Agriculture Reference
In-Depth Information
determine the contract that maximizes joint (farmer-landowner) wealth by comparing the
net values of the two contracts as important parameters change. We assume there are just
two inputs—farmland owned by landowners and farm capital (both human and physical)
owned by farmers—and that both parties are risk neutral. As we stressed in the introduction,
we also assume a random input to account for factors as weather and pests. Because of this
uncertainty and because all of the attributes of the farmer and land inputs cannot be perfectly
specified in a contract, there are opportunities for farmer moral hazard.
In all cases, we consider the use of a tract of farmland of fixed acreage that is contracted
for use by a single farmer for a single growing season.
12
Following our general production
discussion in chapter 1, let
Q
=
h(e
,
l)
+
θ
, where
Q
is the harvested output (with unit
price) per tract;
is a composite input of farmer inputs, including labor time and effort,
equipment, and other farming materials;
e
is a composite input of land attributes, such
as fertility and moisture content that are not specified in the contract; and
l
2
)
is a randomly distributed composite input that includes weather and pests. We assume
that
θ
∼
(
0,
σ
h
e
>
0,
h
l
>
0,
h
ee
<
0,
h
ll
<
0, and
h
el
=
0, where the subscripts denote partial
derivatives.
13
The opportunity cost of the farmer's input is the competitive wage rate
w
per unit of farmer's effort, and the opportunity cost of the unpriced land input (
per
unit. In a farmland contract the priced land attribute is acres, which for our purposes is
ignored. Therefore it is worth stressing that
l
)is
r
r
is not the price of land per acre, but the cost
of the composite unpriced land input.
If contracts could be enforced without cost, there would be no input distortion and no
output measurement. With risk-neutral landowners and farmers, the expected profit from the
farming operation is maximized, resulting in the employment of
l
∗
units of farmer
and landowner inputs. These first-best, full-information input levels are identical for the
cropshare and cash rent contracts and satisfy the standard conditions that marginal products
equal marginal costs for both inputs.
14
When contract enforcement is costly, however, the input choices will be second-best. In
either contract, farmers have an incentive to exploit the land's unpriced attribute (
e
∗
and
l
) because
they do not face the full costs,
. In addition, farmers have an incentive to underreport the
output in the cropshare contract. We examine the differential outcomes of the cash rent and
cropshare contracts by modeling these incentives. For both contracts, the farmer chooses
the inputs, which depend on the type of contract. Once the input levels are determined, the
net value of each contract can be evaluated.
r
Cash Rent Contracts
For the cash rent contract, the farmer hires a tract of farmland for a lump-sum fee paid just
prior to the growing season.
15
He owns the entire crop and chooses his inputs to maximize
expected profit. Because the farmer does not have indefinite tenure of the land, he does not
