Limited liability, contractual choice, and the tenancy ladder

Transcription

1 Jornal of Development Economics Vol Limited liability, contractal choice, and the tenancy ladder Tridip Ray a, Nirvikar Singh b,) a ong Kong UniÕersity of Science and Technology, ongkong, China b Department of Economics, UniÕersity of California, Santa Crz, CA 95064, USA Received April 998; accepted November 2000 Abstract We re-examine the connection between limited liability, contractal form and the agricltral tenancy ladder in a model with only labor moral hazard. We show that ex post limited liability does not explain sharecropping in this model, bt that ex ante limited liability can do so. We characterize the natre of the tenancy ladder in either case. q 200 Elsevier Science B.V. All rights reserved. JEL classification: O2 Keywords: Limited liability; Sharecropping; Tenancy ladder; Moral hazard. Introdction In a well known contribtion to the literatre on agricltral contracts, Shetty Ž 988. has demonstrated the role of limited liability in explaining the observed positive relationship between tenants wealth and their retrns from tenancy contracts. is main contribtion is the recognition of the ex post limited liability constraint for sfficiently adverse realizations of otpt the rent cannot be paid completely, the liability of the tenant is limited by his amont of wealth in ) Corresponding athor. Tel.: q address: boxjenk@cats.csc.ed N. Singh r0r$ - see front matter q 200 Elsevier Science B.V. All rights reserved. PII: S

2 290 T. Ray, N. SinghrJornal of DeÕelopment Economics inflencing the terms of contracts and tenants effort levels. owever, Shetty does not flly characterize the complete strctre of tenancy contracts in his model. We provide that analysis in this paper. In particlar, we re-examine the implications of limited liability for contractal strctre and the tenancy ladder. We start with the case of an ex post limited liability constraint, as considered by Shetty Ž Restricting orselves to linear contracts as is standard in this literatre we show that if the tenant s cropshare is nconstrained, wealthier tenants receive a fixed-rent contract, bt less wealthy tenants receive a contract with cropshare greater than. Interestingly, the first-best otcome can be attained in this nconstrained cropshare case, even when the limited liability constraint binds. The reason is that if the cropshare can exceed, the problem of limited liability can be avoided by raising the fixed-rent and, at the same time, raising the cropshare above, withot increasing the risk of defalt on this higher rental payment, and withot redcing the tenant s incentive to apply the first-best effort. owever, as we discss later in the paper, there are many reasons as to why in reality tenant s cropshare will be restricted to not greater than. Incorporating that restriction, we find that some potential bt very poor tenants do not get any tenancy contract. All other tenants, who are wealthy enogh to receive a tenancy contract, receive a fixed-rent contract. Ths, there is no room for sharecropping when there is a limited liability constraint in the ex post sense. We define a range of wealth sch that, for tenants with wealth levels within that range, their effort levels increase with wealth, and the landlord prefers the wealthier tenants as his expected earning increases with the tenant s wealth. The wealthiest tenants, with wealth levels beyond this range, receive a fixed-rent contract, apply the efficient effort level, and the landlord earns the highest expected earning. Ths, a version of a tenancy ladder emerges, where the landlord prefers to do bsiness with wealthier tenants. Shetty Ž 988. establishes that for the tenants with wealth levels sfficient to garantee landlords fll payment for all otpt realizations, the optimal contract is a fixed-rental contract. Bt he does not derive the strctre of contracts received by the less wealthy tenants. Singh Ž 989. tries to address this qestion, bt his argment that the contracts for the poorer tenants are share contracts, with the cropshare of the tenants between 0 and, has an error. Since then, there appears to be a possible misinterpretation in the literatre: 2 limited liability a la Shetty gives e does seem to implicitly assme that they will be share contracts. For example, he states, A... wealthier tenants Žp to A 0. are indced to pt forth greater effort since they bear more of the otpt risk and therefore earn higher shares of their marginal prodct.b Ž Shetty, 988, p. 3.. A similar statement is on p. 2 of his paper. 2 Sengpta Ž 997. is an exception that does not sffer from this misinterpretation. See his footnote 8, p. 405, which also credits Debraj Ray.

