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[null,"choosen global path:",null,{"$f":"'global path'!C2","v":3},null,"macro is to be used EPM?",null,{"$f":"EPM!AM101","v":1.3260197182857576E-3}]
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[null,{"$f":"'pc20'!A2","v":"pc20"},{"$f":"'pc20'!A1","v":"Allocation per capita starting 2020"}]
[null,{"$f":"'SPF-eq'!A2","v":"SPF-eq"},{"$f":"'SPF-eq'!A1","v":"Smooth Pathways Formula - equity (spk = 100%)"}]
[null,{"$f":"'SPF-in'!A2","v":"SPF-in"},{"$f":"'SPF-in'!A1","v":"Smooth Pathways Formula - inertia (spk = 0%)"}]
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[null,{"$f":"EPM!B3","v":"EPM"},{"$f":"EPM!B2","v":"Cap Model"}]
[null,{"$f":"CDC!A2","v":"CDC"},{"$f":"CDC!A1","v":"Common but Differentiated Convergence"}]
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[null,"per capita emissions 2019",{"$f":"C8/C6","v":17.5},{"$f":"D8/D6","v":4.875},{"$f":"E8/E6","v":0.72218653017956425},{"$f":"F8/F6","v":6.047495232073226},null,"per capita emissions 2019",{"$f":"I8/I6","v":17.5},{"$f":"J8/J6","v":4.875},{"$f":"K8/K6","v":0.72218653017956425},{"$f":"L8/L6","v":6.047495232073226}]
[null,"emissions key 2019",{"$f":"C8/$F$8","v":0.5032626143677319},{"$f":"D8/$F$8","v":0.46731528477003675},{"$f":"E8/$F$8","v":2.9422100862231352E-2},{"$f":"F8/$F$8","v":1}]
[null,"population key",{"$f":"C6/$F$6","v":0.17391304347826086},{"$f":"D6/$F$6","v":0.57971014492753625},{"$f":"E6/$F$6","v":0.24637681159420294},{"$f":"F6/$F$6","v":1}]
[null,"population growth",{"$f":"C7/C6-1","v":8.3333333333333481E-2},{"$f":"D7/D6-1","v":7.4999999999999956E-2},{"$f":"E7/E6-1","v":1.3529411764705879},{"$f":"F7/F6-1","v":0.39130434782608692}]
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[null,"Which population size is to be used for the convergence year 2050?",null,null,null,null,"frozen"]
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[null,null,"Country"]
[null,null,"A","B","C","global"]
[null,"population 2050 bn",{"$f":"IF($G$14=\"forecast\",C7,C6)","v":1.2},{"$f":"IF($G$14=\"forecast\",D7,D6)","v":4},{"$f":"IF($G$14=\"forecast\",E7,E6)","v":1.7000000000000004},{"$f":"IF($G$14=\"forecast\",F7,F6)","v":6.9}]
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[null,"input data models"]
[null,{"$f":"'C&C-exp'!A2","v":"C&C-exp"},4,"parameter a of the weighting formula C_t",null,"The author of the model recommends a = 4."]
[null,{"$f":"CDC!A2","v":"CDC"},null,null,null,"Percentage threshold",null,"change rates BAU"]
[null,{"$f":"LEFT('SPF-eq'!A2,LEN('SPF-eq'!A2)-3)","v":"SPF"},"Reduction rate at the beginnging of 2020 for each country",null,null,null,null,"share population key (spk)"]
[null,"EPM","Input of the quantiles of the Lorenz curve possible."]
[null,{"$f":"GQWF!A2","v":"GQWF"},"C2020","weighting of per capita in 2020"]

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[null,"Which global path will you select?",3,null,"input fields"]
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[null,"Sum 2018 - 2100",{"$f":"SUM(C6:C88)","v":767.19392249194743},{"$f":"SUM(D6:D88)","v":767.26170169773968},null,{"$f":"SUM(F6:F88)","v":766.91194032249405},null,{"$f":"SUM(H6:H88)","v":767.19392249194743},null,{"$f":"SUM(J6:J88)","v":767.25185268824043},null,{"$f":"SUM(L6:L88)","v":766.7740498339831},null,{"$f":"SUM(N6:N88)","v":767.05195395951716}]

{"sheet":"RF","index":4,"n_rows":132,"n_cols":19,"rows_kept":132,"cut":false,"hidden":false,"merged":[[128,11,131,12],[102,14,105,16],[107,16,110,18],[118,18,121,19],[0,14,0,26],[4,10,4,13],[4,1,4,3],[4,4,4,6],[4,7,4,9],[0,8,0,13],[0,6,0,7],[2,7,2,8]]}
["Regensburg Formula",null,null,null,null,null,"source:",null,"www.save-the-climate.info",null,null,null,null,null,"Climate Policy, Volume 17, 2017 - Issue 5: The Regensburg Model: reference values for the (I)NDCs based on converging per capita emissions"]
["RF",null,null,null,null,null,"convergence period: 2020 - 2050"]
["Sargl/Wolfsteiner/Wittmann"]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
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[2082,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C70","v":0},0]
[2083,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C71","v":0},0]
[2084,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C72","v":0},0]
[2085,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C73","v":0},0]
[2086,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C74","v":0},0]
[2087,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C75","v":0},0]
[2088,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C76","v":0},0]
[2089,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C77","v":0},0]
[2090,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C78","v":0},0]
[2091,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C79","v":0},0]
[2092,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C80","v":0},0]
[2093,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C81","v":0},0]
[2094,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C82","v":0},0]
[2095,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C83","v":0},0]
[2096,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C84","v":0},0]
[2097,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C85","v":0},0]
[2098,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C86","v":0},0]
[2099,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C87","v":0},0]
[2100,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C88","v":0},0]
["∑",null,{"$f":"SUM(C46:C95)","v":4.730879831791162},null,null,{"$f":"SUM(F46:F95)","v":15.769599439303878},null,null,{"$f":"SUM(I46:I95)","v":6.7020797617041437},null,null,{"$f":"SUM(L46:L95)","v":27.202559032799176}]
[]
["2020-2100",null,{"$f":"C96+C41","v":310.2396613075353},null,null,{"$f":"F96+F41","v":331.22226247336766},null,null,{"$f":"I96+I41","v":42.504281609739252},null,null,{"$f":"L96+L41","v":683.96620539064224}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,"control:",null,{"$f":"L98-L100","v":0}]
["global path:",{"$f":"'global path'!C2","v":3},"A",null,null,"B",null,null,"C"]
[2,null,337.40212079995524,null,null,321.77251336679808,null,null,24.509589054435224,null,null,{"$f":"SUM(B103:I103)","v":683.68422322118852},"RM",null,"Transfer values for the individual global paths from above."]
[1,null,265.3497569937802,null,null,346.58484600311886,null,null,72.099381599535207,null,null,{"$f":"SUM(B104:I104)","v":684.03398459643427},"RM"]
[3,null,310.2396613075353,null,null,331.22226247336766,null,null,42.504281609739252,null,null,{"$f":"SUM(B105:I105)","v":683.96620539064213},"RM"]
[6,null,303.21816594113892,null,null,333.5277134009965,null,null,47.078357516076792,null,null,{"$f":"SUM(B106:I106)","v":683.8242368582122},"RM"]
[]
[2,null,{"$f":"$L108*'input data'!$C$11*$L$98+(1-$L108)*'input data'!$C$10*$L$98","v":337.54128063247742},null,null,{"$f":"$L108*'input data'!$D$11*$L$98+(1-$L108)*'input data'!$D$10*$L$98","v":321.90522684519641},null,null,{"$f":"$L108*'input data'!$E$11*$L$98+(1-$L108)*'input data'!$E$10*$L$98","v":24.519697912968507},null,null,2.9624532704857931E-2,"share population key",null,"solver",null,"Solver must be performed manually for each global path: Minimisation of the quadratic deviation."]
[1,null,{"$f":"$L109*'input data'!$C$11*$L$98+(1-$L109)*'input data'!$C$10*$L$98","v":265.32346415425593},null,null,{"$f":"$L109*'input data'!$D$11*$L$98+(1-$L109)*'input data'!$D$10*$L$98","v":346.55050378309681},null,null,{"$f":"$L109*'input data'!$E$11*$L$98+(1-$L109)*'input data'!$E$10*$L$98","v":72.092237453289599},null,null,0.35021647856759081,"share population key",null,"solver"]
[3,null,{"$f":"$L110*'input data'!$C$11*$L$98+(1-$L110)*'input data'!$C$10*$L$98","v":310.2396613075353},null,null,{"$f":"$L110*'input data'!$D$11*$L$98+(1-$L110)*'input data'!$D$10*$L$98","v":331.22226247336772},null,null,{"$f":"$L110*'input data'!$E$11*$L$98+(1-$L110)*'input data'!$E$10*$L$98","v":42.504281609739252},null,null,0.15082286978316475,"share population key",null,"solver"]
[6,null,{"$f":"$L111*'input data'!$C$11*$L$98+(1-$L111)*'input data'!$C$10*$L$98","v":303.26956150947331},null,null,{"$f":"$L111*'input data'!$D$11*$L$98+(1-$L111)*'input data'!$D$10*$L$98","v":333.60090043537042},null,null,{"$f":"$L111*'input data'!$E$11*$L$98+(1-$L111)*'input data'!$E$10*$L$98","v":47.095743445798512},null,null,0.18176478918877273,"share population key",null,"solver"]
[]
[2,null,{"$f":"(C103-C108)^2/C103^2","v":1.7011091423007309E-7},null,null,{"$f":"(F103-F108)^2/F103^2","v":1.7011091422984717E-7},null,null,{"$f":"(I103-I108)^2/I103^2","v":1.7011091422942648E-7},null,null,{"$f":"C113+F113+I113","v":5.1033274268934674E-7},"square deviation"]
[1,null,{"$f":"(C104-C109)^2/C104^2","v":9.8183292791335879E-9},null,null,{"$f":"(F104-F109)^2/F104^2","v":9.8183292790692399E-9},null,null,{"$f":"(I104-I109)^2/I104^2","v":9.818329279176234E-9},null,null,{"$f":"C114+F114+I114","v":2.9454987837379062E-8},"square deviation"]
[3,null,{"$f":"(C105-C110)^2/C105^2","v":0},null,null,{"$f":"(F105-F110)^2/F105^2","v":2.9452444265918564E-32},null,null,{"$f":"(I105-I110)^2/I105^2","v":0},null,null,{"$f":"C115+F115+I115","v":2.9452444265918564E-32},"square deviation"]
[6,null,{"$f":"(C106-C111)^2/C106^2","v":2.8730349734532455E-8},null,null,{"$f":"(F106-F111)^2/F106^2","v":4.8150904174135291E-8},null,null,{"$f":"(I106-I111)^2/I106^2","v":1.3638080018749283E-7},null,null,{"$f":"C116+F116+I116","v":2.1326205409616058E-7},"square deviation"]
[]
[null,null,null,null,null,null,null,null,null,null,null,"A","B","C"]
[2,null,{"$f":"$L119*'input data'!$C$11*$L$98+(1-$L119)*'input data'!$C$10*$L$98","v":337.47216874699632},null,null,{"$f":"M119*'input data'!$D$11*$L$98+(1-M119)*'input data'!$D$10*$L$98","v":321.83931645600848},null,null,{"$f":"N119*'input data'!$E$11*$L$98+(1-N119)*'input data'!$E$10*$L$98","v":24.514677482427359},null,null,2.9931336689374654E-2,2.8767153825506736E-2,2.9590699959921283E-2,"share population key",null,"solver",null,"There is an implicit population weighting that is the same for all countries."]
