Agrarian Reforms in Developing Rural Economies Characterized by Interlinked Credit and Tenancy Markets World Bank Staff Working Paper No. 433 October 1980 Prepared by: Avishay Braverman T. N. Srinivasan (Consultant) Development Research Centre Copyright © 1980 The World Bank 1818 H Street, N.W. Washington, D.C. 20433, U.S.A. The views and interpretations in this document are those of the authors and should not be attributed to the World Bank, to its affiliated organizations, or to any individual acting in their behalf. The views and interpretations in this document are those of the author and should rLot be attributed to the World Bank, to its affiliated organizations, or to any individual acting in their behalf. WORLD BANK Staff Working Paper No. 433 October 1980 AGRARIAN REFORMS IN DEVELOPING RURAL ECONOMIES CHARACTERIZED BY INTERLINKED CREDIT AND TENANCY MARKETS The paper concentrates on a model of linkage between land, labor and credit transactions in the context of sharecropping. Our proof follows from our result that ceteris paribus, the tenant's optimaZ effort per hectare is a decreasing function of the size of the plot he cultivates. The utility equivalence result has the fundamental implication that policies other than land reform will leave the welfare of each potential tenant unaltered while affecting the level of output, extent of tenancy and the welfare of landlords. With the possibility of linking tenancy and credit contracts, it is shown that the landlord will resort to linking only in a situation where it will Lower the cost of credit to the tenant. If the government offers the tenant subsidized credit at a cost lower than the landlord's opportunity cost of funds, the landlord will move out of the tenant's credit market and allow the tenant to borrow from the government. The increase in surplus due to government subsidization of tenant's credit will fully accrue to the landlord as a consequence of the utility equivalence result. Hence, government subsidization of tenant's credit resuZts only in the subsidization of landlords. Other partial reforms by the government, however, may force the landlord to link credit and tenancy contracts even if the government provides the cheaper source o:f credit; this, thereby, leaves the tenant's utility unaltered at its pre-reform level while affecting total output and the extent of tenancy. Our model is also able to provide a theoretical underpinning for two almost opposite phenomena that are sometimes observed: low interest consumption loans from landlord to tenant and the opposite, high interest, low volume loans. One major result of the paper is valid both in the context of interlinked credit and tenancy contracts and in that of sharecropping contracts alone. 'It states that, as long as the landlord can vary thie size of the plot given to a tenant and there are enough potential tenants, the equilibrium will be characterized by "utility-equivalent" contracts even if the landlord does not control any other term of contract such as crop share, interest rate on credit, etc. That is, in equilibrium, a tenant's utility obtained through sharecropping will be the same as that which he could have obtained as a full- time wage laborer. Prepared by: Copyright @ 1980 Avishay Braverman The World Bank T. N. Srinivasan (Consultant) 1818 H Street, N.W. Development Research Centre Washington, D.C. 20433 U.S.A. 1. Introduction It is often claimed that because the rural economy of developing countries is characterized by a non-competitive market structure, policy analysis in such an environment will differ significantly from a similar analysis of a competitive world. We discuss here the possible impact of policies such as land reform, as well as alternative tenancy and credit reforms in a rural economy characterized by interlinked land, labor and credit markets. One of the many contributors to the literature on interlinking states, "It is misleading when talking about individual operators to hypothesize that each producer confronts technical data and market prices in an impersonal environment and all are equally free to take behaviour in any one single market without knowing how the markets are interlinked by price and non-price relations, for the fields of feasibZe choices in the different markets are not, as assumed under competition, definable a priori independently of each other."-'/ While this description is suggestive, it is by no means a complete definition of interlinking. After all, the typical consumer's choice problem as usually formulated in micro-economic theory implies that the consumer's actions in the market, for each of the set of goods, are interlinked through his budget constraint. Similarly, in a typical producer's choice problem, profit maximiza- tion links his choice of inputs and outputs given his technology. In any case, at the economy-wide level, general equilibrium implies simultaneous equilibrium in ael markets, with the supply and demand in each market being dependent on all relevant prices. 1/ See K. Bharadwaj [19741. A possible definition of interlinked contracts could be the following: contracts made between the same pair of individuals relating exchanges in more than one commodity or service, the contracts being linked in an essentiaZ way. In other words, contracts between a pair of individuals in two or more commodities that are linked by coincidence, i.e. contracts that could as well have taken place without change at different points in time and not necessarily between the same individuals, are not interlinked in this sense. This definition, however, is not meant to exclude intertemporal linking of contracts. On the contrary, a very important aspect of interlinking is the interlinkage of present and future transactions. In the present paper we concentrate on one form of linkage between land, labor and credit contracts in the context of sharecropping. In this context, the following conditions lead to interlinking: (a) There is an incen- tive problem due to the cost of monitoring and supervising effort; (b) The tenant has no accumulated savings; hence, he must borrow at the beginning of the produc- tion period; and (c) There are imperfections in the capital market in the form of differing costs of capital to the landlord and to the tenant. One major result of the paper is valid both in the context of interlinked credit and tenancy contracts and in that of sharecropping contracts alone. It states that, as long as the landlord can vary the size of the plot given to a tenant and there are enough potential tenants, the equilibrium will be charac- terized by "utility-equivalent" contracts even if the landlord does not control any other term of contract such as crop share, interest rate on credit, etc. That is, in equilibrium, a tenant's utility obtained through sharecropping will be the same as that which he could have obtained as a full-time wage laborer. 