World Bank Reprint Series: Number 229

Avishay Braverman and Joseph E. Stiglitz

3,iareckoppinr andf1'4I'vnterfinkin,-'k Abraria MAX Ma

R eprinttcd with permission from The AMicrican Ectitionomic Reiview, vol. 72, no. 4X-wptemnber 1982), pp. 695-715.

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Sharecropping and the Interlinking of Agrarian Markets

By AvisHAY BRAVERMAN AND JOSEPH E. STIGLITZ*

One of the often noted features of less-de- Our analysis is based on two features com-veloped agrarian economies is the existence monly found in less-developed agrarian econ-of interlinkages among the land, labor, credit, omies:and product markets.' The l.1ndlord is often (a) Inldividuals are not paid on the basisthe supplier of credit; he frequenitly purchases of their input (effort) since this, in general, isand markets the output of the tenant farmers; not observable; and they conventionally doand he often sells raw materials (fertilizers) not rent land for a fixed sum since thatand even consumption goods to his tenant imposes too much risk on them.3 Hence thefarmers. contractual arrangements involve at least

How do we explain this phenomenon? some form of sharecropping;4 as a result,What are the welfare consequences of at- workers do not obtain the full marginaltempts to restrict these practices, which often product of their efforts.seem to constitute restraints on free trade? (b) The landlord cannot completelyThese are the questions to which this paper is specify the actions to be taken by the worker;addressed. the worker has considerable discretion both

Jn the past, theoretical discussions of inter- with respect to the level of effort and itslinked contracts viewed them as a form allocation, and the choice of technique ofof exploitation of less-powerful agents by production. Some of these decisions may, ofmore-powerful agents (for example, see Amit course, be easily monitored by the landlord,Bhaduri, 1973, 1977). The argument, how- but there are other actions, perhaps equallyever, was never very convincing: if a land- important, for which the cost of monitoringlord could exploit his tenants to the point of would be very high.reducing them to their subsistence level (as These two facts-that the worker has con-these arguments often suggested), why could siderable discretion over his own actions,the landlord not do so simply by reducing and that, because of the nature of the con-the share on the share contract? What more tractual arrangements between the workercould he get through these other devices? and the landlord, the worker's actions have

In this paper we present a general set of an important effect on the landlord's ex-arguments applicable to both competitive and pected profits-have, in turn, some furthernoncompetitive environments, to situationswhere all the terms of the contract are de-termined in an optimal way, as well as to man-Srinivasan (1981). In particular, Mitra's study raisessituations where many of the terms are the central issue discussed, of the relationship betweenspecified institutionally.2 interlinking and moral hazard. For a more general dis-

cussion of equilibrium with moral hazard, includingimplications of moral hazard for the decentralization of

'World Bank and Princeton University, respectively. the economy, see Richard Arnott and Stiglitz (1980).Views expressed in this paper are our own, and do not 3Moreover, if there is some probability of their notnecessarily reflect those of our affiliated organizations. being able to pay the fixed rent, which can be affectedWe thank Hans Binswanger, T. N. Srinivasan, and an by the actions of the tenant, rental arrangements mayanonvmous referee for helpful comments, and Vivianne not be desirable from the point of view of the landlordLake and Tribhuwan Narain for editorial assistance. (see Stiglitz and Andrew Weiss, 1981), and even with a

'For a survey of such phenomena, see Pranab rental agreement tenants do not obtain the full marginalBardhan (1980) and Hans Binswanger et al., forthcomn- benefit (or cost) of their actions.ing For the nineteenth-centuryUnited States, see Joseph 4See Alfred Marshall (1920), Steven Cheung (1969),Rei'd (1979). Bardhan and T. N. Srinivasan (1971), Reid (1973),

' Other recent studies which have addressed this Stiglitz (1974), Bell-Zusman (1976), David Newberyquestion include those of Clive Bell and Pinhas Zusman (1977), and Newbery-Stiglitz (1979) for earlier discus-

198(), Pradeep Mitra (1982), Reid (1976), and Braver- sions of sharecropping.

695

6I) THE AMERICAN ECONOMIC REVIEW SEPTEMlfBER 1982

important implications. In particular, it offer a tenancy contract which is much moremeans that the landlord has an incentive to attractive in some other dimensions.attempt to induce workers to behave in the The arguments for interlinkage with prod-way he would like them to behave. The be- uct markets are similar. The tenants mayhavior of the worker is affected, in important purchase less of inputs, such as fertilizer,ways, by the amount he borrows and the than the landlord desires; some of theterms at which he obtains credit, and by the increased return to the input is appropri-goods he can purchase and the prices he ated by the landlords. As we show else-pays. where (19°81a), conventional cost-sharing

Much of the formal analysis of this paper rules, where the landlord pays a share of thefocuses on showing how the landlord, by cost equal to the share he receives of output,altering, say, the terms at which he makes alleviate but do not fully correct for thisloans available to his tenants, not only can distortion. When an increase in fertilizer in-induce the tenant to borrow more but, more duces tenants to increase their effort, there isimportantly, can induce the tenant to work an incentive for the landlord to encourageharder or to undertake projects which are the utilization of fertilizer by contributing amore to the liking of the landlord. For in- higher share of the cost.stance, if the landlord makes credit less ex- Sinmilarly, consumption of certain com-pensive, the tenant (under quite reasonable modities serves to increase effort while theconditions) will be induced to borrow more; consumption of other commodities (alcohol)under somewhat more restrictive condftions may reduce it. It may be worthwhile for thethe tenant will be induced to increase his landlord to subsidize the consumption of theborrowing to such an extent that the amount former class of commodities, and to attemptwhich he must repay (including interest) in- to restrict the consumption of the latter classcreases. If there are severe penalties associ- (either by charging high prices for these com-ated with default (for example, the tenant is modities at the landlord's store or by pro-put 'ito bonded labor), the tenant will then viding wages in kind).need to work harder to avoid this con- Tlhus we establish that:tingencv.5 (i) Interlirnking markets can increase

Similarly the landlord may observe that the expected utility of both landlords andhis tenants are employing techniques of pro- workers; it unambiguously shifts the utilityduction which are too safe; the landlord's possibilities schedule outward;income rmight be increased if his tenants (ii) Accordingly, both competitive andwould be willing to employ techniques with monopoly markets will, in general, be char-higher means but higher variances. Again, he acterized by interlinkages;may note that his tenants are acting in a (iii) Although interlinkage shifts theparticularly risk-averse manner because they utility possibility frontier outwards, the com-are concerned about the consequences of de- petitive equilibrium with interlinkage mayfaulting on outstanding loans. Thus, the (but need not) entail tenants being worse off;landi.)rd may require that his tenants only (iv) While even with a monopoly land-borrow from him. He will charge them an lord, interlinkage may (but need not) entailinterest rate which is above the market rate tenants being better off.and this will induce them to restrict their In providing a general analysis of inter-borrowing. As a result, he may be able to linkage of markets, we are able at the same

time to obtain answers to several questions'It is important to note that in our analysis, the concerning the design of contractual

*korker is not myopic; at the time he undertakes the arrangements between landlords and ten-loan, he knows that he will want ("need") to work ants. In particular, we show that:harder next period, and takes this into account in de- '') A monopolist gains nothing fromtermining his demand for loans. If workers are i( . othic,the case for interlinkages may be even stronger than that controlling the markets for inputs and out-presented here. puts, if he is unrestricted in adopting cost

VOL. 72 NO. 4 BRA/f VERMANAND STIGLITZ: AGRARIAN MARKETS 697

and crop sharing rules; if he is restricted, competition, and equilibria with surpluscontrolling the market for inputs and out- laborputs can be a valuable additional instrumentfor the monopolist; I. Interlinked Credit and Tenancy Contracts

(vi) A monopolist only gains from con-trolling the consumption goods market to the In this section we establish that wheneverextent that he uses it to change relative prices there is not a pure rental system so that theof different consumption goods. landlord's income depends, in part, on the