[1,null,{"$f":"$L120*'input data'!$C$11*$L$98+(1-$L120)*'input data'!$C$10*$L$98","v":265.40484617247648},null,null,{"$f":"M120*'input data'!$D$11*$L$98+(1-M120)*'input data'!$D$10*$L$98","v":346.65680037282016},null,null,{"$f":"N120*'input data'!$E$11*$L$98+(1-N120)*'input data'!$E$10*$L$98","v":72.114350129229109},null,null,0.34985520456552466,0.35159921127633165,0.35036549617052259,"share population key",null,"solver"]
[3,null,{"$f":"$L121*'input data'!$C$11*$L$98+(1-$L121)*'input data'!$C$10*$L$98","v":310.30407006499593},null,null,{"$f":"M121*'input data'!$D$11*$L$98+(1-M121)*'input data'!$D$10*$L$98","v":331.29102742198609},null,null,{"$f":"N121*'input data'!$E$11*$L$98+(1-N121)*'input data'!$E$10*$L$98","v":42.513105910132381},null,null,0.15053694409485299,0.15171738148779024,0.15088233685516142,"share population key",null,"solver"]
[6,null,{"$f":"$L122*'input data'!$C$11*$L$98+(1-$L122)*'input data'!$C$10*$L$98","v":303.28111696817865},null,null,{"$f":"M122*'input data'!$D$11*$L$98+(1-M122)*'input data'!$D$10*$L$98","v":333.59695698354915},null,null,{"$f":"N122*'input data'!$E$11*$L$98+(1-N122)*'input data'!$E$10*$L$98","v":47.088131438914758},null,null,0.18171349177807361,0.18171349177807627,0.18171349177807397,"share population key",null,"solver"]
[]
[2,null,{"$f":"(C103-C119)^2/C103^2","v":4.3101780104039456E-8},null,null,{"$f":"(F103-F119)^2/F103^2","v":4.3101780103981586E-8},null,null,4.3101780104066819E-8,null,null,{"$f":"C124+F124+I124","v":1.2930534031208785E-7},"square deviation"]
[1,null,{"$f":"(C104-C120)^2/C104^2","v":4.3101780103989885E-8},null,null,4.3101780103960113E-8,null,null,4.310178010406177E-8,null,null,{"$f":"C125+F125+I125","v":1.2930534031201175E-7},"square deviation"]
[3,null,4.3101780104014528E-8,null,null,4.3101780104024997E-8,null,null,4.3101780104034989E-8,null,null,{"$f":"C126+F126+I126","v":1.2930534031207451E-7},"square deviation"]
[6,null,4.3101780104053353E-8,null,null,4.3101780104057958E-8,null,null,4.3101780103976828E-8,null,null,{"$f":"C127+F127+I127","v":1.2930534031208815E-7},"square deviation"]
[]
[{"$f":"A124","v":2},null,{"$f":"(C119-(RF!$L103*'input data'!$C$10))/(RF!$L103*('input data'!$C$11-'input data'!$C$10))","v":2.931344506831363E-2},null,null,{"$f":"(F119-(RF!$L103*'input data'!$D$10))/(RF!$L103*('input data'!$D$11-'input data'!$D$10))","v":3.049388246125272E-2},null,null,{"$f":"(I119-(RF!$L103*'input data'!$E$10))/(RF!$L103*('input data'!$E$11-'input data'!$E$10))","v":2.9658837828622175E-2},null,null,"Budgets via the solver"]
[{"$f":"A125","v":1},null,{"$f":"(C120-(RF!$L104*'input data'!$C$10))/(RF!L104*('input data'!$C$11-'input data'!$C$10))","v":0.34997194892301275},null,null,{"$f":"(F120-(RF!$L104*'input data'!$D$10))/(RF!$L104*('input data'!$D$11-'input data'!$D$10))","v":0.35115238631595025},null,null,{"$f":"(I120-(RF!$L104*'input data'!$E$10))/(RF!$L104*('input data'!$E$11-'input data'!$E$10))","v":0.35031734168332135}]
[3,null,{"$f":"(C121-(RF!$L105*'input data'!$C$10))/(RF!L105*('input data'!$C$11-'input data'!$C$10))","v":0.15053694409485249},null,null,{"$f":"(F121-(RF!$L105*'input data'!$D$10))/(RF!$L105*('input data'!$D$11-'input data'!$D$10))","v":0.1517173814877914},null,null,{"$f":"(I121-(RF!$L105*'input data'!$E$10))/(RF!$L105*('input data'!$E$11-'input data'!$E$10))","v":0.1508823368551615}]
[6,null,{"$f":"(C122-(RF!$L106*'input data'!$C$10))/(RF!L106*('input data'!$C$11-'input data'!$C$10))","v":0.18143397928197483},null,null,{"$f":"(F122-(RF!$L106*'input data'!$D$10))/(RF!$L106*('input data'!$D$11-'input data'!$D$10))","v":0.18261441667491465},null,null,{"$f":"(I122-(RF!$L106*'input data'!$E$10))/(RF!$L106*('input data'!$E$11-'input data'!$E$10))","v":0.18177937204228298}]

{"sheet":"C&C-exp","index":5,"n_rows":123,"n_cols":29,"rows_kept":123,"cut":false,"hidden":false,"merged":[[0,7,0,10],[119,11,122,12],[109,16,112,20],[104,16,107,18],[114,16,117,20],[6,1,6,3],[6,4,6,6],[6,7,6,9],[6,10,6,13]]}
["C&C: exponential approach",null,null,null,null,null,"source:","www.gci.org.uk",null,null,null,"convergence period: 2020 - 2050"]
["C&C-exp"]
[]
[]
[null,"Parameter a:",null,null,{"$f":"'input data'!C21","v":4},null,"Input value sheet \"input data\":",null,null,null,null,"parameter a of the weighting formula Ct"]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
[]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita","Ct"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t"]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C11/B11","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F11/E11","v":4.875},{"$f":"K11-E11-B11","v":1.7000000000000004},{"$f":"'global path'!$C$7-C11-F11","v":1.2277171013052595},{"$f":"I11/H11","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I11+F11+C11","v":41.727717101305259},{"$f":"L11/K11","v":6.047495232073226},{"$f":"EXP(-$E$5*(1-((A11-2019)/(2050-2019))))","v":1.8315638888734179E-2},null,null,null,null,null,null,null,null,null,null,null,null,null,"a","CBY = exp(-a)"]
[{"$f":"A11+1","v":2020},{"$f":"B$11*(B$42/B$11)^(($A12-2019)/31)","v":1.2},{"$f":"((1-$N12)*(C11/$L11)+$N12*(B12/$K12))*'global path'!$C8","v":20.299348173457769},{"$f":"C12/B12","v":16.916123477881474},{"$f":"E$11*(E$42/E$11)^(($A12-2019)/31)","v":4},{"$f":"((1-$N12)*(F11/$L11)+$N12*(E12/$K12))*'global path'!$C8","v":19.205776116276603},{"$f":"F12/E12","v":4.8014440290691507},{"$f":"H$11*(H$42/H$11)^(($A12-2019)/31)","v":1.7000000000000004},{"$f":"((1-$N12)*(I11/$L11)+$N12*(H12/$K12))*'global path'!$C8","v":1.3880384695447761},{"$f":"I12/H12","v":0.81649321737927982},{"$f":"B12+E12+H12","v":6.9},{"$f":"I12+F12+C12","v":40.89316275927915},{"$f":"L12/K12","v":5.9265453274317608},2.0838193670452695E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,0,{"$f":"EXP(-AB12)","v":1}]
[{"$f":"A12+1","v":2021},{"$f":"B$11*(B$42/B$11)^(($A13-2019)/31)","v":1.2},{"$f":"((1-$N13)*(C12/$L12)+$N13*(B13/$K13))*'global path'!$C9","v":19.521385297798155},16.267821081498465,{"$f":"E$11*(E$42/E$11)^(($A13-2019)/31)","v":4},{"$f":"((1-$N13)*(F12/$L12)+$N13*(E13/$K13))*'global path'!$C9","v":18.862857647432392},4.715714411858098,{"$f":"H$11*(H$42/H$11)^(($A13-2019)/31)","v":1.7000000000000004},{"$f":"((1-$N13)*(I12/$L12)+$N13*(H13/$K13))*'global path'!$C9","v":1.5568836003390056},0.91581388255235607,{"$f":"B13+E13+H13","v":6.9},{"$f":"I13+F13+C13","v":39.941126545569553},5.788569064575297,2.3708171911730948E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AB12+0.1","v":0.1},{"$f":"EXP(-AB13)","v":0.90483741803595952}]
[2022,1.2,{"$f":"((1-$N14)*(C13/$L13)+$N14*(B14/$K14))*'global path'!$C10","v":18.672672024741754},15.560560020618128,4,{"$f":"((1-$N14)*(F13/$L13)+$N14*(E14/$K14))*'global path'!$C10","v":18.474499695651041},4.6186249239127601,1.7000000000000004,{"$f":"((1-$N14)*(I13/$L13)+$N14*(H14/$K14))*'global path'!$C10","v":1.7330337548617245},1.0194316205068965,6.9,38.88020547525452,5.6348123877180463,2.6973423142389763E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AB13+0.1","v":0.2},{"$f":"EXP(-AB14)","v":0.81873075307798182}]
[2023,1.2,{"$f":"((1-$N15)*(C14/$L14)+$N15*(B15/$K15))*'global path'!$C11","v":17.760802304126091},14.800668586771744,4,{"$f":"((1-$N15)*(F14/$L14)+$N15*(E15/$K15))*'global path'!$C11","v":18.044179784242694},4.5110449460606734,1.7000000000000004,{"$f":"((1-$N15)*(I14/$L14)+$N15*(H15/$K15))*'global path'!$C11","v":1.9149143082875297},1.1264201813456054,6.9,37.71989639665631,5.46665165168932,3.0688387056043043E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,0.30000000000000004,0.74081822068171788]
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[2067,1.2,5.0683910508547897E-2,4.2236592090456583E-2,4,0.16894636836182633,4.2236592090456583E-2,1.7000000000000004,7.1802206553776199E-2,4.2236592090456576E-2,6.9,{"$f":"'global path'!C55","v":0.2914324854241504},4.2236592090456576E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.1999999999999975,5.5165644207607863E-3]
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[2069,1.2,3.4151958116388603E-2,2.8459965096990503E-2,4,0.11383986038796201,2.8459965096990503E-2,1.7000000000000004,4.8381940664883862E-2,2.8459965096990499E-2,6.9,{"$f":"'global path'!C57","v":0.19637375916923447},2.8459965096990503E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.3999999999999968,4.5165809426126824E-3]
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[2071,1.2,2.2645899072934614E-2,1.8871582560778845E-2,4,7.5486330243115393E-2,1.8871582560778848E-2,1.7000000000000004,3.2081690353324047E-2,1.8871582560778845E-2,6.9,{"$f":"'global path'!C59","v":0.13021391966937404},1.8871582560778845E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.5999999999999961,3.6978637164829455E-3]
[2072,1.2,1.8329247211639352E-2,1.5274372676366128E-2,4,6.1097490705464517E-2,1.5274372676366129E-2,1.7000000000000004,2.5966433549822421E-2,1.5274372676366126E-2,6.9,{"$f":"'global path'!C60","v":0.10539317146692628},1.5274372676366128E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.6999999999999957,3.3459654574712872E-3]
[2073,1.2,1.4775275294181562E-2,1.2312729411817968E-2,4,4.9250917647271873E-2,1.2312729411817968E-2,1.7000000000000004,2.093164000009055E-2,1.2312729411817968E-2,6.9,{"$f":"'global path'!C61","v":8.4957832941543979E-2},1.2312729411817967E-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.7999999999999954,3.0275547453758288E-3]
[2074,1.2,1.1221303376723769E-2,9.3510861472698072E-3,4,3.7404344589079236E-2,9.351086147269809E-3,1.7000000000000004,1.5896846450358677E-2,9.3510861472698072E-3,6.9,{"$f":"'global path'!C62","v":6.4522494416161674E-2},9.3510861472698072E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.899999999999995,2.7394448187683827E-3]
[2075,1.2,7.6673314592659771E-3,6.3894428827216479E-3,4,2.5557771530886592E-2,6.3894428827216479E-3,1.7000000000000004,1.0862052900626803E-2,6.389442882721647E-3,6.9,{"$f":"'global path'!C63","v":4.408715589077937E-2},6.3894428827216479E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.9999999999999947,2.4787521766663715E-3]
[2076,1.2,4.1133595418081856E-3,3.4277996181734881E-3,4,1.3711198472693951E-2,3.4277996181734877E-3,1.7000000000000004,5.8272593508949299E-3,3.4277996181734873E-3,6.9,{"$f":"'global path'!C64","v":2.3651817365397065E-2},3.4277996181734877E-3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.0999999999999943,2.2428677194858151E-3]
[2077,1.2,5.5938762435039317E-4,4.6615635362532766E-4,4,1.8646254145013108E-3,4.6615635362532771E-4,1.7000000000000004,7.9246580116305713E-4,4.661563536253276E-4,6.9,{"$f":"'global path'!C65","v":3.2164788400147609E-3},4.6615635362532766E-4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.199999999999994,2.0294306362957466E-3]
[2078,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C66","v":0},0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.2999999999999936,1.8363047770289186E-3]
[2079,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C67","v":0},0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.3999999999999932,1.6615572731739456E-3]
[2080,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C68","v":0},0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.4999999999999929,1.5034391929775832E-3]
[2081,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C69","v":0},0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.5999999999999925,{"$f":"EXP(-AB78)","v":1.3603680375479036E-3}]
[2082,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C70","v":0},0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.6999999999999922,{"$f":"EXP(-AB79)","v":1.2309119026734908E-3}]
[2083,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C71","v":0},0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6.7999999999999918,{"$f":"EXP(-AB80)","v":1.1137751478448121E-3}]
[2084,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C72","v":0},0]
[2085,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C73","v":0},0]
[2086,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C74","v":0},0]
[2087,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C75","v":0},0]
[2088,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C76","v":0},0]
[2089,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C77","v":0},0]
[2090,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C78","v":0},0]
[2091,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C79","v":0},0]
[2092,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C80","v":0},0]
[2093,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C81","v":0},0]
[2094,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C82","v":0},0]
[2095,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C83","v":0},0]
[2096,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C84","v":0},0]
[2097,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C85","v":0},0]
[2098,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C86","v":0},0]
[2099,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C87","v":0},0]
[2100,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C88","v":0},0]
["∑",null,{"$f":"SUM(C48:C97)","v":4.730879831791162},null,null,{"$f":"SUM(F48:F97)","v":15.769599439303878},null,null,{"$f":"SUM(I48:I97)","v":6.7020797617041437},null,null,{"$f":"SUM(L48:L97)","v":27.202559032799176}]
[]
["∑",null,{"$f":"C98+C43","v":247.13531484852703},null,null,{"$f":"F98+F43","v":352.75744825313285},null,null,{"$f":"I98+I43","v":84.073442288982534},null,null,{"$f":"L98+L43","v":683.96620539064224}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,"control:",null,{"$f":"L100-L102","v":0}]
["global path:",null,{"$f":"'global path'!C2","v":3}]
[2,null,255.22874577056143,null,null,349.81525521751695,null,null,78.640222233110137,null,null,{"$f":"SUM(C105:I105)","v":683.6842232211884},"C&Cexp",null,null,null,"Transfer values for the individual global paths from above."]
[1,null,229.76727745111626,null,null,358.72783377581874,null,null,95.538873369499271,null,null,{"$f":"SUM(C106:I106)","v":684.03398459643427},"C&Cexp"]
[3,null,247.13531484852703,null,null,352.75744825313285,null,null,84.073442288982534,null,null,{"$f":"SUM(C107:I107)","v":683.96620539064236},"C&Cexp"]
[6,null,247.22172582296673,null,null,352.63723292884146,null,null,83.965278106403829,null,null,{"$f":"SUM(C108:I108)","v":683.82423685821198},"C&Cexp"]
[]
[2,null,{"$f":"$L110*'input data'!$C$11*$L$100+(1-$L110)*'input data'!$C$10*$L$100","v":255.32123806618557},null,null,{"$f":"$L110*'input data'!$D$11*$L$100+(1-$L110)*'input data'!$D$10*$L$100","v":349.9638946048799},null,null,{"$f":"$L110*'input data'!$E$11*$L$100+(1-$L110)*'input data'!$E$10*$L$100","v":78.681072719576704},null,null,0.39461872279080773,"share population key",null,"solver",null,"Solver must be performed manually for each global path: Minimisation of the quadratic deviation."]
