Agriculture Reference
In-Depth Information
dividing inputs are more likely to be worth overcoming as the share of the farmer's harvest
decreases because the costs are lump sum.
Pure Cropshare Contracts and Input-Output Cropshare Contracts
(q
∗
=
s
∗
<
The choice between a pure cropshare contract
1,
1
)
and an input-output cropshare
(q
∗
=
s
∗
<
contract
is a dichotomous one that can be examined by comparing the
expected net return to the land in both contracts.
10
The trade-off between the two contracts
is straightforward. The pure cropshare contract has the advantage of avoiding the input
division costs,
1
)
. The input-output share contract further reduces the input distortion that
arises in any share contract. With the input-output cropshare contract, each input
m
is used
at its first-best level, allowing for a further reduction in the output share in order to abate
soil exploitation. The effect of parameter changes
k
on the net value of each contract
can illuminate this trade-off and lead to hypotheses about contract choice.
Consider exogenous changes in
(m
,
r)
. The net value of the pure cropshare contract does
not depend on input division costs, but the net value of the input-output cropshare contract
declines as these costs increase. Let
m
V
P
be the indirect objective functions for
input-output sharing and pure cropsharing contracts, respectively. Then for any input
V
IO
and
k
,
∂V
IO
/∂m
=
∂V
P
/∂m<
the Envelope Theorem yields
0. For low costs, the input-
output cropshare contract maximizes net value; for high costs, the pure cropshare contract
maximizes net value. This analysis parallels that in chapter 4 and implies the following:
0 and
PREDICTION 5.5
As input division costs
(m)
increase, it is more likely that the pure
(q
∗
=
cropshare contract will be chosen
1
)
.
r
k
The comparative statics for
are similar. For any input
, the Envelope Theorem yields
∂V
IO
/∂r
=−
l
1
∂V
P
/∂r
=−
l
2
, where
1
2
,
1
2
l
>l
l
q
=
l
and
is derived when
1, and
is
1
or
2
derived when 0
<q<
1. Because neither
l
l
depends on
r
, the second derivatives of
V
IO
and
V
P
with respect to
V
IO
and
V
P
are declining linear functions
r
are zero. Thus,
of
. An increase in the costs of land attributes will lower the value of the input-output
cropshare contracts, but it will lower the value of the pure cropshare contract even more
because the land is used more intensively in the pure cropshare contract
r
1
2
(l
>l
)
as a result
of a larger cropshare. This implies the following:
PREDICTION 5.6
As the costs of land attributes increase or as land exploitation becomes
r
−
r
more costly (
increases), the chosen contract will more likely be an input-output
(q
∗
=
s
∗
)
cropshare contract
.
By recognizing how land attributes may be exploited in various situations, we derive
specific implications. The problem of land exploitation tends to be less serious for irrigated
land than for dry-farming land because tilling is not as important and soil moisture storage
