2: The Model
In this section, we outline a principal-agent model that explains how owner-farming, sharecropping
and fixed-rent tenancy allocate farming skills and time. We treat skills and time as separate inputs
because there are large variations in their relative distributions across households. In addition, the many
different farm labor tasks require different complementary combinations of skills and time. For simplicity,
we divide these tasks in to two types according to their relative time and skill intensities. The first type
(M1) includes skill-intensive tasks that involve management and decision making elements (crop and input
choices, timing decisions, land and asset management, technological change etc.). The second type (M2)
consists of time-intensive unskilled activities such as the application of water, pesticides and fertilizer,
preparation of seeds, protection of assets, inputs and crops, animal care and the supervision of casual
labor.9 The provision of both M1 and M2 is not enforceable with fixed payments because their
contribution to output is not easily and immediately observed. The difficulties in identifying the inputs
shares has been attributed to the spatial, temporal and uncertain nature of agricultural production. The M1
input differs from M2 because it depends heavily on the skills of the provider and relatively less on the
time spent providing it.
Suppose the agricultural production function is
Q= ΘF[M1,M2,H] [1]
where F is increasing and twice differentiable in its arguments, and H is land. The multiplicative
uncertainty term, θ, with E[θ]=l, makes the enforcement difficult but plays no other role due to the risk
9 We ignore casual labor tasks such as harvesting, threshing, weeding etc. which are easily monitored and enforced
with fixed wage contracts.