3 Newbery and Stiglitz [1978] assert, without providing a satisfactory proof, the same result in the context of sharecropping alone, while a similar, though not identical, conclusion has been obtained in a different setting by Cheung [19691. Our proof follows from our result that ceteris paribus, the tenant's optimal effort per hectare is a decreasing function of the size of the pZot he cuZtivates. The utility equivalence result has the fundamental implication that policies other than land reform (i.e., reform that confers ownership to the tenant of the piece of land he is cultivating) will leave the welfare of each potential tenant unaltered while affecting the level of output, extent of tenancy and the welfare of landlords. With the possibility of linking tenancy and credit contracts, it is showm that the landlord will resort to linking only in a situation where it will Zower the cost of credit to the tenant. If the government offers the tenant subsidized credit at a cost lower than the landlord's opportunity cost of funds, the landlord will move out of the tenant's credit market and allow the tenant to borrow from the government. The increase in surplus due to government subsidization of tenant' s credit will fuZly accrue to the landlord as a consequence of the utility equivalence result. Hence, governent subsidization of tenant's credit resuZts onZy in the subsidization of landZords. Other partial reforms by the government, however, may force the landlord to link credit and tenancy contracts even if the government provides the cheaper source of credit; this, thereby, leaves the tenant's utility unaltered at its pre-reform level while affecting total output and the extent of tenancy. Our model is also able to provide a theoretical underpinning for two almost opposite phenomena that are sometimes observed: low interest consumption loans from landlord to tenant and the opposite, high interest, low volume loans. 4 We begin in Section 2 with an extended discussion of the various possible forms of linked contracts and the circumstances in which they are likely to arise. In Section 3, we present the model followed by a characterization of the equilibrium in Section 4. Section 5 discusses policies of credit, land and tenancy reforms as well as the impact of taxation and technological progress. Finally, in Section 6 we briefly summarize and relate our conclusions to the literature on sharecropping and on interlinked credit and tenancy contracts. 2. Types of Interlinked Contracts As stated in the introduction, interlinked contracts may be defined as transactions in more than one commodity or service made between the same pair of individuals and linked in an essential way. An example will perhaps make the concept of interlinking clearer: suppose a landlord and a tenant enter into a contract in which the tenant rents a piece of land at a stipulated rent, and at the same time the landlord extends the tenant credit, again on specified terms. If the contract in land (credit) could have taken place independently of that in credit (land) with no additional cost to either party, the two contracts are not interlinked. An essential feature of this definition, therefore, is that delinking the contracts would be infeasible or costly for at least one party: in the first case, if it is infeasible, the two parties either transact in all the relevant goods and services or do not transact in any of them: and in the second, if it is costly, linking rather than not linking, will benefit at least one party. The infeasibility of delinking for both parties can arise from the nonexistence of certain markets (e.g., the market for bullocks' services) 5 however, interlinking covers a much wider range of contracts than those simply created to circumvent the absence of certain markets. Quite often the linking of contracts occurs when there is a moral hazard problem, which results in an "inappropriable" externality.-/ "Moral hazard" arises in a risk-sharing contract when one party, often called the agent (tenant, insuree), can affect the probability distribution of the outcome (output, accident) through his action (effort, driving habits) which the other party, often called the principal (landlord, insurer) cannot effectively or cheaply monitor. In such a situation, the agent has an incentive to change the probability distribution of the outcome, in his favor, once the parties have agreed on the terms of the contract. Since both parties know this, the form of contract as well as its terms will often include provisions that address the moral hazard problem, such as for instance, the deductible feature of an insurance contract. Consider the case of sharecropping. The tenant's effort, which cannot be perfectly monitored or inferred by the landlord through observation, is affected by his capital endowmeat. If the tenant lacks capital he will try to borrow some. The borrowing affects his effort and, consequently, output and the landlord's profits. Since the landlord can neither perfectly monitor nor enforce the tenant's effort level (i.e., it is too costly), there is an inherent externality from the credit market into the production process. Since, the landlord is aware of this externality he can internalize it (i.e., address the moral hazard problem) by linking the credit and tenancy contracts, thus promoting greater efficiency in production and increasing his own profits. This linking may constitute a Pareto superior move as opposed to a delinked situation, since the increase in total surplus allows for an 1/ In the broader sense, even this class of contracts can be defined as arising due to nonexistence of markets where the missing markets are themselves defined as the markets for the externalities. 6 improvement in welfare of at least one party, without making the other party worse-off. Such linking is clearly voLuntary. Linking, however,may not necessarily constitute a Pareto improving move if one party, which possesses more market power, decreases the other party's welfare through interlinking of contracts. Such linking could be termed as forced Zinking, where the weaker party would prefer delinking if that option were open to him; however, since this option is not allowed by the powerful party, the weaker party chooses to accept the "tie-in" package rather than not to transact at all. There are two more classes of interlinked contracts: one class arising from voluntary linking is due to Lowering transaction costs for both parties. Many examples of linking-often found in developed countries, such as "ttie-in-sales," supplier's credit, and shopping for unrelated items in a large store-result, to some degree, from lower transaction costs. Another class constitutes a screening device resulting from imperfect information regarding the attributes of a heterogenous population. For example, in a world where some attributes, such as tenant's managerial skills, are unobservable, interlinked credit and tenancy contracts may serve as a screening device for landlords to identify more able tenants. The equilibrium, in all of the above cases, is achieved in the context of an incomplete set of markets, imperfect markets, or both. Hence, welfare propositions relating to such equilibria are often of the "second- best" kind; for instance, in an environment characterized by market distortions, a move toward eliminating a subset of distortions does not necessarily imply an improvement of welfare. Therefore, policy intervention, either by creating some, but not all, nonexistent markets or by eliminating market power through reform will not necessarily lead to a more efficient allocation of resources as compared to the pre-intervention equilibrium. 