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(i) g=1 and b=0 we have the Marshallian model;

(ii) g=1 and 0

(ii) g=b=0 we have the Cheungian model;
Proof

(i) If g=1, the first order condition for (6) is U1af’(L)+U2=0. In the first stage of the bargain, when b=0, a is chosen to maximize V(y,L) subject to this constraint. But this is exactly the Marshallian model, see (3).
(ii) Again, if g=1 the first order condition for (6) is U1af’(L)+U2=0. In the first stage of the bargain, a is chosen to maximize [U(y,L)b V(y,L)(1-b)] subject to this constraint. But this is exactly the Bell and Zusman model, see (5).
(iii) The tenant has no influence over a and L. The landlord chooses both a and L to maximize V(y,L) subject to the constraint U(y,L)=U0. But this is exactly the Cheungian model, see (4).


Before we proceed and show some further implications of the model, it can be appropriate to discuss briefly some of the assumptions underlying it. The first assumption which needs to be justified is the assumption that the rental share and labor input are determined by a bargain between the landlord and the tenant.

The most common assumption in the sharecropping literature is that the tenants have no bargaining power vis á vis the landlord. In most cases it turns out that the contract is such that it yields the tenants no gain over the utility from alternative employment. The source of the landlord’s power to arrange matters to his liking appears to lie in the assumption that he faces a perfectly elastic supply of identical agricultural workers who wish to become sharecroppers. If a single tenant refuse the landlord’s offer, there are plenty more who will accept, and this will not make the landlord any worse off. In view of what is known about peasant agriculture this is, however, a rather strong assumption.

One input, besides land and labor, that is essential for production in agriculture is draft power. In poor agrarian economies draft animals, like bullocks, are usually the only source of draft power. Despite their importance for cultivation, an efficient market for animal draft power seldom exists in rural areas.8 No cultivator can thus rely on the market for this service, nor indirectly, can any landlord. When a landlord decides to lease out his land on a sharecropping basis, he will therefore be interested in finding a tenant who possesses sufficient bullocks (and other agricultural equipment) to cultivate the land properly.9 But, a poor agricultural worker usually cannot afford, and does not own, any bullocks. Landlords therefore generally do not face any perfectly elastic supply of identical workers who have the means to cultivate the land. As Platteau (1994) comments; “The interpretation of the sharecropping contract as a partnership venture - as opposed to a buyer-seller arrangement- in which households (...) pool productive resources is gaining ground in the abundant literature addressing the thorny issue of the rationale of this particular arrangement.” (p. 8).10 This implies that there are potential gains from co-operation for both the landlord and the tenant. By having access to a tenant who has sufficient bullocks, the landlord maximizes expected rent from the leased out land. By entering into a sharecropping contract, the tenant may be able to make a fuller utilization of his bullocks capacity that are otherwise not tradeable in efficient markets.

In such a situation it is rather arbitrary to assume that the terms of the contract are decided unilaterally by the landlord, especially if he captures all the gains from co-operation. Instead it is more reasonable to assume that the terms are decided through a bargaining between the two parties’.




What then are the possible explanation for the sequence of decision-making; that the share is determined prior to labor input? One explanation can be that in the presence of uncertainty and the impossibility of complete contracting, it may be optimal to agree on the share first and then bargain over labor input later in response to a changing environment. Preparing the land for cultivating, e.g. ploughing, are done during a relatively short period at the beginning of a crop season. Thus all landlords will search for tenants who possess bullocks, at about the same time. This tends to make the markets for tenants tight during this period. Hence, a landlord may not be successful in hiring tenants that are able to cultivate the land properly. A strategy to ensure that tenants are available when needed may therefore be to make a deal, that is determine how the crop should be shared, in advance. When the crop season starts, and the “state of nature” is known to the parties involved, labor input can be bargained over. If there has been a drought for example, this probably calls for different labor services from the tenant compared to a situation with normal weather.

4. Sharecropping and efficiency


We have shown how a two-stage bargaining model can encompass some popular models of sharecropping that traditionally have been treated as completely separate in the literature. In this section we introduce some specific utility functions in order to show some further implications of the model. In particular we look at the relationship between the power of the landlord and efficiency in sharecropping. As Cheung (1968), among others, have argued sharecropping will give an efficient outcome only if the landlord has the power to decide the amount of labor (and other variable inputs) to be used on the land. As will be shown, this is not the case in our model.

Assume that the tenant has the following utility function






where the tenant’s total labor time is normalized to one, and z is the tenant’s opportunity cost of labor. One possible justification of this last feature is that there exists a casual labor market where the tenant can always sell labor at the fixed wage z.11 This means that the level of labor input chosen is Pareto-efficient if it meets the condition f’(L)=z. That is, the marginal product of the tenant’s effort is equal to the marginal cost to the tenant of providing that effort.

The landlord is interested in maximizing income






If the two parties fail to reach an agreement, the tenant will fall back on wage labor, and the plot of land earmarked for the tenant under consideration lies uncultivated. In other words, we assume that U1=z and V1=0 are the two parties disagreement points.

In the labor input determination stage, L is chosen to solve the following problem






The first-order condition for (10) can be written




From (11) we see that for a given a, labor input depends on the bargaining power of the landlord and the tenant. If g=1, so that the landlord has no influence over labor input, then we have that af'(L)=z. The tenant will chose labor input so that the marginal income from sharecropping equals the opportunity cost of labor. If, on the other hand, g=0, so that the tenant has no influence over labor input, labor input will be chosen so that the tenant’s net income is zero, that is af(L)=zL.
In the first stage of the bargaining, a will be chosen in the following way




where L(a;g) is given by the solution to (11). The first-order condition for (12) can be written







(11) and (13) will give a solution for L and a dependent on the two parties bargaining power, and the following proposition can be proved
PROPOSITION 2

In the share-labor input bargain between a landowner and a tenant

(i) The optimal labor input rule says that

(a) if g>b labor input is too low, i.e., f’(L)>z.

(b) if g

(c) if g=b we have efficiency, i.e., f’(L)=z.
(ii) When g=b the optimal share solves




Proof. See Appendix



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