Double Moral Hazard, Monitoring, and the Nature of Contracts

Double Moral Hazard, Monitoring,and the Nature of Contracts

Pradeep Agrawal

Received September 19, 2000; revised version received October 30, 1997

We consider the choice of contract between an entrepreneur and a worker: in asituation where the worker cannot readily observe the outcome (such as profit oroutput) of their joint endeavor, while the entrepreneur cannot easily observe theeffort supplied by the worker. We analyze this problem using a generalizeddouble-sided moral-hazard model, with risk-averse parties who mutually monitoreach other (to get a reasonable idea of outcome/effort). The model considerstrade-off between monitoring costs and moral hazard costs, which are endoge-nously determined by the extent of monitoring.

Using this model, we formally prove a generalized version of Coase’s con-jecture – that the optimal contract minimizes the agency and risk costs. We thenshow how varying assumptions about the feasibility or cost of monitoring of theoutcome or the worker’s effort lead to different contracts being optimal. Theanalysis is then used to explain the nature of contracts observed in practice undermany different situations. We will give an explanation as to why industrialworkers typically work under wage contracts, while share contracts are commonin agriculture and will explain why profit sharing is more common for seniormanagers than for the production workers.

Keywords: contracts, double moral hazard, incentives, monitoring, transactioncosts, risk-premium.

JEL classification: D23, D82, L14, L20.

1 Introduction

This paper attempts to provide insights into the choice of two-party

contracts commonly observed in industry and agriculture. For example,

industrial workers typically work under wage contracts; but share con-

tracts, in which the worker’s compensation for his work depends to some

extent on the output he produces, are common in agriculture (see, for

Vol. 75 (2002), No. 1, pp. 33–61

example Cheung, 1969a; Stiglitz, 1974; Eswaran and Kotwal, 1985;

Otsuka et al., 1992). A fixed fee, possibly along with a royalty payment

proportional to the revenue or profits, is common in franchise arrange-

ments (see, for example Mathewson and Winter, 1985; Lafontaine, 1993;

Bhattacharyya and Lafontaine, 1995). Furthermore, some form of share

contract (e.g., part remuneration in the form of company shares) is much

more common for senior managers than for production workers and more

common for firms with publicly traded shares than for others. Thus a

central question, and one which will be the focus of this paper, is to

explain why particular types of contracts (wage, share or fixed rent) are

used in certain situations but not in others.

Previously, two-party contracts have been extensively analyzed using,

(i) the principal-agent framework in which (only) the agent is subject to

moral hazard (see Stiglitz, 1974; Shavell, 1979; Holmstrom, 1979; Harris

and Raviv, 1979) and, (ii) the ‘‘standard’’ double-sided moral hazard

framework in which both parties (usually assumed to be risk-neutral) may

shirk in providing their effort which cannot be observed by the other party

due to various uncertainties involved (see, for example Cooper and Ross,

1985; Eswaran and Kotwal, 1985; Lal, 1990; Romano, 1994, and Bhat-

tacharyya and Lafontaine, 1995). While these frameworks have proved

very fruitful and have been used extensively for analyzing optimal two-

party contracts, their conclusion that only share contracts can be optimal

(with a few exceptions, such as Eswaran and Kotwal, 1985) is not con-

sistent with the nature of contracts observed in practice, as mentioned

above.

Since the choice of optimal contract could affect the way the firm is

organized, this paper can also be related to the literature on the ‘‘nature of

the firm’’, which tries to explain why firms are organized the way they

are. Coase (1937, 1960) argued that the firm exists when the transaction

cost of organizing production via the firm are lower than organizing it via

the market1 and that the optimal structure of the ownership of the firm

minimizes these transaction costs. These ideas were further developed by

Williamson (1975), and Klein, Crawford and Alchian (1978) who argued

that the firm matters when parties must make specific investments and the

1 Cheung (1983) extended this argument further, arguing that the firm does notnecessarily replace themarket with a non-market institution. In some cases, it mightreplace themarket for intermediate goodswith themarket for labor hired to producethe intermediate goods. Then the firm emerges if the transaction costs are higher intrading intermediate goods than in trading the labor hired to produce it.

34 P. Agrawal

quasi rents from these investments cannot be divided in advance due to

the unfeasibility of writing long term contracts about the subsequent

actions of the parties. They suggested that vertical integration was a way

of reducing the opportunistic behavior. Grossman and Hart (1986) and

Hart and Moore (1990) built on this work to show that change in own-

ership brings benefits as well as costs. Thus, they established that the

ownership makes a difference and thereby developed a theory of optimal

ownership structure in the context of the asset specificity argument. Yang

and Ng (1995) did the same in the context of indirect pricing of intangible

intellectual property rights.

In this paper we focus on the optimal contractual structure for a given

ownership structure. Thus, we consider two parties, one of whom (the

‘‘entrepreneur’’) owns an asset such as land (agricultural landlord), ma-

chinery (firm), production technique or brand name recognition (fran-

chiser). In addition to the asset (which is easily observable to both

parties), production also requires labor effort from the worker (which is

not readily observed by the entrepreneur). On the other hand, the outcome

is easily observed by the entrepreneur but not by the worker (and could be

under-reported by the entrepreneur when the worker’s reward depends on

it). Thus, both parties are subject to moral hazard. While the case of the

entrepreneur being subject to moral hazard due to supplying unobservable

effort has been considered in the literature, we believe that our specifi-

cation is new in the literature and more realistic since entrepreneurs often

do not supply effort (except supervisory). Furthermore, we assume that

both parties mutually monitor each other to restrict moral hazard by the

other, with the extent of moral hazard determined endogenously by the

level of monitoring by the other party2, and that both agents are risk

averse in general.3

2 Cheung (1983), Barzel (1987), and Milgrom and Robert (1994) also considersome aspects of such tradeoffs.3 Our framework differs from that of Grossman and Hart, Hart and Moore

(GHM) and Yang and Ng (YN) in that (i) we consider an endogenous level ofmonitoring and allow for the tradeoff between monitoring and the extent of moralhazard, which is treated as exogenously fixed by the GHM and YN models; (ii)the structure of ownership is richer in GHM and YN models which allows themto analyze the optimal ownership structure while this paper focuses on analyzingoptimal contract structure for a given ownership structure; and (iii) in GHM andYN models both parties are assumed risk neutral while we consider the moregeneral case where both parties are risk adverse.

Double Moral Hazard, Monitoring, and the Nature of Contracts 35

Using this generalized double moral-hazard model, we formally

prove (for the case of two party contracts) a generalized version of

Coase’s hypothesis, namely that the optimal contract minimizes the

sum of the risk and agency costs of both the parties, the latter in-

cluding the monitoring, expected penalty and residual shirking costs.

Thus, when risk costs are small, the optimal contract would minimize

the agency (or transaction) costs. However, more generally, both risk

and agency costs should be considered as also emphasized by several

other authors (see, for example Cheung, 1969b; Stiglitz, 1974; Barzel,

1987).4 We also consider how the optimal contract varies with the

ability to monitor the effort or outcome levels and obtain some inter-

esting results, such as: (i) when mutual monitoring is allowed, not only

share contracts, but also the fixed wage and fixed rent contracts may be

optimal, and (ii) when the outcome cannot be observed by one of the

parties, the optimal contract will involve a fixed payment to that party.

These results help resolve the anomaly mentioned earlier. They also

allow us to provide explanations for several features of the contracts

observed in practice that were mentioned in the opening paragraph of

the paper.