It should be emphasized that our analysis actions of the tenant, and the actions ofapplies equally well to situations where the the tenant cannot be perfectly monitored,9terms of the tenancy contract (the share, plot the returns to the landowner are affectedsize, etc) are endogenous as well as institu- by the borrowing decisions of the tenant.'°tionally determined.6 The employm lent of In the following discussion we will be con-sharecropping arrangements need not, how- cerned both with the tenant's allocation ofever, be viewed (as interpreters of Marshall effort and his choice of technique of produc-did)7 as an inefficient contractual arrange- tion, for example, when and how often hement, even where it gives rise to the vtariety weeds, when he plants and harvests, the typeof problems which are the subject of this of seed he plants, the amount and kind ofpaper. When information is costly and there fertilizer he uses, when and how he applies it,are significant risks, sharecropping provides etc. Some of these decisions may be easilya method by which some of the risks are monitored by the landlord, but there areborne bv the landlord, and which, at the other actions, perhaps equally important, forsame time, maintains incentives for the ten- which the cost of monitoring would be veryant. high. The fact that the tenani has some dis-

This paper is divided into the following: cretion over his effort and choices, and thatSection I examines interlinked credit and his behavior can thus affect the returns totenancy contracts; Section II examines inter- the landlord, is referred to as the morallinked marketing and tenancy contracts; Sec- hazard problem.tion III points out the possible interlinkingbetwveen labor contracts and consumptiongoods markets; and Section IV presents the 9Although our results only require that the actions ofdifferent equilibrium frameworks discussed the tenant not be perfectly monitored (and that thein this paper, that is, monopoly, monopsony, contractual arrangements, which could accordingly

specify compensation based on the observed actions beperfectly enforced), in our model we will assume thatthese actions (effort or the choice of technique) cannot6This applies to the situations which xere previously be monitored at all. Clearly. some actions (such as what

discussed in the literature where interlinkage provides a crop is planted) are easily monitored, and thus theremechanism by which legal restrictions (such as limits on would, prc,umiahbl, be little difficulty in enforcing devi-usurious interest rates) and conventions (such as "fair" ations from the contract. Other actions, however, aredivision of output between landlords and tenants) may more difficult to specify (either implicitly or explicitly)be evaded (for example, Braverman-Srinivasan, 1981). in a contract, to monitor and to enforce; for example,Such situations can be viewed as special cases of the the "optimal" time to harvest will, in general be aanalysis provided here. complicated function of the weather conditions during

7Marshall recognized the importance of share con- the growing season as well as the expectations con-tracts in a world dominated by market imperfections cerning weather during the harvest season. By harvest-and the absence of certain markets (see Christopher ing earlier, the mlean harvest may be smaller but there isBliss and Nickolas Stern, 1981, ch. 3, and Jerald Jaynes, likely to be less risk (of the crop being destroyed beforeforthcoming. it is harvested).

8The optimal linear contractual arrangements are tOThe argument is. in fact, even stronger; these moraldiscussed in Stiglitz (1974) and Newbery (1977); the hazard problems arise even with rental tenancy arrange-optimal nonlinear contract is discussed in Stiglitz (forth- ments, if renters have insufficient capital to pay the rentcoming); in these studies the only variable which the in advance, and if there is sufficient variability in outputworker alters is effort; in this paper, we also consider that it may not be feasible for the renter to repay thethe problem of the choice of technique. promised rent.

698 THE A MERICAN ECONOMIC REVIEW Sl:PTE,IBER 1982

A. A Getneral Model ual's consumption of other commodities, wecan write

We 'uegin our discussion by presenting ageneral model. The following subsections (2') U=U(c, e, S2, z)=U( y-zq, e, Q2, z).focus on a number of special, but important,specializations of this model. Similarly, consider an individual with initial

We assume that there is a pure sharecrop- wealth WO who wishes to borrow to financeping agreement.1 ' The tenant receives a share current consumption. Assume the landlorda e the gross output, the landlord receives charges an interest rate r and the tenantI - a. Output, Y, is a function of: (a) the borrows an amount B; denote the ith periodeffort of the tenant, which we denote by e; 12 consumption by c,. We can then write(b) environmental factors (the weather) de-noted by 6; and (c) the choice of teclinique, (3) U= U(co, cl, e, I)denoted by Q. We let an increase in Q repre-sent an increase in risk (see discussion be- = U(Wo + B, y-(1 + r)B, e, 0),low). Thus

(which is of the form (2)). 14(i) y Y(e, 0, ,). The tenant chooses e, z, and ,Q to maxi-

mize his expected utility, taking into accountIt will greatly simplify the analysis, howvever, the production relationship (1),if we write( 1I',) Y=g ()(4) max Eu(y, e, f, z, q)-V(a, q),

where g is a positive random variable with a where a, the tenant's crop share, can bedensity function (Eg g): h = h(g, 2). determined in a variety of ways, it may, for

The tenant's utility'3 can be expressed as a instance, be directly controlled by the land-function of his income y = aY, his effort e, lord. From the first-order conditions for thishis technique of production, S2, of the other maximization, problem, we can solve for thevariables which are under his control, z, level of effort, the choice of technique, andand of a set of variables which are under the level of z as a function of the controlhe control of the landlord which we denote variables at the disposal of the landlord, that

by q: is: e = e(a, q), z z(a, q), 0 = 9(a, q).For simplicity, we shall assume that the

(2) u = u(y, e, 2, z, q). landlord is risk neutral. His expected income,P, has two parts: the direct receipts from the

In the subsequent analysis, we shall investi- sharecroppers, (1 - a)f(e)Eg, and the returngate several special cases of this general from the interlinked activities (which may bespecification. For instance, if z is the individ- negative), ?n(q, z). Henceual's consumption of some commoditypurchased from the landlord, q is the price (5) P= (1-o&)f(e)k + 7(q, z),charged by the landlord, and c is the individ- Thus, for instance, in the first example where

the landlord sold, say, alcohol to his tenants''The m )del, however, is far from being the most at a price of q,

general one for which our conclusions are valid. Thus,although we limit ourselves to discussing pure share- (6) T(q, z) = (q -qo)z(q)cropping contracts, the results apply for virtually anycontractual arrangement other than fixed rental con-tracts when there is no possibility of bankruptcy. 14In these two examples "q" is the price at which the

-2It should also be clear that e could represent a landlord makes goods or credit avaif%ale to his tenant.vector of inputs, including fertilizer, machinery, etc. The landlord need not, howeve., restrict himself to

XAs the following discussion will make clear, this is a linear price systems; he may i-ulpose a variety of restric-d/rtl ed utility function, analogous to the indirect utility tions on his tenants, emplo' a nonlinear price system,function. etc. See fn. 21 below.

VOL, 72 NO. 4 BRA VERMANAND STIGLITZA GRRIARN MARKETS 699

where qo is the price at which the landlord Although there is a kind of formal similar-can purchase (or produce) the given com- ity between those cases where the landlordmodity. In the second example, where the wishes to induce borrowing and thus sub-tenant borrows at the rate of interest r, the sidizes the rate of interest, and those casesreturn to the interlinked activity is simply where he wishes to restrict borrowing activ-the difference between the rate of intern-t ity, there are imnportant asymmetries in theclharged and what the landlord could obtain costs of implementation. The latter requiresfrom his funds lent elsewhere, times the a kind of monitoring of the tenant which theamount borrowed.15 former does not.