7 Clearly, equity or the distributional aspects of such intervention will depend very much on the prior structure. Nonexistence of markets is the rule rather than the exception, particularly in less developed countries. For example, landless rural households endowed with the labor of women and children for which there is no market or because social taboos prevent them from working for others, often lease in land. The leased in land is farmed mostly by non-marketable family labor, while those members of the household who can work as wage laborers outside the household farm do so, to a significant extent. In this case, transactions in land and family labor get linked. There are several other examples of linkage of a similar nature arising from the nonexistence of markets for draught power and of tenants' managerial input. Intertemporal linking is quite prominant, especially in the labor market. If wage labor in peak agricultural seasons is either uncertain in its availability or its cost, a landlord may wish to employ a permanent or attached farm laborer whose services are available to him throughout the year. In this case, the linking occurs in the contracts relating to peak season and off-peak season labor: an attached labor contract is-an agreement to buy and sell labor in both seasons. The unlinked alternative is to hire wage labor in each season separately.L/ 1/ For more examples see Bardhan [1980]. 8 3. The Model 3.1 The Tenant The form of rental contract discussed here is sharecropping. If onZy incentive problems exist (i.e., the landlord can neither force the worker to contribute a specified level of effort nor can he monitor it), the fixed-rent contract will be best suited to remedy them: It will, in fact, dominate a fixed-wage or a sharecropping contract. The tenant obtains all the fruits of his effort after paying the fixed rent. Fixed rents, however, imply that the tenant must bear all risk resulting from output uncertainty due to exogenous conditions (e.g. weather, illness). If the tenant is risk averse, such a contract will be inefficient, in which case a sharecropping contract will dominate it. It follows that risk-sharing effects seem to be necessary to explain the phenomena of sharecropping. In addition, incentive problems due to the cost of supervision are also necessary, since any risk-sharing posture obtained through a share contract can also be obtained by a linear combination of wage and fixed-rent contracts (Stiglitz [1974], Newbery [1977]). However, we shall not consider risk elements here, but focus instead only on the relations between incentive effects and the tenant's lack of funds. We assume that all workers are identical, facing two employment alternatives: first, as tenants on the landlords' land, or secondly, as wage laborers outside the farm. Each tenant is offered a plot of land of size H hectares for cultivation, in return for which he agrees to pay the landlord a share (1-a) of the harvest. None of the workers possess any savings at the beginning of the production year. Wage wort.3:rs are paid 9 wages, W , during the production period and, therefore, have no need to borrow for consumption. The tenant, however, borrows at the beginning of each season his entire consumption needs for the coming season and repays his loan with interest at the end of the season after harvest. He does not store any grain from one season to the next nor does he have any in- vestment opportunity. The tenant obtains a proportion v of his borrowings (either as a voluntary or "tie-in" package with a tenancy contract - see Section 2.2 below) from his landlord at an interest rate rT per season. He obtains the remaining proportion (1-v) of his borrowings from an alternative source (e.g., local moneylender, cooperative, government credit) at an interest rate rA . He treats rT and rA as parameters over which he has no influence. We assume that he cannot default (a) in order to simplify the argumentation, and (b) because in many areas landlords virtually hold the harvested crop as collateral. Clearly, if the tenant can borrow all the present value of his consumption at either rT or rA . he will choose to borrow the entire sum from the cheaper source. However, since our dis- cussion focusses on linking, we start by assuming that the tenant takes v as given, so that v > 0 will represent linking over which he has no influence. Labor provided by the tenant for cultivation (including all operations from land preparation to harvesting) is denoted by eL, where L denotes the number of man-days per season and e denotes the effort per man-day of labor. Thus, eL represents labor in efficiency units. Out- put Q is a concave function exhibiting constant returns to scale in H 10 and eL. l Thus: Q - F(E, eL) (1) Assuming the number of man-days, L , (i.e. labor in natural units) to be exogenously fixed, we can set (without loss of generality) L - 1. Thus we can rewrite (1) as: Q I F(1, ex) _ (2) I X where x is man-days of labor per hectare of land. Given that L - 1, x represents the reciprocal of the size of the plot he is allotted. The function f represents the average product per hectare of land. By as- sumption, f' is positive and f" is negative where the primes (single and double) denote the first and second derivatives of f , respectively. The tenant's share of the harvest Q is a and his income is therefore aQ. By our assumption that the tenant borrows his entire consumption needs at the beginning of the season and has no carry-over stock or invest- ment opportunities, it follows that his consumption c in any season equals his income aQ at the end of the season, discounted by (1 + i) where i is the effective interest rate on his borrowing. Of course, i equals vrT + (1 - v) rA. Thus: 1/ Bell and Braverman [1978] show that landlords will prefer cultivation with wage labor to sharecropping, if the production function is of constant returns to scale and there is no uncertainty. Since we do not allow the landlord the option of self-cultivation with wage labor, the Bell-Braverman result does not apply to our analysis for this and other reasons having to do with the modelling tenant's effort and behavior. 11 + vrT + (1 v)rA where 1 + vrT + (1 - v)rA ~discounted share of the tenant.