The paper is organized as follows. In Sect. 2, we develop the

generalized double-sided moral-hazard model. In Sect. 3, we analyze

the model and prove the basic proposition that the optimal contract

minimizes the sum of agency and risk costs of both the parties. In Sect.

4, we consider how the optimal contract varies with the ability to

monitor and use these results to explain the nature of contracts ob-

served in practice. Section 5 summarizes the main conclusions of the

paper.

2 The Model

We develop a ‘‘generalized double-sided moral-hazard framework’’,

which analyzes a general linear5 contract for sharing an uncertain out-

4 Especially, the work of Barzel (1987) is quite close to the spirit of the presentpaper and addresses some of the same issues less formally.

5 Previously, Bhattacharyya and Lafontaine (1995), and Romano (1994) haveestablished that any optimal sharing rule can be represented by a linear contractin the context of the standard double-sided moral-hazard model with risk neu-tral parties. Their proof does not seem to be extendable to the case when the

36 P. Agrawal

come (such as profit, revenue or output) between two parties. For ease

of exposition, we refer to the two parties as entrepreneur and worker.

However, the analysis is much more general and can be applied to a

variety of other situations involving two parties including a franchiser

and franchisee and an agricultural landlord and tiller/tenant. The detailed

assumptions of the model are as follows:

A.1) The Outcome Function: Our analysis will be over one period. Both

parties are assumed to have access to identical production technology.6

The production process uses the asset (such as land, machinery or brand

name recognition) owned by the entrepreneur and the labor effort of the

worker (L) to produce a risky outcome (such as profit, revenue or output),

Q. The asset is assumed fixed and easily observable by both parties. Thus,

there is no moral-hazard problem regarding its use and, for simplicity, we

suppress it from the production function. However, the labor effort of the

worker is subject to moral hazard due to the entrepreneur’s inability to

observe it directly or infer it from a knowledge of the outcome because

of various uncertainties of the production process. Thus, the outcome

function can be written as:

Q ¼ HF ðLÞ ; ð1Þ

where F is the production function which is linearly homogeneous, in-

creasing and concave in its arguments and H is a multiplicative risk factor

with an expected value of 1:

EH ¼ 1 : ð1:1Þ

contracting parties are risk averse, as assumed here (other nonstandard features ofour model, such as monitoring and the penalty for being detected shirking, do notpose any problem). Thus one has the trade-off between assuming risk averseparties and sticking to linear contracts or assuming risk neutrality and knowingthat the results obtained are actually applicable to nonlinear sharing rules as well.We have chosen the former option because we believe that risk aversion of theparties is important in many situations and that this aspect has not been analyzedadequately in the literature. When risk aversion is not important, the resultsobtained in this paper (with all income and marginal risk premia set to zero)are valid for nonlinear sharing rules as well.6 The model can be generalized to the case of different efficiency levels for the

two parties. This results in a term which generally favors the more efficient partyas the manager.


The risk factor H captures various uncertainties relating to production,

prices of various inputs and outputs etc. We assume that the distribution

of H is known to both parties but exact value for the period is unknown to

either party.

Furthermore, the worker cannot observe the outcome directly and this

gives rise to the possibility of moral hazard by the entrepreneur, who

could easily under-report the actual outcome to the worker (when his

reward depends on it). Thus, the outcome reported by the entrepreneur to

the worker, QQ can be written as:

QQ ¼ HeF ðLÞ ; ð2Þ

where e is the extent of under-reporting and lies in the interval [0,1].

Thus, due to the uncertainty about the outcome, there is scope for moral

hazard by both the worker as well as the entrepreneur.

A.2) Utility Functions of the Worker and the Entrepreneur: The

worker maximizes the expected utility, EU, of his income Y. The worker

has a fixed supply of total labor effort per period which is normalized to 1

and a market determined opportunity cost of w per unit of labor from

working in the casual (or short-term) labor market where he can sell as

much labor as he wants. Thus the worker has a market determined

reservation utility level, U , given by:

U ¼ UðwÞ : ð3Þ

Similar assumptions are made for the entrepreneur – he maximizes the

expected utility, EV, of his income Z, and has a market determined op-

portunity cost of we per unit of labor effort. U and V are assumed to be

increasing functions of the income of the respective party for all finite

levels of incomes, concave and twice differentiable in their respective

arguments. Note that the concavity assumption implies that both parties

are risk averse (except in the case of linear utility functions).

A.3) Mutual Monitoring by the Worker and the Entrepreneur: As

noted earlier, both parties are subject to moral hazard. However, by

monitoring each other, they can control the moral-hazard problem. If

increased moral hazard by a party then results in a higher probability of

38 P. Agrawal

having to incur a penalty, both parties can be dissuaded from shirking. We

will assume that the penalty levels (denoted Pw and Pe for the worker and

the entrepreneur respectively) are fixed exogenously by social norms – for

example, the penalty can be thought of as (the present value of ) the loss

of future income of the party found shirking due to loss of reputation as a

sincere partner in one or more succeeding periods. Note that the penalty

on one party does not accrue to the other party. This is similar to the

concept of dichotomous returns in Harris and Raviv (1979).

We assume that each party randomly inspects the effort of the other.

The probability of detection of shirking by the worker, /w, will be a

function of the monitoring time expended by the entrepreneur, s (which isassumed to be observable to the worker) and the amount of shirking by

the worker, DL ¼ LL� L, where L is the actual level of effort supplied by

the worker and LL is the bench-mark or critical level stipulated by the

entrepreneur – we will assume that this is the first best level7 of his effort

(what the worker will supply if labor could be observed perfectly and

costlessly – see (16) below). That is,

/w ¼ /wðLL� L; sÞ : ð4Þ

If s ¼ 0 or if there is no cheating ðLL� L ¼ 0Þ, /w ¼ uw1 ¼ uw

2 ¼ 0

(where the subscripts 1 and 2 on /wðLL� L; sÞ denote its first partial

derivative with respect to its first and second arguments, respectively); /w

is assumed to be increasing and concave in its arguments.

Identical assumptions are made for the monitoring of the entrepreneur

by the worker with the associated probability, /e, of detection of under-

reporting being:

/e ¼ /eðee � e; T Þ ; ð4aÞ

7 Requiring a lower level is clearly sub-optimal given the opportunity cost ofthe worker’s effort. Requiring a higher level is also problematic since the mar-ginal product of effort would then be less than its marginal cost, w, and theworker’s utility level would fall below the reservation level U (if there were noshirking). Stipulating higher labor inputs in anticipation of shirking would in-evitably lead to disagreements between the entrepreneur and the worker aboutwhether and how much the worker shirks and would provide the worker hisreservation utility only if he was not actually forced to provide more labor thansuggested by the opportunity cost of w. Thus, the assumption made here seemsreasonable.


where T is the time spent on monitoring by the worker, e is the fraction ofactual outcome reported to the worker by the entrepreneur and ee ¼ 1 is

the benchmark level. If T ¼ 0 or if there is no cheating ðee � e ¼ 0Þ, then/e ¼ /e

1 ¼ /e2 ¼ 0; /e is also assumed to be increasing and concave in

its arguments.

The monitoring costs, Ce and Cw, of the entrepreneur and the worker

are simply given by the time, s and T, spent in monitoring multiplied by

the opportunity cost of the monitoring party’s time:

Ce ¼ wes; Cw ¼ wT : ð5Þ

Remark: Note that even though the entrepreneur undertakes monitoring,

the worker may still be able to shirk in his labor effort, at least to some

extent – thus he still controls the effective labor input, L. Similarly the

entrepreneur still controls the extent of under-reporting, e, despite mon-

itoring by the worker.