The problem of the landlord is now sim- The analysis proceeds in a number of steps.ple: he chooses q and a (if a is a control First, we analyze how the behaviorvariable; q may in fact represent a vector of of the tenant is affected by the presence ofcontrol variables) to maxinmze his expected outstanding loan commitments. We analyzeincome, subject to the constraint of being separately the effect on the level of effortable to obtain workers; that is: (Parts B and C) and on the choice of tech-

nique (Part D). We then use these restults to(7) maxP; such that V(a, q) > U. determine the optimal policy of the landlord

mq, (Parts E and F). Part G considers the partic-ular problems raised by default clauses

The first-order conditions for this problem (bonded labor). Part H argues that there is a(for q) can be written as symmetric argumcnt, when there is a positive

probability of default, for why lenders would(8) dP/dq = (1- a) wish to effect borrowers behavior in the

land-tenancy market, thus strengthening theXl g( te) de + ( (e) dg 1 argument for interlinkage,

l dq d2 dqJ Although most of our discussion is couchedin partial equilibrium terms, Part I shows

+ *7q h dz av how it may be extended to a general equi-q dq aq' librium framework.

where X is the Lagrange multiplier associated B. The Impact of the Tenanit's Borrowingwith the constraint in (7). What is critical on his Effort Supplyabout (8) is that the landlord realizes thatchanging q has not only a direct effect (an In this section, we ask: How does the facteffect on his return as a lender or as a that the individual must repay an amount,shopkeeper), but an indirect effect on his (I+r)B, to a lender affect his supply ofincome, through its effect on the level of effort?effort or the choice of technique of the ten- To analyze this question we specialize theant. It is this which provides the fundamen- general model presented earlier by assumingtal motivation for interlinkage in our analy- separability between consumption and effortsis. at one date, and those at any other date. This

The subsequent sections attempt to analyze enables us to address the question of thein greater detail this argument, to ascertain, effect of outstanding loans, without askingin particular, the conditions under which th!e how the outstanding debt was determined.landlord 1 likely to subsidize, say, borrow- We focus here only on effort, taking theing, or those under which he will attempt to choice of teclhnique of production as given.restrict it. Defining B = (1 + r)B as the fixed amount

the tenant must pay to the landlord and15The returns from interlinked activities may be ran- letting c denote the tenant's consumption,

dom; 7r then denotes the mean value, also 7r may be a thenfunction of e and 2. This would necessitate oniy minormodifications to the analysis. (9) c= aY-

700 THIEAMERICAN ECONOMIC REV/ElII' SEPTEMtfBER 1982

and the individual now chooses effort to this implies that he will try to avoid situa-ma:imizc tions or decisions which would increase the

probability that his output will fall below a(10) maxEU(c, e) certain level such that he would no longer be

able to repay his debt and would have tomaxEU(agf(e) - 3, e), offer bonded labor services. Clearly, there-

{e) fore, the impact of adding a bornded labor

where Uis, a concave function of c and e. We clause to the loan agreement is to inicreaseobtain the first-order condition'6 the tenant's effort.

i tOne formal way to model the bonded labor(11) af'(e)EU g + EU = 0 clause for a risk-averse tenant (Figure 1(a)) is

by assuming that the tenant's marginal util-

By total differentiation of (11) and using ity of consumption, (or, alternatively, of in-the concavity of U, it is evident that de/dB come, for a given level of debt), Uc, is veryZ0 as high, that is, approaching infinity for verylow values of c. (See Figure l(b).) In the

1 rextreme, we can depict the tenant as choos-(12) d f (Ucagf + Ue)h dgI/dB ing the minimum level of effort required to

avoid bondage. Thus, e is chosen so that

E E(Uc,a.gf '+ U,.c) -:° (13) atf(e)gmi ,,

Since Uc

VOL. 72 NO. 4 BRA 1VERMAVNAND STIGLJTZ: AGRARIANMA RKETS 701

U U' U

c Ic C

(a) (b) (c)

FIGURE 1. UTILITY AS FUNCTION OF INCONE (FOR GIVEN LEVEL OF DEBT) UNDER ALTERNATIvE DEFAULT CLAUSES

Let rowing on tenants' effort can still be positiveonly if the second set of terms dominates the

(16) g-(c + )/af(e) first term. The following proposition andremark summarize this subsection.

be the critical value of g below which bank-ruptcy occurs. Then the tenant's objective PROPOSITION 2: If the tenant's loanfunction (10) becomes agreement includes a bonded labor clause, in-

creased borrowing will increase the effort of(10') max |(XfU(, e)h dg teniantis and, hence, the return to the landlords.

0 Remark: If the tenant's loan agreement in-

+ | U( agf(e) - B, e)h dg cludes a bankruptcy clause instead of agj bonded labor clause, increased tenant bor-

rowing may not increase his effort supply.which leads to the first-order condition Since landlords' expected returns are clear-

ly dependent on the tenants' level of effort, it(11') f [UCXgf'+Ue]hdg+ fUehdg=o, is clear that, in general, tenants' borrowing

g fo has an effect on larndlords' expected returns;this effect is beneficial under the bonded

and hence to labor system, but if bankruptcy is possiblethen increased borrowing may have a dele-

(12) de 0 -Uagf 1 terious effect on landlords' returns.dB a xg fe(2 0af(e) D. The Impact of the Tenant's Borrowz'ing

- f[ Uccagf'+ Uce] h dg 0 0. on His Choice of Technique of ProductionNow, let us assume that the only set of

An increase in borrowing makes bank- decisions available to the tenant is the choiceruptcy more likely. This effect reduces the of technique, S1. Effort is fixed (for example,marginal return to effort and is expressed by to obtain any outpuit requires -given level ofthe first term of (12') which is always nega- effort; increased effort beyond that pointtive. The sum total effect of increased bor- bears little fruit). Since our main concern

702 TIlEAMERICAN ECONOMIC REVIEW SEPTEXfBER 1982

here is with risk taking, let us first consider a hset of projects, all of which have the samemean, that is,

(17) f gh dg = constant,0 h

or hl

(18) Ighndg=0. g0 a) MPS, expressed in densities, h

Therefore, riskier projects represent mean-preserving spreads (MPS)1 9 of less-risky iiprojects, that is, lettinig H represent the dis-tnrbution function, riskier projects are de-scribed by

(19) f Ha dg 0 for all x > 0; H h20

(20) f H,,dg 0o.o g

In Figure 2 we graphically express an MIPS b) MPS. eApressed in cumulative distributions, H

of the H distribution, that is, the shifting of FIGURE 2. MEAN-PRESERVING SPREADweight from the center to the tails. It is INDISTBUTIONOFgexpressed both in terms of densities andcumulative distributions.

Making the same kind of separability as- and (20), we obtainsumption employed in Part B, the first-ordercondition for the tenant's choice of technique (23) d0l/dB - 0is given by

(21) f Uhn dg + f Uh dg = 0, as- f 0 HrdgJdx 0-

and assuming 'a = 0,20 it immediately fol- Using (19), it is thus apparent thatlows that

(24) d2/dBO as U, 5°(22) d2ldh:0 as - Ufhtdgt0.

0 From (24) it is clear that an increase inborrowing will leave risk taking unaffected if

Integrating twice by parts, and using (18) and only if the utility function is quadratic,so U .. = 0. Othernvise, risk taking may either

"Consult Rothschild-Stiglitz (1970) and Diamond- It is worth creatse v seialStiglitz ( 1974) for discussions of mean-preser-ving (a Assumet a bondedrl claseitsproads. (a) Assume a bonded labor clause in the

2"Throughout the reinainder of the paper we assume loan agreement, so that Ub for very low val-U,,= 0: if we write U=U(c, e)-V(Q2), V(f2) can be ues of c is very high, that is, approachingthought of as the "cost" of technology Q. Furthermore, infinity. Then from (22) it is apparent thatif all available technologies have the same mean, then an increase in borrowing reduces risk taking:for an interior solution (i.e., £2> £2i,where £2m,n is theleast risky technology), we require that V'(Q2) be suffi- individuals are concerned with only the lowerciently large. tail of the distribution where U, is very high

[01.. 72 NO. 4 BRA VERWL4,VAND STIGLITZ:AGRARIAN AfARKETS 703

and ha, the shift in the density, is positive (see fn. 9 for another example). 21 If mean(see Figure 2(a)). Hence an increase in bor- output is not increased too much, it will stillrowing induces tenants to be more conserva- be true that if tenants have decreasing abso-tive. lute risk aversion (or if there is bonded labor),

In the limiting case described earlier, Q2'* is an increase in tenant's borrowing wil! resultthe largest value of 2 such that in a roduction in risk taking. This reduction

in risk taking, however, will now have an(25) agmtn(R*) effect on landlords; their expected income

will be lowered.where g( Q*) is the minimum value of g for Formally, we postulate thatthe technique Q*. Thus, (27) Y= gX(Q)f(e)

(26) dQI*/dB = l/ag'in < 0, with '> 0 (recall that we have adopted theconvention that an increase in S2 represents

since gJ,n( Q) is negative; increasing Q means an increase in risk). Now the first-order con-an increasing spread of risk which implies dition for the tenant's modified objectivethat the smallest value of g for given S2 function will be (instead of (21))decliines.