(4) We assume that the tenant's utility function U(c,e) is strictly quasi-concave in consumption and leisure, where leisure is defined as e -e. Further, both consumption and leisure are assumed to be normal goods. The potential tenant's choice or control variable is e. He will not choose to work as a tenant unless U(c, e) is at least as large as U , the utility he could have assured himself by working as a wage laborer. The supply of tenants is assumed to be infinitely elastic at U, i.e. U is exogenous. Thus, we can solve the potential tenant's choice problem in two steps. First, let the tenant maximize: Max U(c(e),e) s.t. (2) and (3) (5) e Let he maximized value of U be U*. Secondly, he compares U* with U. If U* > U, he works as a tenant, otherwise as a wage laborer. It is immediately apparent from (2)-(5) that the parameters a, v, rT and rA enter the tenant's constraint set and utility function only through their effect on his discounted share B. By substituting (2), (3) and (4) in (5), maximizing with respect to e, we get the first order 12 condition:i/ Of'(ex) 1 + U2 = (6) i.e., at the margin the change in the tenant's utility of consumption due to a change in effort must compensate the change in his disutility due to the same change in effort. Now, define effort per hectare as z E ex. and rewrite (6), to obtain U2 Of'(z) = _ 2 (7) U1 On the L.H.S. of (7) we have the marginal rate of transformation between consumption and leisure through production (MRT) and on the R.H.S. of (7) we have the marginal rate of substitution between consumption and leisure through consumption (MRS). While MRT is a function of a and z, MRS is a function of 8, z and x. The relation (7) is crucial to the understanding of the utility equivalence result and tothe impact of land reform on output. We present it graphically in Figure 1. The MRT curve, given 3, is downward sloping in effort per hectare z, due to diminishing marginal productivity (i.e. f' < 0). The MRS, given 8 and x, is an increasing function due to the normality of both consumption and leisure (See Braverman-Srinivasan [19801 for a proof of this and all other propositions discussed below.) 1/ It can be shown that the second order condition is satisfied from our strict quasi-concavity assumption on U, and the strict concavity of f. 13 MRS (x ) MRS MRT MRS (x; x1 > X I~~~~( *~~~~~~~~~~~~~~~~~~~~~~~~~~~ af'(z) MRT a 1 z Figure I TIenant's Optimal Effort per hectare Now consider the impact of a ceteris paribus reduction in plot size (an increase in x) on tenant's welfare, effort e, and effort per hectare, z. Clearly, his welfare declines. The impact on e cannot be determined * ~~unambiguously since it depends on the relative absolute magnitudes of the income and substitution effects which are opposite in sign. However, there is no ambiguity in the impact on z. Consider Figure 1: a change in the plot size does not affect the MRT curve. A reduction in plot size, however, shifts the MRS curve outside and downward, since ceteris pari1bus, such a reduction results in a decline in the tenant?'s income E consumption, thereby, increasing 14 the marginal utility of consumption vis-a-vis leisure and calling for larger effort per hectare to restore equality between MRS and MRT. This leads, there- fore, to the following proposition: Proposition 1: The tenant's effort per hectare increases with a reduction in the size of his plot. This holds even if the tenant's effort declines with such a reduction in plot size. Remark: The instrument other than plot size, namely a , shifts both curves; thus, in order to derive the impact of policies that change 8 (e.g. land reform) we need to specify the relative movements of the two curves. 3.2. The Landlord With an infinitely elastic supply of identical tenants, and con- stant returns to scale in production, maximizing profits is equivalent to maximizing profits per hectare. Hence, our model yields the same results whether different landlords possess different amounts of land or not. There- fore, without loss of generality, we assume that all landlords are identical and possess one hectare of land each, which they divide into plots of size l/x to give each of x tenants. As stated earlier, the landlord may require that each of his tenants get a proportion v of his borrowings from him at an interest rate rT. Assuming that an alternative use of funds would have earned the landlord an interest of rL per season (e.g. deposits in the city's bank), his income g can be shown as: f( z 9 + vrL + (~1 - v)r A} 15 Multiplying g by the number of tenants, x , we get the landlord's income G: G - [1 - {1 + vrL + (1 - v)rA}f(z) (8) The interest rate, rT , charged by the landlord on his loans to his tenant is seen from (8) to affect his income onl through its effect on , the discounted share. The landlord maximizes G with respect to his choice variables given the tenant's effort function e(ex, 8). The choice variables include the plot size 1/x, and may include the tenant's crop share a, v (if there are no laws against the landlord providing credit) and r T , the rate of interest charged. 4. Utility Equivalence For the moment, let us focus only on the choice of x (the number of tenants or, equivalently, the plot size per tenant). The landlord's in- come, G , is an increasing function of output per hectare, f , and f is an increasing function of its argument, effort per hectare, z , (see (8)). Furthermore, Proposition 1 states that z is an increasing function of x Therefore, the landlord's income increases with x . Thus a decrease in each tenant's plot size, with a corresponding increase in the number of tenants, increases the landlord's income. On the other hand, a tenant's welfare clearly decreases as x increases. Thus, if at any value of x the tenant's utility U* exceeds his utility U in the alternative use of his labor (so that he chooses to be a tenant), the landlord, by reducing plot size (increasing x), can increase his income while pushing the tenant towards U. As long as there are enough potential tenants, the landlord's choice, x 16 will be to push the tenant to a utility level equalling U.