[1,null,{"$f":"$L111*'input data'!$C$11*$L$100+(1-$L111)*'input data'!$C$10*$L$100","v":229.74451038992731},null,null,{"$f":"$L111*'input data'!$D$11*$L$100+(1-$L111)*'input data'!$D$10*$L$100","v":358.69228833770262},null,null,{"$f":"$L111*'input data'!$E$11*$L$100+(1-$L111)*'input data'!$E$10*$L$100","v":95.529406663012338},null,null,0.50815985840525313,"share population key",null,"solver"]
[{"$f":"A107","v":3},null,{"$f":"$L112*'input data'!$C$11*$L$100+(1-$L112)*'input data'!$C$10*$L$100","v":247.11038842685213},null,null,{"$f":"$L112*'input data'!$D$11*$L$100+(1-$L112)*'input data'!$D$10*$L$100","v":352.76595472141446},null,null,{"$f":"$L112*'input data'!$E$11*$L$100+(1-$L112)*'input data'!$E$10*$L$100","v":84.089862242375688},null,null,0.43106862381840344,"share population key",null,"solver"]
[{"$f":"A108","v":6},null,{"$f":"$L113*'input data'!$C$11*$L$100+(1-$L113)*'input data'!$C$10*$L$100","v":247.27305144687446},null,null,{"$f":"$L113*'input data'!$D$11*$L$100+(1-$L113)*'input data'!$D$10*$L$100","v":352.71044383266837},null,null,{"$f":"$L113*'input data'!$E$11*$L$100+(1-$L113)*'input data'!$E$10*$L$100","v":83.982710111099394},null,null,0.43034652425001507,"share population key",null,"solver"]
[]
[2,null,{"$f":"(C105-C110)^2/C105^2","v":1.313263713755029E-7},null,null,{"$f":"(F105-F110)^2/F105^2","v":1.8054701957019677E-7},null,null,{"$f":"(I105-I110)^2/I105^2","v":2.6983917545966801E-7},null,null,{"$f":"C115+F115+I115","v":5.8171256640536766E-7},"square deviation",null,null,null,{"$f":"RF!S119","v":"There is an implicit population weighting that is the same for all countries."}]
[1,null,{"$f":"(C106-C111)^2/C106^2","v":9.8183292791245551E-9},null,null,{"$f":"(F106-F111)^2/F106^2","v":9.8183292791148887E-9},null,null,{"$f":"(I106-I111)^2/I106^2","v":9.818329279171668E-9},null,null,{"$f":"C116+F116+I116","v":2.945498783741111E-8},"square deviation"]
[{"$f":"A107","v":3},null,{"$f":"(C107-C112)^2/C107^2","v":1.0173028401025335E-8},null,null,{"$f":"(F107-F112)^2/F107^2","v":5.8149527368122311E-10},null,null,{"$f":"(I107-I112)^2/I107^2","v":3.8143995388546979E-8},null,null,{"$f":"C117+F117+I117","v":4.8898519063253537E-8},"square deviation"]
[{"$f":"A108","v":6},null,{"$f":"(C108-C113)^2/C108^2","v":4.3101780104030946E-8},null,null,{"$f":"(F108-F113)^2/F108^2","v":4.3101780103945243E-8},null,null,{"$f":"(I108-I113)^2/I108^2","v":4.3101780103916484E-8},null,null,{"$f":"C118+F118+I118","v":1.2930534031189269E-7},"square deviation"]
[]
[{"$f":"A115","v":2},null,{"$f":"(C110-($L$105*'input data'!$C$10))/($L$105*('input data'!$C$11-'input data'!$C$10))","v":0.39415124467471369},null,null,{"$f":"(F110-($L$105*'input data'!$D$10))/($L$105*('input data'!$D$11-'input data'!$D$10))","v":0.39649634509297338},null,null,{"$f":"(I110-($L$105*'input data'!$E$10))/($L$105*('input data'!$E$11-'input data'!$E$10))","v":0.39483741465840644},null,null,"Budgets via the solver"]
[{"$f":"A116","v":1},null,{"$f":"(C111-($L$105*'input data'!$C$10))/($L$105*('input data'!$C$11-'input data'!$C$10))","v":0.50773920976782072},null,null,{"$f":"(F111-($L$105*'input data'!$D$10))/($L$105*('input data'!$D$11-'input data'!$D$10))","v":0.51008431018608102},null,null,{"$f":"(I111-($L$105*'input data'!$E$10))/($L$105*('input data'!$E$11-'input data'!$E$10))","v":0.5084253797515137}]
[3,null,{"$f":"(C112-($L$105*'input data'!$C$10))/($L$105*('input data'!$C$11-'input data'!$C$10))","v":0.43061617928333834},null,null,{"$f":"(F112-($L$105*'input data'!$D$10))/($L$105*('input data'!$D$11-'input data'!$D$10))","v":0.43296127970159887},null,null,{"$f":"(I112-($L$105*'input data'!$E$10))/($L$105*('input data'!$E$11-'input data'!$E$10))","v":0.43130234926703132}]
[6,null,{"$f":"(C113-($L$105*'input data'!$C$10))/($L$105*('input data'!$C$11-'input data'!$C$10))","v":0.42989378188856187},null,null,{"$f":"(F113-($L$105*'input data'!$D$10))/($L$105*('input data'!$D$11-'input data'!$D$10))","v":0.432238882306822},null,null,{"$f":"(I113-($L$105*'input data'!$E$10))/($L$105*('input data'!$E$11-'input data'!$E$10))","v":0.43057995187225473}]

{"sheet":"C&C-lin","index":6,"n_rows":115,"n_cols":17,"rows_kept":115,"cut":false,"hidden":false,"merged":[[0,6,0,9],[106,16,109,20],[101,16,104,18],[111,16,114,20],[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13]]}
["C&C: linear aproach",null,null,null,null,"source:","www.gci.org.uk",null,null,null,"convergence period: 2020 - 2050"]
["C&C-lin"]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
[]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita","Ct"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t"]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C8/B8","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F8/E8","v":4.875},{"$f":"K8-E8-B8","v":1.7000000000000004},{"$f":"'global path'!$C$7-C8-F8","v":1.2277171013052595},{"$f":"I8/H8","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I8+F8+C8","v":41.727717101305259},{"$f":"L8/K8","v":6.047495232073226},{"$f":"(A8-2019)/(2050-2019)","v":0}]
[{"$f":"A8+1","v":2020},{"$f":"B$8*(B$39/B$8)^(($A9-2019)/31)","v":1.2},{"$f":"((1-$N9)*(C8/$L8)+$N9*(B9/$K9))*'global path'!$C8","v":20.145543690094133},{"$f":"C9/B9","v":16.787953075078445},{"$f":"E$8*(E$39/E$8)^(($A9-2019)/31)","v":4},{"$f":"((1-$N9)*(F8/$L8)+$N9*(E9/$K9))*'global path'!$C8","v":19.258263913217},{"$f":"F9/E9","v":4.81456597830425},{"$f":"H$8*(H$39/H$8)^(($A9-2019)/31)","v":1.7000000000000004},{"$f":"((1-$N9)*(I8/$L8)+$N9*(H9/$K9))*'global path'!$C8","v":1.48935515596802},{"$f":"I9/H9","v":0.8760912682164822},{"$f":"B9+E9+H9","v":6.9},{"$f":"I9+F9+C9","v":40.89316275927915},{"$f":"L9/K9","v":5.9265453274317608},{"$f":"(A9-2019)/(2050-2019)","v":3.2258064516129031E-2}]
[{"$f":"A9+1","v":2021},{"$f":"B$8*(B$39/B$8)^(($A10-2019)/31)","v":1.2},{"$f":"((1-$N10)*(C9/$L9)+$N10*(B10/$K10))*'global path'!$C9","v":18.855227532125213},15.712689610104345,{"$f":"E$8*(E$39/E$8)^(($A10-2019)/31)","v":4},{"$f":"((1-$N10)*(F9/$L9)+$N10*(E10/$K10))*'global path'!$C9","v":19.090192720963646},4.7725481802409115,{"$f":"H$8*(H$39/H$8)^(($A10-2019)/31)","v":1.7000000000000004},{"$f":"((1-$N10)*(I9/$L9)+$N10*(H10/$K10))*'global path'!$C9","v":1.9957062924807036},1.1739448779298254,{"$f":"B10+E10+H10","v":6.9},{"$f":"I10+F10+C10","v":39.94112654556956},5.7885690645752979,{"$f":"(A10-2019)/(2050-2019)","v":6.4516129032258063E-2}]
[2022,1.2,{"$f":"((1-$N11)*(C10/$L10)+$N11*(B11/$K11))*'global path'!$C10","v":17.232526440604612},14.360438700503844,4,{"$f":"((1-$N11)*(F10/$L10)+$N11*(E11/$K11))*'global path'!$C10","v":18.965968262312259},4.7414920655780648,1.7000000000000004,{"$f":"((1-$N11)*(I10/$L10)+$N11*(H11/$K11))*'global path'!$C10","v":2.6817107723376541},1.577476924904502,6.9,38.880205475254527,5.6348123877180472,9.6774193548387094E-2]
[2023,1.2,{"$f":"((1-$N12)*(C11/$L11)+$N12*(B12/$K12))*'global path'!$C11","v":15.407508356214873},12.839590296845728,4,{"$f":"((1-$N12)*(F11/$L11)+$N12*(E12/$K12))*'global path'!$C11","v":18.847272205072766},4.7118180512681915,1.7000000000000004,{"$f":"((1-$N12)*(I11/$L11)+$N12*(H12/$K12))*'global path'!$C11","v":3.465115835368676},2.0383034325698088,6.9,37.71989639665631,5.46665165168932,0.12903225806451613]
[2024,1.2,{"$f":"((1-$N13)*(C12/$L12)+$N13*(B13/$K13))*'global path'!$C12","v":13.517394882479739},11.264495735399782,4,{"$f":"((1-$N13)*(F12/$L12)+$N13*(E13/$K13))*'global path'!$C12","v":18.693828830703772},4.6734572076759431,1.7000000000000004,{"$f":"((1-$N13)*(I12/$L12)+$N13*(H13/$K13))*'global path'!$C12","v":4.2592296425411504},2.5054292014947936,6.9,36.470453355724658,5.2855729501050224,0.16129032258064516]
[2025,1.2,{"$f":"((1-$N14)*(C13/$L13)+$N14*(B14/$K14))*'global path'!$C13","v":11.687191306623342},9.7393260888527848,4,{"$f":"((1-$N14)*(F13/$L13)+$N14*(E14/$K14))*'global path'!$C13","v":18.469918025570887},4.6174795063927219,1.7000000000000004,{"$f":"((1-$N14)*(I13/$L13)+$N14*(H14/$K14))*'global path'!$C13","v":4.9856260588803289},2.9327212111060752,6.9,35.142735391074559,5.0931500566774721,0.19354838709677419]
[2026,1.2,{"$f":"((1-$N15)*(C14/$L14)+$N15*(B15/$K15))*'global path'!$C14","v":10.014369030652567},8.3453075255438058,4,{"$f":"((1-$N15)*(F14/$L14)+$N15*(E15/$K15))*'global path'!$C14","v":18.149501255848826},4.5373753139622064,1.7000000000000004,{"$f":"((1-$N15)*(I14/$L14)+$N15*(H15/$K15))*'global path'!$C14","v":5.5841776609268319},3.2848103887804885,6.9,33.748047947428226,4.8910214416562647,0.22580645161290322]
[2027,1.2,{"$f":"((1-$N16)*(C15/$L15)+$N16*(B16/$K16))*'global path'!$C15","v":8.5603258401562119},7.1336048667968432,4,{"$f":"((1-$N16)*(F15/$L15)+$N16*(E16/$K16))*'global path'!$C15","v":17.719032528280632},4.429758132070158,1.7000000000000004,{"$f":"((1-$N16)*(I15/$L15)+$N16*(H16/$K16))*'global path'!$C15","v":6.0186228095873817},3.5403663585808118,6.9,32.297981178024223,4.6808668373948148,0.25806451612903225]
[2028,1.2,{"$f":"((1-$N17)*(C16/$L16)+$N17*(B17/$K17))*'global path'!$C16","v":7.3494408750296536},6.1245340625247113,4,{"$f":"((1-$N17)*(F16/$L16)+$N17*(E17/$K17))*'global path'!$C16","v":17.177677658260507},4.2944194145651267,1.7000000000000004,{"$f":"((1-$N17)*(I16/$L16)+$N17*(H17/$K17))*'global path'!$C16","v":6.2771298685772834},3.6924293344572248,6.9,30.804248401867444,4.4643838263575999,0.29032258064516131]
[2029,1.2,{"$f":"((1-$N18)*(C17/$L17)+$N18*(B18/$K18))*'global path'!$C17","v":6.3746171963655991},5.3121809969713327,4,{"$f":"((1-$N18)*(F17/$L17)+$N18*(E18/$K18))*'global path'!$C17","v":16.535321688978975},4.1338304222447437,1.7000000000000004,{"$f":"((1-$N18)*(I17/$L17)+$N18*(H18/$K18))*'global path'!$C17","v":6.3685890060440338},3.746228827084725,6.9,29.278527891388606,4.2432649117954497,0.32258064516129031]
[2030,1.2,{"$f":"((1-$N19)*(C18/$L18)+$N19*(B19/$K19))*'global path'!$C18","v":5.6068552339544651},4.672379361628721,4,{"$f":"((1-$N19)*(F18/$L18)+$N19*(E19/$K19))*'global path'!$C18","v":15.809204767965593},3.9523011919913982,1.7000000000000004,{"$f":"((1-$N19)*(I18/$L18)+$N19*(H19/$K19))*'global path'!$C18","v":6.3162509929018933},3.7154417605305246,6.9,27.732310994821951,4.0191755064959347,0.35483870967741937]
[2031,1.2,{"$f":"((1-$N20)*(C19/$L19)+$N20*(B20/$K20))*'global path'!$C19","v":5.0059531766383136},4.1716276471985951,4,{"$f":"((1-$N20)*(F19/$L19)+$N20*(E20/$K20))*'global path'!$C19","v":15.020179251230354},3.7550448128075886,1.7000000000000004,{"$f":"((1-$N20)*(I19/$L19)+$N20*(H20/$K20))*'global path'!$C19","v":6.150626924733424},3.6180158380784837,6.9,26.176759352602094,3.7937332395075498,0.38709677419354838]
[2032,1.2,{"$f":"((1-$N21)*(C20/$L20)+$N21*(B21/$K21))*'global path'!$C20","v":4.5298605343140244},3.7748837785950204,4,{"$f":"((1-$N21)*(F20/$L20)+$N21*(E21/$K21))*'global path'!$C20","v":14.189433807554249},3.5473584518885621,1.7000000000000004,{"$f":"((1-$N21)*(I20/$L20)+$N21*(H21/$K21))*'global path'!$C20","v":5.9032793158935508},3.4725172446432642,6.9,24.622573657761826,3.5684889359075109,0.41935483870967744]
[2033,1.2,{"$f":"((1-$N22)*(C21/$L21)+$N22*(B22/$K22))*'global path'!$C21","v":4.141202900531578},3.4510024171096485,4,{"$f":"((1-$N22)*(F21/$L21)+$N22*(E22/$K22))*'global path'!$C21","v":13.336191599097296},3.3340478997743239,1.7000000000000004,{"$f":"((1-$N22)*(I21/$L21)+$N22*(H22/$K22))*'global path'!$C21","v":5.6024815483166268},3.2955773813627207,6.9,23.079876047945501,3.3449095721660145,0.45161290322580644]
[2034,1.2,{"$f":"((1-$N23)*(C22/$L22)+$N23*(B23/$K23))*'global path'!$C22","v":3.8106127374506555},3.1755106145422132,4,{"$f":"((1-$N23)*(F22/$L22)+$N23*(E23/$K23))*'global path'!$C22","v":12.476508236895699},3.1191270592239246,1.7000000000000004,{"$f":"((1-$N23)*(I22/$L22)+$N23*(H23/$K23))*'global path'!$C22","v":5.2709868395239488},3.100580493837616,6.9,21.558107813870301,3.1243634512855505,0.4838709677419355]