A.4) The General Contract: We consider the general linear contract in

which the entrepreneur pays the worker a fixed income A (which is

unrelated to his effort level and can be positive, negative or zero) and a

share, s ð0 � s � 1Þ, of the outcome, in return for his labor. Note that the

linear contract reduces to: (a) a fixed-rent contract when s ¼ 1 (and

A < 0), (b) a wage labor contract when s ¼ 0 (and A > 0), and (c) a share

contract when 0 < s < 1.

Given above assumptions, the worker’s income, Y, for the period is

given by:

Y ¼ Aþ seHF ðLÞ � dwPw/wðLL� L; sÞ þ ð1� L� T Þw ; ð6Þ

where dw is a stochastic variable that has the value 1=/w with proba-

bility /w and the value 0 with the probability ð1� /wÞ; thus it has a

mean of one, just as H does (see (1.1)). Overall, the term8 HPw/w

simply implies that the worker faces a penalty of Pw with a probability

/w, and zero with a probability of ð1� /wÞ. L is the time spent by the

8 As with the preceding term in (6), ~HH is included here to take into account therisk aversion of the worker. If he was risk neutral, as in the standard double-sidedmoral hazard model, only the mean of this term, i.e. Pw/w, would need to beconsidered.

40 P. Agrawal

worker in working under the contract under consideration, T in moni-

toring the entrepreneur and the remainder, ð1� L� T Þ, in working in

the labor market at a wage rate w. Similarly, the entrepreneur’s income,

Z, is given by:

Z ¼ �Aþ ð1� seÞHf ðLÞ � deP e/eððee � e; T Þ þ ð1� sÞwe : ð7Þ

3 Behavior of the Two Parties and the Optimal Outcome Share

To analyze this generalized double moral hazard problem, we consider the

two-stage game played by the parties to the contract. In the first stage, the

entrepreneur signs a binding contract with the worker with respect to the

outcome share s, and the fixed payment A. As in the standard double

moral-hazard model, we assume that these terms of the contract are easily

enforceable. The worker accepts the contract subject to his expected

utility, EU, from the contract being no less than his reservation utility, U .

The second stage takes A and s as given and the entrepreneur and the

worker choose their effort and monitoring levels noncooperatively (we

assume that monitoring levels of each party are announced at the be-

ginning of the period and are observable to the other party9). We focus on

the Nash equilibrium of this noncooperative game. The model applies to

many types of contracts often observed in practice (such as fixed wage,

share-tenancy and franchise arrangements) where the terms of the con-

tracts are easily enforceable but actions or effort levels of the two parties

are not.

We first analyze the second stage of the game and consider the Nash

equilibrium of strategies whereby effort/under-reporting and monitoring

levels of the two parties ðe; sÞ and ðL; T Þ are chosen for arbitrary A

and s (Sect. 3.1). Then we consider the first stage of the game where

the optimal outcome share, s, and fixed payment, A, are chosen (Sect.

3.2).

9 In practice the ‘‘period’’ of a contract may last for many months (for ex-ample, the contract period between a landlord and his tenants is often one crop-cycle). Thus, the parties have a chance to observe, over the length of the period,as to what extent they are being monitored and to adjust their effort levelaccordingly. This is being modeled here by the assumption of pre-announcing ofthe monitoring effort by each party.


3.1 Choice of L, T and e, s for a Given Contract

We begin by analyzing the second stage of the game for a given con-

tract, that is, for a given outcome share, s, and fixed payment, A. The

linearity of the problem implies that the second stage equilibrium is

independent of the fixed payment A and depends only on the share

payment, s. For a given outcome share, s, the worker chooses his labor

effort, L, and monitoring effort, T, so as to maximize his expected

utility, EU, for a given level of entrepreneur’s monitoring s (assumed to

be observable to the worker) and a given conjecture about entrepreneur’s

under-reporting, e [recall that the optimal choice of L and T depends on

s and e]:

MaxL;T EU ½Aþ seHF ðLÞ � dwPw/wðLL� L; sÞ þ ð1� L� T Þw� :ð8Þ

The first-order condition with respect to L yields:

EU 0:½seHFL þ dwPw/w1 ðLL� L; sÞ � w� ¼ 0

or

ð1� qwÞseFL þ ð1� rwÞPw/w1 ðLL� L; sÞ ¼ w ; ð9Þ

where a prime on a function denotes its first derivative with respect to its

argument and

qw ¼ 1� EHU 0=EU 0; and rw ¼ 1� EU 0HEU 0 ð10Þ

are the marginal risk premia of the worker associated with the outcome

and penalty risks, respectively (with 0 � qw 1, and 0 � rw 1).

Equation (9) suggests that the worker has to balance the benefit of in-

creasing his effort, L, which accrues in the form of his share of the

increased outcome (the first term on the left-hand side) and reduced

probability of being detected as a shirker (the second term on the

left-hand side) against the cost of additional effort, w.

Likewise, the first-order condition with respect to T yields:

EU 0:½sHF :eT � w� ¼ 0

42 P. Agrawal

or

ð1� qwÞsF :eT ¼ w : ð9:1Þ

This implies that the worker should choose monitoring effort, T, so as

to balance the benefit of monitoring (reduced under-reporting by the

entrepreneur) against the cost per unit of monitoring, w.

Similarly, for a given s and A, the entrepreneur chooses the extent of

under-reporting of outcome, e, and monitoring effort, s, for a given level

of monitoring, T, by the worker (assumed observable to the entrepreneur)

and a conjecture about the worker’s effort level, L, to maximize his

utility, V:

Maxe;s ¼ EV ½�Aþ ð1� seÞHF ðL; eÞ� deP e/eððee � e; T Þ þ ð1� sÞwe� : ð11Þ

The first-order condition with respect to s is:

EV 0:½ð1� seÞHFLLs � we� ¼ 0

or

ð1� qeÞð1� seÞHFLLs ¼ we ; ð12Þ

where

qe ¼ 1� EHV 0=EV 0 ð10:1Þ

is the marginal risk premium of the entrepreneur.

Likewise, the first-order condition with respect to e yields:

�sð1� qeÞF þ ð1� reÞPe/e1ðee � e; T Þ ¼ 0 ; ð12:1Þ

where re ¼ 1� EV 0de=EV 0 is the entrepreneur’s marginal risk premium

for the risk of facing the penalty Pe. Equation (12.1) suggests that, in

equilibrium, the entrepreneur has to balance the cost of reducing the

under-reporting, e, in the form of a reduced share of the outcome (the first

term on the left-hand side), against the benefit of reduced probability of

being detected as a shirker (the second term).


The Nash Equilibrium: Now consider whether there exists a Nash equi-

librium to the system of simultaneous Eqs. (9), (9.1), (12) and (12.1). A

solution to Eqs. (9) and (9.1) would exist if the worker’s utility, U, is

concave in L and T, see Eq. (8). Concavity of U with respect to L follows

from the concavity of the worker’s utility function, U, with respect to its

argument, the concavity of the outcome function, F, with respect to L, and

the concavity of /w in its arguments (which means /w is convex in L and

)Pw/w is concave in L). This implies that U in Eq. (8), being a concave

function of the sum of two functions that are concave in L (plus terms

independent of L), is concave in L. Thus, a solution of Eq. (9) does exist.