3 T. Ray, N. SinghrJornal of DeÕelopment Economics rise to a separate explanation of the existence of sharecropping. 3 Ths, or paper clarifies this possible misinterpretation of Shetty Ž 988., and demonstrates that all contracts are rental contracts in his model. The idea of the limited liability constraint affecting contract choice has remained qite inflential in the literatre. Bas Ž 992. ses the ex post limited liability constraint to explain the existence of share tenancy when there is moral hazard in the tenant s choice of techniqe. Sengpta Ž 997., sing a slightly different model, clarifies Bas s point: moral hazard in the choice of techniqe is not in general sfficient; we also need moral hazard in the choice of effort to develop a consistent theory of sharecropping arising ot of the limited liability constraint. Laffont and Matossi Ž 995. have taken an approach close to Shetty Ž 988., in the sense that they have considered a limited liability constraint and moral hazard in the choice of effort only. Bt they have interpreted the limited liability constraint in a very different way. They postlate an ex ante financial constraint the fixed component of the rent has to be paid in advance. In Section 3 we illstrate how this ex ante limited liability constraint explains the emergence of sharecropping and the associated tenancy ladder throgh a simple example. Section 4 provides a smmary conclsion for or analysis. Throghot the paper, we follow the notation of Singh Ž Contracts nder ex post limited liability 2.. The set-p Both the landlord and the tenant are risk-netral. The prodction fnction is Y Q s QŽ L,. Q ) 0, Q - 0, where is a random variable with distribtion w x 4 fnction F, g, and E s. The tenant has wealth W and receives an 5 income aq LyC from the contract, where a is the tenant s cropshare and C represents the fixed component of the contract, being the payment from the tenant to the landlord when C)0. The liability of the tenant is limited, ex post, by the amont of his wealth, and we define to be the vale of sch that the tenant 3 For instance, Laffont and Matossi Ž 995. comment, AIn a contribtion which is closest to or paper Shetty Ž 988. develops a model where sharecropping is explained by an ex post liability constraint... Even with risk-netral tenants limited liability introdces non-concavities in the landlord s and tenant s payoff fnctions. Sharecropping mitigates within the relationship the associated insrance problem.b Ž p See also ayami and Otska Ž 993, p. 29., Sadolet et al., Ž 994, p. 226., and Bas Ž 997, p This assmption simplifies the algebra, and is inessential. 5 This seems to be a more common notation. Note that a is the landlord s share in Shetty s notation.

4 292 T. Ray, N. SinghrJornal of DeÕelopment Economics cannot make the agreed-on payment, Ž ya. QLqC, for any realization of less than or eqal to. Formally, is defined by: a Q Ž L. qwsc Ž a,c, L;W.: ½ if aqž L. qwgc. Note that is decreasing in W, ceteris paribs. In the presence of ex post limited liability, the expected earning of the tenant w x 6 is aq LyC d F q yw d F yl, and that of the landlord is wž ya. QLqC xd FŽ. q w QLqW xd FŽ.. In order to facilitate ftre reference, let s denote by L )) the efficient Ž first-best. level of labor inpt, that is, the amont of labor that maximizes the )) total expected earnings of the landlord and tenant, QLy L. Ths, L is defined by Q Ž L )). s Contracts withot the cropshare constraint We first analyze the contracting problem withot imposing any restriction on the cropshare, a. It will be interesting to see that the efficient effort choice can be achieved in this case even when the limited liability constraint is binding. The contracting problem is: Maximize Ž ya. QŽ L. qc d FŽ. q QŽ L. qw d FŽ. a,c, L4 sbject to: Ž i. aqž L. yc d FŽ. q Ž yw. d FŽ. ylgk, ii aq L d F ys0. Constraint Ž. i is the participation constraint, and Ž ii. is the incentive constraint. Before we start analyzing the contracting problem, we shold clarify the following point. Throghot this paper we characterize the contracting problems by assming that tenants compete for landlords, so tenants are driven down to their opportnity income, K. This is qite a standard in the principal-agent literatre. Shetty Ž 988. assmes instead that landlords compete for tenants. This difference has no effect on the analysis of contract form since soltions to both approaches characterize points on the same tility-possibility-frontier, the qalitative properties of the soltions are also the same. Since the cropshare is nconstrained, it is possible for the landlord to psh the tenant to his reservation income, K, so that the participation constraint holds with 6 We assme that labor is measred in distility nits. This is withot loss of generality.