-/ Thus share- cropping will be utility equivalent to the best alternative use of the tenant's labor. Hence, Proposition 2: The equilibrium in the land-labor market will be characterized by utility equivalent contracts. It should be noted that this proposition does not depend for its validity on the presence or absence of any linkage between tenancy and credit transactions. The landlord's use of plot size as his sole instrument variable is sufficient to result in a utility equivalent contract equilibrium, an outcome obtained by Cheung [1969] in a different model. Our model is that of Stiglitz [1974], subsequently utilized by Newbery and Stiglitz [1978]. Assuming the tenants' utility function to be separable in consumption and leisure, they claimed that competition between landlords will drive the inequality U* > U to equality, thereby achieving utility equivalence. We have shown above that the utility equivalence outcome results from profit maximization by landlords and not from competition. That there is an in- finitely elastic supply of potential tenants at U does not render the proposition insignificant, since the possibility of an excess applicants equilibrium at U* > U can occur if the output share, instead of the plot size, is the only control variable of the landlord. A well-known case of excess applicants equilibrium arose under the efficiency-wage hypothesis (e.g., see Leibenstein [1957], Mirrlees [1976] and Stiglitz [1976]), primarily because the landlord is not allowed to use an instrument completely 1/ It can also be argued that if at an initial x , U* is less than U the potential tenant will not choose sharecropping. As such, in order to obtain someone to cultivate his land, the landlord will have to in- crease the plot size, i.e., reduce x . We are ignoring the fact that a tenant is "indivisible" while land is divisible. 17 orthogonal to effort to reduce U* to U without affecting effort. In our model, the use of the power to vary the plot size, although non- orthogonal to effort, guarantees the utility equivalent contract result since the tenant's effort per hectare increases with a reduction in his plot size. Additional instruments such as cropshare and interest rate are not needed for this purpose. Of the two assumptions used in deriving our result, namely, that both consumption and leisure are normal goods, and that the tenant is prohibited, as part of his contract, from working as a part-time laborer outside the farm, the latter is perhaps more controversial. Its actuality is primarily an empirical issue. It is true that tenants work as part-time laborers in many villages, butthe extent of such work is often limited. There is also some evidence to suggest that landlords believe that a tenant will put greater effort into cultivation, the smaller his plot size; From utility equivalence U[cCx, $). e(x, 6)1 = U, x can be solved as a function of the discounted share 0. It is easily shown that x'ta) > 0; i.e., in order to maintain the tenant on his iso-utility curve, the landlord must increase the tenant's discounted share if he reduces the plot size. Thus, when analyzing changes in $, unless otherwise specified, we assume that the landlord changes x along the curve x(S) so as to maintain the tenant at a welfare level of U. Consider the impact of change in S both on effort per hectare, z , and total effort e. It can be shown that effort per hectare increases with an increase in 0. Total effort, however, will increase (decrease) 18 with an increase in a if the elasticity of substitution between effective labor and land, a , is bigger (smller) than 1. Formally, it can be shown that: de A 1a) where A < 0 The results derived so far do not utilize the credit aspects of the model. Turning to the landlord's credit instruments (v, rT) and crop share x , we can write his income G as G = (1 - $O)f(ex) (10) where e 1 + vrL + (l-v)rA. It is seen that (a, vt rT) enter G only through their effect on 8 and 6, since e and x are functions of 8 . Now it is clear from (10) that G is decreasing in 6 for given 8. Hence an income maximizing landlord will, first, choose his optimal 0 ( 6)* to be the minimum feasible 6 for any given 8 and then choose 8 to maximize (l-8e*)f(ex). Since e depends only on v which lies between 0 and 1, if the given value of $ does not restrict the choices of 0 and 1 for v, then: 0* =(1 + r ) and v* - 1 if r rA Recalling that v is the proportion of borrowing by the tenant from the land- lord, we can state (11) as the following proposition. Proposition 3: The landlord, with no restriction on his choice of crop shares, will ensure that the tenant gets credit from the cheaper source. He does this by linking credit to tenancy if he is the cheaper source (rL c rA) and by not offering any credit, if he is not. 19 Remark: In the case of rL ' rA where linking is optimal, it remains optimal even if there is an institutionally imposed floor on the tenant's crop share. The reason is that with full linking, any given 8 l+rT (and a fortiori the optimal 8) can be achieved with an infinite set consisting of pairs (a, rT), of which, an infinite subset will meet the required floor. Proposition 3 is consistent with empirical observations (Bardhan and Rudra [19781) that landlords often offer interest-free loans to their tenants. For example, where the landlord is the cheaper credit source and, hence, there is linking (i.e., rL I rA), the interest rate rT charged by the landlord is essentially arbitrary and could as well be zero. In this case, linking is essentially voluntary. However, this will not be the case, as we will show later, if the environment faced bydhe parties is subject to certain constraints such as government regulations. Returning to the case where there is no floor on a, it can be derived and shown that: 6* S according as a 1 (12) where S is the imputed share of labor in output. In the case r rA,0* (1 + rA) and 8* - a*/(l + rA). Since in the first case rT can be chosen to be rL' 8*e* becomes the crop share a* in either case. Using (12) we can thus state: 20 Proposition 4: If there is no restriction on the landlord's choice of instruments (a, v, rT) , his optimal strategy involves offering his tenant a crop share a* such that a* S , according as a 1. a*(l + rL) Remark: In the case of rL < rA' since O*e (1 + rT) can offer an a* which is less (greater) than S, even if a is greater (less) than unity by choosing (a* ,'rT) with rT sufficiently less (greater) than rL L. Newbery and Stiglitz [1978] established Proposition 4 without incorporating credit or its linkage to tenancy. The above remark extends their result to a case where it is optimal for the tenant to borrow from his landlord It also implies that it is possible to observe crop shares lower than the imputed share of labor even for a production function with an elasticity of substitution larger than 1. 5. Policy Analysis 5.1 Tenancy Reforms Consider a reform which imposes a floor, a on the tenant's share a of the harvest. This is a common feature of many agrarian reform laws in India. In the case where rL ' rA , if in an equilibrium (a* , 1 , r*) prior to the promulgation of the reform law a* < a the landlord will respond to the reform by raising the crop share to aF while simultaneously raising the interest rate to rT so that in the new equilibrium * 1 , 1 + r** = +* . Since output (aF Tr1 r) 1 + r* T T depends only on B* , it is unaffected by reform. Given utility equivalence, the tenant's welfare is unaffected anyway. 