profit, productivity, and profit-sharing

Profit, Productivity, Profit-Sharing

and

Chun-Hao Chang and David J. Bjornstad

ABSTRACT

This study is an investigation of the effect of profit-sharing on labor productivity. When monitoring labor performance is costly for management, a regular wage/salary contract is insufficient to induce profit-maximizing behavior from the worker. The authors demonstrate that when this profit-maximizing behavior can be induced only through profit-sharing, a linear profit-sharing program will increase productivity and the welfare of both management and labor. The benefit from profit-sharing is increasing up to the point where the utility of additional income is offset by the negative utility of extraordinary effort (working harder or providing higher quality work). The income effect, i.e., the change in negative utility of extraordinary effort given a change in income, can potentially either increase or decrease the point at which the income-effort tradeoff reaches zero.

Introduction

Profit-sharing is not a new topic in economics, but it has recently attracted new attention as firms seek innovative ways to increase labor productivity. Although fixed wage/salary rules continue to dominate compensation negotiations and many firms retain traditional profit-sharing arrangements linked to savings or retirement plans, integrating profit-sharing with base salary concepts is increasingly looked upon as an option to allow workers to capture a portion of productivity gains (Business Week 1983). The purpose of this paper is to investigate the effect of introducing an explicit profit-sharing rule into a wage/salary labor contract. Will profit-sharing increase productivity? What factors will affect employers' decisions on profit-sharing rules.'?

Early analyses of profit-sharing were more concerned with equity than efficiency and were viewed as a means for distributing extraordinary profits among workers

Chun-Hao Chang is Assistant Professor of Fintmce, Florida International University, Miami, FL 33199. David J. Bjornstad is Group Leader of Energy and Economic Analysis, Energy l~'vision, Oak Ridge National Laboratory, Oak Ridge, TN.

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(Samuelson 1977). It was also suggested that under highly restricted circumstances profit-sharing could increase worker productivity through monetary incentives. Alchian and Demsetz (1972) argue that a specific reward system could be used to stimulate a specific productivity response. On the other hand, if output is produced by a team, individual cooperating inputs often do not yield identifiable marginal products. This non-measurability of individual productivity in team production results in a "free rider problem" which renders the incentive unworkable (Alchian and Demsetz 1972). For example, Holmstrom (1982) shows that in a partnership firm the efficient Nash equilibria can not be reached with differentiable sharing rules due to free rider problems. This sort of observation has led to the conclusion that profit- sharing improves productivity only in very small partnerships (Samuelson 1977), and has led to much of the profession's considering any form of group incentives redistributive rather than motivational (Alchian 1984). More recently, Weiztman (1985) has reopened the discussion by describing the macroeconomic effects of the greater flexibility and lower marginal costs and hence employers' profit- maximization behavior as a result of employers compensating employees through profit-sharing.

The free rider argument tends to neglect the incentives which groups may impose on their members, which take the form of externalities among workers to cooperate in the pursuit of group goals. A theory of cooperation and group incentives is developed in FitzRoy and Hiller (1978), FitzRoy and Mueller (1984), and is further discussed in FitzRoy and Kraft (1986, 1987). In team production situations where individual performance is difficult to measure and reward, team members usually have better information about each other's effort than supervisors who are outside of the team. Under such circumstances, group incentives could lead to the development of mechanisms to utilize this information to provide horizontal monitoring or peer-group pressure against shirking and encourage cooperation. Under these conditions, profit-sharing and other group incentives would suffice to increase production efficiency.

This reasoning is supported by a number of empirical studies. Cable and FitzRoy (1980) find firms most committed to profit-sharing and worker participation are more efficient and profitable than other firms in a sample of West Germany firms. Jones and Svejnar (1985) find that for manufacturing and construction sectors of Italian producer cooperatives, profit-sharing always affects productivity positively. In a similar study Defourney, Estrin and Jones (1985), who employ firm-level data for French cooperatives, conclude that value added consistently increased with profit- sharing, with collective membership, and with capital stakes. FitzRoy and Kraft (1986 and 1987) find that both profit-sharing and worker's capital ownership have strong effects on productivity and profitability in a sample of medium-sized metalworking capitalist firms in West Germany.

