Agriculture Reference
In-Depth Information
F
V ,
P
V ,
P
F
M
I
V ,V
V
I
V
P
N =3
N =1
V
M
V
F
N =2
1
2
3
1
α
T
δ
α
δ
a) Specialization Effects
b) Task Number Effects
c) Timeliness Effects
Figure 9.2
Farm organization comparative statics
factory-corporate farm (
). We can examine the choice of market connection versus cross-
stage integration in a similar fashion. We derive value functions by evaluating the firm's
objective function at the optimal input levels (see appendix B). Deriving comparative statics
predictions requires examining how changes in various parameters
FC
2
,
(α
,
C
,
δ
,
L
,
σ
T)
affect
the relative values of these indirect objective functions.
Consider the effects of changes in the specialization parameter
(α)
on the value of the
V
α
<
V
αα
>
family farm. By the Envelope Theorem,
0 (see appendix B). This means
that the value of a family farm declines as specialization becomes more important. A
partnership is just the general case of the family farm where
0 and
N
≥
2 and is allowed to vary.
V
F
,
V
α
<
V
αα
>
V
P
is less than the slope of
V
F
As with
0 and
0, but the absolute slope of
V
P
increases as
α
α
N
for low values of
. In addition, the absolute slope of
and
increase.
Furthermore, from equations (9.3) and (9.6), when
α
=
1 the task input choices are the
V
P
>V
F
by an amount equal to
the net savings in capital costs. In the extreme case, when
same for partnerships and family farms, so when
α
=
1,
0 the family farm makes a
first-best task allocation since there are no gains to specialized task effort. The partnership,
on the other hand, is penalized because of partner moral hazard. As long as the savings
in capital costs are smaller than the moral hazard losses in a partnership, then
α
=
V
F
>V
P
0.
17
These value functions, shown in panel (a) of figure 9.2, demonstrate that the
optimal number of owners varies with changes in the importance of specialization: Low
values of
when
α
=
α
lead to family farms; high values of
α
lead to partnerships.
V
FC
is identical to that of the partnership for
For corporate-factory farms, the slope of
all values of
. Since corporate-factory farms have the lowest costs of capital,
but the highest labor costs, whether partnership farms or corporate-factory farms emerge
α
for a given
N