(b) Assume that the individual has de- rf,gf\creasing absolute risk aversion. Absolute risk (28) J ha+Ua+L/gX(f2)f(e)] dgaversion is defined by

and then,

A= -U soA'- U+ 2- (29) d0aldB>O

as -f[Uch + UccgXf ] dg0.

Thus, decreasing absolute risk aversion im-plies U( > 0. Therefore, from (24), risk tak- Thus our earlier results are unaffected, pro-ing is reduced by an increase in borrowing. vided X' is sufficiently small (the bounds on

(c) Assume a bankruptcy clause in the X' are determined by the magnitude of Uccc).loan agreement. If the individual's utility We can summarize this subsection with thefunction is linear in consumption (in the following proposition and remark.absence of bankruptcy, he would be riskneutral) he now becomes a risk lover; this PROPOSITION 3: With a bonded laborholds more generally, provided he is not clause in the loan agreement or with decreas-

too risk averse (see Figure 3 below). Then ing absolute risk aversion, an increase in thethe increase in borrowing may induce more tenant's borrowing will reduce his risk takiiig.risk taking. He will therefore not select some techniques

According to our analysis, in which wefocus on choices of techniques that leave the 21Presumably, the choice of seed as a decision vari-mean output unchanged but increase the able which could be specified by the contract betweenspread of distribution, these changes in landlord and tenant. But as we noted in fn. 9, there arethe choice of technique leave the risk-neutral many other decisions concerning techniques which couldlandlord unaffected. iowever, in many cases not be so casily specified. or if specified, monitored andenforced. A fuller analysis would, of course, not simplytechniques which are riskier also have higher dichotomize the actions into "observables" and "nonob-means. This is true, for instance, of some of servables." There are costs of observation, as well asthe HYV seeds of the "green revolution," costs entailed in decision making, contract specifica-w\hich are more vulnerable to rain falls, un- tions, monitoring and enforcement; these costs will forder which circumstances their output is actu- iS an absentee landlord Ths wance pairtly on whether healIN lower than that of more traditional seeds contract should be treated as an endogenous variable.

'04 THE A MlRI(AN ECONOMTC RE17h'IEI' SE,PTh:MABER 1982

which a/lovtw for higher mean outpul as well as given amount at a "favorable" interest rate,higher risk. This reduces thte reurnis of the but beyond that point, charging a prohibi-risk-neutral lanidlord. tively high interest rate, Even if the landlord

cannot directly monitor loans from the otherRemark: With a bankruptcy clause in the creditors such a scheme may be very effec-loan agreement the tenant may increase his tive. To borrow supplementallv from otherrisk taking with increased borrowing and, lenders may then be very expensive: sincethus, may select riskier and higher mean the loan from his landlord has seniority overoutput techniques than he Nwould have cho- any supplemental loan, any potential lendersen under a bonded labor clause. This choice would have to charge a very high interestincreases a risk-neutral landlord's ref':rns. rate.

The above arguments establish clearly that If the amount which an individual bor-the return to the landlord will depend criti- rows from other lenders is observable, thencalIk' on whether his tenant has borrowed, the competitive equilibrium contract willand if so. how much. Formally, the landlord make the share (or other provisions of thecold effect the same behavior by charging a contract) a function of the size of loans therenl paid at the end of the production period worker has undertaken. In this case thereano equal to B, in additioii to the share. would be no difference between the equi-What is important is that tie individual's librium which would emerge if the twobehavior is affected by the total magnitude markets were linked together, or if they wereof the sum of rents and loan repayments, separated. If there are costs of monitoringand that it is of value to the landlord to and collection, however, there is a naturalknow their magnitude. In other words, al- advantage for the landlord to tindertake thethough the form which the tenants' commit- loan.menits take (whether rents or loans) may In the case where there is a positiue exter-make little difference, it is important for the naliti% there will be an incentive for thelandlords to control the total and it is this landlord to subsidize loans and to encouragewhich provides the motivation for interlink- the tenant to become indebted to him, soing. (Indeed, rent paid at the end of the that he will work harder to repay the loan.production period can be viewed as a rent (Bcirdhan and Rudra. 1978, report that inpaid at the beginning of the period plus a West Bengal landlords quite often offer ten-loan fromn the beginning of the period to its ants loanis at interest rates below the marketend-, in a sense, then, rent and loan comnmit- rate, sometimes even offering interest-freements are equivalent.) consumption loans.)

We now analyze formally the landlord'sE. The Equilibrium Termiis of Loans from optimal contract. We write the tenant's util-

Landlords to Tenants ity function as U*(c 0, cl, e) where c0consumption in the 0th period W0 + B,

Let us first consider the case where an W0 denotes the individual's initial wealth 22increase in borrowing reduces the expected and B denotes the amount borrowed, clreturn to the landlord-a negative exter- af(e)g - B(l ± r) where cl is consumptionnalitv. While he would like to restrict the in the first period, and r denotes the interestamount of borrowing, he would not want to charged to the tenant.23 In general, r will beeliminate it altogether. The restriction on the a function of B; the landlord specifies theamlount of borrowing obviously reduces the "loan functioni" r(B) and the tenant choosesexpected utility of the tenant; thus, in acompetitive environment, the tenant will re-quire an alteration in some other provision 22Forsirnplicity. we take II;,here as Ninply a param-of the contract to compensate for any such eter. It represents, for instance. the amount the tenant

rtfor instance, be able to has been able to .ave. Clearly, in a more general model,restriction. He might, iawould be affccted bN the terms of the contract.induce his tenants to accept a borrowing 2.We ignored here ihc direct effect of horrowing onrestriction by lending to the individual a production. See Part Ci below.

VOL. 72 NO. 4 BRA VERAIANAND STIGLITZ:AGRARIAN MARKETS 705

the loan size, B. Hoxvever, since in our analy- In contrast, in a competitive loan market,sis we assume that all tenants are identical, if the tenant and landlord had equal accessthey will all choose the same value of (r, B).24 to the capital market (an admittedly dubiousThere are a large variety of loan functions assunmption),which will induce the same choices of {r, B}(and indeed, any {r, B) which makes the u'(co)tenant better off than he would be with (32) -(ce) -l+p.B = 0, can be generated by some loan func- EUc(c1, e)tion). Hence, we analyze the behavior of thelandlord assuming he controls r and B (or Comparing (31) and (32) we obtain theequivalently B(l + r) and B) directly. 25 If p following proposition:is the cost of capital to landlords, we candescribe the optimal loan as the solution to PROPOSITION 4: The optimal contract of-the landlord's problem.26 fered by the landlord will entail farmers bor-

rowing more (borrowin-g less) than they would(30) maxP in an unlinked market with equal access to

(B, B(] + r)) capital, if de/dB > ( < ) 0, that is, if increaseda)f(e) + (1 + r - (1 + p)) B, borrowing induces more (less) effort.

In order for the landlord to control simulrwhere, without loss of generality, we have taneously both the amount borrowed (B)absumed Eg-1, subject to and the amount owed (B), he must use a

nonlinear loan function.27 In footnote, 27 weEU*(Wo + B, af(e)g-(I + r)B, e) discuss the case where the landlord is re-

stricted to charging a simple interest rate.As before, we assuame that U* is separable in (Clearly, intermediate cases, for example,c0 and cl, that is, U* = u(c0 )+ U(c1, e). Thenwe obtain the following by using the en-velope theorem and recalling B B(1 + r): 2 7The contract described in the preceding analysis

entailed the landlord specifying B, the amount bor-(31) -(dU*/dB)/(dU*/dB) rowed, and B=(IJ+r)B, the amount paid back. The

landlord does not, however, allow the tenant to borrowEUc(cl, e ,as much as he would like at the interest rate r = (B/B)

EUc 1 , e) - (1- a)f'(e) de/d + 1 -1. Effectively the landlord is employing a nonlinearu'( c0 ) 1 + p interest rate schedule to maintain the individual on the

same expected utility curve. In Section V, below, weconsider what happens if the landlord is not allowed to

-- (dP 1dB)/(idP/dB). use such schedules, and cannot decrease a or plot size tocompensate for lowering in the interest rate. (Thus, theexpected utility constraint will not be binding.) Notethat if the landlord cannot restrict the level of credit or24See Braverman-Guasch (1981) for a discussion of a "force" credit, but can announce an r different from p,

self-selection separating equilibrium, where heteroge- and can alter a, then instead of (31) we obtainneous tenants choose different pairs of {r, B) from aloan function r(B), offercd bY ihe landlords.

