher than jK . Then (i) Firm H uses push while firm ¸ uses pull. (ii) q*'q&"q&'q*.   (iii) Overall productivity measured as vN /[a #a ] is strictly higher for firm ¸. ' $ The perceived quality superiority of successful pull firms (e.g., Toyota) is often linked either to cultural issues or to the prevalence of Just-In-Time in the pull environment. Propositions 2—4 give a different reason. Unless conditions are such that using the pull assignment results in a sufficiently large quality advantage to compensate for the added costs of achieving even a minimum level of quality, it is optimal to assign responsibilities following the push principle and accept lower quality. To provide crisper intuition for the comparison of the two alternative incentive mechanisms and their impact on product quality consider Fig. 2.

 Generally, as in Alles et al. (1995) it is simply a maintained conjecture that JIT leads to improved quality. For an exception, however, see Creme´r (1992).

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Fig. 2. The relation between q and the optimal assignment of responsibilities. 

Fig. 2 illustrates that the pull (push) assignment is, ceteris paribus, more desirable for relatively low (high) levels of q. The solid lines/curves in Fig. 2 depict the certainty equivalents for a pull and a push firm as a function of q, the  product quality which can be achieved ‘for free’, i.e., without any a . AccordO ingly, as long as q4q the maximum achievable total certainty equivalent  under the pull assignment is the peak of the dotted function labeled ¹CEJ(q"q"0). This explains the flat part of the ¹CEJ(q)-function.   For q'q, ¹CEJ is maximized at q and, thus, determined by the (dotted)  total certainty equivalent achievable function TCEJ(q"q"q), which maps the  under the pull if contracts are chosen such that qJ"q. By Observation 2, qF"q  in q. Following Proposi- and by Lemma 4 then, TCEF(q"0)"0 and increasing  everywhere above the ¹CEJ(q  tion 2, then ¹CEF(q) must be "q"q)-curve in   

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Fig. 2. This guarantees that ¹CEF(q) will intersect with ¹CEJ(q) at the flat  section. In addition, that the crossing point is unique. Since the maximum total certainty equivalent achievable is the upper envelope of the ¹CEF(q) and the  ¹CEJ(q) curves (indicated by the dotted bold curve), it follows from this figure  that the pull assignment dominates if and only if q(qL . Beyond this point, the  cost of using the pull to ensure superior quality becomes prohibitively high and the push approach becomes dominant. Part (ii) of Proposition 4 follows directly from the above discussion of Fig. 2. Part (iii) of Proposition 4 highlights additional differences between pull and push firms. Because quality is enhanced, the productivity of agent F is enhanced. This suggests that firms switching to the pull assignment should experience large productivity gains relative to similar firms continuing to rely on the more traditional push approach to the assignment of responsibilities. While not modeled here, this also suggests that the optimal mix of capital and labor would differ according to the choice of the responsibility assignment. This model also provides predictions about differences in the approaches to ‘continuous improvements’ such as industrial robots have led to both higher productivity and improvements between push and pull firms. Investments in equipment in the quality of manufactured goods in both traditional push factories as well as in newer pull type environments over the years. Technological advancement captures only part of the ‘continuous improvement’ discussion, however. Also important is what is being improved and, in particular, the role of workers. Specifically, it seems widely accepted, see, e.g., Aoki (1986), that improving individual specific skills and having workers involved in identifying improvements is more commonplace in the modern manufacturing environment. Proposition 5 suggests which type of improvements are valued under these tow assignments. Proposition 5. Consider two firms, H and ¸, where firm H uses push while firm ¸ uses pull. Then: d¹CE& d¹CE* ' "0, dq dq   d¹CE* d¹CE& (ii) ' "0. dj dj (i)

Following Proposition 5(i), push is the best facilitator of the two assignments for improvements in q while only the pull-system provides economic support for  j. Casually speaking, these differences can be attributed investments to increase to the fact that for the pull firm a portion of product quality is the result of worker involvement while for the push firm quality is fully determined by the technology specific level of q. This is also the reason why improvements that will 

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reduce agent I’s personal cost of achieving a level of product quality in excess of q are valuable under pull but a matter of indifference under the push Proposi tion 5 (ii). Also of direct interest to this study is the difference in the incentives for workers to actively participate in the improvement process. Proposition 6 provides additional insights. Proposition 6. Consider two firms, H and ¸, where firm H optimally uses push while firm ¸ optimally uses pull. Suppose that the contracts with the agents are fixed. Let CEI denote the certainty equivalent of agent I. Then *CEI& *CEI* " "0, *q *j  *CEI* *CEI& (ii) " "0. *j *q  Proposition 6 predicts that agent I’s incentive to actively propose and/or implement improvements with implications for product quality, and thus agent F’s productivity, is a feature inherent to the pull assignment. Such incentives are not present under the push. This feature is present under the pull assignment even when contracts are designed (as in this paper) without the intent of promoting such behavior. This suggests that in a dynamic setting, the pull approach could be more desirable than what is suggested here. However, dynamic extensions of this model to allow for a formal evaluation of this as well as other multi-period aspects of responsibility assignments are left for future research. (i)

