Agriculture Reference
In-Depth Information
Table 7.1
Summary of dynamic contracting incentives
Landowner
Constant effort
committed to
and incentives
consistent contract?
in each period?
Ratchet effect?
Empirical implementation
Case I
Yes
Yes
No
Same farmer in both periods.
Case II
No
No
Yes
Different farmer in each period.
Y
where
Y
is the income to the farmer,
is the farmer's reservation income from another plot
of land,
is
the farmer's effort cost function, and the price of output is normalized to one. In each period
i
∈{
s
is the farmer's share of output
Q
,
β
is a side payment to the landowner,
C(e)
1, 2
}
, observed output is
Q
i
=
e
i
+
θ
i
, where
e
i
is the unobservable effort of the farmer,
2
is a random input.
12
and
θ
i
∼
(
0,
σ
)
A cash rent contract implies
s
=
1 and
β>
0, while
a share contract implies
. A cash rent contract is a pure high-
powered contract, because the farmer is the complete residual claimant. A share contract
has lower-powered incentives since
s
∈
[0, 1] and
β
∈
(
−∞
,
∞
)
1.
We examine two moral hazard cases that generate the second-best outcomes summarized
in table 7.1. In case I the landowner commits to maintaining the contract over two periods,
while in case II there is no such commitment. Case I corresponds to the situation of an
ongoing landowner-farmer relationship, while case II corresponds to a new farmer dealing
with an established landowner in period 2. In both cases farmers exert less than the first-best
level of effort, and the optimal share is less than one. Compared to the first-best optimum,
there is less effort because the farmer does not own the entire output and there is moral
hazard.
s<
Case I: Dynamic Commitment.
First, consider the case where the landowner ignores any
new information when deciding what incentives to set in period 2 so there is no possibility
of a ratchet effect. This is equivalent to having (dynamic) commitment to the terms of
the contract over the two periods. Given the assumption of no wealth effects, the optimal
contract maximizes the total certainty equivalent income of the farmer and the landowner,
subject to the incentive compatibility constraints for each period. The value of the contract
is the certainty equivalent that is equal to total output, minus the farmer's risk premium and
cost of effort. As a result the optimal contract follows from:
max
e
1
,
e
2
V
=
Q(e
1
)
+
Q(e
2
)
−
C(e
1
)
−
C(e
2
)
−
(R/
2
)
Va r
(s
1
θ
1
+
s
2
θ
2
)
,
(7.2)
s
1
=
C
(e
1
)
s
2
=
C
(e
2
)
subject to
,
,
