Geography Reference
In-Depth Information
the non-land cost per unit of output in land use ($/calories or $/m
3
). i is an index
for land use type. l is the region index. p is an index for geographical location
within a region.
Profit rate (pr) calculation for forest products is somewhat different because of
the time lag between planting and harvest. Profit rate expression for forest products
includes a term that allocates future earnings into the pres
en
t and distributes those
earnings over 45 years; this forward price is denoted by P
i
;
l
;
m
,
r
1
þ
r
pr
i
;
lm
;
p
¼
P
i
;
l
;
m
G
i
;
l
;
m
ð
3
:
2
Þ
Þ
45
1
ð
where r is the interest rate (unitless).
To determine the share of land allocated to each land use type, land use shares
would, in general, be calculated numerically by summing the land distributions
implied in Eqs. (
3.1
) and (
3.2
). In integrated modeling context, however, we wish
to work on large regional scales. We use instead a reduced-form expression for
land shares that effectively sums up the index p in Eqs. (
3.1
) and (
3.2
) based on
maximizing profit rate which is the core of finding land shares that provide the
yields leading to maximum profits.
With specific assumptions on the functional form of yield distribution, the share
of land allocated to use i is given by a logit share equation as follows.
pr
i
;
l
;
m
k
p
pr
i
;
l
;
m
;
p
k
S
i
;
l
;
m
¼
ð
3
:
3
Þ
where k is a positive parameter that
de
termines the rate that land shares change in
response to a change in profit rate. pr
i
;
l
;
m
is the average profit r
a
te using land i,
which is the profit rate evaluated at an average or intrinsic yield, y
i
, for land use i.
Land use for a specific purpose is calculated based on this logit-based share of
total land:
Land use
i
;
l
;
m
¼ S
i
;
l
;
m
Total land
l
ð
3
:
4
Þ
3.1.2.3 CO
2
Emissions
Carbon emissions are accounted for in two separate categories, those from industry
and fossil fuel use and those as net land-use emissions. Land-use emissions have
different implications for carbon-cycle than industrial emissions, which are the
sum of emissions from fossil-fuel and cement production.
