Cap Model input values solver original scenario global path: 3 choosen scenario global path: 3 start macro
EPM cap model; based on: Chakravartya et al. / Sharing global CO2 emission reductions among
one billion high emitters / 11884–11888   PNAS   July 21, 2009   vol. 106   no. 29 / doi 10.1073 pnas.0905232106		 Description
source data: http://data.worldbank.org/indicator/SI.DST.04TH.20/countries?display=default Chakravarty et al. insinuate that the income and emissions distribution correlated. Each person is attributed his emissions or a cap, whatever is the least. The cap is calculated for each year such that the emissions of the global pathway are met.
Country A Country B Country C
Data of the probability density functions Data of the probability density functions Data of the probability density functions
If you change the quantile values of countries, you have to do the following optimization with the help of the Excel solver:
G income G emissions G income G emissions G income G emissions - For each country: minimize the target value by adjusting the parameter a (variable)
a 1.57 1.57 a 0.78 0.78 a 2.79 2.79 - Redefine caps for each year. Target = 0 by adjusting the caps of the individual years (variables).
b 34,866.14 11.17 b 15,014.72 6.24 b 153.43 0.26
E 54,625 17.50 E 11,727 4.88 E 427 0.72 Limitations
- The per capita emissions converge far into the future. So is it comparable with the models with converging per capita emissions upto 2050 to a limited extent only.
Data of the Lorenz curve Data of the Lorenz curve Data of the Lorenz curve - Actual correlation between emission and income distribution?
≈ USA ≈ Brazil   ≈ Niger Global   Country A Country B Country C Global
population
share		 income
share		 quantiles squares population
share		 emission
share		 population
share		 income
share		 quantiles squares population
share		 emission
share		 population
share		 income
share		 quantiles squares population
share		 emission
share		                                
0.00 0.000     0.00 0.000 0.00 0.000     0.00 0.000 0.00 0.000     0.00 0.000 Year
t		 Popu-lation
Pt		 Et Per capita Cap Per capita Popu-lation
Pit		 Eit Per capita Popu-lation
Pit		 Eit Per capita Popu-lation
Pit		 Eit Et square
0.05 0.004     0.05 0.004 0.05 0.001     0.05 0.001 0.05 0.009     0.05 0.009   bn Gt t   t bn Gt t bn Gt t bn Gt Gt  
0.10 0.012 0.017 2.42E-05 0.10 0.012 0.10 0.003 0.010 5.30E-05 0.10 0.003 0.10 0.024 0.0380 1.90E-04 0.10 0.024 2019 6.9 41.7 6.05   17.50 1.2 21.0 4.88 4.0 19.5 0.72 1.7 1.2 41.7  
0.15 0.024     0.15 0.024 0.15 0.007     0.15 0.007 0.15 0.044     0.15 0.044 2020 6.9 40.9 5.93 43.64 16.81 1.2 20.2 4.87 4.0 19.5 0.72 1.7 1.2 40.9 0.00
0.20 0.040 0.051 1.26E-04 0.20 0.040 0.20 0.014 0.033 3.78E-04 0.20 0.014 0.20 0.067 0.0890 5.00E-04 0.20 0.067 2021 6.9 39.9 5.79 34.35 16.06 1.2 19.3 4.86 4.0 19.4 0.72 1.7 1.2 39.9 0.00
