Agriculture Reference
In-Depth Information
Farmer's Effort ( e
Priced Attribute ( l
Unpriced Attribute (
k/l
)
w
w
r
v
h
h
h
h
e
e
l
k
[1 − (θ)]
X
X
X
h
h
[1 − (θ)]
h
[1 − (θ)]
e
l
k
o
r
o
o
w
w
o
w*
w*
r*
v = v*
e
e
′
o
′
o
o
′
o
k/l
e
o
e
e
o
o
e*
e*
l
l
l*
l
k
k*=
k
Panel (a): Ownership
Farmer's Effort ( e
Priced Attribute ( l
Unpriced Attribute (
k/l
)
w
w
r
v
h
h
h
h
k
e
e
l
o
o
o
l
s
r
w
w = w = w
{
D
l
r
c
w
{
D
s
c
r*= r = r
v*= v
c
w*
w*
D
l
s
v = v
e
e
c
k*= k = k
c
o
k = k
s
o
c
l
s
l
k/l
l
s
e
e*
e*
l
l
l* = l
l
e
e = e = e
Panel (b): Contracting
Figure 8.1
Optimal inputs with ownership and contracting
The first-order necessary conditions are
=
w
o
h
e
[1
−
X(θ)
]
(8.2)
=
r
o
h
l
[1
−
X(θ)
]
(8.3)
=
v
∗
.
h
k
[1
−
X(θ)
]
(8.4)
The right-hand side of each equation is the marginal cost of each input for an (unspecialized)
owner of the farm. The left-hand side of each equation is the marginal product faced by the
owner who borrows. This marginal product is less than the true marginal product because
the term in square brackets is the probability (less than one) that the farmer has a crop that
can pay off the loan. Because of the shift in marginal products caused by borrowing, these