251f the population is heterogeneous, then the precise EU g/EU, = I I-a f'e 8/ne -(r-p) 8Bspecification of the loan function becomes more im- e a f 8/na f aajportant. Even then, provided that there are only a finitenumber of types of borrowers, the same sets of choices + (I - a) f'e 8lne 8/nB f dB (r-p) 1can be induced by a large variety of loan functions. a f + - li -B -Only in the limiting case of a continuum of types, does a f 8/nA 8/nr rB dr B jthe optimal loan function become determinate,

26 In the calculation below, we take the share and the Whether the landlord will set r! p depends on tenants'plot size as exogenously given; alternatively, we could risk aversion, as well as the elasticity of effort withview them as having been optimally chosen. For pur- respect to share (a) and with respect to indebtednessposes of the ensuing analysis it makes no difference. See (B), and the elasticity of indebtedness with respect tothe Appendix. the interest rate.

706 THEA AfERJCAN ECONOMIC REVIEW SEPTEMBER 1982

where the landlord can restrict the maximum in his choice of technique, then a bondedborrowing, can be treated within the same labor clause will be preferred by the land-framework.) lord.

In all of the above cases, notice that thetenant could have elected to keep some of his G. Production Loansinitial wealth in savings, or could have elect-ed to borrow less to ensure adequate con- For simplicity, the analysis to this pointsumption in period one; yet the landlord has assumed that loans are only used formanages to induce him to borrow the amount consumption purposes. There is no interac-B even though the tenant is fully aware of tion between the amount lent in the previousthe consequences.28 period and output in the current period. The

modifications required to take this intoF. Default Clauses account are straightforward;2 9 we let output

be a function not only of effort but of theThe discussion in Section I.E did not cover amount borrowed: 30

default clauses. As previously discussed, abonded labor clause increases the tenant's (33) Y= gf(e, B).effort but reduces his risk taking. Thus, thetwo effects go in opposite directions in their Then, the first-order condition for the (ap-impact on the return to the risk-neutral propriately modified version of the) maximi-landlord. The bankruptcy clause produces zation problem (30) can be written asthe opposite result: it reduces effort andincreases risk taking. Hence the landlord's (34) EUI/EUcagfBpreference for one clause over another de- (1- a)fae/aB+Ipends on the extent of the significance of the ( emoral hazard problem regarding effort supply (I1-a) [tfeae/aB + fsI + (1+ p)compared with the tenant's choice of tech-nique. For example, if effort can be relatively Thus the landlord takes into account that (a)easily monitored and enforced, and the moral he appropriates a fraction of the return fromnhazard problem mainly involves the tenant's the increased input ((1- a)fB); (b) the in-choice of technique, then a risk-neutral creased inputs alter the level of effort; andlandlord will tend to prefer a bankruptcy (c) an increase in the amount lent increasesclause to a bonded labor clause. On the other the expected utility of the tenant (and thushand, if the moral hazard problem is more enables him to alter some other term of thesignificant in the tenant's effort supply than contract more to his liking while still bcinrg

able to recruit tenants). The effect of in-28 1t is possible, of course, that creased inputs on effort is ambiguous;3 1 if

E(I -( af e ) ( -a)fJ( e) d + 1 2 9 Similar modifications need to be made in the analy-g,dB B B==O sis of the consumption loan model when the utility

u'( WO) I + P function is not separable, so that changes in co affectef fort, e.

In that case the landlord would like to induce the tenant 30This formulation assumes that the marginal incre-to lend to him, but if this is not feasible, then B = B = 0. ment in input from a marginal increase in borrowing isNotice that it is still possible that unity. More generally, if output is a function of effort

EU( c1, e) and an input, z,f(e, z) and z is a function of B, z(B),< 1e-then f(e, B) -f(e, z(B)), Equation (34) below is un-u'(co) B=O p affected, although the interpretation of fB needs to be

modified.in which case the tenant may attempt to borrow 3difee h -elsewhere. The landlord will attempt to restrict this with respect to B (keeping B fixed) yieldsborrowing, if he rcn. If he cannot, he may still lend tothe tenant. In either case, there is a kind of interlinking, ae/aB =-{afBeEUfg + ct2fBfe [ E(U,,g + Uc) g] }although in the first case, no transactions occur in thenterlinked market. (-xfe,EU.g+ cafE[(U,af.+ UcLe)g] f EULee-.

VOL. 72 NO. 4 BRA VERMANAND STIGLITZ.AGRARIANMARKETS 707

effort and other inputs are complements (feB Uliliiy pwisibilities schedule> 0), as we might expect, the increased in- 3 withinterlinkingputs increase the marginal return to effort. /But the increased output has an additional %income effect which normally decreases the D Alevel of effort.le e oKfor. Utility possibilities schedule

In the absence of subsidization, the tenant w' 0 without interlinkingwould have set c C

(35) EU(I + p) = EUag.Landlord's Expected Income

Thus, whether the landlord prefers to sub- FIGURE 3. WELFARE COMPARISON OF EQUILIBRIUMsid'.; or to restrict borrowing depends on WITH INTERLINKING TO EQUILIBRIUMwhether WITHOUT INTERLINKING

EU,agfB aeI fee/B fB_E U e I. General vs. Partial Equilibrium

Clearly either is possible, depending on the The preceding analysis shows that, for anydegree of complementarity (feB) and the fixed level of expected utility of workers, thespecifics of the utility function. landlord can increase his expected income by

simultaneously controlling the credit market.H. Externalities from the Landlord to the This argument establishes that the utility

Lender in the Absence of Linkages possibilities schedule, in an economy in wherethe two markets are linked together, will be

Our previous discussion emphasized the above that of an economy where (for exam-externality associated with the lending activ- ple, as a result of legal restrictions) the twoity on the income of the landlord. There is are kept separate, and it establishes that in aalso a reverse externamity in situations where competitive equilibrium such linkages will, inthere is a positive probability of default, so fact, exist. However, it does not necessarilylong as the return to the lender is affected by imply that landlords are the only benefi-default. (Normally, we would assume that ciaries, or indeed, in general equilibrium,default reduces the expected income of the that landlords will be better off at all. Thelender, but it is possible that, with bonded new equilibrium with linkages may lie to thelabor, it increases his expected income.) The northeast of the one without linkages (pointanalysis is similar to that presented earlier. A, Figure 3), making both workers and land-What is relevant now, however, is not the lords better off, but it need not.mean output of the farn, but the probability In Figure 3 we depict four possible situa-that the income of the tenant, after paying tions: in A, the landlords and workers arethe landlord's share, is sufficiently low so both better off; they share in the gains fromthat the tenant goes into default. This is interlinking markets; in B, tenants have aclearly affected by the terms of the contract subsistence utility level to which they are(the share, the plot size, the supply of com- always driven; thus all the gains from inter-plementary inputs), but the landlord, in linking accrue to landlords; in C, tenants arechoosing the optimal contract, ignores the worse off as a result of interlinking markets;impact on the lender. Since the landlord who all the gains accrue to landlords-and thenlends funds to his own tenants can internal- some; while D is the converse situation, whereize this externality, he can obtain a higher landlords are worse off as a result of inter-return from lending to his own tenants than linking; all the gains accrue to tenants.he can obtain lending elsewhere. This, then, Under competitive conditions, we canprovides a further motivation for interlinking ascertain the conditions for C or D to occu-r.the two markets. The effect of interlinkage on the welfare of