5 T. Ray, N. SinghrJornal of DeÕelopment Economics eqality. As in Singh 989, solving the constraints for L a, C a and sbstitting in the objective fnction, the first-order condition for the maximization becomes: y QŽ L. q Ž ya. Q Ž L. La d FŽ. q Ca d FŽ. q Q Ž L. L d FŽ. s0. Now sing ii we can derive from i : a QŽ L. yc a d FŽ. s0. Ž 2. Then from Eqs. Ž. and Ž. 2, we get: Q Ž L. L ya d FŽ. s0. Ž 3. a Bt Q Ž L. and La are non-zero. So finally, we get that the choice of a is given by: as. Ž 4. d FŽ. For the tenants with wealth levels high enogh to garantee fll rental payments for all realizations of otpt, s. ence, for these wealthy tenants, asr d FŽ. s, that is, they receive a fixed-rental contract. Shetty Ž 988. has noted this reslt, which is the standard one with a risk-netral agent. For the less wealthy tenants, however, ). Since d F - d FŽ. s, for these tenants a), that is, they receive a contract with cropshare greater than. 8 Ž. Note that Eq. 4 implies ad FŽ. s, and sbstitting this into the incentive constraint Ž ii., we see that in response to sch a contract the tenant s effort choice is sch that Q Ž L. s, that is, efficiency in labor choice is achieved. Observe that the efficiency of labor choice occrs irrespective of whether the limited liability constraint binds or not. We can determine the wealth level that distingishes the wealthy and less wealthy tenants. Using the binding participation constraint Ž. i, Eq. Ž 4., and the fact that s for the wealthy tenants, we get that, for the wealthy tenants, Ž )). )) C syk q Q L y L. Then, from the definition of, it follows that 7 For more on this argment, see below. 8 Singh Ž 989. fails to get this reslt becase he errs in the calclation of conditional expectations.

6 294 T. Ray, N. SinghrJornal of DeÕelopment Economics Ž )). Ž )). )) WGyaQ L qcsq L yl yky QL Ž )).. We denote this distin- Ž )). )) Ž )) gishing wealth level as W'Q L yl yky QL.. Let s smmarize the above findings with the proposition below. Proposition. In the presence of ex post limited liability, when the cropshare of the tenant is nconstrained, () a tenants with wealth leõel greater than or eqal to W receiõe a fixed-rental contract, () b tenants with wealth leõel less than W receiõe a contract with cropshare greater than, and () c the efficiency in labor choice is achieõed irrespectiõe of whether the limited liability constraint binds or not. For the wealthy tenants in this model, the limited liability constraint does not bind. So, in this model with risk-netral landlords and tenants, it follows from the standard principal-agent analysis that for these tenants the cropshare will be, providing first-best incentives. For the less wealthy tenants, however, the limited liability constraint binds. When there is a crop failre, the landlord appropriates from the tenant his wealth and the entire amont of crop prodced Žthe landlord s share and also the tenant s share.. Ths, since in bad states the tenant gets no marginal benefit, his incentives are redced. A cropshare greater than balances this ot by paying more in good states. Another way of explaining the intition for the reslts is sefl in nderstanding the role of limited liability. 9 Becase the wealth of some tenants is limited, it may not be possible to se the fixed rent instrment alone in pshing sch tenants to their reservation tility levels while attaining the first-best otcome. If a is nconstrained, and, in particlar, can exceed Žthe case nder consideration in this sbsection., this problem posed by the lack of wealth of some tenants can be circmvented. It is possible for the landlord to psh these tenants to their reservation tility levels by raising the fixed rent, C, and, at the same time, raising a above. Since the tenant s cropshare can be raised above, increasing the fixed rent does not increase the risk of defalt on this rental payment or redce the tenant s incentive to apply effort. owever, there are several compelling reasons as to why in reality the tenant s cropshare is restricted to be not greater than. Shetty sggests that the landlord promising a marginal share greater than cannot be conted on to deliver. Certainly this is a possibility: keeping a share of otpt is different from actally receiving more than one has prodced Ž at the margin.. The latter perhaps relies more on the landlord s goodwill to deliver. The problem may be even more severe, however. In sharecropping Ž when a is between 0 and. both landlord and tenant benefit from more otpt, so neither has an incentive to destroy otpt. Bt if the tenant s cropshare is greater than, then the landlord is worse off from 9 We are gratefl to a referee for this sggestion.

