Page 62 - Read Online

Page 4 of 20 Han et al. Carbon Footprints 2025, 4, 25 https://dx.doi.org/10.20517/cf.2025.18

where C represents the emissions of region s embodied in the final consumption of region t, corresponding
st
to the embodied emission export from region s to region t, and d denotes the direct emission intensity,
s
defined as the emissions generated per unit of output in region s. Based on this emission intensity matrix,
PBEs are defined as the direct CH emissions occurring within a nation’s geographical boundaries, while
4
CBEs are defined as the CH emissions embodied in the final demand of the economy.
4
The emissions embodied in imports (EEI) and exports (EEE) of region t can be expressed as Eqs. (4) and
(5):

t
where EEI represents the emissions embodied in imports to region t from other regions, and EEE
t
represents the emissions embodied in exports from region t to other regions. The trade balance of embodied
emissions is obtained by calculating the difference between EEI and EEE. t
t
Lorenz curve and Gini coefficient
The Lorenz curve, a standard analytical tool, is frequently employed to analyze income or wealth disparities.
Extending this principle, it can also be harnessed to measure inequality in CH emissions. The Lorenz curve
4
of CH emissions is a graphical representation where the x-axis shows the cumulative proportion of the
4
sampled population, arranged in ascending order by per capita CH emissions, while the y-axis represents
4
the cumulative percentage of total CH emissions per capita. In an ideal scenario, where every individual
4
contributes equally to CH emissions, the Lorenz curve coincides with the diagonal line, representing
4
absolute equality. In the presence of inequality, however, the curve lies below this line. The degree of
deviation from the diagonal serves as a quantitative indicator, i.e., the greater the deviation, the larger the
disparity in CH emissions.
4

The Gini coefficient, traditionally used to measure differences in income distribution, can similarly be
employed to quantify inequality in CH emissions across countries with different income groups. It reflects
4
the relationship between cumulative population shares and cumulative CH emissions. The Gini coefficient
4
ranges from 0 to 1, where 0 indicates perfect equality and 1 represents complete inequality, calculated as
follows:

where X denotes the cumulative percentage of the population in region i, and Y represents the cumulative
i
i
percentage of CH emissions in region i. When i = 1, X and Y are zero, marking the beginning of the
4
i-1
i-1
cumulative process. Generally, a Gini coefficient below 0.2 indicates a high level of equality, values between
0.2 and 0.3 suggest relative equality, and values from 0.3 to 0.4 are considered acceptable. By contrast, values