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Proof of Proposition 2
(i) It is easier to transform (12) into a problem in labor input using (11). We are able to do this because the one-to-one relationship between a and L. From (11) we have that




and




Using (A1) and (A2) we can write the first stage of the bargain as




From (A3) we can derive the optimal labor input rule in terms of b and g. The first-order condition for (A3) can be written




Some rearrangement of (A4) yields




where




The bracket term of the left hand side of (A5) is positive (being U), which implies that




Consider the case where g>b: Assume f’(L)£ z. This contradict (A6), hence f’(L)>z.

Consider the case where g: Assume f’(L)³ z. This contradict (A6), hence f’(L)>z.



Consider the case where g=b: Then (A6) becomes




which only holds when f’(L)=z.
(ii) In the labor-input determination stage of the bargain, the first-order condition to (10) can be written




Turning to the share determination stage of the bargain, the first-order condition to (12) can be written




When g=b we have from (A7) that the first two terms of (A8) is equal to zero. (A8) is then reduced to




which gives us (14). By replacing a in (11) by using (14) we get f'(L)=z, which confirm part (i) of Proposition 2.



Notes



11. For the whole of Asia, it is estimated that about 16 percent of total cultivated land is farmed under different tenurial arrangements. 85 percent of this land is sharecropped (Hayami and Otsuka, 1993).


22. For recent review articles and books on sharecropping, see Bliss and Stern (1982), Singh (1989), Otsuka et.al. (1992), and Hayami and Otsuka (1993).


33. Hayami and Otsuka (1993) give a broad survey of the empirical literature.


44. This formulation indicates that we are investigating the effects of sharecropping on resource allocation and efficiency given that this arrangements has been adopted. There exists a large body of literature that attempts to identify conditions under which sharecropping is superior to alternative contractual arrangements. As this literature has rigorously shown, sharecropping may perform a variety of functions. It permits risk sharing when insurance markets fail (Stiglitz, 1974), sharecropping can serve as a mechanism to sort workers of different qualities (Hallagan, 1978), and it can correct market imperfections for inputs other than land (Bliss and Stern, 1982). In this paper we abstract from all this by confining ourselves to pure sharecropping under certainty.


55. See also Bell (1988; 1989) who extends this paper in major ways.


66. By using a variety of supposedly realistic production technologies Bell and Zusman get the important result that a takes remarkably stable values, centering around 0.5 in equilibrium. This result appears significant in view of the fact that 50:50 sharing under sharecropping is so common in practice.


77. In the formulation of (4) and (5), we have implicitly assumed that U1=V1=0 is the disagreement points. We have more to say about this is section 3.


88. Bliss and Stern (1982) and Taslim and Ahmed (1990) give evidence from South Asia.


99. This is particularly important in the context of sharecropping. As Johnson (1950) has pointed out, a sharecropper will have an incentive to lease in as much land as he can. While the sharecropper always receives a fixed proportion of the output from the land, the effective cost of holding the land is zero.


1010. See also Bell and Zusman (1976) who report that; "[T]enants are drawn mainly not from the mass of landless laborers, but from the ranks of the small peasantry possessing (...) skills and capital, all of which are traded in imperfect markets. (...) Owning at least one pair of bullocks or buffalo is a sine qua non for obtaining a lease." (p. 579-80). Bliss and Stern (1982, chap. 5) report more or less the same from their in-depth study of an small Indian village.


1111. There are many examples of the coexistence of both casual and permanent labor in poor agrarian economies (see, for example, Bardhan (1984) and Eswaran and Kotwal (1985)). In casual labor markets, contracts are struck for a short duration between the landowners and the workers. Permanent labor contracts are contracts where workers or tenants get into a long-term attachment to landowners. Such contracts can last for around a year and, at times, even for several years. There is evidence that permanent laborers earn a higher income (Eswaran and Kotwal, 1985). Laborers therefore prefer long-term contracts, but such contracts are more difficult to get hold of compared to casual contracts.



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