The authors adopt the proposition that profit-sharing enhances production efficiency through some form of horizontal monitoring or peer pressure. A case where a linear profit-sharing program is introduced into an existing wage labor contract is considered. Profit-sharing is demonstrated to be a necessary component of profit maximization when the worker's profit-maximizing behavior can be induced

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Profit, Productivit T, and Profit-Sharing,

only through profit-sharing. In addition, in the simple case in which the impact on profit-sharing from income effects (the change in disutility of labor given a change in income) is ignored, profit-sharing results in an unambiguous increase in marginal production efficiency. However, changes in the profit-sharing rule have different effects on productivity depending upon the existing profit-sharing rule as well as on the profitability of the firm. These effects are examined with and without the complicating income effects.

A Simple Model of Profit-Sharing

For simplicity, labor is assumed to be the only input in the production process. The labor supplied by a typical worker has two characteristics: an observable effort and an unobservable extraordinary effort, denoted by L and x, respectively. The observable effort L is the effort that can be monitored by the owner/manager without cost. An example of L is the eight-hour-a-day working shown on the punch card. The extraordinary effort x can be interpreted as the "productive cooperation" defined by FitzRoy and Kraft (1986) or extraordinary endeavors performed by an employee. This includes, for example, working harder by taking a short lunch break, making fewer personal phone calls, and skipping coffee breaks; providing higher quality work such as double checking the work performed; and so on. Management cannot generally monitor these efforts or at minimum incurs very high costs in doing so. Assuming homogeneous labor, the per-worker production function is written as

q = q ( L , x ) .

The production function is defined over the non-negative ranges of L and x, i.e., L > 0 and x > 0 . It is also assumed that q(0,0)=0, and q(L,0) > 0 for L > 0 ; that is, one can produce without extraordinary effort x. However, extraordinary effort may help enhance the total productivity. The marginal productivity of L and x are both positive and decreasing (qL>0, oh>0, and qta.<0, q~<0) . Without loss of generality it is assumed that q ~ < 0 , that is, L and x are substitutive input factors in the production process. The labor contract is based on the observable effort L only. The labor market is assumed to be perfectly competitive and w is defined as the market real wage rate for observable effort L. Then a worker's income y is

y = w L + l ,

where I is the worker's exogenous non-wage income. All workers are assumed to have the same utility function:

U(y,L,x) , (1)

which is defined over the non-negative values of y, L, and x with Uy > O, Ut. < O, and U x < O. The first inequality indicates that workers always prefer more income to less. The last two inequalities imply that workers are effort averse since working gives rise to negative utility (disutility hereafter). Marginal utility of income and marginal disutilities of effort are assumed to be decreasing (Up < O, Uu. < O, and U,~, < 0).

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Given the market real wage rate w, a representative worker's problem is to choose the optimal L and x to maximize his/her utility. Formally,

Max U ( w L + I , L , x ) {L,x}

s.t . L ~ O

x ~ O .

(2)

Solving the maximization program in Equation (2), produces the following result:

Proposition 1: If workers are compensated only through regular wages, then they will supply the optimal observable effort, L ~ so as to make their marginal rates of substitution between L and income equal to the real wage rate w:

w-- _ u , (3) v,

Also, workers will choose not to provide any extraordinary effort. [For proofs of all Propositions see Appendix]

When a regular wage compensation scheme is used, the labor compensation can not be contingent on the unobservable extraordinary effort. Since extraordinary effort reduces utility, the worker will not contribute any. The worker's optimal labor supply decision is to furnish only the observable effort according to Equation (3): provide observable effort L until the subjective value of the effort (marginal rate of substitution of L and y) equals the market real wage rate.