[2035,1.2,{"$f":"((1-$N24)*(C23/$L23)+$N24*(B24/$K24))*'global path'!$C23","v":3.5173720897661007},2.9311434081384173,4,{"$f":"((1-$N24)*(F23/$L23)+$N24*(E24/$K24))*'global path'!$C23","v":11.62299766608764},2.90574941652191,1.7000000000000004,{"$f":"((1-$N24)*(I23/$L23)+$N24*(H24/$K24))*'global path'!$C23","v":4.9255739235134808},2.8973964255961646,6.9,20.065943679367223,2.908107779618438,0.5161290322580645]
[2036,1.2,{"$f":"((1-$N25)*(C24/$L24)+$N25*(B25/$K25))*'global path'!$C24","v":3.2483133006934102},2.706927750577842,4,{"$f":"((1-$N25)*(F24/$L24)+$N25*(E25/$K25))*'global path'!$C24","v":10.785163640165072},2.696290910041268,1.7000000000000004,{"$f":"((1-$N25)*(I24/$L24)+$N25*(H25/$K25))*'global path'!$C24","v":4.5777465245025324},2.6927920732367832,6.9,18.611223465361014,2.6972787630957988,0.54838709677419351]
[2037,1.2,{"$f":"((1-$N26)*(C25/$L25)+$N26*(B26/$K26))*'global path'!$C25","v":2.9959488020215299},2.4966240016846082,4,{"$f":"((1-$N26)*(F25/$L25)+$N26*(E26/$K26))*'global path'!$C25","v":9.9700056297704798},2.4925014074426199,1.7000000000000004,{"$f":"((1-$N26)*(I25/$L25)+$N26*(H26/$K26))*'global path'!$C25","v":4.2349470761908421},2.4911453389357887,6.9,17.200901507982852,2.4928842765192538,0.58064516129032262]
[2038,1.2,{"$f":"((1-$N27)*(C26/$L26)+$N27*(B27/$K27))*'global path'!$C26","v":2.7565587410996013},2.2971322842496678,4,{"$f":"((1-$N27)*(F26/$L26)+$N27*(E27/$K27))*'global path'!$C26","v":9.1826504288719253},2.2956626072179813,1.7000000000000004,{"$f":"((1-$N27)*(I26/$L26)+$N27*(H27/$K27))*'global path'!$C26","v":3.901804602506219},2.2951791779448341,6.9,15.841013772477746,2.2957990974605429,0.61290322580645162]
[2039,1.2,{"$f":"((1-$N28)*(C27/$L27)+$N28*(B28/$K28))*'global path'!$C27","v":2.5286361022102137},2.1071967518418449,4,{"$f":"((1-$N28)*(F27/$L27)+$N28*(E28/$K28))*'global path'!$C27","v":8.4268727751705104},2.1067181937926276,1.7000000000000004,{"$f":"((1-$N28)*(I27/$L27)+$N28*(H28/$K28))*'global path'!$C27","v":3.5811533242251392},2.1065607789559637,6.9,14.536662201605864,2.1067626379138931,0.64516129032258063]
[2040,1.2,{"$f":"((1-$N29)*(C28/$L28)+$N29*(B29/$K29))*'global path'!$C28","v":2.3118085203616379},1.926507100301365,4,{"$f":"((1-$N29)*(F28/$L28)+$N29*(E29/$K29))*'global path'!$C28","v":7.7054637775591388},1.9263659443897847,1.7000000000000004,{"$f":"((1-$N29)*(I28/$L28)+$N29*(H29/$K29))*'global path'!$C28","v":3.2747431723861498},1.9263195131683228,6.9,13.292015470306925,1.9263790536676701,0.67741935483870963]
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[2100,1.2,0,0,4,0,0,1.7000000000000004,0,0,6.9,{"$f":"'global path'!C88","v":0},0]
["∑",null,{"$f":"SUM(C45:C94)","v":4.730879831791162},null,null,{"$f":"SUM(F45:F94)","v":15.769599439303878},null,null,{"$f":"SUM(I45:I94)","v":6.7020797617041437},null,null,{"$f":"SUM(L45:L94)","v":27.202559032799176}]
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["∑",null,{"$f":"C95+C40","v":188.04469928745851},null,null,{"$f":"F95+F40","v":372.92289572789423},null,null,{"$f":"I95+I40","v":122.9986103752896},null,null,{"$f":"L95+L40","v":683.96620539064224}]
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[]
[2,null,{"$f":"$L107*'input data'!$C$11*$L$97+(1-$L107)*'input data'!$C$10*$L$97","v":190.43965666161904},null,null,{"$f":"$L107*'input data'!$D$11*$L$97+(1-$L107)*'input data'!$D$10*$L$97","v":372.10558511648219},null,null,{"$f":"$L107*'input data'!$E$11*$L$97+(1-$L107)*'input data'!$E$10*$L$97","v":121.42096361254102},null,null,0.68264338827503857,"share population key",null,"solver",null,"Solver must be performed manually for each global path: Minimisation of the quadratic deviation."]
[1,null,{"$f":"$L108*'input data'!$C$11*$L$97+(1-$L108)*'input data'!$C$10*$L$97","v":180.60097705651509},null,null,{"$f":"$L108*'input data'!$D$11*$L$97+(1-$L108)*'input data'!$D$10*$L$97","v":375.46316355620399},null,null,{"$f":"$L108*'input data'!$E$11*$L$97+(1-$L108)*'input data'!$E$10*$L$97","v":127.90206477792321},null,null,0.72631961102917653,"share population key",null,"solver"]
[{"$f":"A104","v":3},null,{"$f":"$L109*'input data'!$C$11*$L$97+(1-$L109)*'input data'!$C$10*$L$97","v":188.04469928745849},null,null,{"$f":"$L109*'input data'!$D$11*$L$97+(1-$L109)*'input data'!$D$10*$L$97","v":372.92289572789417},null,null,{"$f":"$L109*'input data'!$E$11*$L$97+(1-$L109)*'input data'!$E$10*$L$97","v":122.99861037528959},null,null,0.69327516977001047,"share population key",null,"solver"]
[{"$f":"A105","v":6},null,{"$f":"$L110*'input data'!$C$11*$L$97+(1-$L110)*'input data'!$C$10*$L$97","v":189.81101095648745},null,null,{"$f":"$L110*'input data'!$D$11*$L$97+(1-$L110)*'input data'!$D$10*$L$97","v":372.32011870742042},null,null,{"$f":"$L110*'input data'!$E$11*$L$97+(1-$L110)*'input data'!$E$10*$L$97","v":121.8350757267344},null,null,0.68543409505204511,"share population key",null,"solver"]
[]
[2,null,{"$f":"(C102-C107)^2/C102^2","v":2.0547072433649496E-7},null,null,{"$f":"(F102-F107)^2/F102^2","v":1.6427767938064629E-7},null,null,{"$f":"(I102-I107)^2/I102^2","v":1.3708479338316843E-7},null,null,{"$f":"C112+F112+I112","v":5.0683319710030966E-7},"square deviation",null,null,null,{"$f":"'C&C-exp'!Q115","v":"There is an implicit population weighting that is the same for all countries."}]
[1,null,{"$f":"(C103-C108)^2/C103^2","v":1.0821506656951386E-8},null,null,{"$f":"(F103-F108)^2/F103^2","v":9.6583178484754672E-9},null,null,{"$f":"(I103-I108)^2/I103^2","v":8.9290070431075488E-9},null,null,{"$f":"C113+F113+I113","v":2.9408831548534405E-8},"square deviation"]
[{"$f":"A104","v":3},null,{"$f":"(C104-C109)^2/C104^2","v":2.284431808511195E-32},null,null,{"$f":"(F104-F109)^2/F104^2","v":2.3233909099903466E-32},null,null,{"$f":"(I104-I109)^2/I104^2","v":1.3348731240900982E-32},null,null,{"$f":"C114+F114+I114","v":5.9426958425916403E-32},"square deviation"]
[{"$f":"A105","v":6},null,{"$f":"(C105-C110)^2/C105^2","v":5.1783334988230039E-8},null,null,{"$f":"(F105-F110)^2/F105^2","v":4.167270324419097E-8},null,null,{"$f":"(I105-I110)^2/I105^2","v":3.5020113570779291E-8},null,null,{"$f":"C115+F115+I115","v":1.284761518032003E-7},"square deviation"]

{"sheet":"CDC","index":7,"n_rows":48,"n_cols":35,"rows_kept":48,"cut":false,"hidden":false,"merged":[[7,32,7,33],[7,28,7,31],[7,19,7,21],[7,22,7,24],[0,9,0,13],[6,1,6,12],[6,19,6,27],[7,1,7,4],[7,5,7,8],[7,9,7,12],[7,25,7,27],[7,13,7,16],[1,9,1,35],[3,10,3,12]]}
["Common but Differentiated Convergence"]
["CDC","Niklas Höhne, Michel den Elzen, Martin Weiss",null,null,null,null,null,null,null,"Climate Policy, Volume 6, 2006 - Issue 2: Common but differentiated convergence (CDC): a new conceptual approach to long-term climate policy"]
[]
["Percentage threshold (PT):",null,null,null,null,null,0.95,null,null,null,"input values"]
["Parameter a (Ct := C&C exp):",null,null,null,null,null,{"$f":"'C&C-exp'!E5","v":4}]
[]
[null,"business as usual",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CDC"]
[null,"Country A",null,null,null,"Country B",null,null,null,"Country C",null,null,null,"Global",null,null,null,null,null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"over threshold",null,null,null,"Global"]
["change rate (CRi)",null,0,null,null,null,0.03,null,null,null,0.02]
["Year\nt","Popu-lation\nPit","Ei_baut"," o TH","Per capita","Popu-lation\nPit","Ei_baut"," o TH","Per capita","Popu-lation\nPit","Ei_baut"," o TH","Per capita","Popu-lation\nPt","Et","Per capita","thres-hold\nTHt",null,"Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPoTH","EoTHt","EPoTHt-1","Per capita","Et","Ct","differ-ence"]
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[{"$f":"A12+1","v":2020},{"$f":"B$12*(B$43/B$12)^(($A13-2019)/31)","v":1.2},{"$f":"C12*(1+C$9)","v":21},{"$f":"IF(E13>$Q13,1,0)","v":1},{"$f":"C13/B13","v":17.5},{"$f":"F$12*(F$43/F$12)^(($A13-2019)/31)","v":4},{"$f":"G12*(1+G$9)","v":20.085000000000001},{"$f":"IF(I13>$Q13,1,0)","v":0},{"$f":"G13/F13","v":5.0212500000000002},{"$f":"J$12*(J$43/J$12)^(($A13-2019)/31)","v":1.7000000000000004},{"$f":"K12*(1+K$9)","v":1.2522714433313646},{"$f":"IF(M13>$Q13,1,0)","v":0},{"$f":"K13/J13","v":0.73663026078315552},{"$f":"B13+F13+J13","v":6.9},{"$f":"'global path'!C8","v":40.89316275927915},{"$f":"O13/N13","v":5.9265453274317608},{"$f":"P13*$G$4","v":5.6302180610601722},null,{"$f":"S12+1","v":2020},{"$f":"B13","v":1.2},{"$f":"IF(D13=1,((1-$AH13)*(U12/AE13)+$AH13*(T13/$AC13))*AD13,C13)","v":19.555891315947786},{"$f":"IF(T13<>0,U13/T13,U13/B13)","v":16.296576096623156},{"$f":"F13","v":4},{"$f":"IF(H13=1,((1-$AH13)*(X12/AE13)+$AH13*(W13/AC13))*AD13,G13)","v":20.085000000000001},{"$f":"IF(W13<>0,X13/W13,X13/F13)","v":5.0212500000000002},{"$f":"J13","v":1.7000000000000004},{"$f":"IF(L13=1,((1-$AH13)*(AA12/AE13)+$AH13*(Z13/AC13))*AD13,K13)","v":1.2522714433313646},0.73663026078315552,{"$f":"N13-((1-D13)*B13+(1-H13)*F13+(1-L13)*J13)","v":1.2000000000000002},{"$f":"O13-((1-D13)*C13+(1-H13)*G13+(1-L13)*K13)","v":19.555891315947786},{"$f":"U12*D13+X12*H13+AA12*L13","v":21},{"$f":"AD13/AC13","v":16.296576096623152},{"$f":"U13+X13+AA13","v":40.89316275927915},2.0838193670452695E-2,0]
[{"$f":"A13+1","v":2021},{"$f":"B$12*(B$43/B$12)^(($A14-2019)/31)","v":1.2},{"$f":"C13*(1+$C$9)","v":21},1,17.5,{"$f":"F$12*(F$43/F$12)^(($A14-2019)/31)","v":4},{"$f":"G13*(1+G$9)","v":20.687550000000002},0,5.1718875000000004,{"$f":"J$12*(J$43/J$12)^(($A14-2019)/31)","v":1.7000000000000004},{"$f":"K13*(1+K$9)","v":1.2773168721979919},0,0.75136286599881863,{"$f":"B14+F14+J14","v":6.9},{"$f":"'global path'!C9","v":39.941126545569553},5.788569064575297,{"$f":"P14*$G$4","v":5.4991406113465322},null,{"$f":"S13+1","v":2021},1.2,17.976259673371558,14.980216394476299,4,20.687550000000002,5.1718875000000004,1.7000000000000004,1.2773168721979919,0.75136286599881863,1.2000000000000002,17.976259673371558,{"$f":"U13*D14+X13*H14+AA13*L14","v":19.555891315947786},14.980216394476296,39.941126545569553,2.3708171911730948E-2,0]
[2022,1.2,21,1,17.5,4,21.308176500000002,0,5.3270441250000005,1.7000000000000004,1.3028632096419519,0,0.76639012331879508,6.9,{"$f":"'global path'!C10","v":38.88020547525452},5.6348123877180463,5.3530717683321436,null,2022,1.2,16.269165765612566,13.557638138010473,4,21.308176500000002,5.3270441250000005,1.7000000000000004,1.3028632096419519,0.76639012331879508,1.2000000000000002,16.269165765612566,17.976259673371558,13.55763813801047,38.88020547525452,2.6973423142389763E-2,0]
[2023,1.2,21,1,17.5,4,21.947421795000004,1,5.486855448750001,1.7000000000000004,1.3289204738347911,0,0.78171792578517107,6.9,{"$f":"'global path'!C11","v":37.719896396656317},5.4666516516893209,5.193319069104855,null,2023,1.2,15.529733548917141,12.941444624097619,4,20.861242373904378,5.2153105934760946,1.7000000000000004,1.3289204738347911,0.78171792578517107,5.2,36.390975922821525,37.577342265612572,6.9982646005426004,37.71989639665631,3.0688387056043043E-2,0]
[2024,1.2,21,1,17.5,4,22.605844448850004,1,5.6514611122125009,1.7000000000000004,1.3554988833114869,0,0.79735228430087446,6.9,{"$f":"'global path'!C12","v":36.470453355724658},5.2855729501050224,5.0212943025997712,null,2024,1.2,14.744919328271566,12.287432773559638,4,20.37003514414161,5.0925087860354026,1.7000000000000004,1.3554988833114869,0.79735228430087446,5.2,35.114954472413174,36.390975922821518,6.7528758600794561,36.470453355724658,3.4915001152429612E-2,0]
