Agriculture Reference
In-Depth Information
(such as planning and marketing decisions) or mostly physical (such as lifting, shoveling,
and operating heavy equipment). Task seasons do not always match stage seasons because
a task may not be stage specific. Truck driving may be a task in several stages and have a
long season compared to any one stage. A given task may be common to any or all stages of
production, like inspecting crops and livestock, or it may be unique to a stage, like operating
a combine.
Effort
, however, does not adequately describe the labor input into farm production.
Because workers learn by doing, we define effective labor in stage
(e)
s
for task
j
as
e
st
=
a
s
t
st
,
t
st
=
n
=
1
t
stn
]
α
. The term
where
indicates that total task effort is
the sum of all of the individual worker's efforts for a given task
and
a
s
=
[
N
s
L
s
/T
s
t
st
t
in stage
s
. The effective
effort parameter
measures the amount of task specialization and is assumed a ratio—
the total number of workers multiplied by the length of the stage, and divided by the total
number of tasks—raised to
a
s
. This means that a worker's marginal productivity
increases when he spends more time working at a particular task, which in turn depends on
how long a stage is and how many other tasks the worker is performing during the stage.
To simplify, we assume that there is only one person working on a task, so
α
s
∈
(
0, 1
)
.We
assume that workers are identical, which means that gains from specialization do not arise
from endowment effects. Instead, gains from specialization arise because, in the words of
Becker and Murphy (1992), “The increasing returns from concentrating on a narrower set
of tasks raises the productivity of a specialist above that of a jack-of-all-trades” (1139). This
formal structure is a more explicit modeling of the same idea first presented in chapter 8.
The parameter
N
≤
T
indicates the degree to which task specialization can potentially in-
crease output. For some tasks (such as shoveling grain) there may be little to be gained
from specialization
α
s
(α
s
≈
)
, while for others (such as management decisions or pesticide
application) these gains may be great
0
(α
s
≈
)
(L)
1
. The length of a stage
can vary across
stages for a single crop and vary across crops for the same stage.
9
Since
L
is determined
by nature and has the same effect on
, we initially normalize it to one to
minimize notation. This also constrains the value of the effective effort parameter,
a
as changes in
N
a
s
∈
[0, 1
)
.
1. This condition could arise for
several reasons. First, there may be only one task and one worker
Specialization effects are at their maximum when
a
s
=
. Second,
there may be many tasks but the number of workers exactly matches the number of tasks
(T
=
N>
(N
=
T
=
1
)
, allowing each worker to completely specialize. Finally, there may simply
be no gains from specialization for some stages
1
)
(α
i
=
0
)
. Under these assumptions, the
full-stage production function becomes
Q
s
=
h
s
(a
s
t
s
1
,
...
,
a
s
t
sT
,
k
s
;
Q
s
−
1
(d))
+
θ
s
s
=
1,
...
,
S
.
(9.1)