The question now is how can the owner use suitable incentives to induce higher productivity from workers. Here one may introduce a profit-sharing program. Let the profit, x, per person be

it = q - w L - k ,

where k is fixed costs, and normalize the price of the product to be one 2. Assume linear profit-sharing, i.e., workers are given a fractional share, ~; and the owner retains the remaining fraction, 1-c~, of profits. With the linear sharing rule, each worker's income is now given by

y = a~ + w L + l (4)

-- (1 - a)wL + ~(q - k ) + I.

Now, the worker's problem is choosing the optimal amount of both observable and extraordinary efforts to maximize utility in Equation (1), subject to the income constraint in Equation (4) and non-negativity constraints. The maximization problem of the worker is now:

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Profit, Productivity, and Profit-Sharin~

Max U([(1-a)wL + a(q-k) + l],L,x) { t,x }

s . t . L ~ O (5) x ~ O

Solving the maximization problem in Equation (5) yields:

Proposition 2: The introduction of a linear profit-sharing scheme in workers' regular wage compensation may induce workers to contribute extraordinary efforts. The worker will furnish optimal extraordinary efforts, x*, and the optimal observable effort, L ~, based on the following condition:

(I - tow + qL _ l'It (6)

~qx Ux"

L" is less than the corresponding optimal observable effort when there is no profit-sharing, i.e., L ~

When the linear profit-sharing scheme comprises part of the worker's compensation, the worker's income is directly associated with the total productivity of the firm through the term q in Equation (4). Thus, the worker is entitled to a share of the productivity increase, if any. This provides the worker an incentive to work harder--furnishing extraordinary efforts. The worker optimally chooses L* and x* so that the objective tradeoff in marginal productivities of observable effort and extraordinary effort equals the subjective tradeoff between the two efforts, as described in Equation (6).

In Proposition 2, the workers are allowed to choose L and x freely. Since the two efforts are substitutes and both give disutility to workers, when workers choose a positive x* in equilibrium they would also choose a lower level of L to reduce some disutility. Therefore, L* is expected to be less than L ~ Consequently, the net effect of profit-sharing on total productivity is ambiguous. To focus attention on how the profit-sharing scheme will affect the total productivity of the firm, hereafter it is assumed that the level of observable effort is fixed at L ~ in a long-term labor contract. Under this contracting arrangement, a profit-sharing program can be treated as a supplement to the labor contract. The following results are obtained.

Proposit ion 3: (a) In a long-term labor contract that sets the level of observable effort at L ~ the linear profit-sharing scheme will induce workers to furnish extraordinary efforts and thus enhance the worker's total productivity. The optimal extraordinary effort, x ~ is determined by

aqx U , + U x = O. (7)

(b) Assuming that the marginal disutility of labor is not affected by the worker's income level ( UyL=Uyx=O or no income effect on labor), then the higher (lower) the observable effort L ~ specified in the long-term

I07


contract, the less (more) extraordinary efforts will be induced in equilibrium.

The long-term labor contract specifies the observable efforts at the optimal level L ~ obtained in Proposition 1. Thus, the worker's wage income is fixed at wL ~ Profit-sharing gives workers an additional source of income: by working extraordinarily, the total productivity of the firm will increase and a share of the additional profit will go to workers as bonus through profit-sharing. This provides an incentive for workers to contribute extraordinary efforts. The extent of extraordinary effort furnished depends on the balance of the marginal utility from profit-sharing bonus and the marginal disutility from working extraordinarily. In Equation (7), c~ch is the portion of the real value of the marginal product of x received by workers. Thus, oeChUy is their marginal value of real income from profit- sharing in utility units, while 13, is the workers' marginal disutility from extraordinary effort 3 . Therefore, the worker will furnish extraordinary effort until the marginal utility from profit-sharing equals the marginal disutility from working extraordinarily.