0.25 0.059     0.25 0.059 0.25 0.023     0.25 0.023 0.25 0.093     0.25 0.093 2022 6.9 38.9 5.63 28.67 15.25 1.2 18.3 4.84 4.0 19.4 0.72 1.7 1.2 38.9 0.00
0.30 0.081     0.30 0.081 0.30 0.035     0.30 0.035 0.30 0.123     0.30 0.123 2023 6.9 37.7 5.47 24.54 14.39 1.2 17.3 4.80 4.0 19.2 0.72 1.7 1.2 37.7 0.00
0.35 0.108     0.35 0.108 0.35 0.051     0.35 0.051 0.35 0.155     0.35 0.155 2024 6.9 36.5 5.29 21.30 13.52 1.2 16.2 4.75 4.0 19.0 0.72 1.7 1.2 36.5 0.00
0.40 0.137 0.154 2.78E-04 0.40 0.137 0.40 0.071 0.109 1.48E-03 0.40 0.071 0.40 0.191 0.2160 6.16E-04 0.40 0.191 2025 6.9 35.1 5.09 18.64 12.64 1.2 15.2 4.69 4.0 18.7 0.72 1.7 1.2 35.1 0.00
0.45 0.171     0.45 0.171 0.45 0.094     0.45 0.094 0.45 0.230     0.45 0.230 2026 6.9 33.7 4.89 16.41 11.76 1.2 14.1 4.60 4.0 18.4 0.72 1.7 1.2 33.7 0.00
0.50 0.209     0.50 0.209 0.50 0.123     0.50 0.123 0.50 0.273     0.50 0.273 2027 6.9 32.3 4.68 14.51 10.90 1.2 13.1 4.50 4.0 18.0 0.72 1.7 1.2 32.3 0.00
0.55 0.251     0.55 0.251 0.55 0.156     0.55 0.156 0.55 0.319     0.55 0.319 2028 6.9 30.8 4.46 12.86 10.06 1.2 12.1 4.38 4.0 17.5 0.72 1.7 1.2 30.8 0.00
0.60 0.298 0.308 1.08E-04 0.60 0.298 0.60 0.196 0.233 1.37E-03 0.60 0.196 0.60 0.368 0.3780 9.36E-05 0.60 0.368 2029 6.9 29.3 4.24 11.42 9.26 1.2 11.1 4.24 4.0 16.9 0.72 1.7 1.2 29.3 0.00
0.65 0.350     0.65 0.350 0.65 0.242     0.65 0.242 0.65 0.422     0.65 0.422 2030 6.9 27.7 4.02 10.16 8.48 1.2 10.2 4.08 4.0 16.3 0.72 1.7 1.2 27.7 0.00
0.70 0.408     0.70 0.408 0.70 0.297     0.70 0.297 0.70 0.480     0.70 0.480 2031 6.9 26.2 3.79 9.04 7.75 1.2 9.3 3.91 4.0 15.7 0.72 1.7 1.2 26.2 0.00
0.75 0.472     0.75 0.472 0.75 0.361     0.75 0.361 0.75 0.543     0.75 0.543 2032 6.9 24.6 3.57 8.04 7.05 1.2 8.5 3.73 4.0 14.9 0.72 1.7 1.2 24.6 0.00
0.80 0.545 0.536 7.61E-05 0.80 0.545 0.80 0.436 0.426 9.60E-05 0.80 0.436 0.80 0.612 0.5920 3.91E-04 0.80 0.612 2033 6.9 23.1 3.34 7.16 6.40 1.2 7.7 3.54 4.0 14.2 0.72 1.7 1.2 23.1 0.00
0.85 0.627     0.85 0.627 0.85 0.526     0.85 0.526 0.85 0.687     0.85 0.687 2034 6.9 21.6 3.12 6.37 5.79 1.2 6.9 3.35 4.0 13.4 0.72 1.7 1.2 21.6 0.00
0.90 0.722 0.698 5.75E-04 0.90 0.722 0.90 0.635 0.582 2.82E-03 0.90 0.635 0.90 0.772 0.7360 1.30E-03 0.90 0.772 2035 6.9 20.1 2.91 5.66 5.22 1.2 6.3 3.14 4.0 12.6 0.72 1.7 1.2 20.1 0.00
0.95 0.836     0.95 0.836 0.95 0.776     0.95 0.776 0.95 0.870     0.95 0.870 2036 6.9 18.6 2.70 5.02 4.69 1.2 5.6 2.94 4.0 11.8 0.72 1.7 1.2 18.6 0.00
1.00 1.000     1.00 1.000 1.00 1.000     1.00 1.000 1.00 1.000     1.00 1.000 2037 6.9 17.2 2.49 4.45 4.20 1.2 5.0 2.73 4.0 10.9 0.72 1.7 1.2 17.2 0.00
    target 1.19E-03 0   target 6.19E-03     target 3.09E-03 2038 6.9 15.8 2.30 3.94 3.75 1.2 4.5 2.53 4.0 10.1 0.72 1.7 1.2 15.8 0.00
