Agriculture Reference
In-Depth Information
PREDICTION 6.2
Share contracts will not be chosen unless farmers are risk averse.
Prediction 6.1 is implied because the model predicts a continuum of contracts ranging
from a fixed wage contract
(s
=
β<
0 and
0) in which the farmer is paid a wage by the
s
=
β>
landowner to a fixed rent contract (
0) in which the farmer retains the crop
and pays rent to the landowner. In between these poles are an infinite number of share
contracts in which crop ownership is split and fixed payments allocate rents
1 and
(s
∈
(
0, 1
)
and
]). Prediction 6.2 is implied because if the farmer were risk neutral, then
the optimal contract would be a fixed rent contract in which the farmer was the complete
residual claimant of the output. Farmer effort would be first-best since there would be no
moral hazard. Thus, by incorporating risk-averse preferences into the model, a rationale for
share contracts emerges. This is because a risk-averse farmer prefers a contract in which he
is not compensated solely on the basis of variable output, as in a fixed rent contract. The
greater the risk aversion of the farmer the more likely a contract will share output.
By examining the comparative statics of the optimal sharing rule, two more predictions
are implied:
β
∈
[
−∞
,
∞
2
) increases the farmer's share of output will
PREDICTION 6.3
As output variability (
σ
decrease.
PREDICTION 6.4 Under declining absolute risk aversion, as farmer wealth increases the
farmer's share of output will increase.
2
Prediction
6.3
follows
directly
from
equation
(6.2),
since
∂s/∂σ
=
(Rc
2
)/
2
2
2
(
1
+
Rc
2
σ
)
<
0. We can see from the same equation that if the crop has zero risk (
σ
=
0),
s
∗
=
then the optimal share is
1; that is, a cash rent contract emerges. Prediction 6.4 also
follows from equation (6.2), since
∂s
∗
/∂R
=−
(c
2
σ
2
2
2
)/(
+
Rc
2
σ
)
<
1
0. If the farmer is
s
∗
=
not risk averse (
R
=
0), then the optimal share is
1, implying a cash rent contract.
R
(W)<
s
∗
and
Since
.
In this standard model, changes in contract form are continuous because changes in
parameters
0, there is also a positive relationship between
W
2
,
, which lead to marginal increases (decreases) in crop shares to the
farmer, are offset by marginal increases (decreases) in payments to the landowner. In the
contract setting we observe in North America and elsewhere, these incremental adjustments
are not always realized. Instead, changes in parameters ultimately lead to discrete changes
in contract choice, as from cropsharing to cash renting or vice versa. As the model stands,
the farmer and landowner would always share the crop
(R
,
σ
W)
(
0
<s<
1
)
because sharing always
has some benefit of spreading risk when farmers are risk averse.
Evidence from earlier chapters and from around the world (Hayami and Otsuka 1993)
shows that the actual range of contracts is much more limited. In particular, farm contracts