The negative 4 relationship between x ~ and L ~ observed in Proposition 3(b) is explained by the fact that the two efforts are substitutes in the production process (q,a <0). Other things being equal, if the level of observable effort is reduced in the long-term contract, the worker's wage compensation is diminished accordingly. Hence, the worker has an incentive to provide more extraordinary effort in order to obtain more bonus through the profit-sharing program. This tradeoff between extraordinary and observable efforts depends on the magnitudes of q~. If ChL is zero (the two efforts are independent input factors), then the tradeoff ratio between the two efforts is expected to be low. If the two efforts are close substitutes in production (q~ is large in absolute value), then the tradeoff between the two efforts is significant.

The next question of interest is how profit-sharing will affect the productivity of the firm through inducing extraordinary efforts.

Proposition 4: (a) If the disutility of extraordinary effort is independent of the level of income (U~=0, or no income effect), then the initial introduction of profit-sharing always increases productivity. Productivity increases with the profit-sharing share ~ until the worker's share of profit becomes large enough: c~r= -Uy/Ur/, and declines with c~ beyond that.

(b) If U~ follows the pattern that it is positive when income is low, decreases with income, and becomes negative eventually; then if the worker's income is low, a higher (lower) linear profit-sharing would increase (decrease) productivity. The worker's productivity would be reduced (increased) by a higher (lower) linear sharing rule if his/her income is high.

Introduction of a profit-sharing scheme provides workers with extra monetary compensation, which gives rise to an incentive for workers to perform extraordinarily. But, note that the worker's marginal utility of income is diminishing

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Profit, Productivity, and Profit-Sharin~g

(Ur:<0) and thus the extraordinary effort has an adverse effect on his/her utility; giving a larger portion of profits may not provide further incentive to increase productivity. Supplying extraordinary effort has two effects on a worker's utility: first, an adverse effect from a higher level of x; second, a favorable effect from a higher profit-sharing income, which results from the worker's additional effort. As long as the adverse effect does not dominate the favorable effect, the worker can be motivated to work harder by being raised the fractional share oc Hence, if workers are given a sufficiently large income increment (a higher fractional share ot or a large profit a" or both); a more aggressive profit-sharing scheme may not further improve productivity. On the other hand, if workers initially benefit only slightly through profit-sharing arrangements (due to a low ot or a small I" or both), then they could easily be stimulated by a higher fractional share of the profits. This suggests the following: a firm with a huge profit margin needs a smaller fractional share et to motivate its workers to work harder than a firm with a smaller profit margin. This conclusion is drawn from the linear sharing framework. Non-linear sharing and uncertainty may lead to different results.

In the above analysis the marginal utility of income is assumed invariant with respect to the change in income (no income effect, or U~=0) . U~ is the variation in the marginal utility of extraordinary effort due to the change in income. U~ > 0 implies that as the worker's income increases he/she feels less uncomfortable with supplying extraordinary effort. Hence, other things being equal, the worker is willing to work harder in terms of providing extra work (which is not observable by the owner) when he/she becomes wealthier. This case may occur for upwardly mobile workers from either poor or comfortable backgrounds. In each case, consumption complementarities in the worker's utility function lead them to obtain increasing satisfaction from additional purchasing power, relative to additional effort. Conversely, U~ < 0 implies that, other things being equal, the worker is willing to work less when he/she is getting a higher monetary compensation. This may be the case where the worker is in a more stable consumption regime, as might occur when some consumption threshold is reached, and supplying less effort is more attractive than additional income. I fU~ satisfies the pattern described in Proposition 4(b), then a low-income worker is easier to be motivated by profit-sharing than a high-income worker. To the extreme, when a worker's income is high enough, one may see the increase in profit-sharing having adverse effect on productivity.