708 THE AMERICAN ECONOMIC RE VIE W SEPTEMBER 1982

supply of tenants, the optimal "interlinked" con-tract entails a plot size for each tenant whichis smaller (larger) than in the noninterlinked

3\ 0 D Interlinkage increases demand contract, then, at that level of expected util-\forlaborers ity of tenants, there is an excess supply (de-

mand) for tenants; hence, in the competitive, D d \ l equilibrium with interlinkage the expected

nd for loborers without utility of tenants must be lower (higher) thann|\erlinkage in the equilibrium without interlinkage. The

\\calculations of the relationship betweenl theC Interlinkage decreases demand optimal plot size and interlinkage are com-

f lborers plicated, and are presented in the Appendix.There we show that interlinkage can, undernot implausible conditions, increase plot size(at a give-n level of utility of tenants) and

Demand, supply for laborers make tenants worse off.FIGURE 4. COMPETITIVE EQUILIBRIA IN THE TENANCY Consider, for instance, an economy with a

MARKET WITH AND WITHOUT TNTERLINKAGE Cobb-Douglas production function. It isknown (see Stiglitz, 1974) that in the optimalcontract, the share of the tenant a equals the

tenants is, in principle, easy to ascertain. We implicit share of labor S,, (where SW is thecan derive a pseudo demand curve for labor. exponent on labor in the Cobb-Douglas func-There is now not a simple price of labor (the tion). This share is optimal for all levels ofwage); but we can, instead, summarize the borrowing. Changes in the credit terms, thus,contract in terms of the expected utility that must be offset by changes in plot size. Ifit generates to the tenant. At higher levels of interlinkage attempts to restrict credit (as itexpected utility, there will be a lower de- would if the conditions of Propositions 1 andmand for labor, as depicted in Figure 4 4 are satisfied) then tenants will be worsewhere the supply of tenants is assumed off; to compensate them (leave them at theperfectly inelastic. 32 The competitive equi- same level of expected utility as they wouldlibrium is just the intersection of the demand have without interiinkage) plot size must beand supply schedules (point 0 in Figure 4). increased; this reduces the demand for te-Interlinkage may shift the demand schedule nants, alnd hence the general equilibrium ef-upwards, in which case the tenants will be fect corresponds to the partial equilibriumbetter off (point D in Figure 4). If it shifts up effect,the demand schedule enough, landlords will Conversely, if interlinkage attempts to en-compete for tenants so fiercely that landlords courage borrowing (see Propositions I and 4)will be worse off. However, it is possible for then tenants will be better off as a result ofthe demand curve to shift down, in which interlinkage; to leave them at the same levelcase tenants are worse off (point C in Figure of expected utility, plot size must.be reduced,4). If at a particular level of expected utility and this increases the demand for labor, and,

again, the general equilibrium effect con-3 forms to the partial equilibrium effect. In

'2The case with elastic supply of laborers may be fom toheprileuibum fec.Ihandled analogously. There is one critical difference: if more general cases, the partial and generalthe supply schedule of tenants is upward sloping (as one equilibrium efects need not be qualitativelymnight expect), and interlinkage increases plot size at a the same. 3fixed level of expected utility, then in equilibrium, whenland area is fixed, plot size will increase. The number oftenants will accordingly decrease. Conversely, if inter-linkage decreases plot size the equilibrium number oftenants will increase. One can, thus, infer the welfare 3 3This is a general property which arises in variety ofimpact from observing the equilibrium effect on plot situa!ions where risk is involved. See, for instance,size. Newbery-SuigliLz (1982).

101_. 72 NO. 4 BRA VERMANAND STIGLITZ: AGRARIAN MARKETS 709

In Section IV below we analyze the effects framework where the lanldlord both pos-of interlinkage in noncompetitive environ- sesses sufficient controls and gains frommerits. pushing the tenant down to his reservation

utility, there is no possibility to extract fur-I1. Interlinking Marketing and ther surplus from the tenant. Hence, in such

Tenancy Contracts a world the following question arises: Doesthe control of output and raw material prices

In the discussion above, we assumed that provide an additional instrument for theoutput and raw material prices are exoge- landlord to motivate the tenant (and extractnously given to both landlords and tenants. surplus) besides those already discussed?Landlords and tenants therefore face identi- Consider the tenant's problem in the ab-cal prices; quite often, however, one observes sence of uncertainty. Assume that both thethat the landlord undertakes the marketing tenant and landlord face the same price foractivity for his tenant and is involved in the the raw material fertilizer, P, (for example,provision of raw material inputs.3 4 Is there the fertilizer purchased from the village co-an explanation for this interlinkage between operative). For notational convenience, wemarketing and tenancy contracts which is shall define the fertilizer units such thatanalogous to that presented earlier, for the P =1. However, the landlord buys t]iie out-interlinkage between credit markets and put from the tenant at the price PT which istenancy.3 5 In this section, we focus on in- different from the market price at which theputs, while in the next we consider interlink- landlord sells the output, PL. Thus, the ten-ages with consumption goods markets. Here ant's income iswe show: (i) if there is a single input, and ifthe contract can specify the cost and output (37) YT= aPTf(e, x)-/3x,sharing formula without restriction, then in-terlinkage provides no advantages; but (ii) if where a and /3 denote the tenant's outputthere are restrictions on the cost-sharing for- share and cost share, respectively, and hemula (and, in particular, if the same cost- maximizessharing formula musXt be employed for avariety of inputs), then there will be inter- (38) max U(YT(e, x), e).linkages. (e,x)

It is widely believed that by marketing the From the first-order conditions we obtainoutput, the landlord may explicitly (by buy- (39) f IB/P .ing the product from the tenant at a lower x T;price than at the market price) or implicitly (40) fe =-U 2 (YT, e)/UI(YT, e).aPT.(bv charging high marketing costs), extractfurther surplus from the tenant. However, in Hence, the tenant's decisions are fully de-a utility equivalent contract equilibrium termined by the set of controls 3, aPT. Let

us therefore define & aPT, and write the

'4 For simplicity we will focus in this section on tenant's effort and input supply functionsinterlinking of marketing of output and tenancy con- e = e(a, /3), x = x(&, /).tracts while similar reasoning applies to discussion re- Now let us move to the landlord's problemgarding marketing raw materials by the landlord to the and determine whether PT plays a separatetcnant role for him, in addition to its role in de-

"There are several other reasons why the landlord refrn him in landd on toi rles de-might market the tenant's output. If the landlord re- terming a. The landlord who faces thequires the tenant to market his output solely through output price, PL, at the market place maxi-himself (the landlord), then he creates a simple way to mizes his income subject to the utility equiv-monitor the output and guarantee that he obtains the alence constraint, that is,agreed share. Another reason is that marketing activityex.hibits increasing returns to scale; hence, it is efficient (4) max (I-a)PLI[e(&, /3), x(&, )]for a specialized agency to market output of many {',xB, Pr)productions units together. The landlord may providesuch an agency. -(0- P)X(&, 8),

"10 THE.A ,tERICAN ECONOMIC REP7EW' SEPTEMBER 1982

subject to which the landlord sells the ith input to thetenant (we normalize the units so the

U[YT(a,I3P PT),e(a)] =F. purchase price of all inputs by the landlordis unity), and /,3 is the share of the i th input's

Equation (41) can be rewvritten as cost borne by the tenant, then the tenant'sbehavior is fully determined by the set of

(42) max PLf -X YT conitrols (ThP,, aPr}. Similarly, the profits of(a,.:, Pr} the landlords are a function of the same

variables. Thus, any equilibrium can be sup-The last term is the tenant's income. By ported by the landlord setting Pi 1 for ev-

inverting the const;~Ant in (41) we obtain ery if (the price the landlord must pay for theinputs). But again, if there are restrictions on

(43) Y = = [V, e(&, /)]. pi (in particular, if the same cost-sharingformula must apply to all inputs), since the

