Agriculture Reference
In-Depth Information
farm or use the market depends on weighing the gains from specialized stage production
against the cost of using the market to connect two firms. In agriculture, a new inter-stage
moral hazard problem emerges because of the timeliness costs that arise between stages of
production. Our emphasis on timeliness is directly related to the discussion introduced in
the last chapter.
15
As discussed in chapter 8, timeliness costs depend on seasonal parameters and can be
examined by letting
is the date at which
the stage's tasks are completed (such as the date at which planting is completed). As before,
we will assume that this timing function is approximately quadratic in
q
s
=
q(d)
, where
q
s
is the output for stage
s
and
d
d
, with a unique
d
∗
(as little as two or three days) for certain
crucial stages (planting, irrigating, spraying, and harvesting) can reduce crop output by
relatively large amounts, possibly to zero (such as when hail falls before harvest). As in
chapter 8 we assume the timing function takes a specific form for the
d
∗
, and that small deviations from
optimum,
th
stage
s
(s
=
1,
...
,
S)
:
1
−
d
L
q(d)
=
δd
q
,
(9.9)
where
is a crop-specific response parameter. All of these
variables are stage specific even though we suppress the subscripts. The stage length,
L
is the length of stage and
δ
,
indicates the possible dates for which the task can be undertaken and still generate positive
output. The term
L
make deviations
from the optimal date more costly.
16
In this specification, the optimal time is exactly in the
middle of the stage; that is,
δ
reflects the crop's sensitivity to timing. Increases in
δ
d
∗
=
L/
2.
Timeliness costs create incentive problems, not simply because deviations from
d
∗
reduce
d
∗
that makes it costly to contract across
output, but because there is temporal variance in
d
∗
means that the optimal date for applying task effort cannot be known
with certainty prior to the stage; variance in
stages. Variance in
d
∗
can arise from variance in the length of
the stage
or simply from variance in the time at which the stage begins. Accordingly,
increases in the variance of
(L)
d
∗
decrease the probability of firm-to-firm contracting between
stages because the farmer in the later stage cannot accurately schedule a specific date.
Obviously, increases in
d
also decrease the probability of firm-to-firm contracting, for any
d
∗
, because the firm producing at the earlier stage can impose severe
losses on the later stage firm by undertaking tasks at a nonoptimal time.
To focus on timeliness and integration incentives, we assume the organization is constant
across two adjacent stages (
level of variation in
s
and
s
−
1). If the farm is integrated and if stage output has a
per-unit value of
p
s
, then the value of the integrated firm is
.
V
I
=
p
s
h
s
(a
s
t
s
q
s
−
1
(d
∗
))
+
θ
s
,
k
s
,
(9.10)
