Agriculture Reference
In-Depth Information
face the true opportunity cost of using the attributes of the land. We denote the reduced costs
he faces as
r
<r
, so the farmer's objective is
l
r
=
h(e
l)
−
we
−
r
l
max
e
,
.
(4.1)
,
e
r
and
l
r
satisfy:
h
e
(e
r
)
≡
w
h
l
(l
r
)
≡
r
. Given that
The second-best solutions
and
h
el
=
0,
e
r
=
e
∗
.
we note that the farmer's input level is identical to the first-best optimum; that is,
l
r
>l
∗
, implying that the land is overworked
because the farmer does not face the full cost of using the land's attributes.
16
r
<r
It is also clear, however, that since
,
Cropshare Contracts
In a cropshare contract, the farmer has exclusive use of the plot of land without paying
the landowner prior to production. At harvest time, the crop is divided between the farmer
and landowner, with the farmer receiving
sQ
and the landowner receiving
(
1
−
s)Q
, where
1.
17
The farmer bears all costs of the variable inputs except the differential cost of
the land's unpriced attributes. The farmer's objective is
0
<s<
e
,
l
s
=
s
−
we
−
r
l
h(e
l)
max
[
,
]
.
(4.2)
sh
l
(l
s
)
≡
r
. These
solutions indicate that the farmer supplies too few of his inputs because he must share the
output with the landowner; that is,
e
s
and
l
s
satisfy:
sh
e
(e
s
)
≡
w
Now the second-best solutions
and
e
s
<e
∗
. As with cash rent, the farmer overuses the land
l
r
>l
s
>l
∗
, the use of the land is less excessive than
it is with cash rent. This means that although a share contract still provides the farmer with
an incentive to overuse the land, this incentive is not as powerful as it is with the cash rent
contract.
Figure 4.1 demonstrates the equilibrium of the model. For simplicity of presentation,
the graphs use identical and linear marginal product curves for each input. When contracts
are enforced without cost, the first-best input levels
l
s
>l
∗
; however, since
attributes, or
l
∗
are chosen. In a cash rent
contract the farmer faces reduced costs of using land attributes and chooses
e
∗
and
l
r
, resulting
in a deadweight cost of DFG. In a share contract the perceived marginal products to the
farmer are lower, and therefore, he reduces the amount of both inputs used to
l
s
,
resulting in two deadweight costs, ABC and DEH. In order to understand the differential
effects of the contract, consider a switch from cash rent to cropshare. In a cropshare contract
the farmer chooses less of both inputs, which has two offsetting effects: the reduction in the
use of land attributes
e
s
and
(e)
lowers it. The optimal share will be the one that just equates the marginal loss (AB) due to
reducing effort to the marginal gain (EH) due to reducing the level of the land attributes.
One obvious implication of the model is that
(l)
increases the value of the contract, while the decrease in effort
l
s
is always greater than
l
∗
since
r
<r
.
18
If
