Skills, Partnerships and Tenancy in Sri Lankan Rice Farms

problem can be restated in terms of time inputs per unit of land.

max hi {a *f (Z1*,z2s ; S) - z2sv- βɔ + v
_z2s        l                      s                               s           s

[13]

where the tenant takes the landlord’s optimal choices of a . β*_s and Zl*_s as given. The assumption here is

that each tenant and the landlord engage in a one-shot non-cooperative Nash game where each party

maximizes his or her income subject to the optimal choices of the other.

Let

a * f ( Z1*, z2_s;S ) - z2_sv = r_s ( a *, Z1*)

[14]

The tenant’s optimal choice of z2s is

z2*_s= argmax r_s(a*, Z1*)

[15]

This is the reaction function of the tenant that is solved simultaneously with the landlord’s choice of Z1s to

obtain the Nash equilibrium levels of time inputs. Once the time inputs are chosen, the tenant’s income is

reduced to

*       *       *      Λ

^hS [^rs (^{a , Z1}s ⁾ - ^β s] + v

[16]

where r_s * = r_s (Z2_s*). The share tenant will lease-in land if r* ≥ β_s.   For those who lease-in, the

maximum amount of land cultivable with the optimal levels of time inputs is

Λ* _  ¹

^h s      ɔ*

z2_s^*

[17]

The Landlord’s Problem:

The landlord maximizes his or her income subject to a time constraint and the reservation incomes
of tenants. The choice variables of the landlord are the time inputs in owner-farmed and sharecropped
land (T1o, T2o,T1s), the amount of land under each type of contract (Hs and Hf) and the contract

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