[2025,1.2,21,1,17.5,4,23.284019782315504,1,5.8210049455788759,1.7000000000000004,1.3826088609777167,0,0.81329932998689203,6.9,{"$f":"'global path'!C13","v":35.142735391074559},5.0931500566774721,4.8384925538435981,null,2025,1.2,13.922376399502946,11.601980332919123,4,19.837750130593896,4.9594375326484741,1.7000000000000004,1.3826088609777167,0.81329932998689203,5.2,33.760126530096841,35.114954472413174,6.4923320250186229,35.142735391074559,3.9723733386441029E-2,0]
[2026,1.2,21,1,17.5,4,23.982540375784968,1,5.9956350939462419,1.7000000000000004,1.4102610381972711,0,0.82956531658662991,6.9,{"$f":"'global path'!C14","v":33.748047947428226},4.8910214416562647,4.6464703695734517,null,2026,1.2,13.070376064895578,10.891980054079649,4,19.267410844335377,4.8168527110838442,1.7000000000000004,1.4102610381972711,0.82956531658662991,5.2,32.337786909230957,33.760126530096841,6.2188051748521067,33.748047947428226,4.5194757040620724E-2,0]
[2027,1.2,21,1,17.5,4,24.702016587058516,1,6.175504146764629,1.7000000000000004,1.4384662589612165,0,0.84615662291836247,6.9,{"$f":"'global path'!C15","v":32.297981178024223},4.6808668373948148,4.4468234955250736,null,2027,1.2,12.197715876714794,10.164763230595662,4,18.661799042348211,4.6654497605870526,1.7000000000000004,1.4384662589612165,0.84615662291836247,5.2,30.859514919063006,32.337786909230957,5.9345220998198087,32.297981178024216,5.1419287409121751E-2,0]
[2028,1.2,21,1,17.5,4,25.443077084670271,1,6.3607692711675679,1.7000000000000004,1.4672355841404408,0,0.86307975537672965,6.9,{"$f":"'global path'!C16","v":30.80424840186744},4.4643838263575999,4.2411646350397199,null,2028,1.2,11.313605496760797,9.4280045806339974,4,18.023407320966207,4.5058518302415518,1.7000000000000004,1.4672355841404408,0.86307975537672965,5.2,29.337012817727,30.859514919063002,5.6417332341782691,30.804248401867444,5.8501102578901121E-2,0]
[2029,1.2,21,1,17.5,4,26.206369397210381,1,6.5515923493025952,1.7000000000000004,1.4965802958232497,0,0.88034135048426432,6.9,{"$f":"'global path'!C17","v":29.278527891388606},4.2432649117954497,4.0311016662056769,null,2029,1.2,10.427526476168079,8.6896053968067335,4,17.354421119397273,4.3386052798493182,1.7000000000000004,1.4965802958232497,0.88034135048426432,5.2,27.781947595565356,29.337012817727004,5.3426822299164147,29.278527891388602,6.6558273663278794E-2,0]
[2030,1.2,21,1,17.5,4,26.992560479126691,1,6.7481401197816728,1.7000000000000004,1.5265119017397146,0,0.89794817749394962,6.9,{"$f":"'global path'!C18","v":27.732310994821948},4.0191755064959338,3.818216731171137,null,2030,1.2,9.5490624127509847,7.9575520106258208,4,16.656736680331246,4.1641841700828115,1.7000000000000004,1.5265119017397146,0.89794817749394962,5.2,26.205799093082234,27.781947595565352,5.0395767486696599,27.732310994821944,7.5725133335070319E-2,0]
[2031,1.2,21,1,17.5,4,27.802337293500493,1,6.9505843233751232,1.7000000000000004,1.5570421397745089,0,0.91590714104382853,6.9,{"$f":"'global path'!C19","v":26.17675935260209},3.7937332395075489,3.6040465775321713,null,2031,1.2,8.6876967697279337,7.2397473081066117,4,15.932020443099645,3.9830051107749114,1.7000000000000004,1.5570421397745089,0.91590714104382853,5.2,24.619717212827581,26.205799093082231,4.7345610024668421,26.17675935260209,8.6154515479536453E-2,0]
[2032,1.2,21,1,17.5,4,28.636407412305509,1,7.1591018530763773,1.7000000000000004,1.5881829825699991,0,0.93422528386470516,6.9,{"$f":"'global path'!C20","v":24.622573657761826},3.5684889359075109,3.3900644891121354,null,2032,1.2,7.8525774322875748,6.5438145269063126,4,15.18181324290425,3.7954533107260624,1.7000000000000004,1.5881829825699991,0.93422528386470516,5.2,23.034390675191826,24.619717212827581,4.4296905144599661,24.622573657761823,9.8020303307621723E-2,0]
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["∑",null,{"$f":"SUM(C9:C39)","v":253.28991557053203},null,null,{"$f":"SUM(F9:F39)","v":333.27303582261447},null,null,{"$f":"SUM(I9:I39)","v":70.200694964696666},null,null,{"$f":"SUM(L9:L39)","v":656.76364635784307}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C90","v":656.76364635784296}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L40-L42","v":0}]

{"sheet":"GQWF","index":10,"n_rows":56,"n_cols":25,"rows_kept":56,"cut":false,"hidden":false,"merged":[[8,21,8,23],[2,6,2,7],[16,1,16,3],[16,4,16,6],[16,7,16,9],[16,10,16,13],[4,0,4,8]]}
["General Quadratic Weigthing Formula",null,null,null,null,null,null,"convergence period: 2020 - 2050"]
["GQWF",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Input value"]
["Sargl/Wolfsteiner/Wittmann",null,null,null,null,null,"input value",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C2020","weighting of per capita in 2020"]
[]
["Determination of Ct",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"convex quadratic",null,null,{"$f":"(1/(2050-2019))^2","v":1.0405827263267429E-3}]
[null,null,null,null,null,"a","b","c","Ct",null,null,null,null,null,null,null,null,null,null,null,null,"conkave quadratic",null,null,{"$f":"-(1/(2050-2019))^2+2/(2050-2019)","v":6.555671175858481E-2}]
["Constraint 1 in 2019:",null,null,"t=2019",null,0,0,1,0,null,null,null,null,null,null,null,null,null,null,null,null,"linear",null,null,{"$f":"1/(2050-2019)","v":3.2258064516129031E-2}]
["Constraint 2 in 2050:",null,null,"t=2050",null,{"$f":"31^2","v":961},31,1,1,null,null,null,null,null,null,null,null,null,null,null,null,"other value",null,null,0.04]
["Constraint 3 in 2020:",null,null,"t=2020",null,1,1,1,{"$f":"Y9","v":0.04},null,null,null,null,null,null,null,null,null,null,null,null,"other value",null,null,{"$f":"VLOOKUP(V9,V5:Y8,4,FALSE)","v":0.04}]
[]
["Remodeled constraint 1",null,null,null,null,{"$f":"MMULT(MINVERSE(F7:H9),F7:I9)","v":1},6.9388939039072284E-18,0,-2.58064516129032E-4]
["Remodeled constraint 2",null,null,null,null,-2.2204460492503131E-16,0.99999999999999989,0,4.0258064516129025E-2]
["Remodeled constraint 3",null,null,null,null,0,0,1,0]
[]
["parameter of the parabola:",null,null,null,null,{"$f":"I11","v":-2.58064516129032E-4},{"$f":"I12","v":4.0258064516129025E-2},{"$f":"I13","v":0}]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
[]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita","Ct"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t"]
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["∑",null,{"$f":"SUM(C22:C52)","v":244.2460906220374},null,null,{"$f":"SUM(F22:F52)","v":336.35935968704138},null,null,{"$f":"SUM(I22:I52)","v":76.158196048764268},null,null,{"$f":"SUM(L22:L52)","v":656.76364635784296}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C90","v":656.76364635784296}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L53-L55","v":0}]

{"sheet":"SPF-eq","index":11,"n_rows":108,"n_cols":23,"rows_kept":108,"cut":false,"hidden":false,"merged":[[1,1,1,26],[10,13,10,16],[6,15,6,16],[4,18,6,30],[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13],[5,10,7,13]]}
["Smooth Pathways Formula - equity (spk = 100%)"]
["SPF-eq","Smooth Pathways Formula; based on: Raupach et al. (2014) / Sharing a quota on cumulative carbon emissions / nature climate change DOI: 10.1038/NCLIMATE2384"]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global",null,null,null,null,null,null,null,"Description"]
[null,"RBA:",{"$f":"W8*'global path'!C89/K11*B11+(1-W8)*'global path'!C89*C11/L11","v":118.95064441576383},"Gt","RBB:",{"$f":"W8*'global path'!C89/K11*E11+(1-W8)*'global path'!C89*F11/L11","v":396.50214805254615},"Gt","RBC:",{"$f":"W8*'global path'!C89/K11*H11+(1-W8)*'global path'!C89*I11/L11","v":168.51341292233215},"Gt","RB:",{"$f":"C5+F5+I5","v":683.96620539064213},"Gt",null,null,null,null,null,"Raupach et al. have developed a formula to convert a budget of a country or global into a smooth emission pathway."]
[null,"TA",{"$f":"C5/C11","v":5.6643164007506588},null,"TB",{"$f":"F5/F11","v":20.33344348987416},null,"TC",{"$f":"I5/I11","v":137.25752678949854},null,"Global path ist different to the path in sheet \"global path\"."]
[null,"rA",0,null,"rB",0.03,null,"rC",0.02,null,null,null,null,null,null,"input values"]
[null,"mA",{"$f":"(1+SQRT(1+C7*C6))/C6","v":0.35308762055293236},null,"mB",{"$f":"(1+SQRT(1+F7*F6))/F6","v":0.11158262777315084},null,"mC",{"$f":"(1+SQRT(1+I7*I6))/I6","v":2.1384904787472729E-2},null,null,null,null,null,null,null,null,null,"share population key:",null,null,null,1]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita",null,null,null,null,null,"Limitations"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t",null,"A","B","C",null,"-","The resulting global pathway ist different to the pathway in sheet \"global path\". So this model is comparable with the other models to a limited extent only."]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C11/B11","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F11/E11","v":4.875},{"$f":"K11-E11-B11","v":1.7000000000000004},{"$f":"'global path'!$C$7-C11-F11","v":1.2277171013052595},{"$f":"I11/H11","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I11+F11+C11","v":41.727717101305259},{"$f":"L11/K11","v":6.047495232073226},"annual change rates",null,null,null,null,"-","The per capita emissions converge far into the future; as you can see on the remaining budgets as of 2051. So this model is comparable with the other models to a limited extent only."]
[{"$f":"A11+1","v":2020},{"$f":"B$11*(B$42/B$11)^(($A12-2019)/31)","v":1.2},{"$f":"-C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A11-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A11-$A$11)+2*C$8+C$7)","v":20.633128463331417},{"$f":"C12/B12","v":17.194273719442847},{"$f":"E$11*(E$42/E$11)^(($A12-2019)/31)","v":4},{"$f":"-F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A11-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A11-$A$11)+2*F$8+F$7)","v":19.733344496566019},{"$f":"F12/E12","v":4.9333361241415048},{"$f":"H$11*(H$42/H$11)^(($A12-2019)/31)","v":1.7000000000000004},{"$f":"-I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A11-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A11-$A$11)+2*I$8+I$7)","v":1.2397280559859212},{"$f":"I12/H12","v":0.72925179763877701},{"$f":"B12+E12+H12","v":6.9},{"$f":"I12+F12+C12","v":41.606201015883357},{"$f":"L12/K12","v":6.029884205200486},{"$f":"L12/L11-1","v":-2.9121191827218285E-3},{"$f":"C12/C11-1","v":-1.74700731746944E-2},{"$f":"F12/F11-1","v":1.1966384439282995E-2},{"$f":"I12/I11-1","v":9.7831615018575402E-3}]
[{"$f":"A12+1","v":2021},1.2,{"$f":"-C$11*EXP(-C$8*($A13-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A13-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)","v":18.883831124220123},15.736525936850104,4,{"$f":"-F$11*EXP(-F$8*($A13-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A13-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)","v":19.98642632965749},4.9966065824143726,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A13-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A13-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)","v":1.26270399098388},0.74276705351992922,{"$f":"B13+E13+H13","v":6.9},{"$f":"I13+F13+C13","v":40.132961444861493},5.8163712238929701,{"$f":"L13/L12-1","v":-3.5409134577306101E-2},{"$f":"C13/C12-1","v":-8.4781003628223051E-2},{"$f":"F13/F12-1","v":1.2825085637941935E-2},{"$f":"I13/I12-1","v":1.8533044313243874E-2},null,"Simplification"]
[2022,1.2,16.349342124287709,13.624451770239759,4,19.966085365526965,4.9915213413817412,1.7000000000000004,1.2841527113546647,0.75538394785568497,6.9,37.599580201169339,5.4492145219085995,-6.312470230169176E-2,-0.13421476729272985,-1.0177389291622374E-3,1.698634083992423E-2,null,null,"We assumed that the emission power at the end of the base year are the emissions in the base year divided by one year."]