2039 6.9 14.5 2.11 3.47 3.34 1.2 4.0 2.33 4.0 9.3 0.72 1.7 1.2 14.5 0.00
2040 6.9 13.3 1.93 3.06 2.96 1.2 3.6 2.13 4.0 8.5 0.72 1.7 1.2 13.3 0.00
2041 6.9 12.1 1.76 2.69 2.61 1.2 3.1 1.94 4.0 7.7 0.72 1.7 1.2 12.1 0.00
2042 6.9 11.0 1.59 2.35 2.30 1.2 2.8 1.75 4.0 7.0 0.72 1.7 1.2 11.0 0.00
2043 6.9 9.9 1.44 2.05 2.02 1.2 2.4 1.58 4.0 6.3 0.72 1.7 1.2 9.9 0.00
2044 6.9 9.0 1.30 1.79 1.76 1.2 2.1 1.41 4.0 5.6 0.71 1.7 1.2 9.0 0.00
2045 6.9 8.0 1.17 1.55 1.53 1.2 1.8 1.25 4.0 5.0 0.71 1.7 1.2 8.0 0.00
2046 6.9 7.2 1.04 1.34 1.33 1.2 1.6 1.11 4.0 4.4 0.69 1.7 1.2 7.2 0.00
2047 6.9 6.4 0.93 1.15 1.15 1.2 1.4 0.98 4.0 3.9 0.67 1.7 1.1 6.4 0.00
2048 6.9 5.7 0.83 0.99 0.99 1.2 1.2 0.86 4.0 3.4 0.64 1.7 1.1 5.7 0.00
2049 6.9 5.0 0.73 0.86 0.85 1.2 1.0 0.75 4.0 3.0 0.60 1.7 1.0 5.0 0.00
2050 6.9 4.4 0.64 0.74 0.73 1.2 0.9 0.65 4.0 2.6 0.56 1.7 1.0 4.4 0.00
2051 6.9 3.9 0.57 0.63 0.63 1.2 0.8 0.57 4.0 2.3 0.51 1.7 0.9 3.9 0.00
2052 6.9 3.4 0.50 0.54 0.54 1.2 0.6 0.49 4.0 2.0 0.46 1.7 0.8 3.4 0.00
2053 6.9 3.0 0.43 0.47 0.46 1.2 0.6 0.43 4.0 1.7 0.41 1.7 0.7 3.0 0.00
2054 6.9 2.6 0.37 0.40 0.40 1.2 0.5 0.37 4.0 1.5 0.37 1.7 0.6 2.6 0.00
2055 6.9 2.2 0.32 0.34 0.34 1.2 0.4 0.32 4.0 1.3 0.32 1.7 0.5 2.2 0.00
2056 6.9 1.9 0.28 0.29 0.29 1.2 0.4 0.28 4.0 1.1 0.28 1.7 0.5 1.9 0.00
2057 6.9 1.7 0.24 0.25 0.25 1.2 0.3 0.24 4.0 0.9 0.24 1.7 0.4 1.7 0.00
2058 6.9 1.4 0.21 0.21 0.21 1.2 0.3 0.20 4.0 0.8 0.21 1.7 0.4 1.4 0.00
2059 6.9 1.2 0.17 0.18 0.18 1.2 0.2 0.17 4.0 0.7 0.18 1.7 0.3 1.2 0.00
2060 6.9 1.0 0.15 0.15 0.15 1.2 0.2 0.15 4.0 0.6 0.15 1.7 0.3 1.0 0.00
2061 6.9 0.9 0.13 0.13 0.13 1.2 0.2 0.12 4.0 0.5 0.13 1.7 0.2 0.9 0.00
2062 6.9 0.7 0.11 0.11 0.11 1.2 0.1 0.10 4.0 0.4 0.11 1.7 0.2 0.7 0.00
2063 6.9 0.6 0.09 0.09 0.09 1.2 0.1 0.09 4.0 0.4 0.09 1.7 0.2 0.6 0.00
2064 6.9 0.5 0.07 0.08 0.08 1.2 0.1 0.07 4.0 0.3 0.08 1.7 0.1 0.5 0.00
2065 6.9 0.4 0.06 0.06 0.06 1.2 0.1 0.06 4.0 0.2 0.06 1.7 0.1 0.4 0.00
2066 6.9 0.4 0.05 0.05 0.05 1.2 0.1 0.05 4.0 0.2 0.05 1.7 0.1 0.4 0.00
2067 6.9 0.3 0.04 0.04 0.04 1.2 0.1 0.04 4.0 0.2 0.04 1.7 0.1 0.3 0.00
2068 6.9 0.2 0.03 0.04 0.04 1.2 0.0 0.04 4.0 0.1 0.04 1.7 0.1 0.2 0.00
2069 6.9 0.2 0.03 0.03 0.03 1.2 0.0 0.03 4.0 0.1 0.03 1.7 0.0 0.2 0.00
2070 6.9 0.2 0.02 0.02 0.02 1.2 0.0 0.02 4.0 0.1 0.02 1.7 0.0 0.2 0.00
2071 6.9 0.1 0.02 0.02 0.02 1.2 0.0 0.02 4.0 0.1 0.02 1.7 0.0 0.1 0.00
2072 6.9 0.1 0.02 0.02 0.02 1.2 0.0 0.02 4.0 0.1 0.02 1.7 0.0 0.1 0.00
2073 6.9 0.1 0.01 0.01 0.01 1.2 0.0 0.01 4.0 0.0 0.01 1.7 0.0 0.1 0.00
2074 6.9 0.1 0.01 0.01 0.01 1.2 0.0 0.01 4.0 0.0 0.01 1.7 0.0 0.1 0.00
2075 6.9 0.0 0.01 0.01 0.01 1.2 0.0 0.01 4.0 0.0 0.01 1.7 0.0 0.0 0.00
2076 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
2077 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
