Agriculture Reference
In-Depth Information
farmer is not observable; the landowner is unable to shirk and the land cannot be exploited
by the farmer; and finally, farm production is variable, depending on both the effort of the
farmer and random forces. Relying on these assumptions, we derive predictions about the
structure of share contracts and the choice between cropshare and cash rent contracts.
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We begin by assuming that for a given plot of land, crop production is
Q
=
(e
+
θ)
,
where
e
is the unobservable effort of the farmer, and
θ
is a random variable with mean 0
2
. This production function is routine in principal-agent analyses applied to
agriculture and to business.
9
The farmer's income from the land contract is
and variance
σ
Y
, and
U(Y)
=
E(Y)
−
(R/
2
)Var(Y)
is the farmer's utility function where
R
∈
[0,
∞
] is the farmer's
coefficient of absolute risk aversion.
10
Following Pratt (1964), we assume decreasing
R
(W)<
absolute risk aversion (DARA), so that
is total individual wealth. In
share contracts only the crop is shared, with both parties selling their shares independently
in competitive markets. As a result,
0 where
W
s
∈
[0, 1] is the contracted share of output owned by the
farmer and
] is the value of any fixed (cash) payments made by the farmer to
the landowner. Farmer income is
β
∈
[
−∞
,
∞
2
]
Y
=
s(e
+
θ)
−
[
c
0
+
c
1
e
+
(c
2
/
2
)e
−
β
, where
c
i
for
i
=
0, 1, 2 are parameters of the effort cost function, and the farmer's expected utility (EU)
2
]
2
2
is
.
The landowner maximizes expected profits subject to the farmer's incentive compatibility
(IC) and individual rationality (IR) constraints, solving
EU
=
se
−
[
c
0
+
c
1
e
+
(c
2
/
2
)e
−
(R/
2
)s
σ
−
β
max
s
β
=
E
[
(
1
−
s)(e
+
θ)
+
β
]
,
e(s)
=
s
−
c
1
subject to (IC)
c
2
=
argmax EU,
and
(6.1)
0
,
(
IR
)U(e)
≥
U
0
is the farmer's reservation utility. The optimal contract parameters
(s
∗
,
β
∗
)
are
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where
U
1
s
∗
=
(6.2)
(
1
+
Rc
2
σ
2
)
β
∗
∈
[
−∞
,
∞
].
(6.3)
Predictions
The equilibrium contract that solves this model also trades off the incentive effects of greater
output shares to the agent against the risk aversion of the agent and generates two predictions
immediately.
PREDICTION 6.1
If a share contract is chosen, it will be normally accompanied by a cash
payment.
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