Further, we make the reasonable assumption that the entrepreneur’s effort,

e, is a concave function of the worker’s monitoring effort, T. Then the

outcome function, F(L, e(T )), which is concave in both its arguments,

would be a concave function of T as well. This implies that U in Eq. (8) is

concave in T as well. Therefore, a solution of Eq. (9.1) also exists. Simi-

larly, the entrepreneur’s utility function, V is concave in e and s in (11)

assuming that the worker’s effort, L, is a concave function of the entre-

preneur’s monitoring effort, s. Thus, solutions to Eqs. (12) and (12.1) alsoexist. Thus solutions exist for the vector strategies (L, T) and ðe; sÞ of theworker and the entrepreneur. Finally, note that each of the variables L, T, eand s are restricted to the convex set [0,1]. Therefore, the existence of the

Nash equilibrium is assured by the usual Kakutani’s fixed-point theorem

(see, for example Friedman, 1986, chap. 2). We shall further assume that

for a given outcome share, s, the Nash solution is unique. Let this Nash

equilibrium be denoted as follows:

L ¼ L0ðsÞ; e ¼ e0ðsÞ; T ¼ T 0ðsÞ; s ¼ s0ðsÞ : ð13Þ

3.2 The Optimal Contract

In Sect. 3.1, we analyzed the second stage of the game and discussed the

Nash equilibrium of strategies whereby ðe; sÞ and (L,T) are chosen for

arbitrary s and A. Here we consider the first stage of the game. In this

stage, the contract (i.e., optimal outcome share, s, and fixed payment, A is

chosen to maximize the entrepreneur’s expected utility subject to the

worker’s participation constraint. We shall assume that the Nash solutions

in (13) are a continuous function of the outcome share, s. This ensures that

a solution to the entrepreneur’s optimization problem with respect to the

44 P. Agrawal

outcome share, s, exists for s lying in the convex set [0,1]. Consideration of

this optimization problem leads to the following proposition:

Proposition 1: (A) The optimal outcome share, s0, satisfies the followingcondition:

(i) For an interior solution, 0 < s0 < 1 (a share contract):

ð1� qeÞð1� se0ÞFL0s þ ð1� qwÞsF e0s� ð1� reÞP/e

2T0s � ð1� rwÞPw/w

2 s0s� o=os½pwðsÞ þ peðsÞ þ CwðsÞ þ CeðsÞ� ¼ 0 : ð14Þ

(ii) At the corner10, s0 ¼ 0 (a fixed-wage contract):

ð1� qeÞFL0s � ð1� reÞPe/e2T

0s � ð1� rwÞPw/w

2 s0s� o=os½pw þ pe þ CwððT 0ðsÞ þ Ceðs0ðsÞ� � 0 : ð14:1Þ

(iii) At the corner, s0 ¼ 1 (a fixed-rent contract):

ð1� qwÞF e0s � ð1� reÞPe/e2T



(B) The equilibrium fixed payment, A0, satisfies the condition:

EU ½A0 þ s0He0F ðL0Þ � dwPw/wðLL� L0; s0Þþ ð1� L0 � T 0Þw� ¼ U ¼ UðwÞ ; ð15Þ

where L0 and e0 are the Nash-equilibrium levels of the worker’s

effort and the entrepreneur’s under-reporting (see Eq. (12)), Cw and

10 Other corner solutions are possible, such as s ¼ 0, A ¼ 0 (the entrepreneurdoes not hire the worker). Such a corner solution would be feasible only when theentrepreneur can provide the entire amount of required labor needed to work theasset by himself and the opportunity cost of his labor does not exceed that of theworker (plus associated agency costs). These (autarkic) corner solutions are notexplored in detail here as the focus of this paper is on understanding the nature oftwo party contracts.


Ce are the equilibrium monitoring costs of the worker and the

entrepreneur and pw, pe are the Arrow–Pratt risk premia of the

worker and the entrepreneur, respectively [see Eqs. (A.13) and

(A.14) in the Appendix].

Proof: See the Appendix.

Intuitive Interpretation of (14): In Eq. (14), the last term is the first

derivative of the sum of the risk premia and monitoring costs of the worker

and the entrepreneur. The first two terms represent the residual incentive

effects on the effort or under-reporting levels of the two parties. Note that L0sand e0s can be re-written as �o=osðLL� L0Þ and �o=osðee � e0Þ, respec-tively, where LL and ee are the (first best) effort levels corresponding to zero

shirking or under-reporting. Then (14) has the intuitive interpretation that

the optimal contract chooses the outcome share which minimizes the sum

of risk premia and the agency costs (of both11 the parties), the latter in-

cluding the monitoring costs and residual shirking (or under-reporting)

costs and the expected penalty costs. Further note that if the monitoring

undertaken by the two parties is sufficient to eliminate moral hazard by

each other, their effort or outcome reporting would be essentially at its first

best level (see Eq. (16)), so that the incentive effects L0s and e0s vanish in

Eq. (14). Then the probability of being detected shirking also approaches

zero, that is,/e2 ¼ /w

2 ¼ 0. Thus, only the last term survives in (14). That is,

monitoring cost will be the only agency cost and the optimal contract would

minimize the sum of monitoring and risk costs.

As mentioned earlier, much of the literature on the ‘‘nature of the firm’’

uses the underlying principle that the optimal size or organizational

structure of the firm minimizes the transactions costs of organizing the

production. Proposition 1 provides a formal proof of a comparable

principle, namely that the optimal contract minimizes the sum of the

agency costs and risk-premia. Obviously, if risk costs are small or not

taken into account, the optimal contract would minimize the agency (or

11 Even though it is the entrepreneur who decides s and A, the worker’s riskpremium (pw(s)) and the cost of monitoring the entrepreneur’s profit (Cw(s)) arestill important in the choice of the optimal outcome share, so, because of theconstraint of providing the risk-averse worker a given reservation utility – asthe worker’s share in profit increases, his risk premium and monitoringcosts, Cw, also increase and his reservation utility cannot be maintainedunless he is compensated for these costs.

46 P. Agrawal

transaction) costs. Although the risk costs have sometimes been ignored

in this branch of literature, there are situations where they play an im-

portant role (see, e.g. Cheung, 1969b; Stiglitz, 1974).

The First-best Solution: It may be worthwhile to consider the optimal

solutions in the first-best world where the effort level of the worker and

the extent of under-reporting are both observable. In this case, monitoring

will obviously not be needed and the entrepreneur will set e ¼ 1 (no

under-reporting). Further, the first-best level of the worker’s efforts would

optimize the entrepreneur’s utility subject to the participation constraint of

the worker, that is,

MaxA;s;LEV ½�Aþ ð1� sÞHF ðLÞ þ we�

subject to:EU ½Aþ HsF ðLÞ þ ð1� LÞw� � U :

Then it easily follows that the optimization conditions with respect to L

are given by:

FL ¼ w=ð1� q�Þ ; ð16Þ

where q� ¼ sqw þ ð1� sÞqe is the weighted average of the marginal risk

premia of the two agents. The solution of (16) is, of course, the first-best

effort levels LL. A comparison of (16) with (9) and (12a) shows that

L0 � LL, that is, the Nash-equilibrium effort level in the second-best world,

when the effort level is not observable, would be less than or equal to

those in the first-best world.

4 Applications: Monitorability of Outcome/Effort

and the Choice of Contracts

In this section, we use the analysis and results of Sect. 3 to consider the

contracts that can be optimal under different assumptions regarding the

monitorability of outcome and effort (Sect. 4.1). Then we use these results

to explain the nature of contracts observed in practice under several

different situations (Sect. 4.2).