2078 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
2079 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
2080 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
2081 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
2082 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
2083 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
2084 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
2085 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
Data of the probability density functions Data of the probability density functions Data of the probability density functions 2086 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
2087 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
income probability cumulative emissions probability cumulative income probability cumulative emissions probability cumulative income probability cumulative emissions probability cumulative 2088 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
0 0.00E+00 0.00 0 0.00E+00 0.00 0 0.00E+00 0.00 0 0.00E+00 0.00 0 0.00E+00 0.00 0 0.00E+00 0.00 2089 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
5,463 9.64E-06 0.04 2 3.01E-02 0.04 1,173 9.08E-05 0.14 0 2.18E-01 0.14 43 3.04E-04 0.01 0 1.80E-01 0.01 2090 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
10,925 1.22E-05 0.10 4 3.81E-02 0.10 2,345 7.21E-05 0.24 1 1.73E-01 0.24 85 7.93E-04 0.03 0 4.69E-01 0.03 2091 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
16,388 1.31E-05 0.17 5 4.10E-02 0.17 3,518 6.10E-05 0.31 1 1.47E-01 0.31 128 1.24E-03 0.07 0 7.33E-01 0.07 2092 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
21,850 1.32E-05 0.24 7 4.12E-02 0.24 4,691 5.30E-05 0.38 2 1.27E-01 0.38 171 1.57E-03 0.13 0 9.27E-01 0.13 2093 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
27,313 1.28E-05 0.31 9 4.00E-02 0.31 5,863 4.67E-05 0.44 2 1.12E-01 0.44 214 1.77E-03 0.20 0 1.05E+00 0.20 2094 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
32,775 1.22E-05 0.38 11 3.79E-02 0.38 7,036 4.15E-05 0.49 3 9.98E-02 0.49 256 1.85E-03 0.28 0 1.10E+00 0.28 2095 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
38,238 1.13E-05 0.44 12 3.54E-02 0.44 8,209 3.71E-05 0.54 3 8.92E-02 0.54 299 1.84E-03 0.36 1 1.09E+00 0.36 2096 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
43,700 1.05E-05 0.50 14 3.26E-02 0.50 9,381 3.33E-05 0.58 4 8.01E-02 0.58 342 1.77E-03 0.44 1 1.05E+00 0.44 2097 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
49,163 9.56E-06 0.56 16 2.98E-02 0.56 10,554 3.00E-05 0.62 4 7.22E-02 0.62 385 1.66E-03 0.51 1 9.80E-01 0.51 2098 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
54,625 8.67E-06 0.61 18 2.71E-02 0.61 11,727 2.71E-05 0.65 5 6.53E-02 0.65 427 1.51E-03 0.58 1 8.95E-01 0.58 2099 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