21 Consider now the following two alternatives: (i) an initial equilibrium in which the landlord is not the cheaper source of credit, i.e., rL > rA so that v* -0, ° * = with a* < aF , or (ii) initially A ~~~~~~1 + r rL ! rA and v* - 1 a with a* < oF but as part of a tenancy reform, the interest rate on the tenant's alternative source of credit is brought below rL . In other words,the imposition of a floor, aF, coincides with a change in rA which brings rA below rL . This joint reform of tenancy and credit could be viewed as two consecutive reforms, first a credit reform with no tenancy reform, so that the landlord switches from a one-asterisk to a two-asterisk equilibrium, and secondly, a tenancy reform imposing a floor. In this way, it suffices to discuss only the first tenancy reform where rL > rA . In this case, it can be shown that the landlord can partially nullify the tenancy reform by forcedZy linking the credit and tenancy contracts. In Braverman-Srinivasan [1980] we demonstrated that although there is no optimal policy for the landlord after reform, there exist policies that will give him an income as close as he wishes to his income prior to reform. By forcing the tenant to take small loans (v is small) with a high interest rate rT- , the landlord ensures that on the whole the tenant will both use the cheaper source of credit, rA , and deduct from him yrT , which increases the income of the landlord. (yrT, however, is not an orthogonal lump sum levy on the tenant). The above discussion implies that, if linking is permitted, the landlord can reduce the tenancy and credit reform to insignificance. Suppose 1/ This is perhaps a rationale for empirical observations of tenants being charged high interest for rather small loans. 22 now that the government bans linking, a2ong with tenancy and credit reforms. Clearly the landlord's income will decline, while the tenant's welfare continues to be at the level he could have achieved while working as a wage laborer. What about the effect on output? Since the landlord no longer has the instrument by which he can maintain the pre-reform discounted share, 0*, of the tenant, the reform will raise S.. Since we know from that dz/dS > 0 , 1/ we can assert that output f(z) will go up.- Thus: Ppopoeition 5. A tenancy reform which imposes a floor on the tenant's share of the crop with or without credit reform (to make credit available to the tenant at a rate lower than the landlord's opportunity cost of capital), will have no effect on output. If it is coupled with a ban on linking of credit and tenancy transactions, it will raise output, reduce the tenant's plot size and increase the number of tenants. Now consider only a ban on linking of credit and tenancy. This is,of course, meaningless when the landlord is not the cheaper source of credit, since no linking will be observed anyway. Suppose the ban is imposed when there is linking, i.e., when r < r and v* - 1 . Clearly, L- A this immediately raises the cost of credit to the tenant to rA . In the landlord's income maximization problem, fixing v at zero (i.e., preventing linking), fixes e at (1 + r ), i.e., raises e from its optimal value of A 1 + rL prior to the ban to (1+ rA). Since G is a monotonic decreasing function of 9 , at any vaZue of G , G is lower than before. Clearly, even with the optimal value of G , G is lower. This means that landlord's income definitely goes down. What about output? As long as f(z) as a function of 6 is concave, optimal 5 for any specified e is a decreasing function of 1/ Recall the interpretation of this result. An increase in 0 raises the the number of efficiency units of labor per hectare, i.e., ex supplied by each tenant, and increases the number of tenants through a reduction in plot size. If the elasticity of substitution is less than unity, effort per tenant will decline, so that output per tenant will decline. But the increase in the number of tenants more than offsets this decline. 23 e . Hence, as e is increased from (1 + rL) to (1 + rA), optimal 6 goes down. This means that firstly, the optimal plot size increases thereby reducing the number of tenants, and secondly, output goes down since f(z) is an increasing function of a Finally, consider a credit reform alone where rL < rA. With this reform, however, the government subsidized credit becomes the cheaper source of credit, i.e., rA < rL . Before the reform the landlord lends to his tenants but afterwards, the landlord withdraws from the tenant's credit market. Yet, by the utility equivalence result, the landlord extracts all the surplus created by the government's cheaper credit. Hence, the government subsidization of tenants' credit results only in the subsidization of Zandlords. 5.2 Land Reform Suppose that starting from an initial equilibrium [a*, v*, r* and x($*), each tenant is given the ownership of the plot he cultivates and has to forego the opportunity to borrow from one landlord. Clearly, the tenant's welfare improves, for if rL > rA ' v* = O and ** = + With reform, a becomes unity, rA remains unchanged so that the tenant's (now a landowning peasant's) discounted share 6 increases, while the size of the plot remains the same. Hence, without changing his effort e , (and its disutility) he will gain in consumption and, hence, total utility. By optimally adjusting his effort to the changed s , he can raise his utility even further. Now if rL I rA * initially v* 1. Since the landlord is indifferent in this case between alternative combinations of V(a, rT) which 24 result in his optimal S* , we can view the land reform as if it, first, changed the interest rate charged by the landlord to rA with a corres- ponding change in a to maintain the same O* , and then raised the tenant's crop share to unity. The two moves together imply that the tenant's post-reform discounted share is higher. From this point, the argument is the same as inthe previous case. Now, what is the effect of land reform on output? Land reform increases the discounted share S while keeping the plot size fixed. Thus output is f[e(O)x] where x is fixed. Hence, output will increase if tenant's effort increases. Braverman-Srinivasan [1980] provides the fol- lowing condition: e < °0 according as -c 21 a= 1. (13) aB < u1 ~~~U2 > This leads to. the following proposition: Propositon 6: A land reform which confers ownership to the plot of land that a tenant used to cultivate in a sharecropping contract with a landlord will increase, not change, or decrease output, according as -c(l ~ U 1. To interpret (13) we can utilize Figure 1 again. Clearly, since the plot size is fixed an increase (decrease) in effort implies an increase (decrease) in effort per hectare. The expression in (13) is the following: The R.H.S. term 1 is the elasticity of the MRT with respect to S for given x and e , while the term on the L.H.S. is the elasticity of the MRS with respect to B , which equals the elasticity of the marginal rate of substitution with respect to consumption. A land reform which increases a shifts the curves in Figure 1 in opposite directions: the dominant effect is obtained by a comparison of the two elasticities. 