Agriculture Reference
In-Depth Information
In equation (9.10) the superscript
denotes variables specific to the integrated case. Al-
ternatively, two separate, specialized firms could produce the two stages and be connected
by a market contract. When separate firms, connected by a market transaction, undertake
different stages the value of the market governance structure is:
I
V
M
=
p
s
h
s
(a
s
t
s
q
s
−
1
(d
M
))
+
θ
s
,
k
s
,
(9.11)
In equation (9.11) the superscript
denotes variables specific to the market connected case.
The trade-off between the values generated in equations 9.10 and 9.11 depends on the
relative importance of timing and specialization. The benefit of the integrated regime is
the guarantee of optimal timing of task effort at each stage. With integration there is no
interstage moral hazard in timing because a single firm controls both stages and applies
task effort at the optimal time
M
(d
=
d
∗
)
. With market-connected stages, however, the date
(d
M
=
d
∗
)
of task efforts are not optimal
because the incentives of the two farms (or “firms”)
are not identical. The magnitude of the loss from suboptimal timing will depend on both the
impact of timing on output
.
The cost of the integrated regime is the forgone gain from task specialization. As long
as the tasks in the two stages are not identical, there must be a loss of specialization across
stages because there are more tasks but the number of farmers is the same. In the simplest
case, the number of tasks increases to
(δ)
and the marginal product of last period's output
(∂h
s
/∂q
s
−
1
)
T
I
=
T
s
+
T
s
−
1
, but this increase is spread over
two stages. In general, the effective effort parameter in the market-connected firms will be
larger than for integrated firms; that is,
a
M
≥
a
I
. This can arise for two reasons since the
effort specialization parameter depends on the number of tasks and the length of a stage,
a
=
]
α
. First, there may be more tasks in the integrated case, or
T
I
>T
M
. Second,
NL/T
[
L
M
>L
I
. For example, a specialized firm
can perform its tasks over a longer period by contracting with many farms (producing stage
s
−
the integrated case may have a shorter stage, or
production as long as the stages for these farms do not perfectly overlap. In
this case, the length of stage
1) for stage
s
for the contracting firm can get large, allowing greater gains
from specialization. Finally, it is clear that stages with high values of
s
α
are more likely to
be contracted for than stages with low values of
α
.
The Comparative Statics of Farm Organization
To generate predictions about the choice of farm organization we examine how various
parameters affect the relative value of the three farm organizations we study. The general
model for choosing which farm organization will maximize the expected value of production
for any stage is as follows: maximize
V
F
,
V
P
,
V
FC
], where
V
F
,
V
P
, and
V
FC
V
=
max[
are the optimal value functions for the family farm (
F
), the partnership farm (
P
), and the