6. The value of an additional performance measure The previous analysis has utilized the perhaps somewhat extreme assumption that no separate measure of the quality of the intermediate product is available. It is certainly conceivable that by acquiring some measurement device, a noisy measure of q could be produced. For the sake of argument, suppose that the owner is presented with a new technology that, if implemented at a cost M'0, will produce the following quality measure: m"q#e , K

(8)

 For detailed specifications of CEI under the push and the pull assignments, see the proofs of Lemma 1 and Lemma 3 respectively.

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where e &N(0,p ) and p is strictly positive and finite. The following proposiK K K tion provides details about the value of this performance measure under the two responsibility assignments. Proposition 7. Consider the opportunity to introduce the measure m in a firm which is organized optimally given m is not available. Further suppose that the firm can not change its assignments. If the firm uses the (i) push assignment, then for any possible value of p there exists a strictly K positive level of q, denoted qF , such that the measure m has value if and only if K q(qF . K  (ii) pull assignment, then for any possible value of p there exists a strictly K positive level of p, denoted pL , such that the measure m has value if and only if p'pL . The features that determine whether or not the measure m has value are, as highlighted by Proposition 7, not identical under the two systems. In both cases, to have value the measure m must reveal q with sufficient precision, i.e., that p is K ‘sufficiently small’. The difference between the push and the pull assignment rests on what determines how small is ‘sufficiently small’. In the case of the push firm, the question is whether introducing m would lead to an improvement in quality over the case where the owner has not measure available that will allow him to contractually elicit levels of q in excess of the base level q. Therefore, the higher  q is, the more precise must m be for this performance measure to be of value in  push firm. Moreover, if m is sufficiently precise to have value under the push the assignment, this value is decreasing in q.  of the measure m is linked to the Under the pull assignment the value volatility of output rather than to the technology-specific base level of quality, q. This difference arises because unlike under the push assignment, under the pull assignment the equilibrium level of qJ does not depend on q. Recall from  pull assignSection 5 that absent the measure m, a necessary condition for the ment to be optimal is that qJ exceeds q. This is feasible since product volume, v,  about q. Accordingly, in the pull setting under the pull assignment is informative m is simply a substitute for v as a measure of product quality. To have value in the pull setting, then, m must provide a cheaper means for eliciting qJ'q than  does v alone. This requires that the precision with which m measures q is sufficiently high relative to the precision with which q is measured by production volume, v. The important point here is, however, that Proposition 7 does not imply that the value of introducing the measure of quality m into a push (pull) firm is measured by the effect on ¹CEF (¹CEJ). Proposition 7 does not even imply that the value of getting the measure m is nil unless the conditions of Proposition 7 is met. That these conclusions are not generally correct is due to the effect m can have on the overall organizational architecture. As is easily verified, it is entirely feasible that introducing the measure m has a more beneficial effect for the pull

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(push) than the push (pull) firm. Accordingly, it is quite likely that some or all the value of the measure m arises from enabling the owner to change the whole architecture of the firm.

7. Summary In this paper I analyze the role of complementarities in the choice of performance measures, explicit (monetary) incentives and responsibility assignment in a two stage, sequential production setting where a principal contracts with two specialized agents. Two responsibility assignments compete for optimality. One assignment makes the agent of the final stage responsible for finishing whatever the agent at the initial stage produces, while the agent at the initial stage is responsible for the overall output level. The other assignment is simply the reverse. These assignments correspond to the traditional push approach and the newer pull approach to manufacturing, respectively. I focus on the determinants as well as the implications of the choice of the optimal responsibility assignment. First, I show that inherent in the pull, but not present under the push assignment, is a costly incentive for the initial stage agent to sabotage the final stage agent by supplying low quality units that are harder to finish. This incentive, however, ensures that output becomes informative about qualityenhancing effort. This allows the principal to design a contract to elicit costly quality-enhancing effort and, in turn, enhance overall productivity. The choice of an optimal assignment therefore is dictated by whether the benefits of having this information available for contracting outweigh the costs of the undesirable incentive that is responsible for its availability. The ability to change the informativeness of available performance measures by changing the responsibility assignment has important implications for our understanding of the demand for independent performance measures. Here, a separate measure of product quality complements volume as a performance measure in the push setting, while in the pull-setting such a measure serves as a substitute for volume, since volume is already informative about quality in this setting. Therefore, the factors that give rise to the value of such a measure differ for the two assignments. Moreover, the preference ordering over the two assignments can change as a result of introducing such a measure. This highlights the need for endogenizing the choice of an organizational design in studies of optimal performance evaluation systems.