25 Furthermore, consider the case of a separable utility function, i.e., U(c, e) - u(t) - v(e). Then (13) becomes ae > 0 according as u < 1=l (14) TO- ~~ut > (4 The negative of the elasticity of marginal utility ( --) is defined by Arrow [19711 as the measure of relative risk aversion. The intuitive explanation for the value of this elasticity to be of relevance in our case, even though there is no uncertainty, is the following: On the one hand, an increase in 6 increases tenant's income; hence, the marginal utility of income declines relative to the marginal disutility of effort, and ceteris pazribus, the new landowver would like to reduce his effort. On the other hand, his share in the marginal productivity of effort increases, with increasing a , thus creating an incentive for more effort. Whether the income effect or the.marginal produttivity effect is the dominant force depends solely on the elasticity of the marginal utility. Where land reform distributes the land to more owners than the original cultivators, it may increase total output even if -c u i 21) > i since ceteris paribus, output per hectare increases with reductions in plot size. Note that the above discussion also applies to analyses of share- cropping contracts by substituting a for B . This holds for the remaining policy analysis as well. 5.3 Taxation and Technological Progress Suppose the government imposes a proportional output tax at the rate t on tenants and landlords (i.e., the rural community) in order to raise food to feed the urban workers. Since, for any a , this tax is 26 equivalent to a reduction in the discounted share of the tenant from S to u E $(l-t) , the tenant's decision function e(x, $) becomes e(x, p). It is also easily seen that the landlord's choice set x(a) becomes x(p). It can be shown (Braverman-Srinivasan [1980]) that du < 0 and dt df(z(u)) d < 0 , i.e., output declines due to the imposition of a dt duidt- proportional tax. The implied decline in the aftertax share, p , necessitates an increase in the tenant's plot size in order to maintain the tenant on his reservation utility U . The increase in plot size implies both a reduction in the number of tenants, x , and a decline in output. We thus obtain the following proposition: Proposition 7: The imposition of a proportional output tax on landlords and tenants will cut the aftertax share of the tenant, increase the plot size per tenant, and reduce the number of tenants as well as total output. Modelling a Hicks neutral technical change is equivalent to modelling a proportional output tax, i.e., a Hicks neutral technical change is a shift in A where the production function is Af(z). The only difference is the direction of the impact. Hence, considering a Hicks neutral technical change and applying Proposition 7, we obtain: Proposition 8: A Hicks neutral technical change will increase the aftertax discounted share of the tenant, decrease the plot size per tenant and increase the number of tenants as well as total output. Now, consider the case of a Cobb-Douglas production function. Given the unit elasticity of substitution, the tenant's effort is independent of v =- (l-t) (see (9)), i.e., the decline in the aftertax share is totally compensated by the increase in plot size so as to leave the tenant's effort 27 unaltered. Furthermore, it is easily seen using (12) that the optimal 8 is unaffected by the tax or technical changes. For the Cobb-Douglas case, all factor-augmenting technical changes can be viewed as Hicks neutral changes. Thus, considering irrigation as a land-augmenting technical change and applying Proposition 8, we obtain: Proposition 9: If the production function is of the Cobb-Douglas type, introducing irrigation will leave the discounted share contract unaltered, decrease the tenant's plot size and increase the number of tenants as well as total output. 5.4 Increase in the Tenant's Utility Level in anAlternitive Occupation Suppose, for example, that through an increase in the non-agricultural wage rate, the utility that the tenant could obtain (i.e., U) in an alternative occupation increases. Assuming once again a Cobb-Douglas production function so that the tenant's effort is independent of 8 , it is clear that the landlord can ieet the higher U only by raising the plot size, therefore reducing the number of tenants and output. Equilibrium 8 is unchanged. Hence: Proposition 20: If the production function is Cobb-Douglas, any increase in the utility that the tenant can obtain in an alternative occupation will raise te.-equilibrium plot size, reduce the number of tenants and output, while leaving the discounted crop share unaltered. 28 5. Conclusions In -conclusion, we summarize our results-and relate them to the literature.-V Our main result is that in a world in which (i) production takes place under constant returns to scale in land and labor in efficiency units, (ii) a landlord can subdivide his land into as many plots as he chooses, and (iii)a tenant chooses his effort, so as to maximize his utility -equilibrium will be characterized by utility equivalent contracts. In other words, even if a landlord has no power over crop shares or terms of credit, by choosing the plot size appropriately, he will force the tenant to a utility'level equal to that uhich he (the tenant) could have obtained in an alternative occupation as long as there-are'enough potential tenants. He is able to do this not only 'ecause there- is a perfectly elastic supply of tenants at this 'reservation' utility level, but also because the tenant's effort per hectare increases with a reduction in his pZot size. This result is similar to that found in Cheungts model (1969), where the tenant's effort per unit of raw labor is invariant. Cheung shows that landlords will provide each tenant a plot of land on which the tenant can earn no more than he could have earned in an alternative occupation. Whereas enforcement of the tenant's labor input is necessary in a Cheungian world, it takes a different form in our model: it ensures that the tenant does not split his working time between sharecropping and an alternative occupation. 1/ Sharecropping contracts have also been analyzed in relation to the post- Bellum South. Discussion of pure sharecropping was initiated by J. Reid [1973], and the interlinkage of credit and tenancy arrangements through the country store was subsequently discussed by Ransom and Sutch [19783. We do not, however, elaborate on these and other works on the post-Bellum South since they are not directly applicable to our model. 