Now, the tenant’s income reduces to
[10]
hf [ rf — β f ] + v
where rf * = rf (z1f *). It is clear from [10] that the tenant will lease-in land if rf* ≥ βf. Therefore the
choice to lease-in land depends on the landlord’s choice of fixed rent, β. Since the technology is constant
returns to scale, there is no optimal farm size. The maximum amount of land the tenant can cultivate using
the optimal levels of time inputs is;
hf*
1
z1f + z2* ,
tif = zi f hf V i = 1,2 and t1f + t2f = 1
[11]
The optimal time inputs and, therefore, the maximum farm size are functions of the tenants’ skill level (s)
and outside option (v).
The Share Tenant’s Problem
Consider a share tenancy arrangement where the landlord and the tenant provide M1 and M2
respectively.14 The share tenant’s problem is
max aF[T1s, 12s,h,;S]+(1 - 12s)v- βs hs [12]
t2
We incorporate the observation made in the empirical literature that there are some fixed payments even
in the case of sharecropping [Otsuka and Hayami 1993]. This limits the role of the share to the
enforcement of work effort, because the tenant’s reservation income constraint can now be met by
adjusting fixed payments.
Notice that the production in sharecropped land takes place at the landlord’s skill level. The
tenant provides only the time for M2 tasks. As in the case of the fixed-rent tenant, the share-tenant’s
14 We assume that both parties cannot provide the same input due to prohibitively high coordination costs.It is quite
possible that the tenant specializes in M1 if his or her skill to time ratio is higher than the landlords. This problem
would be, analytically, a mirror-image of the case considered here.
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