Substituting (43) into (42) we obtain optimal value of ({/3P1} will differ frorm oneinput to another, so, too, must the optimal

(44) max PLAf(&,I )- x(&, /3) price. However, note that it is only thiroughchanges in the relative prices of inputs that

-0(7, a, ,B) nI(a, /3), the landlord achieves the advantages of inter-linkages.

from which it is clear that the landlord caresonly about x rather than about a and PT III Interlinking of Labor and Consumptionseparately. Hence Good Markets

PROPOSITION 5: In a utility equivalence The argument of the previous section sug-world where shares are not restricted, the gested that providing the landlord with addi-landlord can pay the tenant the market price tional instruments for exploiting workersfor his output, that is, PT = PL. However, if through control of the product market wouldshares are restricted either by social norms or not, in fact, enable him to do so any betterlaws, the landlord can extract the tenant's than he could have done by simply alteringsurplut by paying him a price lower than the the "contract" which he imposed on hismarket place, that is, PT < PL, without any workers.3 6 This is not true for the landlord'sloss in effic iency. control of the consumption good market. We

represent the typical worker by his indirectA similar analysis suggests why it may be utility function V= V(C, p). By the usual

in the interests of a monopsonist marketing arguments, V and e are both homogeneousagent to attempt to interlink the credit of degree zero in C and p: so long as themarkets with his marketing activity. Assume monopolist does not change relative prices,that he pays a single price for the output the fact that he may also own the store atwhich he purchases from farmers. He sets which his workers buy their goods has nothis price so the marginal cost of purchasing effect on his ability to exploit his workers,an additional unit equals the marginal reve- The landlord. wil, however, wish to changenue he obtains from selling the good. But the relative prices of goods, to encourage thesince the price he pays is, in general, less consumption of goods which are comple-than the marginal cost, the tenants have (from mentary to effort, and discourage the con-his point of view) insufficient incentives to sumption of goods which are complementaryproduce. If he can induce them to producemore at the given price, this will increase hisprofits. Thus it may, for instanice, be 36This is Newbery's (1975) point in response toworthwhile for him to subsidize credit. Bhaduri's (1973) assertion that interlinked credit and

A similar argument establishes that if there tenancy contracts are an obstacle to technological in-novation. See Srinivasan (1979) and our (1981b) paperare many inputs, and if Pi is the price at on this issue.

I'VL. 72 NO. 4 BRA VERMA N A ND STIGLITZ: A GR R .4 IV MA RKETS 711

to leisure.37 Thus, giving the landlord this model analyzed by Harvey Leibensteinextra degree of control will increase his re- (1957), James Mirrlees (1976) and Stiglitzturn. In addition, this argument provides a (1976), there is a wage which minimizes laborrationale for landlords providing workers costs per efficiency unit. Even though laborwith meals and some in-kind payments, could be obtained at a lower wage, a land-rather than full money wages.38 lord would not do so, since that would in-

crease his labor costs. At a lower wage,IV. Monopoly, Monopsony, Competition, workers are not only less efficient, but are

and Equilibrium with Surplus Labor sufficiently less efficient that wage costs perunit of effective labor are actually larger

For most of the analysis in this paper, we than they would have been at the "efficiencyhave not had to distinguish between a mo- wage." Similarly, a landlord might be able tonopoly landlord and a competitive landlord. reduce the share or the size of plot he pro-In either situation, the contract should be vides workers, but it would not pay him todesigned so as to maximize the expected do so, since his expected profits might beprofits of the landlord, given whatever level reduced as a result of such a move. In thisof expected utility the workers attain. The case, even in a competitive market there mayonlv distinction is the determination of the exist equilibrium in which the supply of laborlevel of expected utility of workers. In the exceeds the demand-that is, there is non-monopoly solution, it is at the subsistence voluntary une-nployment. (For such an un-level of workers; in the competitive equi- employment equilibrium to occur it is re-librium, it is at whatever level equates de- quired that output per hectare increase withmand and supply of tenants. plot size. Braverman-Srinivasan (1981) have

There is, however, another quite different shown that with production functions withregime, in which, in equilibriunm there is un- constant returns to scale in land and laboremployment (surplus labor). In our earlier this can never occur.)discussion, we characterized the equilibrium In such situations, interlinking has somebv having the landlord maximize his ex- interesting implications. Interlinking may in-pected profits subject to the constraint of crease the expected profits of landlords (inbeing able to obtain workers, that is, offering either competitive or noncompetitive situa-tenants a contract which generated a level of tions) if, for instance, the landlord can in-expected utility at least as great as the worker duce a higher level of effort by providingcould obtain elsewhere. In a variety of situa- loans at a subsidized rate. Although thetions, this constraint turns out not to be welfare imtplications for landlords in thishinding. For instance, in the efficiency wage situation are clear, the implications for

workers are ambiguous: (i) The number ofworkers employed may increase or decrease,

We omit the details of the calculations describing depending on the effect of interlinkage onthe optimal pricing policy of the monopolist. That anal- the optimai plot size and (ii) Those workerss'11 1is exactly parallel to the standard analysis of the ' -optimal set of commodity taxes. There, the problem for who do succeed in gettig land may be betterthe government is to maximize the welfare of con- or worse off.\urncrs. subject to a given budget constraint; here, we Consider a case where the worker dividesare concerned with the dual problem, the maximization his consumption between alcohol, which de-of the revenue (of the monopolist) subject to the sub- creases effort, and food, which increases it.slitence level of utility of workers, where the constraint ase that ang the rlive pce ofma% not be binding. Assume that by changing the relative price of

" There is an alternative argument for interlinking alcohol to food, the landlord is able to in-the consumption good market that is based on con- duce a significant change in the relative pro-sumers misperception of their "real" income associated portion of income spent on the two goods%ith the whole interlinked contract, i.e., they may per- (the elasticity of substitution between thecelve certain subsidies which they receive immediatelv

for example, credit, food), more intensely than the two goods iS very high). Then, not only maydisadvantageous terms, the impact of which will be felt this increase the level of effort, but it mayonlk later, also increase the marginal return to increas-

?12 TIIE AM-PRICAN ECONOAf [C RE 'IEzlJ' S EPTEAIlBER 1982

e /lowers the rate to induce workers to borrow

Wt / i nltenng more and is either restiicted from decreasingI h inednkng the share or plot size, or finds it undesirable

to do so, workers will enjoy an expected8A utility level exceeding their subsistence con-

Without interlinking straint. If the landlord could impose a lumpsum tax on his workers, he could again drivethem back to their subsistence constraint.

V. Conclusionc

Fi(,t'Rk 5. EXAMPLE WHEN INTERLINKING GOODS This paper has provided an economic ra-AND LAND/LABOR MARKETS RESULTS IN HIGHER tionale for interlinking contracts in situa-

LEVELS OF CONSUMPTION FOR WORKERS tions where there are important moral hazardproblems. The analysis has focused on thecase where the terms of the tenancy contract

ing plot size, share, etc.; if, for instance, the are determined optimally, but the argumentefficiency wage increases significantly, as de- for interlinkage is even stronger in thosepicted in Figure 5, the inidividual who suc- situations where convention or law restrictsceeds in getting land may be better off. certain contractural arrangemen,ts (for exam-(Clearly, although the level of effort might ple, usury laws which forbid or restrict inter-increase, the marginal return to increasing est rates).39

wages might decrease; the monopolist may We also rnote that our analysis did notthus reduce the wage of his worker and the address the implications of heterogenousinterlinking of the consumption market and population of landlords and tenants for in-the labor market would then lower the welfare terlinking, The interlinkages of credit andof the worker.) Similarly, if the optimal plot tenancy contracts, for example, may servesize increases, the level of un.-rnployment will landlords as a screening device to identifyincrease, likewise if optimal plot size de- more able potential tenants (see Franklincreases so will unemployment. Allen, 1980, and Braverman-Guasch, 1981).