60,088 7.83E-06 0.65 19 2.44E-02 0.65 12,899 2.46E-05 0.68 5 5.91E-02 0.68 470 1.36E-03 0.64 1 8.03E-01 0.64 2100 6.9 0.0 0.00 0.00 0.00 1.2 0.0 0.00 4.0 0.0 0.00 1.7 0.0 0.0 0.00
65,550 7.03E-06 0.69 21 2.19E-02 0.69 14,072 2.23E-05 0.71 6 5.37E-02 0.71 513 1.20E-03 0.70 1 7.10E-01 0.70 ∑   684         252     389     44 target 0.00
71,013 6.29E-06 0.73 23 1.96E-02 0.73 15,245 2.03E-05 0.73 6 4.88E-02 0.73 556 1.05E-03 0.74 1 6.20E-01 0.74
76,475 5.61E-06 0.76 25 1.75E-02 0.76 16,418 1.84E-05 0.75 7 4.44E-02 0.75 598 9.05E-04 0.79 1 5.36E-01 0.79 global path: 3
81,938 4.99E-06 0.79 26 1.56E-02 0.79 17,590 1.68E-05 0.77 7 4.04E-02 0.77 641 7.75E-04 0.82 1 4.59E-01 0.82 2 270     380     36   685 EPM
87,400 4.42E-06 0.82 28 1.38E-02 0.82 18,763 1.53E-05 0.79 8 3.69E-02 0.79 684 6.58E-04 0.85 1 3.89E-01 0.85 1 221 405 58 684 EPM
92,863 3.91E-06 0.84 30 1.22E-02 0.84 19,936 1.40E-05 0.81 8 3.36E-02 0.81 727 5.55E-04 0.88 1 3.28E-01 0.88 3 252 389 44 684 EPM
98,325 3.46E-06 0.86 32 1.08E-02 0.86 21,108 1.28E-05 0.83 9 3.07E-02 0.83 769 4.65E-04 0.90 1 2.75E-01 0.90 6 252     385     47   684 EPM
103,788 3.05E-06 0.88 33 9.51E-03 0.88 22,281 1.17E-05 0.84 9 2.81E-02 0.84 812 3.88E-04 0.92 1 2.29E-01 0.92    
109,251 2.68E-06 0.89 35 8.37E-03 0.89 23,454 1.07E-05 0.85 10 2.57E-02 0.85 855 3.22E-04 0.93 1 1.90E-01 0.93 2 318     328     37   11% share population key solver
114,713 2.36E-06 0.91 37 7.36E-03 0.91 24,626 9.77E-06 0.87 10 2.35E-02 0.87 898 2.66E-04 0.95 2 1.57E-01 0.95 1 276 343 65 30% share population key solver
120,176 2.07E-06 0.92 39 6.46E-03 0.92 25,799 8.95E-06 0.88 11 2.15E-02 0.88 940 2.18E-04 0.96 2 1.29E-01 0.96 3 304 333 47 18% share population key solver
125,638 1.81E-06 0.93 40 5.66E-03 0.93 26,972 8.19E-06 0.89 11 1.97E-02 0.89 983 1.79E-04 0.96 2 1.06E-01 0.96 6 298     335     50   20% share population key solver
131,101 1.59E-06 0.94 42 4.96E-03 0.94 28,144 7.51E-06 0.90 12 1.81E-02 0.90 1,026 1.46E-04 0.97 2 8.65E-02 0.97    
136,563 1.39E-06 0.95 44 4.34E-03 0.95 29,317 6.88E-06 0.90 12 1.66E-02 0.90 1,069 1.19E-04 0.98 2 7.04E-02 0.98 2 0.03     0.02     0.00   0.05 square deviation
142,026 1.22E-06 0.95 46 3.79E-03 0.95 30,490 6.31E-06 0.91 13 1.52E-02 0.91 1,111 9.66E-05 0.98 2 5.72E-02 0.98 1 0.06 0.02 0.01 0.10 square deviation
147,488 1.06E-06 0.96 47 3.31E-03 0.96 31,662 5.79E-06 0.92 13 1.39E-02 0.92 1,154 7.82E-05 0.98 2 4.63E-02 0.98 6 0.04 0.02 0.00 0.07 square deviation
152,951 9.27E-07 0.96 49 2.89E-03 0.96 32,835 5.31E-06 0.93 14 1.28E-02 0.93 1,197 6.31E-05 0.99 2 3.74E-02 0.99 0 0.03     0.02     0.00   0.05 square deviation
158,413 8.08E-07 0.97 51 2.52E-03 0.97 34,008 4.87E-06 0.93 14 1.17E-02 0.93 1,240 5.09E-05 0.99 2 3.01E-02 0.99
163,876 7.04E-07 0.97 53 2.20E-03 0.97 35,180 4.47E-06 0.94 15 1.08E-02 0.94 1,282 4.09E-05 0.99 2 2.42E-02 0.99