Skills, Partnerships and Tenancy in Sri Lankan Rice Farms

Z** = Z 1*0 + Z2*_o = arg max R_o + argmaxR_o
Z1o                  Z2o

Zs = Z1S-(.=²S ) = argmax R

Z1s

However, the two problems are separable only if the landlord’s time constraint is not binding. That is, if A
=0, the exogenous market wage u acts as a separating hyper-plane between the landlord’s time utilization
problems in owner-operated land and sharecropped land, and the three first order conditions are sufficient
to fully identify the time input choice solution. Equation for Z^*s in [23] is the landlord’s reaction function in
the Nash game over the provision of time inputs in sharecropped land. Assuming that a unique solution
exists, the solution to this game (Z1*_s(α), z2*_s(a)) is found by solving the two equations [15] and [23]
simultaneously. The landlord’s time input choices (Z^*o, Z^*s) in the absence of time constraints provide us
with a benchmark “efficient” solution.

If A >0, the problem is analytically more interesting because there is no exogenous market wage
to separate owner-farming from share-cropping. The marginal value of the landlord’s time is now given by
a “shadow wage” w which is the sum of the market wage u and the multiplier Λ which measures the
“magnitude” or the “severity” of the time constraint. Since w does not characterize an exogenous
separating hyper-plane, the landlord’s time constraint is necessary to identify the time input choice
solutions. The landlord’s time constraint is:

ZoHo + Z1_sH_s = 1                                                      [24]

After solving the Nash game with the share-tenants, the landlord’s optimal time inputs choices are
obtained as functions of Hs and Hf.

Z_o (H_s, H_f, α) = arg max R_o + arg max R_o

Z10                 Z20

Z2s (Hs, Hf, α) = arg max Rs

Z1s

Once the optimal input levels are determined, the landlord chooses how much land is leased out to fixed-

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