29 In this world of utility equivalent contracts, it will be in the interest of the landlord to ensure that the tenant gets his credit from the cheapest source, If the landlord's opportunity cost of capital is lower than that charged by the local moneylender, the landlord will ensure tnat the tenant gets credit at the cheapest interest cost by offer- Lug a linked tenancy-cum-credit contract, Unlike the. models of Bhaduri (1973, 1977, 1979), linking credit with tenancy is not an instrument vhich extracts a surplus that would otherwise have accrued to the tenant; linking, where optimal, raises output and the landlord's income (compared to non-linking) by reducing the plot size per tenant, and therefore increases the nuber of tenants, while leaving the utility of each tenant .mhanged. EacE tenant thus cultivates a smaller plot of land devoting less effort per anit of his labor. Ipso facto, a ban on linking, when it is optimal, will reduce the landlord's income and output. In the debate between Srinivasan [1979] and Bhaduri, the issue was the alleged lack of incentive for the landlord to introduce yield-raising innovation, given linked tenancy-cum-credit contracts. Using the Bhaduri model, Srinivasan showed that as long as borrowing was not an "tinferior" good to the tenant (which it was not in the Bhaduri model), there was no such disincentive. In our model, borrowing is, by definition, non-inferior since it equals the tenant's discounted income; and linking is chosen, not imposed,only if it is optimal. The tenant is pushed down to his alternative utility level, not by the credit instrument, but by plot size variations. Finally, in our model, utility equivalence implies that nothing short of land reform will affect the tenant's welfare, as long as he is a tenant. Indeed, other reforms such as setting a floor on the tenant's share of the crop, making credit available to the tenant at a cost below the 30 opportunity cost of capital to the landlord or banning credit and tenancy linkage, either have no effect on the equilibrium at all or have an effect on the number of tenants, output and the landlord's income. Empirically, our model provides a theoretical underpinning for two almost opposite phenomena that are sometimes observed: low interest consumption loans from landlord to tenant (by Bardhan and Rudra [19781) and the opposite, high interest, low volume loans. Our model did not include production credit.and did not allow the tenant any bargaining power given the infinitely elastic supply of tenants at U . Bravernan and Guasch [1980] discuss production credit where inter- linked credit and tenancy contracts are used as a screening device for landlords to distinguish more able tenants. Bell and Zusman [1980], Mitra [1980], and Braverman-Stiglitz [1980] discuss interlinked credit and tenancy contracts in the presence of uncertainty and unequally distributed information. 3 31 REFERENCES Arrow, K.J. [1971], "The Theory of Risk Aversion," Chapter 3 in Essays in the Theory of Risk Bearing. Bardhan, P.K. [1980], Interlocking Factor Markets and Agrarian Development: A Review of Issues," Oxford Economic Papers, March. Bardhan, P.K. and A. Rudra [1980], "Interlinkage of Land, Labour and Credit Relations: An Analysis of Village Survey Data in East India," Economic and Political Weekly, February. Bell, C.L.G. and A. Braverman [1978],' "On the Non-Existence of 'Marshallian' Sharecropping Contracts Under Constant Returns to Scale," World Bank, Development Research Center, July. _______ and-P. Zusman [1980], "On the Interrelationship of Credit and Tenancy Contracts," World Bank, Development Research Center, March. Bhaduri, A. [1973], "Agricultural Backwardness Under Semi-Feudalism," Economic Journal. :__________ [1977], "On the Formation of Usurious Interest Rates in Backward Agriculture," Cambridge JournaZ of Economics, Vol. 1, No. 4, pp. 341-52. __________ [1979], "A Rejoinder to Srinivasan's Comment," Economic Journal, June. Bharadwaj, K. [1974], "Production Relating in Indian Agriculture: A Study Based on Farm Management Surveys," Occasional Paper No. 33, Department of Economics, Cambridge, Cambridge University Press. Braverman, A. and J.L. Guasch [1980], "Draught-Power in Signalling Equilibria with Interconnected Credit and Tenancy Markets in Developing Rural Economies," World Bank (preliminary DRC draft). and J. Stiglitz [1980], "Moral Hazard and Interlinked Contracts in Rural Developing Economies," World Bank (preliminary DRC draft). and T.N. Srinivasan [1980], "Interlinked Credit and Tenancy Markets in Rural Economies of Developing Countries," World Bank, Development Research Center, May. Cheung, S.N. [19691, "The Theory of Share Tenancy," Chicago. Leibenstein, H. [1957], Economic Backoardness and Economic Growth, Wiley. Mirrlees, J.A. [1976], "Pure Theory of Underdeveloped Economies," in (ed.) L. Reynolds, Agriculture in Developing Theory, Yale University Press. 32 Mitra, P. [1980], "A Theory of Interlinked Rural Transactions," World Bank, Development Research Center, draft. Newbery, D.M.G. [1977], "Risk Sharing, Sharecropping and Uncertain Labour Markets," Review of Economic Studies, Vol. 44, No.3,October. and J.E. Stiglitz (1978], "Sharecropping, Risk Sharing and the Importance of Imperfect Information," Cambridge, Economic Theory Discussion Paper. Srinivasan, T.N. [1979], "Agricultural Backwardness under Semi-Feudalism," Economic JournaZ, June. Ransom, R. and R. Sutch [1978], "One Kind of Freedom," Cambridge. Reid, J. [1973], "Sharecropping as an Understandable Market Response: The Post Bellum South," Journal of Economic History, March. Stiglitz, J.E. (1974], "Incentives and Risk Sharing in Sharecropping, Review of Economic Studies. [1976], "The Efficiency Wage Hypothesis, Surplus Labour and the Distribution of Income in LDC's," Oxford Economic Papers. RECENT PAPERS IN THIS SERIES No. TITLE OF PAPER AUTHOR 418 Approaches to Purchasing Power Parity and Real S. Ahmad Product Comparisons Using Shortcuts and Reduced Information 419 Employment Patterns and Income Growth: J. Stern An Application of Input-Output Analysis J. Lewis 420 The Evaluation of Human Capital in Malawi S. Heyneman 421 A ConceptuXal Approach to the Analysis of External R. Aliber Debt of the Developing Countries 422 Estimating Total Factor Productivity Growth in A. Krueger a Developing Country B. Tuncer 423 Rethinking Artisanal Fisheries Development: D. Emmerson Western Concepts, Asian Experience (consultant) 424 Transition toward More Rapid and Labor-Intensive B. de Vries Industrial Deveiopment: The Case of the Philippines 425 Britain's Pattern of Specialization in Manufactured V. Cable Goods with Developing Countries and Trade Protection I. Rebelo 426 Worker Adjustment to Liberalized Trade: Costs and G. Glenday Assistance Policies G. Jenkins J. Evans 427 On the Political Economy of Protection in Germany H. Glismann F. Weiss 428 Italian Commercial Policies in the 1970s E. Grilli 429 Effects of Non-Tariff Barriers to Trade on Prices, C. Hamilton Employment, and Imports: The Case of the Swedish Textile and Clothing Industry 430 Output and Employment Changes in a "Trade Sensitive" J. Mutti Sector: Adjustment in the U.S. Footwear Industry M. Bale 431 The Political Economy of Protection in Belgium P. Tharakan 432 European Community Protection Against Manufactured E. Verrydt Imports from Developing Countries: A Case Study J. Waelbroeck in the Political Economy of Protection