4.1 Monitorability of Outcome/Effort and Choice of Contracts

As mentioned in the introduction, the standard double-sided moral-hazard

models (see, for example, Cooper and Ross, 1985; Romano, 1994;


Bhattacharyya and Lafontaine, 1995, etc.), which does not allow for

mutual monitoring, present us with the anomalous conclusion that only

share contracts can be optimal.12 This conclusion is at variance with the

common use of fixed-wage and fixed-rent contracts in actual practice.

Here we demonstrate that this conclusion follows from the specific as-

sumptions of the standard double moral-hazard model and that in the

presence of mutual monitoring, the fixed wage and fixed rent contracts

can also be optimal (Proposition 2). In fact, under some circumstances

only fixed-wage or fixed-rent contracts can be optimal (Propositions 3 and

4).

Proposition 2: If both parties monitor each other, then all three types of

contracts (fixed-wage, fixed-rent and share contracts) are possible.

Proof: First, consider whether the fixed-wage contract (s = 0) can be

optimal in the case of unobservable outcome. Using (14.1), this can be the

case only if:

ð1� qeÞFLL0s � ðpws þ pe

sÞ � ½Cws ðs ¼ 0Þ þ Ce

s ðs ¼ 0Þ�� ð1� reÞPe/e


2 s0s � 0 : ð14:1Þ

The first term in the above inequality is positive since ð1� qeÞ, FL and

L0s � 0.13 Further pws ðs ¼ 0Þ ¼ 0 and pe

sðs ¼ 0Þ � 0 [see Eqs. (A.13)

and (A.14)]. This implies that the term – ðpws þ pe

sÞ is also non-

negative. Now consider the monitoring costs. The worker’s moni-

toring costs, Cw ¼ wT 0, are zero when s ¼ 0 since he obviously has

no need to monitor the entrepreneur. As the worker’s outcome

share increases from zero, the monitoring costs must increase (i.e.,

12 The economic intuition behind this result is as follows: when there is nomonitoring, the fixed wage contract cannot be optimal because slightly increasingthe worker’s share, s, from zero leads to a positive increase in his effort (andoutcome) while the corresponding decline in the entrepreneur’s share from onedoes not affect the outcome significantly. A similar argument rules out the fixedrent contract as well – so that only share contracts can be optimal in the standarddouble-sided moral hazard models.13 Of course, when monitoring is undertaken, Eqs. (9), (9.1), (12) and (12.1)

need to be solved simultaneously. While L0s ðs ¼ 0Þ > 0 is still likely, note that thefailure of this condition will only strengthen the argument that the fixed wagecontract can be optimal.

48 P. Agrawal

T 0s > 0) because he now has a stake in the outcome and hence has

the incentive to monitor the entrepreneur (see (9.1)). Simulta-

neously, as s increases from zero, the entrepreneur has an in-

creasing incentive to shirk (see (12.1)), which again calls for

increasing monitoring from the worker. This implies that T 0s ðs ¼ 0Þ

and therefore Cws ðs ¼ 0Þ > 0. (Similarly, it can be argued that

s0s ðs ¼ 0Þ and Ces ðs ¼ 0Þ < 0). Further, since T 0

s ðs ¼ 0Þ is positive,

the fifth term, �ð1� reÞPe/e2T

0s , in (14.1) is also negative (because

ð1� reÞ > 0, Pe > 0 and /e2 > 0). Thus, if these monitoring and

expected penalty costs ðwT 0s þ ð1� reÞPe/e

2T0s Þ are sufficiently large

so that (14.1) can be satisfied, then the fixed wage contract ðs ¼ 0Þcan be optimal. Since the shape and magnitude of the worker’s

monitoring effort as a function of his outcome share, s, can vary

with workers and situations and be large in some cases, this is

indeed a possibility.

Next, consider whether the fixed-rent contract ðs ¼ 1Þ can be optimal

in the general case. Using (14.2), this can be the case only if:

ð1� qwÞF e0s � ðpws þ pe

sÞ � ½Cws þ Ce

s �

� ð1� reÞPe/e2T


2 s0s � 0 : ð14:2Þ

The first term in the above inequality is negative since ð1� qwÞ, F � 0

and e0s � 0. Further, pesðs ¼ 1Þ ¼ 0 and pw

s ðs ¼ 1Þ > 0 [see Eqs. (A.13)

and (A.14)]. This implies that the term – ðpws þ pe

sÞ is also negative. Now

consider the entrepreneur’s monitoring costs Ce ¼ wes0. The monitoring

costs are zero when his outcome share 1� s ¼ 0 since he obviously has

no need to monitor the worker. As the entrepreneur’s outcome share

increases from zero, his monitoring effort, s0, must increase because he

now has a stake in the outcome and hence has an incentive to monitor the

worker (see (12)). Simultaneously, as s decreases from one, the worker

has increasing incentive to shirk (see (9)), which again calls for increasing

monitoring from the entrepreneur. This implies that s0s ðs ¼ 1Þ < 0 and

thence, Ces ðs ¼ 1Þ < 0. Further, since s0s ðs ¼ 1Þ is negative, the last term,

�ð1� rwÞPw/w2 s0s , in (14.1) is also positive. Thus, if these monitoring

and expected penalty costs ðwes0s þ ð1� rwÞPw/w2 s0s Þ are sufficiently

large so that (14.2) can be satisfied, then the fixed rent contract ðs ¼ 1Þcan be optimal. Since the shape and magnitude of the entrepreneur’s

monitoring effort will vary with entrepreneurs and situations and be large

in some cases, this is indeed a possibility.


Finally, share contracts can obviously be optimal whenever the in-

centive effects, risk and monitoring costs are such that conditions (14.1)

or (14.2) are not satisfied. This proves that in our more general model, all

three types of contracts – fixed-wage, fixed-rent and share contracts – can

be optimal.

Intuitively, when mutual monitoring is undertaken, an increase in the

worker’s share from zero not only increases his effort, but also increases

his monitoring costs (given his increasing stake in the outcome and the

increasing possibility of moral hazard by the entrepreneur). It is possible

that this increase in the worker’s monitoring costs outweighs the benefits

of his increased effort as his share increases from zero. When that hap-

pens, a fixed-wage contract would be optimal. Similar arguments apply

for the fixed-rent contract. Thus, when mutual monitoring is being un-

dertaken, all three types of contracts would co-exist in an economy where

monitoring costs and risk premia vary across agents so that conditions

(14.1) and (14.2) were satisfied for some pairs of contracting parties but

not for other pairs.

Proposition 3: If the actual outcome is observable only to the entre-

preneur but the worker can neither observe it directly nor monitor it, then

a fixed-wage contract would be optimal.

Proof: When the worker cannot observe the actual outcome and e is

interpreted as the extent of the entrepreneur’s under-reporting of the

outcome, the first-order condition with respect to e satisfies Eq. (12.1)

above. When monitoring or penalizing the entrepreneur for under-

reporting are not possible, ðPe ¼ 0 and/or T ¼ 0Þ, Eq. (12.1) cannot besatisfied as an equality for any s>0. Then the entrepreneur’s expected

utility, EV ½�Aþ ð1� seÞHf ðLÞ þ ð1� sÞwe� will be maximized at the

corner solution, e ¼ 0 for all s>0. And at s ¼ 0, any e will satisfy (12.1).

Thus, the share of actual outcome se ¼ 0 for all s. Note that this solution

does not apply when monitoring of the outcome is possible. Now consider

the worker’s response – from (9) and (6.1), his first-order condition is

easily seen to be:

ð1� qwÞseFL þ ð1� rwÞPw/w1 ðLL� L; sÞ ¼ w : ð17Þ

In a Nash equilibrium, the worker would know the entrepreneur’s optimal

behavior and thus know that his share of actual outcome, esf ðLÞ, is

50 P. Agrawal

always zero since the entrepreneur sets e ¼ 0 for all s > 0. Then (17)

implies that the worker will respond only to monitoring by the entre-

preneur and his effort will be independent of s.