7 T. Ray, N. SinghrJornal of DeÕelopment Economics having more otpt, ex post. So he has an incentive to destroy otpt. For example, he cold send a gang of thgs at night to steal the crop when it is ripe enogh to harvest. This might be another reason why contracts with a tenant s share greater than are not observed. 0 An alternative explanation for the restriction on the share is another kind of tenant moral hazard. A marginal share greater than increases incentives for maniplating otpt. The sharecropper Ž with share less than. has an incentive to hide otpt, akin to the motives for tax evasion. The landlord will certainly try to detect this. The tenant with a pre rent contract has no sch incentive, since he makes only a fixed payment. If a exceeds, however, the tenant has an incentive to overstate otpt in some cases. One can think of monitoring this as being more difficlt Že.g. a neighbor s otpt is borrowed to stake a claim to more payment from the landlord, or last year s stocks are sed, or chaff is inclded with the grain.. These considerations might lead to the tenant s share being restricted to not exceed. In Section 2.3, we characterize the contractal strctre with this additional constraint, that tenant s cropshare is restricted to be weakly between 0 and Contracts with the cropshare constraint Since it is easy to arge that a) 0, we rewrite the contracting problem incorporating the cropshare constraint as follows: Maximize Ž ya. QŽ L. qc d FŽ. q QŽ L. qw d FŽ. a,c, L4 sbject to: Ž i. aqž L. yc d FŽ. q Ž yw. d FŽ. ylgk, ii aq L d F ys0, Ž iii. af. ere, Ž iii. is the cropshare constraint. The incentive constraint can be solved for LŽ a. and sbstitted in the problem as earlier. Bt, since a cannot exceed, the participation constraint may not hold with eqality. Let l and m be the Lagrange mltipliers corresponding to the participation constraint Ž. i and cropshare constraint Ž iii., respectively. Then the 0 This cold well happen in places like Bihar, a state in India. We are gratefl to Kashik Bas for this idea.

8 296 T. Ray, N. SinghrJornal of DeÕelopment Economics first-order conditions with the associated complementary slackness conditions for the problem are given by: a a : y Q L q ya Q L L d F q Q Ž L. L d FŽ. a a a ql QŽ L. qaq Ž L. L d FŽ. yl yms0, Ž 5. C: dfž. yl d FŽ. s0. Ž 6. Now, we consider three exhastive and mtally exclsive cases depending on whether the two constraints bind or not. Case I Ž Participation constraint does not bind.. This case incldes two sb-cases: Ž. a a-, and Ž. b as. Since the participation constraint does not bind, l s 0. ence, Eq. Ž. 6 implies d FŽ. s0, that is, s. Bt if s, it follows from the expression of the tenant s expected earning that ) the tenant s labor choice, L s0. Then, QL Ž ). s0. It follows from the definition of that a QL Ž ). qwsc, implying that CsW, that is, the fixed component of the rent is eqal to the tenant s wealth. Since the participation constraint does not bind and s, we get from the participation constraint that 0q Ž yw. d FŽ. y0)k, that is, W-yK. So this case can arise when the tenant is so poor that his wealth level is less than Ž yk., that is, he is indebted. ) Bt since s and L s0, the landlord s expected earning in this case is W, which is less than yk. If, instead, the landlord does not enter into any contract with sch a poor tenant Ž and presmably leaves the plot fallow., his expected earning is zero. Conclsion: the landlord does not lease ot his plot to tenants with wealth level less than yk, and hence Case I will not arise in a soltion to the contracting problem. Case II Ž Participation constraint binds, and a-.. Since a-, it follows that ms0. Also, Eq. Ž. 6 implies ls. Then it follows from Eq. Ž. 5, after some sbstittions and rearrangement, that Q L La ya d FŽ. s0, implying that as G, a contradic- d FŽ. tion Ž since a- for the case nder consideration..

