Z** = Z 1*0 + Z2*o = arg max Ro + argmaxRo
Z1o Z2o
[23]
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 + Z1sHs = 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.
Zo (Hs, Hf, α) = arg max Ro + arg max Ro
Z10 Z20
Z2s (Hs, Hf, α) = arg max Rs
[25]
Z1s
Once the optimal input levels are determined, the landlord chooses how much land is leased out to fixed-
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