Skills, Partnerships and Tenancy in Sri Lankan Rice Farms

zero, the reservation income constraint for each type of tenant must be binding if that type of contract
exists. The multiplier values of one tell us that if the reservation income constraints are relaxed by a unit,
the landlord can adjust the contract parameters to increase his or her income by the same amount.

Because the constraints must bind in order for a contract to exist, the fixed payments of the
tenants are,

βf = f (z1 *f , z2 f;s) - (z1 f + z2^f )v = r_f

β s = af ( Z1sf, z 2 f ;S ) - z 2sv = r ( a *, Z1^                    [20]

From [10] and [16], we see that the rents in [20] are consistent with the participation conditions of the
tenants. In fact, since the reservation constraint hold with equality, tenants are indifferent to the extent of
land leased for these fixed payments under the assumption that the equalities [11] and [17] are not met.

Using these results, the landlord’s problem reduces to the following form:

max  H[ ( Z1_o, Z2o;S ) - ( Z1_o+Z2o) w]+H_s[f( Z1s,z2 f; S )-z2 f v-Z1_sw]

Z1o,Z2o, Z1_s,Hs,Hι,a

+H_f[f (z1f^{, z2f}_f ;s) - (z1f ^{+ z2}f ) v]+w

where w = u + Λ and Λ is the Lagrange multiplier of the time constraint (marginal value of increasing
the time endowment).

By appropriately reorganizing the terms in expression [21], the landlord’s problem can be
interpreted as maximizing the joint income of both parties minus the opportunity income of tenants.

Let

[ f (Z1o, Z2o;S) - (Z1o + Z2o)w ] = Ro

[ f ( Z1s, z2s ;S ) - z2s v - Z1sw ] = Rs                             [22]

The landlord’s time allocation problem is defined in [22]. The optimal time inputs per unit of land, under the
usual assumptions of concavity of Ro and Rs are,

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