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.