Agriculture Reference
In-Depth Information
5
Sharing Inputs and Outputs
5.1
Introduction
The model and evidence in chapter 4 showed that moral hazard and enforcement costs (over
land quality and output sharing) determined the choice between a cash rent and a cropshare
contract. In this chapter we extend the model developed in chapter 4 to focus solely on
cropshare contracts and, in particular, to determine the optimal sharing rule for both the
crop output and the variable input costs. Though cropshare contracts are common, they
differ from one another in that some include the provision for some or all of the inputs to be
shared, while others contain no such provision. Heady (1947) was one of the first to point
out that sharing input costs in the same proportion as the output share offsets the taxing
effect of the share on that input. His result almost exhausts what economists have had to
say regarding input sharing, save Braverman and Stiglitz (1982). In this chapter we derive
explicit predictions about the relationship between input and output shares. In particular, our
model makes the rather strong prediction that inputs are either shared in the same proportion
as the output or they are not shared at all.
1
5.2
Optimal Cropshare Contracts
The model is developed in three stages. First, we examine the incentives of the farmer
to choose inputs given exogenous input and output shares. Second, we derive the optimal
cropshare and input shares that maximize the expected net value of the contract, taking the
farmer's input choices as constraints in a joint wealth maximization problem. Third, we
derive the comparative statics of various share contract forms by examining the effects of
parameter changes on the joint wealth of a contract. Testable implications are derived at
each stage.
Production and Input Use
We extend the previous analysis by assuming that there are three types of inputs rather than
just two: farmland owned by landowners; farm labor owned by farmers; and other variable
inputs, such as fertilizer and seed, that may be owned by both farmers or landowners. All
other model assumptions remain the same.
2
Hence, output is now
Q
=
h(e
,
l
,
k
i
)
+
θ
, where
all variables are as defined in chapter 4, and
k
i
is one of several
(n)
inputs such as fertilizer,
th
pesticide, or seed. The opportunity cost of the
i
variable input is
c
i
per unit. In general,
we ignore the subscripts on the
inputs and examine one such input at a time. Because the
inputs are assumed to be independent, this causes no problem and clarifies the notation. In
the empirical section, however, we consider many inputs.
k
i