9 T. Ray, N. SinghrJornal of DeÕelopment Economics Conclsion: Case II does not arise in a soltion to the contracting problem. Also, note that Case I and Case II demonstrate decisively that a share contract does not arise when there is a limited liability constraint in the ex post sense. Case III Ž Participation constraint binds, and a s.. Again, Eq. Ž 6. implies that l s. Then, after some sbstittions and rearrangements, we get the following from Eq. Ž. 5 : Q Ž L. L a d FŽ. sm. Since mg0, there is no contradiction. Conclsion: We get that this is the only case that solves the contracting problem. Ths, all the tenants receive a fixed-rent contract when there is ex post limited liability and tenant s cropshare is constrained not to exceed. Next, we demonstrate how this fixed rent changes, and its associated effects on the tenant s labor choice and landlord s expected earning, by considering two sbcases nder Case III: Ž. a limited liability constraint Ž LLC. does not bind, and Ž. b limited liability constraint binds. Case III ()Ž a Participation constraint binds, as, and LLC does not bind.. Since LLC does not bind, s. Then the incentive constraint implies Q Ž L. s, that is LsL )), where L )) denotes the efficient labor choice. Since the participation constraint binds, we get w QLyC xd FŽ. q0yls Ž )). )) K, implying that CsQ L yl yk. Bt, from the definition of, LLC does not bind means aqž L. q W G C, which implies that WGy QL Ž )). qcsq Ž L )). yl )) yky QL Ž )). 'W. Conclsion: ths, we get that when the tenant is rich enogh so that his wealth level is greater than or eqal to W, he receives a fixed-rent contract with the,2 amont of fixed-rent C given as above, and pts the efficient effort. Bt what happens to the less wealthy tenants, that is, to the tenants with wealth Ž. level less than W? Case III b addresses this qestion. Case III ( b) Ž Participation constraint binds, a s, and LLC binds.. Since LLC binds, from the definition of it follows that: QŽ L. qwycs0. Ž 7. Note that this is the same wealth level W that distingishes the wealthy and less wealthy tenants in Proposition. 2 This is exactly Proposition Ž p.. in Shetty Ž The wealth level W is the conterpart of 0 w Ž )). )) x Ž 0 A P and the fixed-rent QL y L y K is the conterpart of R 0, A ;P. L L in that proposition. owever, as noted earlier, Shetty does not characterize the eqilibrim contract in the other cases we analyze.

10 298 T. Ray, N. SinghrJornal of DeÕelopment Economics The incentive constraint implies: Q Ž L. d FŽ. ys0. Ž 8. The participation constraint gives: QŽ L. yc d FŽ. q Ž yw. d FŽ. ylyks0. Ž 9. Considering the wealth level, W, as a parameter, these three first-order conditions determine the fixed-rent Ž C., effort level Ž L. and ct-off level of ncertainty Ž. all as fnctions of wealth level W. It is shown in the Appendix that E EL EC -0, )0, and -0. It is qite intitive that, as the tenant s wealth EW EW EW level decreases, he becomes more prone to defalt, that is, the ct-off level of ncertainty Ž. increases. Since the tenant receives positive vale to his marginal effort only when gw, x,as increases, his benefit from the marginal effort also decreases, and hence he pts less effort. Also, note that for these less wealthy tenants, the fixed rent Ž C. decreases as wealth increases. Since nder adverse realizations of otpt the landlord appropriates the tenant s wealth, the wealthier the tenant, the more the landlord can afford to give him a greater concession in terms of a redced fixed rent. The above findings can be nicely tied p to one version of the tenancy ladder hypothesis. Since the participation constraint binds, sbstitting for the expression of C from Eq. Ž. 9 into the expression for landlord s expected retrn, we get that the landlord s expected retrn is wqlw Ž. ylž W. yk x. ence, it follows from the above that as W decreases, L decreases, and the landlord s expected retrn decreases. It is in this sense that the landlord prefers to have wealthy tenants, sggesting a kind of tenancy ladder where wealthier tenants are preferred. Bt how long will this contine, that is, what is the wealth level below which the landlord will stop leasing ot his plot? ŽRecall from Case I that the landlord does not lease ot his plot to a tenant with wealth level less than yk.. This wealth level is sch that landlord s expected retrn is jst zero: QLW Ž. ylž W. yks0. Therefore, let W be the wealth level sch that QLW Ž. ylž W. yks 0. We may therefore smmarize the findings of this sbsection with the proposition below. Proposition 2 ŽŽ Tenancy Ladder... In the presence of ex post limited liability, when the cropshare of the tenant is constrained to be weakly between 0 and, we haõe the reslts giõen below.