Acknowledgements I thank Sudipto Bhattacharya, Robert Bushman, Leslie Eldenburg, Miles Gietzman, Frank Gigler, Steve Matsunaga, Glenn MacDonald (the referee),

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Jennifer Milliron, Oat O’Brien, Jerry Zimmerman (the editor), and workshop participants at London School of Economics, London Business School and Hong Kong University of Science and Technology for helpful comments, suggestions, and discussions. Financial support from the William S. Fishman research Scholarship at the Graduate School of Business is also gratefully acknowledged.

Appendix A. Proof of Observation 1. This risk-free contract covers exactly agent F’s costs. 䊐 Proof of Observation 2. Under the push assignment agent I solves, using Eqs. (1) and (3):



q for q'q, min (Qu a /j),where Q,  ' '  0 otherwise. O First-order condition: Q(u a /j)"0, which is satisfied when q"q. ' ' 

䊐

Proof of ¸emma 1. Define CEI to be agent I’s certainty equivalent. Then, since from Observation 2, qJ"q ("0), for a given compensation scheme and a given set of actions, CEI"S (v)!a!bR, where R,rp. '  '  ' Similarly, the certainty equivalent of agent F is given by CEF,S !(X /XF )(aF)"h, $ ' $ ' and the certainty equivalent of agent F is given by CEP,u a !s (v)!s (v,t). ' ' ' $ Combining the certainty equivalents of the three parties yields the total certainty equivalent, X ¹CE,u a !(a )! ' (a )!bR ' '  '  ' XF ' $

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and the principal’s problem can be expressed as maximizing ¹CE subject to an incentive compatibility constraint (ICI) for agent I: max ?' s.t.

X u a !a! ' (a )!bR ' '  ' XF '  ' $ a "b u . ' ' '

First-order condition: *¹CE "X !b [X #X/XF #R]"0. 䊐 ' ' ' ' $ *b ' Proof of ¸emma 2 (i)

 

*bF *bF ' ![2u /X !2Ru];[1#X /X #R/X ]\Thus, sgn ' " ' $ ' ' $ ' *u *u ' '

sgn[R/X !X /X ]. ' ' $ (ii) follows from straight forward differentiation. 䊐 Proof of Observation 3. Using Eqs. (1)—(5) agent I’s quality decision can be summarized as min (u aJ /u )#(Qu aJ ).  $ $ O  $ $ ' It is straightforward to confirm that this expression is minimized for q"0. 䊐 Proof of ¸emma 3. When both agent I and agent F are provided with volumebased incentives their respective decision problems be summarized as Agent I:

max CEIJ,bJ u a !X a/X !QX a/K, ' $ $  $ $ '  $ $ O

Agent F:

max CEFJ,bJ u aF!a, $ $  $ ?$

with first-order conditions (using Eqs. (1)—(3)) of Agent I: Agent F:

bJ "u a /X#2Qu a /K ' $ $ $ $ aJ "bJ u . $ $ $

which can be combined to yield bJ "bJ ;[X /X #2X Q/K]. ' $ $ ' $

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Now I can express the principal’s (pull) problem as max ?$ O s.t.

¹CE,u a !a!a!a!P bp!P bp  P $ $  '  O  $  $ a "b u $ $ $ a "u a /u . ' $ $ ' a "Qu a /j O $ $ bJ "bJ ;[X /X #2X Q/K] $ $ ' $ '

First-order condition:









X 4Q 4Q #  bJ " 1#X /X #R/X #RX /X# $ Q#R $ $ ' $ $ ' K K X 

\ . 䊐

Proof of Proposition 1. Only one other form of assignment is a candidate for being optimal: neither of the agents’ contracts is contingent on t. This requires that both have a piece rate contract. This arrangement is always dominated by the pull assignment where both agents have a piece rate but the contract of agent I does depend on t. 䊐 Proof of ¸emma 4. Since by Observation 2 qF"q, the total certainty equivalent  for the push assignment reduces to X #X/X #R X ' ' $ ' ¹CEF" " . 2[1#X /X #R/X ] 2[1#X /X #R/X ] ' $ ' ' $ ' In the case of the pull assignment, in equilibrium a is determined by b . Thus, O $ using [X /X #X/K] $ ' $ bJ " ' 4Q 4Q X 1#X /X #R/X #RX /2X#Q $ Q#R # $ ' $ $ ' X K K ' I obtain







,

X $ ¹CEJ" . 䊐 2[1#X /X #R/X #RX /X#A] $ ' $ $ ' Proof of Proposition 2. Suppose that the optimal pull solution is such that ¹CEJ5¹CEF. Using Lemma 4 then: X X ' ' 5 2[1#X /XJ #R/X #RX /[XJ ]#AX /XJ ] 2[1#X /XF #R/X ] ' $ ' ' $ ' $ ' $ ' which is satisfied if and only if XF (XJ . 䊐 $ $