Finally, in the linear profit-sharing framework, the owner's problem is choosing a profit-sharing share ot to maximize profits; that is,

M a x { a }

= (1 - a X q - w L ~ (S)

s.t. a > 0

(1 - ~ ) >0

The next result is a summary of the optimal linear profit-sharing strategy for the o w n e r :

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Proposition 5: Under the framework of a long-term labor contract with linear profit-sharing, there exists an optimal level of the profit-sharing share, a ~ to maximize the owner's profit. The value of c~ ~ depends on the value of Ox~ If 0x~ is negative or positive but small, then s ~ otherwise, ot ~ > 0.

Proposition 5 allows the owner to obtain the optimal sharing rule ot ~ under the long-term labor contracting. Given the worker's behavior characterized by Propositions 3 and 4, the owner may adopt a linear profit-sharing scheme to motivate workers to work extraordinarily and thus increase the productivity and profit of the firm. The optimal linear profit-sharing scheme is critically dependent upon the relationship between the profit-sharing parameter ot and the equilibrium extraordinary effort x ~ If profit-sharing does not, or does but negligibly, induce workers to work harder, then it would not be worthwhile for the owner to implement profit-sharing. Otherwise, profit-sharing may be a device to induce workers to work harder, thus increasing the owner's profit.

Concluding Remarks

The findings of this paper can be summarized as follows: First, when monitoring extraordinary efforts is costly or impossible for management but can be achieved by peer pressure, a regular wage/salary labor contract is insufficient to induce extraordinary efforts. Workers will instead supply effort levels which are not optimal on the part of both labor and management. Second, the introduction of a linear profit-sharing program into a simple wage/salary labor contract will increase productivity and profit and so benefit both management and labor. Third, in the simple linear profit-sharing setup, an increase (decrease) in profit-sharing will increase (decrease) productivity, up to the point where the utility of additional income is offset by the disutility of extraordinary effort. Finally, the income effect, i.e., the change in the disutility of extra effort given a change in income, can potentially either increase or decrease the point at which the income-effort tradeoff reaches zero.

Due to the complexity of the derivation, several assumptions were made to simplify the analysis. Relaxation of these assumptions may be interesting areas of future research. First, the utility interdependence through cooperation among workers was ignored. A game theoretical model is necessary to capture this interdependence 5. Second, both management and worker were assumed to face no uncertainty of output. Introducing uncertainty will make L unidentifiable. Optimal risk-sharing has been studied extensively in the principal-agent theory literature 6, but no effort has yet combined profit-sharing in the principal-agent model. Third, a linear profit-sharing rule is assumed in Section 2. It is not clear that all the results can be extended with nonlinear sharing rules. It is desirable to investigate this in practice. Fourth, a more realistic alternative is to study profit-sharing in a world of uncertainty with risk-averse employees. Finally, the analysis can be viewed as a short-run one since both wages and observable effort are assumed fixed. In a

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Profit, Productivirg, and Profit-Sharin$

dynamic model, management would not need to monitor extraordinary efforts because they would be able to monitor more general output per worker measures. However, in the absence of some monitoring device, rolling the payment for extraordinary effort into the wage rate could provide incentives to return to the previous condition. Hence, profit-sharing of this type may offer both short and long term advantages.

APPENDIX

A. Proof of Proposition 1: Assuming that the second order sufficient conditions are satisfied, the first order Kuhn-

Tucker conditions for the maximization program in Equation (2) are

= w~],. u, ~ 0, L'---~aL = 0 (A1)

= u, :; 0, x.~ = 0 ( A 2 )

where .~ is the Lagrange function of the maximization program. Note that U z is strictly negative by assumption; hence the second part of Equation (A2) implies that the optimal x, x ~ equals zero. The optimal L, L ~ is determined by Equation (A1) alone. Usually one expects L ~ to be positive and thus a~/aL equals zero. Rewriting this term yields the following equilibrium condition:

UL Q.E.D. u,

B. Proof of Proposition 2: Assume that the second order sufficient conditions are satisfied, the first-order Kuhn-Tucker

conditions for Equation (5) are:

~= [ ~ l - = ) § § u~ ~ o, L.---- ~ =o (,~) aL

---~ = a q = U , �9 r], ~ 0, x . - - ~ = 0 ( A 4 ) ax ax

Note that the equality a~/ax=O may be established in Equation (A4). This implies that x" may be strictly positive in equilibrium. L" and x" are determined by solving Equations (A3) and (A4) simultaneously. The first-order conditions in Equation (A3) and (A4) can be rewritten respectively as

UL (A5) (1 - = ) w § qL = - - - v,

U= (A6) a q x = --~.

