Part (ii) of the proposition says that when g=b, and labor input is at the optimum level, the tenant’s share of the output is determined by his bargaining power vis à vis the landlord. If b=0, we have that af(L)=zL. The tenant’s net income from being a sharecropper is zero, i.e. his income will be exactly the same as what he would have earned as a wage laborer. If b=1, we have that a=1. The tenant receives all the fruits of his work, i.e. his income will be exactly the same as what he would have earned as an owner-cultivator.
We can represent the possible outcomes of the share-labor input bargain in figure 1. On the diagonal (g=b) labor input is at its efficient level, and as we increase ½g-b ½ we have increasing inefficiency. When g=b=0, we have the Cheungian model. When g=1 and 0, we have the Bell and Zusman model, for which the Marshallian model is a special case with b=1. But, as figure 1 shows, not only have we integrated the three models of sharecropping discussed in section 2, the model also open up for several other possibilities depending on the relative bargaining power of the two parties.
Note: The Cheungian model (b=g=0); The Marshallian model (b=0, g=1); the Bell and Zusman model
This framework can also be useful in evaluating recent empirical work on sharecropping (e.g. Bell, 1977; Bliss and Stern, 1982; Nabi, 1986; Shaban, 1987; and Bhuiyan 1987). A central aspect of this work has been to test which is the appropriate model of sharecropping. These papers have, however, restricted the menu of theoretical models to the Marshallian and the Cheungian model. The tests have essentially been based on an examination of whether the intensity of cultivation is lower on sharecropped land compared to land that is owner cultivated or cultivated on a fixed-rent basis. If it is not, the Marshallian inefficiency hypothesis of sharecropping is rejected and the Cheungian hypothesis is accepted. Although the first part of this test is satisfactory, the rejection of the Marshallian model does not, however, automatically justify acceptance of the Cheungian model. As can be seen from figure 1, all points on the diagonal (g=b) give an efficient outcome, i.e. f’(L)=z, and it is only when g=b=0 that we have the Cheungian model. This of course also applies to the opposite case. A rejection of the Cheungian model does not justify acceptance of the Marshallian model since all points above the diagonal (g>b) give an inefficient outcome, i.e. f’(L)>z. If one does not know anything about g and b, one seems in other words to run into an identification problem.
5. Summary and concluding remarks
In this paper, we have shown that some popular models of sharecropping that traditionally have been treated as completely separate, can be viewed as special cases of a more general model of sharecropping. The way we did this integration was to adopt a two stage bargaining framework, developed in another setting by Manning (1987). Some other implications of the framework were also explored. It was shown that it is not the tenant’s control over labor input per se which causes inefficiency in sharecropping (as the traditional argument runs), but differences in the tenant’s influence over different issues in the contract. This result also has some implications for the interpretation of recent empirical work on sharecropping. We have argued that much of this work seems to suffer from an identification problem.
To be able to demonstrate the results above, the model was kept very simple. We looked at a bargain between a single landlord and a landless sharecropper cultivating a given plot of land. There was first a bargain about the rental share and then a bargain about labor input. The two parties bargaining power could differ at different stages of the bargain. An interesting extension of the model would be to take into account that a landlord may bargain with several tenants at the same time, and that there usually exists more than one landlord in the same village. This may have some consequences for the two parties payoff if they fail to reach an agreement (see Bell (1989) for a discussion). In this connection we should also say something about how the landlord distributes his land-holdings between his tenants. There are also other gaps in the model which needs to be filled in. We need a better explanation of why the two parties bargaining power in the different stages should be different, and we should be able to say something more about the determination of the two parties bargaining power. What gives a poor tenant bargaining power vis á vis a wealthy landowner? These questions will hopefully be addressed in future research.