Intuitively, when the worker does not know what is (the amount of

outcome) to be shared, there is no meaningful way of making a share or

fixed-rent contract with him and only wage contracts would be used.

Corollary: If only the worker knows the actual outcome but the entre-

preneur can neither observe it directly nor monitor it, then only the fixed-

rent contract can be optimal.

Proof: From the proof of Proposition 3, it should be obvious that if a

wage or share contract is signed and the entrepreneur can neither directly

observe the outcome nor monitor it (for example, an agricultural tenant

naturally comes to know the output in the process of working while the

landlord may not know unless he takes an active interest), then for any

output share, s < 1, the tenant would under-report the output as much as

he could. Since the entrepreneur also knows this, the only contract ac-

ceptable to both parties would have s ¼ 1, that is, a fixed rent being paid

to the entrepreneur.

Proposition 4: If the effort level of the worker can be observed essen-

tially costlessly and the worker is risk averse while the entrepreneur is

risk neutral, a fixed-wage contract would be optimal.14

Proof: Equation (14.1) gives the condition for the fixed-wage contract

ðs ¼ 0Þ to be optimal. When the worker’s effort (L0) is easily observable,

he cannot shirk for any s so that L0s ¼ 0 and the incentive effect (first term

in (14.1)) vanishes. Further, the monitoring effort of the entrepreneur is

zero (or negligible) for all outcome shares, s, that is, s0s ¼ 0. Finally, risk

neutrality of the entrepreneur implies pe ¼ 0 for all s. Thus (14.1) reduces

to15:

14 Using similar arguments, it is straightforward to prove that if the actualoutcome can be observed essentially costlessly and the entrepreneur is risk aversewhile the worker is risk neutral, a fixed rent contract would be optimal. Whilethese conditions are unrealistic for the case of an entrepreneur and worker, theymay be relevant in other contexts of two party contracts (say, between two firms).15 Using (5) and multiplying both sides of (14.1) by –1 reverses the inequality

sign.


pws ðs ¼ 0Þ þ wT 0

s ðs ¼ 0Þ þ ð1� reÞPe/e2T

0s ðs ¼ 0Þ � 0 ð18:1Þ

Using (a13), pws (s=0) = 0, while the second and the third terms on the left-

hand side are positive since /e2 and T 0

s > 0. Thus, (18.1) is satisfied.

Note that share or fixed-rent contracts (i.e., s > 0), cannot be optimal in

this case since that would require that the following condition be satisfied

(see (14) and (14.2) and note that L0s ¼ s0s ¼ pe ¼ 0):

� ð1� qwÞsF e0s þ pws ðs ¼ 0Þ þ wT 0

s ðs ¼ 0Þþ ð1� reÞPe/e

2T0s ðs ¼ 0Þ � 0 : ð18:2Þ

Equation (18.2) cannot hold since the first term is positive (e0s < 0 for all

s > 0), for risk averse workers pws � 0 (see (A.13)) and the third and

fourth terms on the left-hand side of (18) remain positive (or zero if the

worker does not monitor the entrepreneur) since /e2 and T 0

s ðs ¼ 0Þ � 0.

Intuitively, the fixed wage contract is optimal in this case because as

the worker’s outcome share (s) increases from zero, the incentive effect

on his effort is negligible because, given almost cost-less monitoring,

shirking was not possible to begin with. Further, as s increases, his risk

and monitoring costs increase while the entrepreneur’s risk and moni-

toring costs do not go up, and are zero or negligible for all s.

Thus production processes (such as assembly lines), where the workers

can be supervised at a low cost and where the workers are likely to be

much more risk averse than the entrepreneurs, would be likely to use

fixed-wage contracts.

4.2 On the Nature of Contracts Observed in Practice

The function of the firm based on labor contracts and asymmetric structure

of residual rights is far too sophisticated to be fully explained by any single

model (see, for example Coase, 1937 and 1960; Cheung, 1983; Grossman

and Hart, 1986; Hart and Moore, 1990; and Yang and Ng, 1995). How-

ever, using Propositions 2 to 4, we can provide some understanding of

why different contracts are used under various different circumstances.

Why is it that fixed-wage contracts are so common in industry?

We believe that there are two main reasons for this. One, in many industrial

enterprises, the production workers can be monitored at negligible costs

52 P. Agrawal

(because of the nature of the work, one supervisor can easily monitor a

large number of workers). Further, while workers are generally risk averse,

the entrepreneur (owner of the company), being much wealthier, are es-

sentially risk neutral. Thus, the fixed-wage contracts are optimal as proved

in Proposition 4.

Two, even when the worker’s effort level is not easily observable or the

entrepreneur is not risk neutral, it is often the case that the workers cannot

observe the actual profits because of various uncertainties relating to the

production process and the prices of various inputs and outputs. Further,

monitoring the entrepreneur may be very difficult for the worker as he is

unlikely to have access to detailed accounts on various prices, quantities

purchased and sold, etc. Even when technically feasible, the management

or owners of the firm may frown upon any attempts to monitor the profits

for reasons such as the fear of leakage of vital business information

to business rivals (or tax authorities). Finally, workers often do not really

have the power to penalize the employer in a meaningful way (except in

the cases of highly skilled and hard to replace workers or very strong

trade unions), so that monitoring is not very meaningful. Given these

difficulties, in most industrial enterprises monitoring of profits is unlikely

to be a feasible option for the worker. Therefore, wage contracts likely to

be used as share contracts based on profits are infeasible, as proved in

Proposition 3.

However, in some situations it is possible to find reasonable proxies for

profits that are readily observable to both the parties. These include the

following:

(i) Enterprises (for example, automobile manufacturers), where output

by a particular plant or even a group of workers are readily observable to

both parties (at almost zero cost). In such situations ‘‘incentive contracts’’,

in which a part of the workers’ income depends on the output produced,

are commonly used. The piece rate contracts (see Cheung, 1983) are also

an example of this kind of contract.

(ii) Large firms with publicly traded equity shares. In this case, the

share price acts as a proxy for the profitability of the firm which are

readily observable to the worker costlessly and which minimize the

possibility of moral hazard by the entrepreneur. This explains why share

options are much more common as a part of the remuneration in large

firms with publicly traded shares, than are profit-sharing contracts in firms

lacking publicly traded shares. However, the price of the company shares

is not a very good proxy for the company profits, and is often vulnerable


to price fluctuations due to factors completely unrelated to the effort

levels of the workers such as changes in business sentiments, interest

rates, and many other forces. In other words, share options also expose

workers to exogenous risks, unrelated to their effort levels, which many

of the lower paid workers may not like to face. Thus, the workers who are

low-paid and/or whose effort levels can be monitored relatively easily

would be less likely to be offered the share option. On the other hand, it

would be more common for workers who are well paid and whose effort

level is hard to observe, such as the managers. This is generally consistent

with what is observed in practice.

Further, in some situations, the outcome (profit, revenue, output, etc.) is

easily observable to both parties. These include the following:

(i) The senior managers of a company can often have a reasonably

good knowledge of actual profits of the company in the course of their

work. In such cases, there may be little scope for moral hazard by the

principal (owners of the company), so that the model collapses to the

principal-agent model. Then share contracts are likely to be optimal (see,

for example Shavell, 1979, or Stiglitz, 1974). This explains the much

greater incidence of share contracts for management level employees.