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Proof of Proposition 3 (i) First I calculate




 



3 4R 2Q 8RQ 16RQ X # ! # # ' cq cq K *¹CEJ KX K ' " . (A.1) *q 4[1#X /X #R/X #RX /X#AX /X ] ' $ ' ' $ ' $ Now, suppose that q"0. Then, in the first bracket q appears in the denomin it appears in the numerator and, thus, the numerator is ator while in the second positive (negative) for sufficiently small (large) values of q. Accordingly there exists a unique q'0, denoted q*, for which ¹CEJ is maximized. Following Lemma 3, then ¹CEJ(q"0)'0. By Observation 2, qF"q, and by Lemma 4, then ¹CEF(q"0)"0.  Thus, for q"0, ¹CEJ'¹CEF"0.  *¹CEJ/*q'0 for Q"0,  By Eq. (A.1) the principal always prefer a contract with agent I that implements q over any contract that implements some q(q.  of q, denoted q, where 0(q(q*, such that Also, there exists a unique value  q(q, QJ"q*, while for q(q, qJ"qq. ¹CEJq*"¹CEJ(q). Furthermore for  since by Proposition 1  ¹CEJ(¹CEF Since *¹CEF/*q is strictly positive and  for qJ"qF, there exists a unique value of q, here denoted qL , where 0(qL (q, such that for q"qL , ¹CEJ"¹CEF. Thus,  for q(qL , ¹CEJ'¹CEF, while for   qN 'qL , ¹CEJ(¹CEF.  (ii) NBy (A.1), *¹CEF/*j" '0. Then since ¹CEJ"¹CEF for q"qL and OO  (*¹CEF/*q)'0, this part follows.  Proof of Proposition 4. Part (i) follows directly from Proposition 3 while part (ii) is the joint implication of Proposition 2 and Proposition 3. Part (iii) then follows from part (ii) and Eq. (5). 䊐 Proof of Proposition 5. Straightforward differentiation of the expression for ¹CEF and ¹CEJ in Lemma 4 yields these results. 䊐 Proof of Proposition 6 (i) For the push firm CEI does not (for a given contract) depend on either q or  j. (ii) For the pull approach agent I’s certainty equivalent is given as CEI*"b u a !X a/X!QX a/K, ' $ $  $ $  $ $ where Q'0. Then for a fixed b the results follow from straight forward ' differentiation. 䊐 Proof of Proposition 7 (i) For m to have value in the push setting it must be the case that it is used to induce a level of q'q. Suppose that q"0. The owner’s push problem  

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then becomes: 1 X X 1 u a ! a! ' (a )! ' (Qa )! bR!b !b R ' ' 2 ' XF ' ' K K K K 2 '  $ a "b u . ' ' ' q"b j/u a K ' ' Denote by q the q that solves the above problem. It is straightforward to verify K that q and that q and the ¹CE are strictly decreasing in p . Thus, for any finite K K K p there is a unique q, denoted qF , where qF , such that m is used in the optimal K K K contracts if and only if q(qF . K  in pull setting it must be the case that it can be used to (ii) For m to have value achieve a given level of q more cheaply than can v alone. If the owner base agent I’s contract on m and v (rather than v alone), agent I’s problem is given as max O?' s.t.

max CEIJ,bJ v#bJ q!X a/X !QX a/K, 'K K  $ $ '  $ $ O with first-order condition: ca bJ " #bJ "u ca/X #2Qu ca/K, where $ 'K K $ $ ' $ $ bJ " is the weight on volume given m is used also. 'K Now consider implementing the exact same level of q (and thus a and a ) with ' $ v, m as with v alone. From the proof of Lemma 3 then, bJ "u a /X #2Qu a /K"bJ " #bJ /ca , ' $ $ ' $ $ 'K K $ and we can then find the optimal values of bJ " and bJ which will implement the 'K K same level of q as bJ as ' 1 1 and bJ "ca b ; 1! . bJ " "b ; K $ ' ' 1#p/p 'K 1#p/p K K Thus, the owner would only use m to elicit q if













  1 1 (bJ )(ca ) 1! p #b ((bJ ) p!M, ' $ K ' ' 1#p/p 1#p/p K K i.e., when p'(ca )p . Now, since the left hand side is strictly increasing in p , $ K K m can only be used to improve on the optimal pull solution based on v when p is sufficiently small relative to p. 䊐 K References Alles, M., Datar, S.M., Lambert, R.A., 1995. Moral hazard and management control in just-in-time settings. Journal of Accounting Research 33 (Supplement), 177—204. Aoki, M., 1986. Horizontal vs. vertical information structure of the firm. American Economic Review 76, 917—983.

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