We have argued in this section that there Furthermore, our analysis has focused onis no fundamental difference in the structure interlinkages within a set of markets at aof the analysis of interlinkage of markets given time; similar arguments can be putbetween a competitive market and a market forward for interlinkages across markets overwith a single landowner, but that there is a time. This may lead to the signing of long-significant difference between those situa- term contracts between tenants and land-tions where the expected utility constraint of lords-cum-lenders. In this case, although,workers is binding and those -where it is not. there may be ex ante competition (before theIt is important to recognize, however, that contract has been signed), there is onlywhether the expected utility constraint is or limited ex post competition. 40 The implica-is not binding, is itself affected by the market tions of this are important, but unfortunatelystructure, that is, by whether there is a single cannot be pursued here.landlord, or by the instruments for exploita- Although we have argued that the pres-tion which are at the disposal of the land- ence of interlinkages nieed not be taken aslord. In our earlier discussion, we suggested, evidence that agrarian mark-ets in less-devel-for instance, that the landlord might like toemploy a nonlinear lending schedule, where 39In such situations, it is obvious that inierlinkagethe rate of interest was a function of the provides one way of effectivelv circum\enlino theseamount borrowed. If, however, there is a restrictions. Thus, interlinkages would occur even in thesecondary loan market so individuals can absence of the moral hazard problems, wvhich we have

focused on here. (See Bra%verrnan-Srinivasan. 1981.)re-lend to each other, the landlord may be 'csee Suiglirz-Weiss (1980) on the question of ex anteforced to lend at a single rate. Then, if he vs. expost competitivity in credit markets.

101. 7' NO. 4 BRAV ERMAN AND STIGLITZ:AGRARIAN MARKETS 713

oped countries are noncompetitive, it seems order condition for effortcleai that such linkages have both distribu-tive as well as allocative effects. Attempts to (A3) EUCaf'g + EU, = 0,reduce the landlord's "power" by restrictinghis marketing or credit activities may, in we observe that along the iso-utility contract,certain circumstances, lower agrarian output assuming for simplicity an additive utilityand make tenants worse off. In other circum- function,stances, 4' total agrarian output might in-crease, tenants could be better off, and only I upe af'[1 -y - S.EU Ugthe landlords suffer. Further empirical work (A4) d =- - iis clearly needed to distinguish which of the e u elEUaf`(e1)g + EUevarious possibilities is relevant in any partic- -ular situation. Yet, one of the conclusions of 1-S-our study is that in many situations competi- 'Y + Ptive and noncompetitive markets may lookquite similar (say, with respect to the kinds where -y =-f"el/f' and v = EUeee/EUe,of interlinkages employed). Thus, distin- which is the elasticity of effort supply.guishing among the various possibilities may Expected profits (per hectare) of the land-require greater subtlety than is frequently lord are (1- a)f(el). Hence, the optimalemployed in empirical and policy work in contract is such thatthis area. We hope our study has shown thatsimplistic models (whether competitive or (A5)noncompetitive) which involve anonymousmarket places, homogeneouls goods and per- f4(1-)Sw 1 + di n -e (1-Sw) =,fect monitoring of inputs are likely to be dn1 u Jvery misleading. that is,

APPENDIX: DETERMINATION OF THEEQUILIBRIUM PLOT SIZE, WITH (A6) a = 1W (1+ dlneVARIABLE SHARES IN UTILITY 1-a 1-SW dln l U

EQIJIVALENT CONTRACT EQUILIBRIUMFor example, if d1ne/d1n1lj 0, a=S ,

Let f(el) = output per hectare, so f/l= and from (A4), if there is a Cobb-Douglasoutput per worker. Let a and / be variable. production function, that is, y = 1-S-,, thenLet Eg = . T he landlord must choose {a, 1) d In e/d In l l - = 0. Hence, for a Cobb-Doug-to yield las production function, the optimal share

remains unchanged, as we change (1+r)B.

(Al) EU -f(e) ,e) Thus, to obtain the same level of expectedI * utility, as we increase the interest rate charged

on a fixed level of borrowing, we increaseWe thus obtain plot size. Therefore, interlinkage reduces the

demand for labor; and it leads tenants to be(A2) daldl u a(f-f'el)/lf worse off.

More generally, we observe that a-a(l - S)/1, elasticity of substitution =(1- Sw)/y. Sub-

stituting back into (A4), we obtainw here I - S,, = (f- f'el)/f = implicit shareof landlord. Moreover, recalling the first- (A7) dlne - (1-Sw)(l-1/a)

41 When there is a single landlord, and the expected (I - Sw)(a - 1) 2(1 - Sw)utlit\ constraint is not binding. (1- s)+ va I 1-SW -v .

714 THEAMERICAN ECONOMIC REf 'IEI' SEPTEMBER 1982

Hence eo, Nuffield College, Oxford, 1980.Arnott, Richard and Stiglitz, Joseph E., "Equi-

(A8) a/(I - a) = S/(1 - S) librium in Competitive Insurance Markets-The Welfare Economics of Moral Haz-

+ S.(a-1)/(- S, + vao). ard," paper presented to NSF-BellLaboratories Conference on Information

Although (A8) always characterizes the and Decenitralization, May 1980.equilibrium, it is important to note that -y, a, Bardhan, Pranab K., "Interlocking FactorSw, a, and v are all endogenous variables Markets and Agrarian Development: A(except in some special cases). We can still Review of Issues," Oxford Economicuse (A8), however, to 6btain certain results Papers, March 1980, 32, 82-98.concerning the effects of interlinking. First, -_-_._and Rudra, A., "Interlinkage of Land,let us assume that B is unchanged, but the Labour and Credit Relations: An Analysisrate of interest charged is increased. (The of Village Survey Data in East India,"borrowing was for an emergency which oc- Economic and Political W`eekly, Februarycurred the preceding period.) Assume I were 1978, 13, 367-84.unchanged to keep U at the same level, then . and Srinivasan, T. N., "Crop Sharinga must be increased. Thus, e will be in- Tenancy in Agriculture: A Theoretical andcreased, both because of the increased a and Empirical Analysis," American Economicthe inmreased value of (1 + r)B. If the elastic- Review, March 1971, 61, 48-64.ity of substitution exceeds unity, this in- Bell, Clive and Zusman, Pinhas, "A Bargainingcreases Sw. Both the left-hand and the right- Theoretic Approach to Cropsharing Con-hand sides of (A8) have thus increased. If the tracts," A merican Economic Reviewv, Sep-right-hand side has increased mhore, it means tember 1976, 66. 578-88.that at the contract which generates equal , "On the Interrelationship of Creditexpected utility with unchanged plot size, a and Tenancy Contracts," World Bank.is too small; thus a must be increased, and Development Research Center, mimeo.,plot size decreased. Therefore the demand March 1980.for tenants will increase and their expected Bhaduri, Amit, "Agricultural Backwardnessutility will also increase. This will occur if Under Semi-Feudalism," Economic Jour-the elasticity of substitution is very large. But nal, March 1973, 83, 120-37.if the elasticity of substitution is just slightly ,_ "On the Formation of Usurious In-greater than unity, the left-hand side will terest Rates in Backward Agriculture,"exceed the right, and hence a will need to be Camrrzbtidge Journal of Economics, Decem-reduced and plot size correspondingly in- ber 1977, 1, 341-52.creased (if individuals are to be at the same Binswanger, Haans P. et al., "Common Featureslevel of expected utility). These changes will and Contrasts in Labor Relations inincrease effort, but less than proportionately the Semi-Arid Tropics of India," in H.to the increase in plot size; hernce, el will be Birtsvanger and M. Rosenweig, eds., Ruralreduced, which will reduce the right-hand Labor Mar.kets in Asia: Contiracturalside of (A8); a will continue to be reduced Arrangements, Employmnient and Wages,until the left- and right-hand sides of (A8) Yale University Press, forthcomin.are equal. In this case, therefore, intezlinkage Bliss, Christopher J. and Stern, Nickolas H.,has resulted in a decrease in the demand for Palanpur-Studies in the Econiomy of a Northlabor and tenants expected utility is de- Indian Yillage, New Delhi: Oxford Uni-creased. (Other cases are left as exercises to versity Press, 1981.the reader.) Bia'veanan, AMishay aiid Guaseli, Jose Luis,

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