Agriculture Reference
In-Depth Information
fixed cost (or tax) of methane emission,
x
is the
vector of solutions and
S
is the feasible region.
For a detailed description of
S
, refer to Moraes
et al
. (2012).
The formulation of the REDM model can be
described mathematically as:
Results generated by the model structure
are deterministic, i.e. there is no uncertainty in
the determination of the vector of solutions
and in the determination of the sensitivity
analysis components. Results are limited to the
inputs from which they were generated because
the model was solved for one hypothetical herd
at a fixed level of production, with a singular
set of feed prices. The results are useful in the
exploration of the uses of this optimization
model in reducing the environmental impacts
of livestock. For instance, when methane emis-
sions were taxed at the level of current prices
on the carbon credit market in the USA and
Europe, diets were not significantly altered, and
reductions of methane emissions were practi-
cally zero. These results suggest that current
prices of the carbon dioxide equivalent are not
sufficiently onerous to force a diet manipula-
tion that would reduce methane emissions,
i.e. force a change in the vector of solutions. In
this context, the TAXM model can be used to
investigate the effect of tax-based policies on
diet formulation, demand for feeds by the dairy
industry, environmental impacts and system
profitability. In the scenario examined by
Moraes
et al
. (2012), enforcing a tax-based policy,
with current carbon credit prices used as tax
values, did not alter diets and methane emis-
sions; however, total costs were increased due
to methane tax liabilities.
In the second model (REDM), methane emis-
sions were reduced through a model constraint,
which forced predetermined reductions in emis-
sions. When emissions were reduced by 5%, 10%
and 13.5% from the baseline scenario, dietary
costs were greatly increased and nitrogen and
mineral excretion were altered due to the selec-
tion of different feeds in diet formulation. When
emissions were reduced by 13.5% from the base-
line scenario, which was the maximum reduction
for a feasible solution, nitrogen and potassium
excretions were increased by 16.5% and 16.7%,
and dietary costs were increased by 48.5%. The
animal categories, which comprised the hypo-
thetical dairy herd, were differently affected by
the policy implementation. For example, when
methane emissions were reduced by 10%, the
mid- to late lactation cows group was the cate-
gory that exhibited the largest proportional
increase in nitrogen intake and when emissions
were reduced by 13.5%, the dry cows group
7
19
∑
∑
min
xc
ja
j
a
=
1
j
=
1
Subject to
7
19
∑
∑
x
p NDF
(6.11)
ja
1
j
a
=
1
j
=
1
7
19
∑
=
∑
+
xpME
≤
ACH
1
−
Int
ja
2
j
T
4
a
1
j
=
1
x
∈
S
where
x
ja
is the amount of feed
j
for animal cate-
gory
a, c
j
is the cost of feed
j, p
1
and
p
2
are the
methane emission prediction equation parame-
ters,
NDF
j
is the neutral detergent fibre content
of feed
j, ME
j
is the metabolizable energy content
of feed
j, A
T
is the predetermined reduction in
methane emissions,
CH
4
1 is the amount of
methane emitted in the baseline scenario,
Int
is
the intercept of the methane emission prediction
equation representing the total herd,
x
is the
vector of solutions and
S
is the feasible region.
For a detailed description of
S
, refer to Moraes
et al
. (2012).
Equations 6.10 and 6.11 are complemen-
tary in the sense that, conceptually, a tax that
achieves any desired mandated emissions
reduction can be derived. Therefore, it is possi-
ble to establish a tax that leads to an exact pre-
determined reduction in methane emissions.
In this context, the formulation of the REDM
enabled shadow price calculations of the
methane emissions constraint under different
regulatory scenarios. Shadow prices can be
interpreted as the marginal costs of reducing
one unit of methane emissions through die-
tary manipulation. Therefore, the cost of miti-
gation strategies could be examined in relation
to different policy intensities. Similarly, this
model can be easily adapted to minimize any
environmental impact that can be mitigated by
dietary manipulation. For example, if a con-
straint equation is set to restrict the amount of
nitrogen excreted by livestock, the marginal
cost of reducing nitrogen excretion through
dietary manipulation can be derived.