[2023,1.2,13.65163342114294,11.376361184285784,4,19.727237665418045,4.9318094163545112,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A15-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A15-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A14-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A14-$A$11)+2*I$8+I$7)","v":1.3041285570104719},0.76713444530027741,6.9,34.682999643571456,5.0265216874741236,-7.7569497903787199E-2,-0.16500411347666388,-1.1962670485287541E-2,1.5555662094685285E-2]
[2024,1.2,11.112110172479731,9.2600918103997767,4,19.316250965259087,4.8290627413147718,1.7000000000000004,1.3226842520956836,0.77804956005628434,6.9,31.751045389834502,4.6016007811354349,-8.4535774986821188E-2,-0.18602339883593177,-2.083346422491883E-2,1.4228424786393745E-2,null,"Input values"]
[2025,1.2,8.8753959634722399,7.3961633028935339,4,18.77213759704523,4.6930343992613075,1.7000000000000004,1.3398709490343492,0.78815938178491107,6.9,28.987404509551819,4.2010731173263505,-8.7040941372201197E-2,-0.2012861800584862,-2.8168683933153638E-2,1.2993801741749467E-2,null,"-","reduction rate at the beginnging of 2020 for each country"]
[2026,1.2,6.9860689389819903,5.8217241158183253,4,18.127590800832422,4.5318977002081056,1.7000000000000004,1.3557382714355981,0.79749310084446934,6.9,26.469398011250011,3.8361446393115957,-8.686553835725741E-2,-0.21287242082111069,-3.4335290420748898E-2,1.1842425878913598E-2,null,"-","Share that is distributed over the population key"]
[2027,1.2,5.4353869662107996,4.5294891385089997,4,17.409884199471776,4.352471049867944,1.7000000000000004,1.3703343558887013,0.80607903287570648,6.9,24.215605521571277,3.5095080466045325,-8.5147100388185182E-2,-0.22196774556839061,-3.9591946290385649E-2,1.076615211109111E-2]
[2028,1.2,4.189066502771448,3.49088875230954,4,16.641651778874007,4.1604129447185016,1.7000000000000004,1.3837058926726229,0.81394464274860157,6.9,22.214424174318076,3.2194817643939238,-8.2640153081059542E-2,-0.22929746698572329,-4.4126222311178687E-2,9.757864368254765E-3]
[2029,1.2,3.2032525887308232,2.6693771572756861,4,15.841563579804244,3.9603908949510611,1.7000000000000004,1.3958981654093634,0.82111656788786058,6.9,20.440714333944431,2.962422367238323,-7.9844961384334057E-2,-0.23533021339919513,-4.8077451066813381E-2,8.8113180707722893E-3]
[2030,1.2,2.4332475295649916,2.027706274637493,4,15.024910428331424,3.756227607082856,1.7000000000000004,1.4069550896863063,0.82762064099194466,6.9,18.865113047582721,2.7340743547221331,-7.7081517828622159E-2,-0.24038224830434596,-5.155129715313822E-2,7.9210106803888625E-3]
[2031,1.2,1.8378933269474773,1.5315777724562312,4,14.204109380395209,3.5510273450988024,1.7000000000000004,1.4169192506745389,0.83348191216149325,6.9,17.458921958017225,2.5302785446401774,-7.4539234724897541E-2,-0.24467473834195153,-5.4629347166588627E-2,7.0820746598629913E-3]
[2032,1.2,1.3814212797031327,1.1511843997526106,4,13.389140104518759,3.3472850261296898,1.7000000000000004,1.4258319397667663,0.83872467045103882,6.9,16.196393323988659,2.3473033802882113,-7.2314237789968816E-2,-0.24836699744837232,-5.7375598430781327E-2,6.2901884408617104E-3]
[2033,1.2,1.0338878777282527,0.8615732314402107,4,12.587921151585022,3.1469802878962554,1.7000000000000004,1.4337331902616484,0.843372464859793,6.9,15.055542219574923,2.1819626405181047,-7.043858972750483E-2,-0.25157669646551617,-5.9840956676772028E-2,5.5415019642319763E-3]
[2034,1.2,0.77087441631554388,0.64239534692961997,4,11.806633940780358,2.9516584851950896,1.7000000000000004,1.4406618121162182,0.8474481247742458,6.9,14.018170169212119,2.0316188651032054,-6.8903001647727558E-2,-0.2543926349060448,-6.2066420769269492E-2,4.8325740811687723E-3]
[2035,1.2,0.57284981893722375,0.47737484911435313,4,11.050001307689627,2.7625003269224067,1.7000000000000004,1.4466554257915618,0.85097377987738909,6.9,13.069506552418412,1.8941313844084655,-6.7673855099665059E-2,-0.25688308392019876,-6.4085380887206722E-2,4.1603196704016465E-3]
[2036,1.2,0.42442363213675027,0.3536863601139586,4,10.321526597741197,2.5803816494352994,1.7000000000000004,1.4517504952135027,0.8539708795373544,6.9,12.197700725091451,1.7677827137813695,-6.6705336106636759E-2,-0.25910139428138479,-6.5925305315709615E-2,3.5219647547743982E-3]
[2037,1.2,0.31361092492831188,0.26134243744025992,4,9.6236985312820309,2.4059246328205077,1.7000000000000004,1.4559823598716832,0.85646021168922526,6.9,11.393291816082026,1.6512017124756559,-6.5947585298162248E-2,-0.26108986120908151,-6.7608997550021477E-2,2.9150082415216882E-3]
[2038,1.2,0.23116811756569766,0.19264009797141474,4,8.9581664027847978,2.2395416006961995,1.7000000000000004,1.4593852660772484,0.85846192122191056,6.9,10.648719786427744,1.5432927226706874,-6.5351791358779443E-2,-0.26288244703675345,-6.9155546210628582E-2,2.3371891716221782E-3]
[2039,1.2,0.17002259308263074,0.14168549423552562,4,8.3258895948105618,2.0814723987026404,1.7000000000000004,1.461992397401616,0.85999552788330336,6.9,9.9579045852948092,1.4431745775789577,-6.4873075354411003E-2,-0.26450673703171657,-7.058105191902686E-2,1.7864585760656304E-3]
[2040,1.2,0.12479907091446757,0.10399922576205631,4,7.7272648774927006,1.9318162193731752,1.7000000000000004,1.4638359043167384,0.86107994371572827,6.9,9.3158998527239074,1.3501304134382475,-6.4471870268668074E-2,-0.26598536905142134,-7.1899189930524354E-2,1.2609551994926527E-3]
[2041,1.2,9.1435649826009935E-2,7.6196374855008284E-2,4,7.1622345177297433,1.7905586294324358,1.7000000000000004,1.4649469330565807,0.86173349003328259,6.9,8.7186171006123345,1.2635676957409179,-6.4114338019309103E-2,-0.26733709509202697,-7.3121650250236425E-2,7.5898448491806825E-4]
[2042,1.2,6.6878084200854365E-2,5.5731736834045309E-2,4,6.6303778313131971,1.6575944578282993,1.7000000000000004,1.4653556537197403,0.86197391395278822,6.9,8.1626115692337926,1.1829871839469264,-6.3772215818434286E-2,-0.2685775807563614,-7.4258485267406749E-2,2.7900032003658204E-4]
[2043,1.2,4.8839726317282672E-2,4.0699771931068898E-2,4,6.1309884690987104,1.5327471172746776,1.7000000000000004,1.4650912876327595,0.86181840448985836,6.9,7.6449194830487528,1.1079593453693843,-6.3422359595831423E-2,-0.26972001514572774,-7.5318386812894267E-2,-1.8041086906761539E-4]
[2044,1.2,3.5615121017186641E-2,2.9679267514322202E-2,4,5.6631394290987558,1.4157848572746889,1.7000000000000004,1.4641821339920682,0.86128360823062811,6.9,7.1629366841080104,1.0381067658127552,-6.3046157648808943E-2,-0.27077558162762072,-7.6308908809402998E-2,-6.2054402231848105E-4]
[2045,1.2,2.5936575647633783E-2,2.1613813039694819E-2,4,5.2257375247924571,1.3064343811981143,1.7000000000000004,1.4626555958038239,0.86038564459048439,6.9,6.7143296962439152,0.9730912603252051,-6.2628919903674918E-2,-0.27175382514865865,-7.7236647584343121E-2,-1.0425876349701158E-3]
[2046,1.2,1.8864632634453919E-2,1.5720527195378267E-2,4,4.8175688113977202,1.20439220284943,1.7000000000000004,1.4605382051382776,0.8591401206695749,6.9,6.2969716491704517,0.9126045868362973,-6.2159301963819136E-2,-0.27266294167962157,-7.8107388949074208E-2,-1.4476344750061765E-3]
[2047,1.2,1.3704966804251456E-2,1.1420805670209547E-2,4,4.4373362722729368,1.1093340680682342,1.7000000000000004,1.4578556477170537,0.85756214571591372,6.9,5.908896886794242,0.85636186765133937,-6.1628793013119854E-2,-0.27351000839417206,-7.8926228977820534E-2,-1.8366910305984696E-3]
[2048,1.2,9.945678398719137E-3,8.2880653322659481E-3,4,4.0836908934418972,1.0209227233604743,1.7000000000000004,1.4546327868498992,0.85566634520582285,6.9,5.5482693586905159,0.80409700850587185,-6.1031277920873928E-2,-0.27430116827179318,-7.9697673814090209E-2,-2.2106858605660529E-3]
[2049,1.2,7.2102013154229372E-3,6.008501096185781E-3,4,3.7552571023224388,0.9388142755806097,1.7000000000000004,1.450893686737345,0.85346687455137915,6.9,5.2133609903752065,0.75555956382249367,-6.0362672873970458E-2,-0.27504177931678253,-8.0425722634124619E-2,-2.570476993476456E-3]
[{"$f":"A41+1","v":2050},{"$f":"RF!B40","v":1.2},5.2220853804066329E-3,4.351737817005528E-3,{"$f":"RF!E40","v":4},3.4506534143351359,0.86266335358378399,{"$f":"K42-E42-B42","v":1.7000000000000004},1.4466616351549391,0.85097743244408164,{"$f":"RF!K40","v":6.9},4.9025371348704816,0.71051262824209871,-5.9620627859563347E-2,-0.27573653606087767,-8.1113936992202373E-2,-2.9168584997586455E-3]
["∑",null,{"$f":"SUM(C12:C42)","v":118.93706757499594},null,null,{"$f":"SUM(F12:F42)","v":359.89841936167005},null,null,{"$f":"SUM(I12:I42)","v":43.715461898851572},null,null,{"$f":"SUM(L12:L42)","v":522.5509488355176}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A42-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A42-$A$11)+2*C$8+C$7)","v":1.3576840767910424E-2},null,null,{"$f":"F$11*EXP(-F$8*($A42-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A42-$A$11)+2*F$8+F$7)","v":36.603728690876181},null,null,{"$f":"I$11*EXP(-I$8*($A42-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A42-$A$11)+2*I$8+I$7)","v":124.79795102348058},null,null,161.41525655512467]
["∑",null,{"$f":"SUM(C43:C44)","v":118.95064441576385},null,null,{"$f":"SUM(F43:F44)","v":396.5021480525462},null,null,{"$f":"SUM(I43:I44)","v":168.51341292233215},null,null,{"$f":"SUM(L43:L44)","v":683.96620539064224}]
[]
[null,null,null,null,null,"global path 2020 - 2100 sheet \"global path\":",null,null,null,null,null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L45-L47","v":0}]
[]
[]
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[2095,1.2,1.5440462735841471E-9,1.2867052279867893E-9,4,5.0037737762467727E-2,1.2509434440616932E-2,1.7000000000000004,1.0075853388879921,0.59269725816940699,6.9,1.057623078194506,0.15327870698471099,-1.5526025594554627E-2,-0.28839652151962858,-9.4615296224842438E-2,-1.1236664013052122E-2]
[2096,1.2,1.0985694968083121E-9,9.1547458067359352E-10,4,4.5296754893722091E-2,1.1324188723430523E-2,1.7000000000000004,0.99616313695281633,0.5859783158545977,6.9,1.041459892945108,0.15093621636885624,-1.5282557257535023E-2,-0.28851258177759365,-9.4748145714568022E-2,-1.1336212918482635E-2]
[2097,1.2,7.8149409029286265E-10,6.5124507524405228E-10,4,4.0999097752564495E-2,1.0249774438141124E-2,1.7000000000000004,0.98477322288403002,0.57927836640237051,6.9,1.0257723214180885,0.14866265527798384,-1.5063058724860912E-2,-0.28862571501998979,-9.4877815226300677E-2,-1.1433783931843911E-2]
[2098,1.2,5.5584858872746599E-10,4.6320715727288836E-10,4,3.7104002348991194E-2,9.2760005872477985E-3,1.7000000000000004,0.97341934360726157,0.57259961388662428,6.9,1.0105233465121013,0.14645265891479728,-1.4865847505912577E-2,-0.2887360305960045,-9.5004417586961765E-2,-1.1529435420184586E-2]
[2099,1.2,3.9529526325330057E-10,3.2941271937775051E-10,4,3.3574370574372792E-2,8.3935926435931979E-3,1.7000000000000004,0.96210507304051873,0.56594416061206976,6.9,0.99567944401018671,0.14430136869712851,-1.4689321679849821E-2,-0.28884363247503919,-9.512806034830279E-2,-1.1623223476138089E-2]
[2100,1.2,2.8107524261236595E-10,2.3422936884363833E-10,4,3.0376450518908693E-2,7.5941126297271733E-3,1.7000000000000004,0.95083381773758191,0.55931401043387163,6.9,0.98121026853756588,0.14220438674457475,-1.4531961626469858E-2,-0.28894861957337392,-9.5248846091698924E-2,-1.1715202028107496E-2]
["∑",null,{"$f":"SUM(C51:C100)","v":1.3576840077360335E-2},null,null,{"$f":"SUM(F51:F100)","v":36.318564962148869},null,null,{"$f":"SUM(I51:I100)","v":60.943941575908291},null,null,{"$f":"SUM(L51:L100)","v":97.276083378134544}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A100-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A100-$A$11)+2*C$8+C$7)","v":6.9055009037044834E-10},null,null,{"$f":"F$11*EXP(-F$8*($A100-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A100-$A$11)+2*F$8+F$7)","v":0.28516372872732182},null,null,{"$f":"I$11*EXP(-I$8*($A100-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A100-$A$11)+2*I$8+I$7)","v":63.854009447572288},null,null,{"$f":"I102+F102+C102","v":64.139173176990155}]
["∑",null,{"$f":"SUM(C101:C102)","v":1.3576840767910426E-2},null,null,{"$f":"SUM(F101:F102)","v":36.603728690876189},null,null,{"$f":"SUM(I101:I102)","v":124.79795102348058},null,null,{"$f":"SUM(L101:L102)","v":161.4152565551247}]
[]
["∑",null,{"$f":"C103+C43","v":118.95064441576385},null,null,{"$f":"F103+F43","v":396.50214805254626},null,null,{"$f":"I103+I43","v":168.51341292233215},null,null,{"$f":"SUM(C105:I105)","v":683.96620539064224}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L105-L107","v":0}]

{"sheet":"SPF-in","index":12,"n_rows":108,"n_cols":23,"rows_kept":108,"cut":false,"hidden":false,"merged":[[4,18,6,30],[5,10,7,13],[10,13,10,16],[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13]]}
["Smooth Pathways Formula - inertia (spk = 0%)"]
["SPF-in",{"$f":"'SPF-eq'!B2","v":"Smooth Pathways Formula; based on: Raupach et al. (2014) / Sharing a quota on cumulative carbon emissions / nature climate change DOI: 10.1038/NCLIMATE2384"}]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global",null,null,null,null,null,null,null,"Description"]
[null,"RBA:",{"$f":"W8*'global path'!C89/K11*B11+(1-W8)*'global path'!C89*C11/L11","v":344.21462066407162},"Gt","RBB:",{"$f":"W8*'global path'!C89/K11*E11+(1-W8)*'global path'!C89*F11/L11","v":319.62786204520938},"Gt","RBC:",{"$f":"W8*'global path'!C89/K11*H11+(1-W8)*'global path'!C89*I11/L11","v":20.123722681361119},"Gt","RB:",{"$f":"C5+F5+I5","v":683.96620539064213},"Gt",null,null,null,null,null,"Raupach et al. have developed a formula to convert a budget of a country or global into a smooth emission pathway."]
