Agriculture Reference
In-Depth Information
r
s
=
r
∗
. The
the marginal cost of the asset's priced attribute (
l
) is at its lowest level, so that
cost of exploiting the unpriced attribute (
k
) remains the same for short and long-term simple
k
l
=
k
s
>k
∗
. Since the moral hazard on
k
leases, so that
again creates a per-unit deadweight
r
s
and
D
h
l
D
loss of area
, a wedge is driven between
of distance
, such that the full cost of
r
s
+
D
l
s
asset usage where
l
l
<l
s
<l
∗
. Finally, because
short-term renting is
. This leads to
w
s
=
w
l
>w
∗
, which leads
the farmer is not a specialized operator, the costs of effort are
e
s
<e
∗
.
A short-term contract also offers the potential for timeliness costs, which have long been
recognized in the agricultural literature. For example, in a well-known agricultural finance
topic, Nelson, Lee, and Murray (1973) state, “One of the most important disadvantages
of operating leases, such as custom hiring, is that the machine may not be available when
needed. Crop losses arising from delayed harvest can be very costly” (88).
17
There is, for
instance, an optimal time to plant a crop, and deviating from it lowers the eventual output,
often at an increasing rate. Moreover, the optimal time to employ the controllable inputs
is uncertain. Weather, pests, and other natural forces make it nearly impossible to know
the optimal time until it is upon the farmer. For example, when deciding when to harvest
wheat, farmers test the grain daily for moisture content and pay close attention to weather
forecasts. The combination of uncertainty over the optimal time and significant timeliness
costs dramatically increases the costs of specifying ex ante the correct delivery date for a
contracted input.
Timeliness costs change the production function and can be examined with a simple
modification to our production framework. Let
to less than the first-best level of effort, or
d
be the date for which
e
,
l
, and
k
are
indicates the
period for which output is positive given an application of effort and asset use. Numerous
studies of crop production have shown that output is approximately quadratic in the delivery
of all inputs to a particular stage of production (see Nass, Gupta, and Sterling 1973;
Kay and Edwards 1994, 416-417). Thus, in a simple quadratic framework, where
employed during a particular stage (for example, planting) of length
L
.
L
q(d)
=
2
d
∗
=
L/
(d
−
(d
/L))
[
h(e
,
l
,
k
,
θ)
], the optimal time is
2—the midpoint of the stage. The
chosen, however, is constrained by the contract period established ex ante by
the two parties for the delivery of
actual date
d
.
Figure 8.2 shows the relationship of timeliness to output and shows how timeliness costs
may arise with contracting. Ex ante, the farmer and asset owner choose a delivery date of
d
=
( L
+
d
0
)/
l
and
k
L
d
0
is the expected beginning
2, where
is the expected length of the stage and
of the stage. In this case,
is the output that would be produced if there were no change in
beginning or length of the stage. Even this output,
q
, is not first best because of the other
incentive and specialization effects discussed above. In general, the entire
q
q(d)
function
will lie below an unattainable first-best
function. Ex post, however, this particular date
may not be optimal given the realized values of
q(d)
0
and
d
L
.