Combining Equations (A5) and (A6), the equilibrium condition is

(1 -~,)w § q z u L = q , v="

Note that the equilibrium condition in Equation (AS) differs from the equilibrium condition in Equation (3), it is obvious that L" is different from L ~ Since L and x are substitutes in

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production, the increase in one usually leads to a decrease of the other. Therefore, one expects L" to be less than L ~ in general. Q.E.D.

C. Proof o f Proposition 3: Given the long-term contract and the linear profit-sharing scheme, the worker's problem

in Equation (5) now becomes

Max Ui[(1-a)wLo*tt(q-k)*/],LO, x} (x}

$.t. x ~0 Assuming interior solution and the second-order sufficient condition are satisfied, the first order condition of the above problem is

=tq~U, * v, - o. (A7)

Solving the first-order condition obtains the optimal level of x, x ~ In general, x ~ is strictly positive and thus the total productivity is strictly increased. The second-order sufficient condition is

a22 - =2q==u,,. ,q=u~, . =u,e= �9 u=<0. (A8) ax z

To examine bow the change in L ~ on the equilibrium level of x ~ the first-order condition at x ~ is totally differentiated and terms are rearranged. This yields

a:._~ = _ , , q ~ u , . =q ,u , [ (1 - = ~ § = q j § =~=u,~ § u . ,

aL ~ " q = + U =

By assumption UyL=Uyx=O, the above equation reduces to

~__oo = _ , ,q. ,U, + =q.U.[(l - cow * aqj aL o =q= § U=

It is evident that ax~176 since q ~ < 0 , q=<0 , U,.,<0 and Uyy <0. Q.E.D.

D. Proof o f Proposition 4: (a) To obtain ax~ Equation (6) is partially differentiated with respect to c~, obtaining

ax o = _ u , q , , =lcq, Vy~ + g v . . ( A g )

aa a2 q2z uyy 4. =q=l.] . + = Uyq= 4. I.]=

Note that the denominator in Equation (Ag) is negative by the second-order condition in Equation (A8). Hence the sign of axo/o~ is determined by sign of the numerator. Assuming that U~y=0, Equation (A9) is reduced to

a~-~ e = qz(u , * " g u , , ) (AIO) a= =~q~rJ,, § = U , q = . u =

From Equation (A10), the sign of Ox~ is determined by the term (Uy+~rUry). I f there is no profit-sharing initially, i.e., ~ =0, then it is doubtless that (ax0/a~)> 0. Furthermore, the effect of profit-sharing on the total productivity is also positive:

= ~ . ~ § .a:__*, o. a= aL a= ax o a=

If a > 0 , then the sign of ax0/a~ is determined by the relative values of the positive term Uy and negative term (o~xUyy). It is evident that if otx < -Uy/Ury, then (ax~ if o~r> - uy/.u.yy then (ax~

Co) If u ~ 0 , then the sign of ax*/aot is determined by the sign of the numerator in Equation (A9). If U ~ > 0 , axO/a~ is more likely to be positive than the case where U~y=0.

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Profit, Productivit),, and Pro~t-Sharin~

On the other hand, U~ < 0 will give rise to the conclusion that 0x~ is even more negative. The results are consistent with those derived under the assumption that U~=0 . Q.E.D.

