Skills, Partnerships and Tenancy in Sri Lankan Rice Farms

parameters (α, β_s and βf). Without loss of generality, we focus on the landlord’s choice of H_i and H_f
without consideration to how this land is allocated among tenants. As long as tenants’ time constraints
(equations [11] and [17]) are not met, the tenants are indifferent to the size of plot they obtain.
Therefore, with a large enough number of tenants, the landlord is also indifferent to how the land is
distributed among tenants of each type once the choice of Hs and Hf is made.¹⁵ The optimization problem
is,

max L = F ( Tio, T 2 ^l∣S ) + [ (i-a )F (t 1 „t 2 ,,h,.s ) + β sHsJ
T1 oT 2 O, T1s, HsHf.a.β ,.β f

⁺ βfHf ⁺ (^1-T1o - T2o^- T1s)^{u + λ}[¹ - Tio - T2o - T1s] ⁺

Λ s [OF ( T1 s .t2 ,_tH,.S ) -12 s V - β sHs] + Λ f [F[tif. t2f, H_f ; s] - (tif + t2f ) v - β fHf]

where H = H_o + H_s + H_f . The first four terms are the landlord’s income from owner-farming,
sharecropping, fixed-rent leasing and non-farm employment. The fifth term is the landlord’s time
allocation constraint, and the next two terms are the reservation income constraints of agents. The landlord
takes tenants’ choices per-unit labor time inputs (z2s^*. zif^* .z2f^* ) as given.

The first order conditions with respect to βf, β_s and α are

β f :      H_f [ Λ f - 1] = 0

βs :        Hs [Λ s - 1] = 0                                                               ^[19]

a ::         F ( T1 s, 12 s, H_s ; S )[ Λ s - 1] = 0

From the first two first order conditions, we see that Λ_f =1 for fixed-rent farming to exist (Hf ≥ 0)
and Λs =1 for sharecropping to exist (Hs ≥ 0). The first order condition with respect to the share-rent also
tells us that Λs =1 if production takes place in the sharecropped land (F>0). Since the multipliers are non-

¹⁵ This indeterminacy arises from our assumptions of a production function that is linear homogeneous in T1, T2 and
H, and a non-binding time constraint for tenants. When these assumptions are relaxed, the landlord may choose a
small enough farm size for each tenant in order to maximize their time inputs. We abstract from this because our focus
is on the allocation of contracts.

11

<<   10   11   12   13   14   15   16   >>

More intriguing information