11 T. Ray, N. SinghrJornal of DeÕelopment Economics () a Tenants with wealth leõel below W are exclded from receiõing any tenancy contract. () b All the tenants with wealth leõel aboõe W receiõe a fixed-rental contract. () c For the tenants with wealth leõels greater than W bt less than W, the effort leõels increase with wealth, and the landlord prefers the wealthier tenants as his expected earning increases with the tenant s wealth leõel. () d Tenants with wealth leõel greater than or eqal to also receiõe a fixed-rent ) ) )) contract with the amont of fixed-rent giõen by: Q L yl yk. These tenants proõide the efficient effort leõel, and the landlord s expected earning is the highest from entering into tenancy contracts with these rich tenants. The intition for the fixed-rent contract for less wealthy tenants Žtenants with wealth levels greater that W bt less than W. can be nderstood as follows. Recall from or discssion of Proposition that becase the wealth of these tenants is limited, the first-best otcome is attained only by raising their cropshares above. Now that a is constrained not to exceed, it is clear that the first-best otcome cannot be achieved, that is, these tenants pt too little effort when there is a cropshare constraint and the limited liability constraint binds. Since a fixed-rent contract indces the highest effort level among all possible tenrial contracts, the landlord offers the fixed-rent contracts to these less wealthy tenants in order to get as close as possible to the first-best. So far, we have seen that there is no room for share contracts when there is limited liability in the ex post sense. In Section 3, we show, throgh an example, how sharecropping can arise when there is ex ante limited liability. 3. Ex ante limited liability and sharecropping: an example Laffont and Matossi Ž 995. have posed the limited liability constraint in a very different way. They postlate an ex ante financial constraint that says that the tenant mst pay the fixed component of the rent. The logic is that the landlord wants to obtain as mch of a cash advance from the tenant as possible in the form of the fixed rent. Ths, this amont of fixed rent is bonded above by the tenant s wealth. 3 That is, in or notation, CFW. To illstrate how this ex ante limited liability constraint explains the emergence of sharecropping and the associated tenancy ladder, we consider the following example. 3 Laffont and Matossi 995 consider the pper bond to be the tenant s working capital. We eqate this working capital to the tenant s wealth in order to provide a clean exposition of the tenancy ladder.

12 300 T. Ray, N. SinghrJornal of DeÕelopment Economics Both the landlord and the tenant are risk-netral. The prodction fnction is 2 Q s L, with E s. The tenant s distility from work is r2 bl, so his 2 expected tility is alycyr2bl, while that of the landlord is Ž ya. LqC. So the contracting problem is: Maximize a,c, L4 Ž ya. LqC 2 sbject to, Ž. i LsMax al ycyr2bl : Incentive constraint, L 4 2 Ž ii. alycyr2bl GK : Participation constraint, Ž iii. C F W : Limited liability constraint. The incentive constraint gives the soltion: L s arb. Sbstitting this into the objective fnction and the participation constraint, the contracting problem becomes: Maximize a,c4 a Ž ya. b qc a 2 sbject to, ii y C G K : Participation constraint, 2b iii C F W : Limited liability constraint. This problem can be analyzed straightforwardly Ždetails are omitted, bt available from the athors.. First, we can show that at least one of the constraints mst bind. Next, if only participation constraint binds, it mst be the case that W)C, that is, W)r2byK. If only the limited liability constraint binds, then W- r8b y K. For intermediate vales of wealth, both constraints bind. We smmarize the fll reslts in the following table: Tenant s Tenant s cropshare Fixed Landlord s expected wealth Ž a. component tility Ž U L. Ž W. of rent Ž C. 3 W - y K W UL - y K 8b 2 8b 3 W s yk W y K 8b 2 8b 3 y K -W - y K -' 2bŽ KqW. - W y K -UL - y K 8b 2b 2 8b 2b W G yk y K y K 2b 2b 2b

