Agriculture Reference
In-Depth Information
Assuming risk neutrality and zero contract enforcement costs, the farmer and landowner
jointly maximize expected profit by employing the first-best, full-information input levels
e
∗
,
k
∗
. These input choices do not depend on the contracted input and output shares
and satisfy the standard conditions that marginal products equal marginal costs.
It is not surprising that the nature of the solution here is similar to the one found in
chapter 4. When contract enforcement is costly, the chosen input levels will be second best.
Because farmers do not have indefinite tenure of the land, they face lower opportunity costs
of the land attributes,
l
∗
, and
r
<r
. As a result, they exploit the land's unpriced attributes,
l
, just
as they did in chapter 4. When the crop is shared the farmer owns
sQ
and the landowner
owns
, and the farmer supplies less of his own labor and capital than he would if
he owned the entire crop—again, as they did in chapter 4. For each shared input, however,
the farmer pays
(
1
−
s)Q
q(ck)
and the landowner pays
(
1
−
q)(ck)
, where
q
∈
[0, 1] is the farmer's
share of input costs. If
1, the farmer overuses the shared inputs because he bears less
than their full marginal cost.
Extending the analysis of the last chapter, we find that there are costs of measuring and
dividing both the shared output and each shared input. However, two crucial inputs—the
farmer's effort and the landowner's land—are not shared because the division costs are
prohibitively high. Thus, for a single tract of farmland under a cropshare contract, the
farmer's objective is
3
q<
k
s
=
s
−
we
−
r
l
−
qck
max
e
[
h(e
,
l
,
k)
]
.
(5.1)
,
l
,
e
s
,
l
s
, and
k
s
satisfy
sh
e
(e
s
)
≡
w
sh
l
(l
s
)
≡
r
, and
The second-best optimal input levels
,
sh
k
(k
s
)
≡
qc
. From the first-order conditions and the assumption of independent inputs, it
is clear that the optimal input choices differ from the first-best, or zero transaction cost, case.
It follows that the farmer supplies too few of his inputs because he must share the output
with the landowner; that is,
e
s
<e
∗
. Similarly, the farmer overworks the land because he
does not face the full cost of using the land's attributes; that is,
l
s
>l
∗
.
4
Finally, it is evident
that, depending on the relative size of
, the farmer may use too much, too little, or
the optimal amount of the other inputs. For these inputs, if
q
and
s
k
s
=
k
∗
;if
q
=
s
, then
q>s
,
k
s
<k
∗
; and if
k
s
>k
∗
.
then
q<s
, then
Measurement Costs and Input Sharing
k
s
—effectively constrain the potential value
of the cropshare contract. To maximize joint wealth, the farmer and landowner contract for
the optimal output share
e
s
,
l
s
, and
The farmer's optimal input choices—
(s
∗
)
(q
∗
)
and input share
in recognition of these constraints. Their
joint problem is
q
V
=
h(e
s
,
l
s
,
k
s
)
−
we
s
−
rl
s
−
ck
s
−
m
max
s
,
(5.2)
,