(ii) An agricultural worker comes to know about the likely production

output simply from working in the field. This is an important reason why

share contracts are so much more common in agriculture as compared to

industry where workers often have difficulty knowing the actual outcome

(but there could be other reasons as well for the popularity of share-

cropping in agriculture – see, for example, Otsuka and Hayami, 1988 and

Otsuka et al., 1992).

Finally, there also arise circumstances where only the worker knows

the outcome but the entrepreneur does not – an example would be the

case of an agricultural tenant who leases in land from an absentee land-

lord (who does not reside in the same village and is therefore unable to

observe the yield from the leased land). The corollary to Proposition 3

implies that only fixed rent contracts should be observed in such cases,

which is consistent with the empirical evidence (see, for example, Bliss

and Stern, 1982; Otsuka et al., 1992).

Even when the outcome or effort can be monitored, the cost of doing

so would vary from situation to situation and this affects the choice of

the contract made. For example, landlords who cultivate their own land

often hire some additional labor on a fixed-wage basis since the cost of

54 P. Agrawal

monitoring the worker is low, given that the landlord is present on the

land anyway. Landlords who do not cultivate themselves would find

continuous supervision of workers too costly. Thus those who can un-

dertake limited monitoring usually hire workers as sharecroppers (who

need less supervision because they are partial recipients of residual

rights), while landlords for whom the cost of monitoring is prohibitive

(such as absentee landlords or those with large landholdings) usually

lease land on fixed-rent basis. In industry, workers such as assembly line

workers, who can be supervised at little cost, typically work for fixed

wages, while those whose labor is hard to monitor, such as managers,

lawyers, salesman, writers and doctors, are more likely to have some

form of share (or incentive) contract. Agents for life insurance (which are

often long term policies and therefore require less monitoring) are more

likely to be employees or agents of one insurance company (with in-

centive contracts for getting new customers), while agents for automobile

or fire and casualty insurance, which tend to be more short-term policies

and thus require greater monitoring, are more likely to work as inde-

pendent agents (see Grossman and Hart, 1986, for a more detailed

analysis).

Thus, the analysis developed in this paper can help shed some light on

the prevalence of different types of contracts under various different

conditions.

5 Conclusion

In this paper, we have developed a generalized double-sided moral-

hazard model with risk-averse parties who mutually monitor each other

and where the outcome (profit output, revenue, etc.) or effort may not be

observable. Using this model, we formally proved that the optimal con-

tract minimizes the sum of the agency and risk costs of the two parties,

where the agency costs include the monitoring costs, the residual shirking

and the expected penalty costs.

Our analysis helps resolve the anomaly that while most standard double

moral-hazard models conclude that a share contract should be optimal,

fixed-wage contracts are actually the norm in industry. We show that when

mutual monitoring is allowed, share contracts need not be the only type of

contract that can be optimal. It was also shown that when the outcome

cannot be observed by one of the parties, the optimal contract will involve

a fixed payment to that party.


Our analysis is able to explain the nature of contracts observed in

practice under many different situations. For example, the analysis can

explain: (i) why industrial workers typically work under wage contracts

while share contracts are common in agriculture, (ii) some form of share

contract (e.g., part remuneration in the form of company shares) is

much more common for senior managers than for the lower level

workers and more common for firms with publicly traded shares than

for others.

Appendix

Proof of Proposition 1

The entrepreneur’s optimization problem is:

MaxA;sEV ½�Aþ ð1� seÞHF ðLÞ� deP e/eððee � e; T Þ þ ð1� sÞwe� ; ðA:1Þ

subject to:

EU ½Aþ seHF ðLÞ � dwPw/wðLL� L; sÞ þ ð1� L� T Þw� � U

ðA:2Þ

and

L ¼ L0ðsÞ; e ¼ e0ðsÞ; T ¼ T 0ðsÞ; s ¼ s0ðsÞ : ð13Þ

Substituting constraints (13) into the problem, the Lagrangean, £, for this

constrained optimization problem is:

£ ¼ EV ½�Aþ ð1� se0ÞHF ðL0Þ � deP e/eððee � e0;T0Þ

þ ð1� s0Þwe� þ kfEU ½Aþ se0HF ðL0Þ

� dwPw/wðLL� L0; s0Þ þ ð1� L0 � T 0Þw� � Ug : ðA:3Þ

Differentiating with respect to A yields:

EV 0 ¼ kEU 0 ; ðA:4Þ

56 P. Agrawal

where a prime on a function denotes its first derivative with respect to its

argument.

And differentiating with respect to the worker’s outcome share, s,

yields (assuming an interior solution, s 2 ð0; 1Þ):

EV 0:f�He0F þ ð1� se0ÞHFLL0s þ ½�sHF e0s þ deP e/e1e

0s ��

deP e/e2T

0s � s0sw

eg þ kEU 0:fHe0F þ sHF e0s þ ½se0HFLL0sþdwPw/w

1L0s � wL0s � � dwPw/w

2 s0s � T 0s wg ¼ 0 : ðA:5Þ

Collecting terms containing e0sEV0 and using Eq. (12.1), it is seen that

they add up to zero. Similarly, terms containing L0sEU0 add up to zero

because of Eq. (9) [this is the envelope theorem in action here]. Then

(A.5) simplifies to:

f�ð1� qeÞe0F þ ð1� qeÞð1� se0ÞFLL0s�ð1� reÞPe/e

2T0s � s0sw

eg þ fð1� qwÞe0F þ ð1� qwÞsFee0s�

ð1� rwÞPw/w2s0s � T 0s wg ¼ 0 ; ðA:6Þ

where qe and qw are the marginal risk premia of the entrepreneur and the

worker, respectively, for the production risks and re and rw are the

marginal risk premia of the entrepreneur and the worker respectively for

the penalty risks [see Eqs. (10) and (10.1)].

Recalling the definitions of the monitoring costs (see (5)), the equi-

librium monitoring costs of the entrepreneur and the worker will be

denoted as:

Ce ¼ wes0; Cw ¼ wT 0 : ðA:7Þ

Then, noting that �ð1� qeÞe0F þ ð1� qwÞe0F ¼ qee0F � qwe0F , we

can rewrite (A.6) as:

ð1� qeÞð1� sÞFLL0s þ ð1� qwÞsFee0s � ð1� reÞPe/e

2T0s

� ð1� rwÞPw/w2 s0s � f�qee0F þ qwe0F þ Cw

s þ Cesg ¼ 0 :

ðA:8Þ

Finally, qe and qw can be expressed in an alternative and more intuitively

appealing form by making use of the following Lemma:


Lemma: For an agent facing a risky income of the form

HGðs; L; e; . . .Þ þ X ðL; e; . . .Þ ; ðA:9Þ

where H is the multiplicative risk factor which has an expected value of

one (see (1.1)) and X ðL; e; . . .) represents terms independent of H, the

following relation holds in equilibrium:

q ¼ ps=Gs ; ðA:10Þ

where q is the marginal risk premium [see (10) and (10.1)], p is the

Arrow-Pratt income risk premium [see (A.13) and (A.14) below] and a

subscript on a function denotes partial differentiation with respect to the

subscript.

Proof: See Agrawal (1993).