13 T. Ray, N. SinghrJornal of DeÕelopment Economics The above example can be generalized to the following proposition, which presents a variant of Proposition of Laffont and Matossi, bt with a novel interpretation of possible eqilibria in terms of a tenancy ladder: Proposition 3. When there is an ex ante limited liability constraint, () a wealthier tenants ( for whom the limited liability constraint does not bind) receiõe a fixed-rent contract and pt forth the efficient effort leõel, () b less wealthy tenants ( for whom the limited liability constraint binds) receiõe a share contract, and make an inefficient effort choice, and () c as the tenant s wealth increases, his cropshare ( and effort leõel) increases and the landlord s expected tility also increases. Ths, sharecropping arises in the presence of an ex ante limited liability constraint. Also, note that the landlords prefer to have wealthy tenants since their expected tility increases with the tenant s wealth. Again this might be interpreted as a tenancy ladder. The intition for this otcome, and its difference from the ex post constraint case, is as follows. 4 In the ex ante constraint case, landlords have less scope to extract srpls from tenants by sing the fixed rent component of the contract. This pshes them to se share contracts, where otherwise they wold set the tenant s share at Ž or higher if that is possible. and se the fixed component for collecting income. 4. Conclsion In this paper, we have provided a complete characterization of contracts in Shetty s model of a tenancy ladder with ex post limited liability. We have shown that sharecropping can never arise in that model. owever, as we demonstrated in Section 3, sharecropping does come abot with ex ante limited liability. In either case, a version of a tenancy ladder can be characterized, as we have shown above. Acknowledgements We are gratefl to Debraj Ray for first bringing this isse to the attention of the second athor. We wold like to thank two anonymos referees for very helpfl comments and sggestions. 4 We are indebted to one of the referees for this intition.

14 302 T. Ray, N. SinghrJornal of DeÕelopment Economics Appendix A. Comparative static reslts nder Case III b We assme that the sfficient condition for maximization is satisfied, so that the Jacobian determinant of the first-order conditions Ž.Ž. 7, 8 and Ž. 9, denoted by D, has a negative sign, that is, D- 0. Differentiating the first-order conditions totally, we get: Q Ž L. y QŽ L. Y Q Ž L. d FŽ. 0 yq Ž L. f Ž. d L dc d 0 y d FŽ. 0 ydw 0 s. d FŽ. dw Note that the partial derivative of Eq. Ž. 9 with respect to L is Q Ž L. d FŽ. y, which is eqal to zero by Eq. Ž 8., and the partial derivative of Eq. Ž. 9 with respect to is yfž.w QLyCqW x, which is again eqal to zero by Eq. Ž. 7. Now we can derive the following comparative static reslts: Y yq Ž L. d FŽ. E Y s -0, since Q Ž L. -0, and D-0. EW D EL yq Ž L. f s )0, since Q Ž L.)0, and D-0. EW D EC yf s -0. EW yfž. References Bas, K., 992. Limited liability and the existence of share tenancy. Jornal of Development Economics 38, Bas, K., 997. Analytical Development Economics: The Less Developed Economy Revisited. MIT Press, Cambridge, MA. ayami, Y., Otska, K., 993. The Economics of Contract Choice: An Agrarian Perspective. Clarendon Press, Oxford.

15 T. Ray, N. SinghrJornal of DeÕelopment Economics Laffont, J.J., Matossi, M.S., 995. Moral hazard, financial constraints and sharecropping in El Olja. Review of Economic Stdies 62, Sadolet, E., Fki, S., de Janvry, A., 994. Efficient share tenancy contracts nder risk: the case of two rice-growing villages in Thailand. Jornal of Development Economics 45, Sengpta, K., 997. Limited liability, moral hazard and share tenancy. Jornal of Development Economics 52, Shetty, S., 988. Limited liability, wealth differences and tenancy contracts in agrarian economies. Jornal of Development Economics 29, 22. Singh, N., 989. Theories of sharecropping. In: Bardhan, P. Ž Ed.., The Economic Theory of Agrarian Instittions. Oxford Univ. Press, Oxford.