[null,"TA",{"$f":"C5/C11","v":16.391172412574839},null,"TB",{"$f":"F5/F11","v":16.391172412574839},null,"TC",{"$f":"I5/I11","v":16.391172412574839},null,"Global path ist different to the path in sheet \"global path\"."]
[null,"rA",{"$f":"'SPF-eq'!C7","v":0},null,"rB",{"$f":"'SPF-eq'!F7","v":0.03},null,"rC",{"$f":"'SPF-eq'!I7","v":0.02}]
[null,"mA",{"$f":"(1+SQRT(1+C7*C6))/C6","v":0.12201689724559649},null,"mB",{"$f":"(1+SQRT(1+F7*F6))/F6","v":0.13552210013743388},null,"mC",{"$f":"(1+SQRT(1+I7*I6))/I6","v":0.1313092293852946},null,null,null,null,null,null,null,null,null,"share population key:",null,null,null,0]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita",null,null,null,null,null,"Limitations"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t",null,"A","B","C",null,"-","The resulting global pathway ist different to the pathway in sheet \"global path\". So this model is comparable with the other models to a limited extent only."]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C11/B11","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F11/E11","v":4.875},{"$f":"K11-E11-B11","v":1.7000000000000004},{"$f":"'global path'!$C$7-C11-F11","v":1.2277171013052595},{"$f":"I11/H11","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I11+F11+C11","v":41.727717101305259},{"$f":"L11/K11","v":6.047495232073226},"annual change rates",null,null,null,null,"-","The per capita emissions converge far into the future; as you can see on the remaining budgets as of 2051. So this model is comparable with the other models to a limited extent only."]
[{"$f":"A11+1","v":2020},{"$f":"B$11*(B$42/B$11)^(($A12-2019)/31)","v":1.2},{"$f":"-C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A11-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A11-$A$11)+2*C$8+C$7)","v":20.950957341623223},{"$f":"C12/B12","v":17.459131118019354},{"$f":"E$11*(E$42/E$11)^(($A12-2019)/31)","v":4},{"$f":"-F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A11-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A11-$A$11)+2*F$8+F$7)","v":19.711563813975829},{"$f":"F12/E12","v":4.9278909534939572},{"$f":"H$11*(H$42/H$11)^(($A12-2019)/31)","v":1.7000000000000004},{"$f":"-I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A11-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A11-$A$11)+2*I$8+I$7)","v":1.2356653493811827},{"$f":"I12/H12","v":0.72686197022422494},{"$f":"B12+E12+H12","v":6.9},{"$f":"I12+F12+C12","v":41.898186504980231},{"$f":"L12/K12","v":6.0722009427507579},{"$f":"L12/L11-1","v":4.0852798934845058E-3},{"$f":"C12/C11-1","v":-2.3353646846084875E-3},{"$f":"F12/F11-1","v":1.0849426357734782E-2},{"$f":"I12/I11-1","v":6.4740061594588116E-3}]
[{"$f":"A12+1","v":2021},1.2,{"$f":"-C$11*EXP(-C$8*($A13-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A13-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)","v":20.67950971092813},17.232924759106776,4,{"$f":"-F$11*EXP(-F$8*($A13-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A13-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)","v":19.849273463877751},4.9623183659694377,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A13-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A13-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)","v":1.2362760275915718},0.72722119270092445,{"$f":"B13+E13+H13","v":6.9},{"$f":"I13+F13+C13","v":41.765059202397453},6.0529071307822395,{"$f":"L13/L12-1","v":-3.1774001141303687E-3},{"$f":"C13/C12-1","v":-1.2956335420329812E-2},{"$f":"F13/F12-1","v":6.9862366680559784E-3},{"$f":"I13/I12-1","v":4.9421003081051573E-4},null,"Simplification"]
[2022,1.2,20.193988698158591,16.82832391513216,4,19.635448358799124,4.908862089699781,1.7000000000000004,1.2180257831567864,0.7164857547981095,6.9,41.047462840114505,5.9489076579876095,-1.7181739377056915E-2,-2.3478361893317201E-2,-1.077243988137655E-2,-1.4762273171582296E-2,null,null,"We assumed that the emission power at the end of the base year are the emissions in the base year divided by one year."]
[2023,1.2,19.547155631688383,16.28929635974032,4,19.156983585694576,4.789245896423644,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A15-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A15-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A14-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A14-$A$11)+2*I$8+I$7)","v":1.1855471721172659},0.6973806894807445,6.9,39.889686389500227,5.781113969492786,-2.8205798129934956E-2,-3.2030971005207576E-2,-2.4367397390757106E-2,-2.6664961849448665E-2]
[2024,1.2,18.782475367855142,15.652062806545953,4,18.484394765794463,4.6210986914486156,1.7000000000000004,1.1426182414787203,0.67212837734042352,6.9,38.409488375128326,5.5665925181345397,-3.7107286327563549E-2,-3.9119771604703368E-2,-3.5109327984305772E-2,-3.6210225664727425E-2,null,"Input values"]
[2025,1.2,17.935555848468368,14.946296540390307,4,17.674574124860555,4.4186435312151389,1.7000000000000004,1.0923026829132656,0.64253098994897961,6.9,36.702432656242188,5.319193138585824,-4.4443594307065126E-2,-4.5090942636678011E-2,-4.3811044461812054E-2,-4.4035318830844772E-2,null,"-","reduction rate at the beginnging of 2020 for each country"]
[2026,1.2,17.035379604947138,14.196149670789282,4,16.773111058378674,4.1932777645946686,1.7000000000000004,1.0370684327733741,0.61004025457257283,6.9,34.845559096099187,5.0500810284201716,-5.0592656283430126E-2,-5.0189481225255794E-2,-5.1003382605632863E-2,-5.0566798932121015E-2,null,"-","Share that is distributed over the population key"]
[2027,1.2,16.105356011848102,13.421130009873419,4,15.816243312701005,3.9540608281752512,1.7000000000000004,0.97888790070096121,0.57581641217703583,6.9,32.900487225250068,4.7681865543840676,-5.5819792286439851E-2,-5.4593652426092931E-2,-5.7047720148474479E-2,-5.6100957500773596E-2]
[2028,1.2,15.164219220719673,12.636849350599729,4,14.832495138325783,3.7081237845814456,1.7000000000000004,0.91932255230190663,0.54077797194229793,6.9,30.916036911347362,4.4805850596155592,-6.0316745472988154E-2,-5.8436261231112785E-2,-6.219859892931956E-2,-6.085002006501572E-2]
[2029,1.2,14.226793342847856,11.85566111903988,4,13.844050419758247,3.4610126049395618,1.7000000000000004,0.85959417878144961,0.5056436345773232,6.9,28.930437941387552,4.1928170929547175,-6.4225533681874336E-2,-6.1818275258838429E-2,-6.6640488289356425E-2,-6.4969986182653927E-2]
[2030,1.2,13.30464353058909,11.087202942157575,4,12.867901646403027,3.2169754116007567,1.7000000000000004,0.80064484920769274,0.47096755835746623,6.9,26.973190026199809,3.9091579748115666,-6.7653587517516489E-2,-6.481782577676598E-2,-7.0510345148848907E-2,-6.8578093045398192E-2]
[2031,1.2,12.406629074093985,10.338857561744987,4,11.916809487694749,2.9792023719236873,1.7000000000000004,0.74318725151077913,0.43716897147692879,6.9,25.066625813299513,3.6328443207680454,-7.0683675570015869E-2,-6.7496318441787162E-2,-7.3911985407048686E-2,-7.1764150801410742E-2]
[2032,1.2,11.539372433154071,9.6161436942950598,4,11.000102524564781,2.7500256311411952,1.7000000000000004,0.68774687980996152,0.40455698812350666,6.9,23.227221837528813,3.3662640344244656,-7.3380597351669685E-2,-6.9902681522962085E-2,-7.6925536493350544E-2,-7.4598119906007954E-2]
[2033,1.2,10.707656218918785,8.9230468490989878,4,10.124342240745236,2.5310855601863089,1.7000000000000004,0.63469731247250039,0.3733513602779413,6.9,21.466695772136521,3.1111153292951479,-7.5795808801712328E-2,-7.2076381887602459E-2,-7.9613829222395793E-2,-7.713530790880474E-2]
[2034,1.2,9.9147584892280918,8.262298741023411,4,9.2938745817460102,2.3234686454365026,1.7000000000000004,0.58428964251602977,0.34369978971531157,6.9,19.792922713490132,2.8685395236942219,-7.7970688941282007E-2,-7.4049606513306387E-2,-8.2026825965742511E-2,-7.9420014810059003E-2]
[2035,1.2,9.1627352910575013,7.6356127425479183,4,8.5112861525673509,2.1278215381418377,1.7000000000000004,0.53667696531722164,0.31569233253954204,6.9,18.210698408942072,2.6392316534698654,-7.993889166604351E-2,-7.5848867018558974E-2,-8.4204754679574889E-2,-8.1488141726732577E-2]
[2036,1.2,8.4526581451687264,7.0438817876406059,4,7.7777803666188277,1.9444450916547069,1.7000000000000004,0.49193469441826299,0.2893733496578017,6.9,16.722373206205816,2.4235323487254803,-8.17280682659286E-2,-7.7496197732764838E-2,-8.618036954700059E-2,-8.3369091260535377E-2]
[2037,1.2,7.7848130962745472,6.4873442468954563,4,7.0934865087046859,1.7733716271761715,1.7000000000000004,0.45007736136835153,0.26475138904020673,6.9,15.328376966347584,2.2215039081663162,-8.3361148723849143E-2,-7.9010062565454398E-2,-8.7980609590242231E-2,-8.5087174222200024E-2]
[2038,1.2,7.1588670249446977,5.9657225207872484,4,6.4577126749310949,1.6144281687327737,1.7000000000000004,0.41107245727848829,0.24180732781087541,6.9,14.02765215715428,2.0329930662542433,-8.4857308249200569E-2,-8.040605003470136E-2,-8.9627834351049929E-2,-8.6662666105396302E-2]
[2039,1.2,6.5740061159814189,5.4783384299845164,4,5.8691518511317184,1.4672879627829296,1.7000000000000004,0.37485178975851996,0.22050105279912935,6.9,12.818009756871657,1.8576825734596603,-8.6232705710890478E-2,-8.1697412024187899E-2,-9.114075732792748E-2,-8.8112610997506002E-2]
[2040,1.2,6.0290506854735355,5.0242089045612799,4,5.3260489452827429,1.3315122363206857,1.7000000000000004,0.34132075712714816,0.20077691595714592,6.9,11.696420387883427,1.6951333895483225,-8.7501054396292188E-2,-8.2895485780443035E-2,-9.2535160040926878E-2,-8.9451440669317761E-2]
[2041,1.2,5.5225499707265513,4.6021249756054594,4,4.8263353610501909,1.2065838402625477,1.7000000000000004,0.31036588049987124,0.1825681649999242,6.9,10.659251212276613,1.5448190162719728,-8.8674067895271547E-2,-8.4010027642884677E-2,-9.3824444605441704E-2,-9.0691456587111863E-2]
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[2043,1.2,4.6182069834742236,3.8485058195618533,4,3.9478579527386515,0.98696448818466287,1.7000000000000004,0.25567155333374103,0.15039503137278881,6.9,8.8217364895466162,1.2785125347169009,-9.0772984048590022E-2,-8.6021182102563154E-2,-9.6131872712444277E-2,-9.2915797841162773E-2]
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["∑",null,{"$f":"SUM(C12:C42)","v":321.55839680052622},null,null,{"$f":"SUM(F12:F42)","v":303.78217631684129},null,null,{"$f":"SUM(I12:I42)","v":19.031754323347027},null,null,{"$f":"SUM(L12:L42)","v":644.37232744071457}]
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["∑",null,{"$f":"SUM(C43:C44)","v":344.21462066407167},null,null,{"$f":"SUM(F43:F44)","v":319.6278620452095},null,null,{"$f":"SUM(I43:I44)","v":20.123722681361119},null,null,{"$f":"SUM(L43:L44)","v":683.96620539064224}]
[]
[null,null,null,null,null,"global path 2020 - 2100 sheet \"global path\":",null,null,null,null,null,{"$f":"'global path'!C89","v":683.96620539064213}]
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[]
[]
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[2081,1.2,9.8420998319919017E-2,8.2017498599932515E-2,4,5.2365609355169374E-2,1.3091402338792343E-2,1.7000000000000004,3.937835606975186E-3,2.3163738864559911E-3,6.9,0.15472444328206358,2.242383235971936E-2,-0.10615518377238065,-0.1019798151196627,-0.11361436990586571,-0.10998381577245808]
[2082,1.2,8.8365842326849964E-2,7.3638201939041636E-2,4,4.6405945400765092E-2,1.1601486350191273E-2,1.7000000000000004,3.5039816569944204E-3,2.0611656805849528E-3,6.9,0.13827576938460948,2.0039966577479633E-2,-0.10630947217220277,-0.10216474293813405,-0.11380873874651021,-0.11017573948802462]