Comparing (A.9) with (6) and (7), it is seen that G ¼ seF for the

worker and G ¼ ð1� seÞF for the entrepreneur. Thus, the Lemma implies

that at the equilibrium (i.e., at s ¼ s0; e ¼ s0, and L ¼ L0, etc),

qw ¼ pws =eF ðA:11Þ

and

qe ¼ �pes=eF : ðA:12Þ

The Arrow–Pratt income risk premium ðpÞ is defined by the condition

that the expected utility of the risky income with no insurance should equal

the utility of the expected income minus the risk premium. For small

variances of income, the risk premium of the worker, pwðsÞ, and the

entrepreneur, peðsÞ, are given by (see Pratt, 1964):

pwðsÞ ¼ 1

2Awv½shF � ¼ 1

2s2AwvðhF Þ ¼ s2pwðs ¼ 1Þ ; ðA:13Þ

peðsÞ ¼ 1

2Aev½ð1� sÞhF � ¼ 1

2ð1� sÞ2AevðhF Þ

¼ ð1� sÞ2peðs ¼ 0Þ ; ðA:14Þ

58 P. Agrawal

where Ae and Aw are the degree of absolute risk aversion of the entre-

preneur and the worker, respectively, and v represents the variance of its

argument.

Using (A.11) and (A.12) in (A.8) yields (14), the condition that the

optimal outcome share, s0, must satisfy:

ð1� qeÞð1� se0ÞFLL0s þ ð1� qwÞsFee0s � ð1� reÞPe/e

2T0s �

ð1� rwÞPw/w2 s0s � o=os½pw þ pe þ CwððT 0ðsÞ þ Ceðs0ðsÞ� ¼ 0 :

ð14Þ

Corner Solutions16: Equation (14) has to be satisfied as an equality only

for an interior solution, where the worker’s outcome share s 2 ð0; 1Þ. TheLagrangean can achieve its maximum at the corner s ¼ 0 (a fixed wage

contract) even if o£=os � 0 at s ¼ 0, that is if (since the second term in

(14) vanishes at s ¼ 0)

ð1� qeÞð1� se0ÞFLL0s � ð1� reÞPe/e2T



And the Lagrangean can achieve its maximum at the corner s ¼ 1

(a fixed rent contract) if o£=os � 0 at s ¼ 1, that is, if (since the first term

in (14) vanishes at s=1)

ð1� qwÞsFee0s � ð1� reÞPe/e



Finally, note that in Eq. (A.4) EV0 as well as EU0 are positive for all

finite income levels, so that k > 0, which implies that the constraint (A.2)

must be satisfied with an equality. Therefore, the equilibrium fixed pay-

ment, A0, must satisfy (also see (3)):

EU ½A0 þ s0e0HF ðL0Þ � dwPw/wðLL� L0; s0Þþ ð1� L0 � T 0Þw� ¼ U ¼ UðwÞ : ð15Þ

16 For a brief discussion of other corner solutions, see footnote 12.


Acknowledgements

I would like to thank Sugata Marjit, Kaushik Basu, Ali Khan, Bibhas Saha,Anindya Sen, Mukesh Eswaran and two anonymous referees of this journal forhelpful discussions and/or comments on an earlier draft of this paper.

References

Agrawal, P. (1993): ‘‘Relationships Among Some Risk Premia.’’ EconomicLetters 43: 65–70.

Alchian, A., and Demsetz, H. (1972): ‘‘Production, Information Costs andEconomic Organization.’’ American Economic Review 62: 777–795.

Barzel, Y. (1987): ‘‘The Entrepreneur’s Reward for Self-Policing.’’ EconomicInquiry. 25: 103–116.

Bhattacharyya, S., and Lafontaine, F. (1995): ‘‘Double Sided Moral Hazard andthe Nature of Share Contracts.’’ RAND Journal of Economics 26: 761–781.

Bliss, C. J., and Stern, N. H. (1982): Palanpur: The Economy of an IndianVillage. Oxford: Oxford University Press.

Cheung, S. N. S. (1969a): The Theory of Share Tenancy. University of ChicagoPress.

Cheung, S. N. S. (1969b): ‘‘Transaction Cost, Risk Aversion, and the Choice ofContractual Arrangements.’’ Journal of Law and Economics XII(1): 23–42.

Cheung, S. N. S. (1983): ‘‘The Contractual Nature of the Firm.’’ The Journal ofLaw and Economics 1: 1–21.

Coase, Ronald (1937): ‘‘The Nature of the Firm.’’ Economica 4: 386–405.Coase, Ronald (1960): ‘‘The Problem of Social Costs.’’ Journal of Law andEconomics 3: 1–44.

Cooper, R., and Ross, T. W. (1985): ‘‘Product Warranties and Double MoralHazard.’’ RAND Journal of Economics 16: 103–113.

Eswaran, M., and Kotwal, A. (1985): ‘‘A Theory of Contractual Structure inAgriculture.’’ American Economic Review 75: 352–367.

Grossman, S. J., and Hart, O. D. (1986): ‘‘The Costs and Benefits of Ownership:A Theory of Vertical and Lateral Integration.’’ Journal of Political Economy94: 691–719.

Harris, M., and Raviv, A. (1979): ‘‘Optimal Incentive Contracts With ImperfectInformation.’’ Journal of Economic Theory 20: 232–255.

Hart, O., and Moore, J. (1990): ‘‘Property Rights and the Nature of the Firm.’’Journal of Political Economy 98: 1119–1158.

Holmstrom, B. (1979): ‘‘Moral Hazard and Observability.’’ Bell Journal ofEconomics 10: 74–91.

Lafontaine, F. (1993): ‘‘Contractual Arrangements as Signalling Devices: Evi-dence from Franchising.’’ Journal of Law Economics and Organization V9,N2.

Lal, R. (1990): ‘‘Improving Channel Coordination Through Franchising.’’Marketing Science 9: 299–318.

Mathewson, G. E., and Winter, R. A. (1985): ‘‘The Economics of FranchiseContracts.’’ Journal of Law and Economics 28: 503–526.

60 P. Agrawal

Otsuka, K., and Hayami, Y. (1988): ‘‘Theories of Share Tenancy: A CriticalSurvey.’’ Economic Development and Cultural Change 37: 31–69.

Otsuka, K., Chuma, H., and Hayami, Y. (1992): ‘‘Land and Labor Contracts inAgrarian Economies: Theories and Facts.’’ Journal of Economic Literature30: 1965–2018.

Otsuka, K., Chuma, H., and Hayami, Y. (1993): ‘‘Permanent Labour and LandTenancy Contracts in Agrarian Economies: An Integrated Analysis.’’ Econo-mica 60: 57–77.

Pratt, J. W. (1964): ‘‘Risk Aversion in the Small and the Large.’’ Econometrica32: 112–136.

Romano, R. E. (1994): ‘‘Double Moral Hazard and Resale Price Maintenance.’’RAND Journal of Economics 25: 455–466.

Shavell, S. (1979): ‘‘Risk Sharing and Incentives in the Principal and AgentRelationship.’’ Bell Journal of Economics 10: 55–73.

Stiglitz, J. E. (1974): ‘‘Incentives and Risk Sharing in Agriculture.’’ Review ofEconomic Studies 41: 209–256.

Williamson, O. (1975): Markets and Hierarchies. New York: Free Press.Williamson, O. (1985): Economic Institutions of Capitalism. New York: Free

Press.Yang, Xiaokai, and Ng, Yew–Kwang (1995): ‘‘Theory of the Firm and Structure

of Residual Rights.’’ Journal of Economic Behavior and Organization 26:107–128.

Address of author: Pradeep Agrawal, RBI Chair Unit, Institute of EconomicGrowth, University Enclave, Delhi 110 007, India (e-mail: [email protected].)


Double Moral Hazard, Monitoring, and the Nature of Contracts

Documents

Transcript of Double Moral Hazard, Monitoring, and the Nature of Contracts