General Quadratic Weigthing Formula convergence period: 2020 - 2050
GQWF Input value
Sargl/Wolfsteiner/Wittmann input value C2020 weighting of per capita in 2020
Determination of Ct convex quadratic 0.1%
      a b c Ct conkave quadratic 6.6%
Constraint 1 in 2019: t=2019 0.00E+00 0.00E+00 1.00E+00 0% linear 3.2%
Constraint 2 in 2050: t=2050 9.61E+02 3.10E+01 1.00E+00 100% other value   4.0%
Constraint 3 in 2020: t=2020 1.00E+00 1.00E+00 1.00E+00 4.0%[1]   other value 4.0%
         
Remodeled constraint 1     1.00E+00 6.94E-18 0.00E+00 -2.58E-04
Remodeled constraint 2   -2.22E-16 1.00E+00 0.00E+00 4.03E-02
Remodeled constraint 3     0.00E+00 0.00E+00 1.00E+00 0.00E+00
               
parameter of the parabola:   -0.0003 0.0403 0.0000  
Country A Country B Country C Global
                           
Year
t		 Popu-lation
Pit		 Eit Per capita Popu-lation
Pit		 Eit Per capita Popu-lation
Pit		 Eit Per capita Popu-lation
Pt		 Et Per capita Ct
  bn Gt t bn Gt t bn Gt t bn Gt t  
2019 1.2 21.0 17.50 4.0 19.5 4.88 1.7 1.2 0.72 6.9 41.7 6.05 0.0%
2020 1.2 20.0 16.70 4.0 19.3 4.82 1.7 1.6 0.92 6.9 40.9 5.93 4.0%
2021 1.2 19.1 15.88 4.0 19.0 4.76 1.7 1.9 1.10 6.9 39.9 5.79 7.9%
2022 1.2 18.1 15.04 4.0 18.7 4.67 1.7 2.1 1.26 6.9 38.9 5.63 11.8%
2023 1.2 17.0 14.19 4.0 18.3 4.57 1.7 2.4 1.41 6.9 37.7 5.47 15.7%
2024 1.2 16.0 13.34 4.0 17.8 4.46 1.7 2.6 1.54 6.9 36.5 5.29 19.5%
2025 1.2 15.0 12.50 4.0 17.3 4.34 1.7 2.8 1.65 6.9 35.1 5.09 23.2%
2026 1.2 14.0 11.66 4.0 16.8 4.20 1.7 3.0 1.74 6.9 33.7 4.89 26.9%
2027 1.2 13.0 10.84 4.0 16.2 4.05 1.7 3.1 1.82 6.9 32.3 4.68 30.6%
2028 1.2 12.0 10.03 4.0 15.6 3.89 1.7 3.2 1.88 6.9 30.8 4.46 34.1%
2029 1.2 11.1 9.25 4.0 14.9 3.73 1.7 3.3 1.91 6.9 29.3 4.24 37.7%
2030 1.2 10.2 8.50 4.0 14.2 3.56 1.7 3.3 1.94 6.9 27.7 4.02 41.2%
2031 1.2 9.3 7.77 4.0 13.5 3.39 1.7 3.3 1.94 6.9 26.2 3.79 44.6%
2032 1.2 8.5 7.08 4.0 12.8 3.21 1.7 3.3 1.93 6.9 24.6 3.57 48.0%
2033 1.2 7.7 6.43 4.0 12.1 3.03 1.7 3.2 1.91 6.9 23.1 3.34 51.3%
2034 1.2 7.0 5.81 4.0 11.4 2.85 1.7 3.2 1.87 6.9 21.6 3.12 54.6%
2035 1.2 6.3 5.23 4.0 10.7 2.67 1.7 3.1 1.83 6.9 20.1 2.91 57.8%
2036 1.2 5.6 4.69 4.0 10.0 2.49 1.7 3.0 1.77 6.9 18.6 2.70 61.0%
2037 1.2 5.0 4.19 4.0 9.3 2.32 1.7 2.9 1.70 6.9 17.2 2.49 64.1%
2038 1.2 4.5 3.72 4.0 8.6 2.15 1.7 2.8 1.63 6.9 15.8 2.30 67.2%
2039 1.2 4.0 3.30 4.0 7.9 1.99 1.7 2.6 1.55 6.9 14.5 2.11 70.2%
2040 1.2 3.5 2.91 4.0 7.3 1.83 1.7 2.5 1.47 6.9 13.3 1.93 73.2%
2041 1.2 3.1 2.55 4.0 6.7 1.67 1.7 2.4 1.39 6.9 12.1 1.76 76.1%
2042 1.2 2.7 2.23 4.0 6.1 1.53 1.7 2.2 1.30 6.9 11.0 1.59 78.9%
2043 1.2 2.3 1.94 4.0 5.6 1.39 1.7 2.1 1.21 6.9 9.9 1.44 81.8%
2044 1.2 2.0 1.68 4.0 5.0 1.26 1.7 1.9 1.12 6.9 9.0 1.30 84.5%
2045 1.2 1.7 1.45 4.0 4.5 1.14 1.7 1.8 1.04 6.9 8.0 1.17 87.2%
2046 1.2 1.5 1.24 4.0 4.1 1.02 1.7 1.6 0.95 6.9 7.2 1.04 89.9%
2047 1.2 1.3 1.06 4.0 3.7 0.92 1.7 1.5 0.87 6.9 6.4 0.93 92.5%
2048 1.2 1.1 0.90 4.0 3.3 0.82 1.7 1.3 0.79 6.9 5.7 0.83 95.0%
2049 1.2 0.9 0.76 4.0 2.9 0.73 1.7 1.2 0.72 6.9 5.0 0.73 97.5%
2050 1.2 0.8 0.64 4.0 2.6 0.64 1.70 1.1 0.64 6.9 4.4 0.64 100.0%
∑   244     336     76     657  
global path: 657
0
[1]
GW:
Determination of a parabola with the following run:
(2019;0), (2020; Value in Cell I9); (2050;100).

The value determines the beginning of the run of the parabola.
Only values between 0 and 100 are possible for Ct.