Agriculture Reference
In-Depth Information
1
T
α
∂h
∂t
j
(t
t
m
F
,
k
F
)
≡
wt
=
...
T
,
1,
,
;
and
(9.3)
∂h
∂k
(t
t
m
F
,
k
F
)
≡
r
max
.
,
(9.4)
These solutions have clear implications. Since the family farmer is the complete residual
claimant in both activities, there is no moral hazard for task effort. The family farm is,
however, hindered by a lack of specialization, which reduces the marginal product of task
labor in every given task, as long as there is more than one task
(T >
)
. In addition, though
family farms equate marginal costs and benefits for capital, they face higher costs for capital
compared to partnerships or corporations, and therefore use less capital, implying a smaller
farm with less equipment compared to partnership and factory-corporate farms.
1
Partnership Farms.
Like the family farmer, the partner allocates his time on and off
the farm and among the various farming tasks. Because each partner shares farm output but
keeps all of his off-farm income, he shifts more effort into off-farm activities than he would if
he had no partner. Partners share tasks equally, because partners and tasks are homogeneous.
This means that each partner allocates his farm labor over
tasks. Furthermore, because
the combined resources of the partners exceed that of a single (family) farmer and because
of a higher rate of use of those resources, partnerships have lower capital costs than do
family farms.
12
As in our analysis of contract choice, we model the partnership contracting problem in
two stages. In the first stage, partners jointly maximize the expected wealth of the farm in
choosing capital and partners, subject to the task allocations chosen by each partner. In the
second stage, each partner maximizes his expected profits
T/N
(π
P
)
by choosing how to allocate
his effort over
farm tasks and his own nonfarm labor, holding constant the joint choice
of capital and the number of partners. Using backward induction, we solve the second stage
first, so that for each partner, the problem is
T/N
N
T
α
1
N
h
;
k
m
π
P
=
max
t
t
,
q
−
1
(d)
+
wm
(9.5)
t
1
,
...
,
t
(T/N)
,
subject to
T/N
1
t
t
+
m
=
L
=
1,
t
=
k
where
is a fixed amount of capital owned jointly by the partners,
w
is the (shadow)
]
α
is the
wage for the partner,
m
is each partner's labor market effort, and
a
t
=
[
N/T
t
t
specialization scalar. Each partner takes
, the task effort of all other partners for the
remaining
T(N
−
1
/N)
tasks, as given. The optimal task effort vector for each partner