E. Proof of Proposition 5: The first-order Kuhn-Tucker conditions for Equation (8) are

are - x § - " ~ ' - ~ a § - v - 0 ,

�9 , 20, a13 *0,

( A l l )

(A12)

(A13) (1 - a) ~ 0, ~,(1 - a) ~ 0 ,

where/3 and 3' are Lagrange multipliers for respective constraints. Note that the optimal ,v ~ critically depends on the sign and value of 0x~ If 0x~ is negative, then equality (A1 I) holds only if B is positive. This implies that the first constraint is binding and thus ~ = 0 . We can obtain the same result when 0x~ is positive and small, i.e., 0x~ < 7r/~. If ax~ is positive and sufficiently large, that is, #x~ > ~r/ech, where e is an arbitrarily small real number, then there must be/3=0 and 3" > 0 in (A11). This suggests that the first constraint is binding and thus ,v ~ 1. If 0x~ is positive and takes the value between the above two eases, one may expect ,v ~ to be between 0 and 1. Q.E.D.

NOTES

tNo separate compensation for over-time working is assumed.

:This is consistent with the definition that w is the real wage rate of L.

3An alternative interpretation is to rewrite the first-order condition in Equation (7) as ~ = - U,/Uy. This equality can be read as the real marginal gain from profit-sharing equals the marginal rate o f substitution between extraordinary efforts and income, or the subjective value of extraordinary efforts.

*This relationship may be positive only if the two efforts are close complementary factors, i.e., q , a>0 and large in value. In this case the increase in one factor vastly enhances the productivity of the other, which implies that the two efforts have to be combined in the production. Therefore, the increase in the observable effort will lead to the increase in the extraordinary effort.

SSee FitzRoy and Kraft (1986) for a simple non-cooperative game analysis.

6See MacDonald (1984) for a survey of the literature.

REFERENCES

Alchian, Armen A. "Specificity, Specialization, and Coalitions." Zeitschriflfur die gesamte Staatswissenschafl (Zgs) 140 (1984): 34-39.

Aichian, Alanen A., and Harold Demsetz. "Production, Information Costs, and Economics Organization." American Economics Review 62 (1972): 77-95.

Cable, J o h n , a n d Felix R. FitzRoy. "Productivity Efficiency Incentives and Employee Participation." Kyklos 33 (1980): 100-121.

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Defourney, Jacques, Saul Estrin, and Derek Jones. "The Effect of Workers' Participation on Enterprise Performance." International Journal of Industrial Organization 3 (1985): 197-217.

FitzRoy, Felix R., and John Hiller. "Efficiency and Motivation in Productive Organization." Berlin: International Institute of Management, Discussion Paper 78-15, 1978.

FitzRoy, Felix R., and John Hiller. "Cooperation, Productivity, and Profit Sharing." Quarterly Journal of Economics 102 (1987): 23-35.

FitzRoy, Felix R., and Kornelius Kraft. "Profitability and Profit-Sharing." Journal of Industrial Economics 35 (1986): 113-130.

FitzRoy, Felix R., and Dennis Mueller. "Cooperation and Conflict in Contractual Organization." Quarterly Review of Economics and Business 24, no. 4 (Winter 1984): 23-49.

Holmstrom, Bengt. "Moral Hazard in Teams." Bell Journal of Economics 13 (Autumn 1982): 324-340.

Jones, Derek, and Jan Svejnar. "Participation, Profit-Sharing, Worker Ownership and Efficiency in Italian Producer Co-operatives." Economica 52 (1985): 449-467.

MacDonald, Glenn M. "New Directions in the Economic Theory of Agency." Canadian Journal of Economics 17, no. 3 (1984): 415-440.

Samuelson, Paul A. "Thoughts on Profit-Sharing." Zeitschrift fur die gesamte Staatswissenschafl (Zgs) (1977, Special Issue on Profit-Sharing): 9-18.

Weizanan, Martin L. "The Simple Macroeeonomics of Profit Sharing." American Economic Review (December 1985): 937-953.

"Why Labor and Management Are Both Buying Profit Sharing." Business Week, 10 January 1983, 59.

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