[2083,1.2,7.9322089825552666E-2,6.6101741521293889E-2,4,4.1115786652366371E-2,1.0278946663091593E-2,1.7000000000000004,3.1172748546174842E-3,1.8336910909514609E-3,6.9,0.12355515133253653,1.7906543671382103E-2,-0.10645840639749427,-0.10234443833903628,-0.1139974350853652,-0.11036210809066804]
[2084,1.2,7.1190058956557389E-2,5.9325049130464491E-2,4,3.642115720036293E-2,9.1052893000907326E-3,1.7000000000000004,2.7726814437078473E-3,1.6309890845340274E-3,6.9,0.11038389760062817,1.5997666318931618E-2,-0.1066022224881521,-0.10251912029649579,-0.1141807036722049,-0.11054315932366554]
[2085,1.2,6.3879623296054455E-2,5.3233019413378713E-2,4,3.2256078265140542E-2,8.0640195662851355E-3,1.7000000000000004,2.4656926009999809E-3,1.4504074123529297E-3,6.9,9.8601394162194975E-2,1.4290057124955792E-2,-0.10674114336008134,-0.1026889957341377,-0.11435877537633221,-0.11071911755478725]
[2086,1.2,5.7309331890962878E-2,4.7757776575802401E-2,4,2.8561729362024724E-2,7.1404323405061809E-3,1.7000000000000004,2.192271468395221E-3,1.2895714519971886E-3,6.9,8.8063332721382823E-2,1.2762801843678669E-2,-0.1068753797078924,-0.10285426034278744,-0.1145318681567169,-0.11089019470386208]
[2087,1.2,5.1405605373542773E-2,4.2838004477952316E-2,4,2.5285693635967554E-2,6.3214234089918886E-3,1.7000000000000004,1.9488052723620163E-3,1.1463560425658916E-3,6.9,7.8640104281872347E-2,1.1397116562590195E-2,-0.10700513083378238,-0.10301509933238406,-0.11470018795195713,-0.1110565910942708]
[2088,1.2,4.6102002288086197E-2,3.8418335240071835E-2,4,2.2381279504861851E-2,5.5953198762154627E-3,1.7000000000000004,1.7320620805142684E-3,1.0188600473613342E-3,6.9,7.0215343873462316E-2,1.0176136793255408E-2,-0.10713058540986775,-0.10317168812462252,-0.11486392949783786,-0.11121849623541302]
[2089,1.2,4.1338550106410188E-2,3.4448791755341823E-2,4,1.9806911390999549E-2,4.9517278477498872E-3,1.7000000000000004,1.539151779141372E-3,9.053833994949245E-4,6.9,6.2684613276551115E-2,9.0847265618190023E-3,-0.10725192217932611,-0.10332419299078888,-0.11502327707864402,-0.11137608954271383]
[2090,1.2,3.706113575127451E-2,3.0884279792728758E-2,4,1.7525582924665717E-2,4.3813957311664292E-3,1.7000000000000004,1.3674908876830667E-3,8.0440640451945084E-4,6.9,5.5954209563623292E-2,8.1093057338584469E-3,-0.10736931060314148,-0.10347277164112245,-0.11517840521922507,-0.11152954100086721]
[2091,1.2,3.3220950783625525E-2,2.7684125653021273E-2,4,1.5504366571140835E-2,3.8760916427852087E-3,1.7000000000000004,1.2147708567347669E-3,7.1457109219692154E-4,6.9,4.994008821150113E-2,7.2376939436958158E-3,-0.10748291145608524,-0.10361757376841652,-0.1153294793224936,-0.11167901177539297]
[2092,1.2,2.9773986737173908E-2,2.481165561431159E-2,4,1.3713974162109427E-2,3.4284935405273567E-3,1.7000000000000004,1.0789295250468491E-3,6.3466442649814632E-4,6.9,4.456689042433018E-2,6.4589696267145181E-3,-0.10759287737768775,-0.10375874155144926,-0.11547665625785497,-0.11182465477732273]
[2093,1.2,2.6680576400212652E-2,2.2233813666843877E-2,4,1.212836330511019E-2,3.0320908262775476E-3,1.7000000000000004,9.5812543810427832E-4,5.6360319888486949E-4,6.9,3.9767065143427122E-2,5.7633427744097276E-3,-0.10769935338101833,-0.10389641012028195,-0.11562008490435605,-0.11196661518492157]
[2094,1.2,2.3904977147769541E-2,1.992081428980795E-2,4,1.0724385101055167E-2,2.6810962752637918E-3,1.7000000000000004,8.5071475623418012E-4,5.0042044484363524E-4,6.9,3.548007700505889E-2,5.142040145660708E-3,-0.1078024773240478,-0.10403070798803993,-0.11575990665314817,-0.11210503092644963]
[2095,1.2,2.1414992716236814E-2,1.7845827263530678E-2,4,9.4814690213091551E-3,2.3703672553272888E-3,1.7000000000000004,7.5523050381273021E-4,4.4425323753690001E-4,6.9,3.1651692241358699E-2,4.5872017741099558E-3,-0.10790238034585786,-0.10416175745079326,-0.11589625587239705,-0.11224003312711495]
[2096,1.2,1.9181630086610224E-2,1.5984691738841855E-2,4,8.3813411838502411E-3,2.0953352959625603E-3,1.7000000000000004,6.7036393307152824E-4,3.9433172533619301E-4,6.9,2.8233335203531995E-2,4.0917877106568107E-3,-0.10799918727125746,-0.10428967495904207,-0.11602926033786842,-0.11237174652342408]
[2097,1.2,1.7178788401153222E-2,1.4315657000961018E-2,4,7.4077726243387543E-3,1.8519431560846886E-3,1.7000000000000004,5.9494779629762698E-4,3.4996929193978051E-4,6.9,2.5181508821789603E-2,3.6494940321434204E-3,-0.10809301698655172,-0.1044145714630943,-0.11615904163255253,-0.11250028984756599]
[2098,1.2,1.5382977081556781E-2,1.2819147567963984E-2,4,6.5463544843298097E-3,1.6365886210824524E-3,1.7000000000000004,5.2794133895039692E-4,3.1055372879435107E-4,6.9,2.2457272904836987E-2,3.2546772325850702E-3,-0.10818398278801034,-0.10453655273359597,-0.11628571551706313,-0.11262577618441938]
[2099,1.2,1.3773060544561455E-2,1.1477550453801213E-2,4,5.7842973371969725E-3,1.4460743342992431E-3,1.7000000000000004,4.6841684346063221E-4,2.7553931968272478E-4,6.9,2.0025774725219062E-2,2.9022861920607332E-3,-0.10827219270663158,-0.10465571966076148,-0.11640939227427949,-0.11274831330334101]
[2100,1.2,1.2330027123982401E-2,1.0275022603318668E-2,4,5.1102521445029123E-3,1.2775630361257281E-3,1.7000000000000004,4.1554756931475728E-4,2.4443974665573951E-4,6.9,1.7855826837800071E-2,2.5878009909855175E-3,-0.10835774980961466,-0.10477216853220483,-0.11653017702936719,-0.11286800396689467]
["∑",null,{"$f":"SUM(C51:C100)","v":22.551884926092182},null,null,{"$f":"SUM(F51:F100)","v":15.807264645149509},null,null,{"$f":"SUM(I51:I100)","v":1.0887306265605419},null,null,{"$f":"SUM(L51:L100)","v":39.447880197802228}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A100-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A100-$A$11)+2*C$8+C$7)","v":0.10433893745325071},null,null,{"$f":"F$11*EXP(-F$8*($A100-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A100-$A$11)+2*F$8+F$7)","v":3.8421083218675517E-2},null,null,{"$f":"I$11*EXP(-I$8*($A100-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A100-$A$11)+2*I$8+I$7)","v":3.2377314535498615E-3},null,null,{"$f":"I102+F102+C102","v":0.14599775212547608}]
["∑",null,{"$f":"SUM(C101:C102)","v":22.656223863545431},null,null,{"$f":"SUM(F101:F102)","v":15.845685728368185},null,null,{"$f":"SUM(I101:I102)","v":1.0919683580140918},null,null,{"$f":"SUM(L101:L102)","v":39.593877949927702}]
[]
["∑",null,{"$f":"C103+C43","v":344.21462066407167},null,null,{"$f":"F103+F43","v":319.6278620452095},null,null,{"$f":"I103+I43","v":20.123722681361119},null,null,{"$f":"SUM(C105:I105)","v":683.96620539064224}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L105-L107","v":0}]

{"sheet":"SPF-spk","index":13,"n_rows":108,"n_cols":26,"rows_kept":108,"cut":false,"hidden":false,"merged":[[10,13,10,16],[3,22,3,23],[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13],[4,18,6,30],[5,10,7,13]]}
["Smooth Pathways Formula - equity (spk variabel); free input weighting population"]
[{"$f":"CONCATENATE(\"SPF-\",ROUND(W8*100,0))","v":"SPF-50"},{"$f":"'SPF-eq'!B2","v":"Smooth Pathways Formula; based on: Raupach et al. (2014) / Sharing a quota on cumulative carbon emissions / nature climate change DOI: 10.1038/NCLIMATE2384"}]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global",null,null,null,null,null,null,null,"Description",null,null,null,"input value"]
[null,"RBA:",{"$f":"W8*'global path'!C89/K11*B11+(1-W8)*'global path'!C89*C11/L11","v":231.58263253991771},"Gt","RBB:",{"$f":"W8*'global path'!C89/K11*E11+(1-W8)*'global path'!C89*F11/L11","v":358.06500504887777},"Gt","RBC:",{"$f":"W8*'global path'!C89/K11*H11+(1-W8)*'global path'!C89*I11/L11","v":94.31856780184664},"Gt","RB:",{"$f":"C5+F5+I5","v":683.96620539064213},"Gt",null,null,null,null,null,"Raupach et al. have developed a formula to convert a budget of a country or global into a smooth emission pathway."]
[null,"TA",{"$f":"C5/C11","v":11.027744406662748},null,"TB",{"$f":"F5/F11","v":18.362307951224501},null,"TC",{"$f":"I5/I11","v":76.824349601036701},null,"Global path ist different to the path in sheet \"global path\"."]
[null,"rA",{"$f":"'SPF-eq'!C7","v":0},null,"rB",{"$f":"'SPF-eq'!F7","v":0.03},null,"rC",{"$f":"'SPF-eq'!I7","v":0.02}]
[null,"mA",{"$f":"(1+SQRT(1+C7*C6))/C6","v":0.1813607503263894},null,"mB",{"$f":"(1+SQRT(1+F7*F6))/F6","v":0.12227978157380519},null,"mC",{"$f":"(1+SQRT(1+I7*I6))/I6","v":3.374757155179052E-2},null,null,null,null,null,null,null,null,null,"share population key:",null,null,null,0.5,null,{"$f":"B11/K11","v":0.17391304347826086},{"$f":"C11/L11","v":0.5032626143677319}]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita",null,null,null,null,null,"Limitations"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t",null,"A","B","C",null,"-","The resulting global pathway ist different to the pathway in sheet \"global path\". So this model is comparable with the other models to a limited extent only."]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C11/B11","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F11/E11","v":4.875},{"$f":"K11-E11-B11","v":1.7000000000000004},{"$f":"'global path'!$C$7-C11-F11","v":1.2277171013052595},{"$f":"I11/H11","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I11+F11+C11","v":41.727717101305259},{"$f":"L11/K11","v":6.047495232073226},"annual change rates",null,null,null,null,"-","The per capita emissions converge far into the future; as you can see on the remaining budgets as of 2051. So this model is comparable with the other models to a limited extent only."]
[{"$f":"A11+1","v":2020},{"$f":"B$11*(B$42/B$11)^(($A12-2019)/31)","v":1.2},{"$f":"-C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A11-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A11-$A$11)+2*C$8+C$7)","v":20.894772381654917},{"$f":"C12/B12","v":17.412310318045765},{"$f":"E$11*(E$42/E$11)^(($A12-2019)/31)","v":4},{"$f":"-F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A11-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A11-$A$11)+2*F$8+F$7)","v":19.723983954892105},{"$f":"F12/E12","v":4.9309959887230264},{"$f":"H$11*(H$42/H$11)^(($A12-2019)/31)","v":1.7000000000000004},{"$f":"-I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A11-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A11-$A$11)+2*I$8+I$7)","v":1.2394923721104334},{"$f":"I12/H12","v":0.72911316006496063},{"$f":"B12+E12+H12","v":6.9},{"$f":"I12+F12+C12","v":41.858248708657456},{"$f":"L12/K12","v":6.0664128563271671},{"$f":"L12/L11-1","v":3.1281751416041281E-3},{"$f":"C12/C11-1","v":-5.0108389688134913E-3},{"$f":"F12/F11-1","v":1.1486356661133623E-2},{"$f":"I12/I11-1","v":9.5911922971951835E-3}]
[{"$f":"A12+1","v":2021},1.2,{"$f":"-C$11*EXP(-C$8*($A13-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A13-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)","v":20.334486613652501},16.945405511377086,4,{"$f":"-F$11*EXP(-F$8*($A13-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A13-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)","v":19.927139169977409},4.9817847924943521,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A13-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A13-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)","v":1.2610930543153955},0.74181944371493835,{"$f":"B13+E13+H13","v":6.9},{"$f":"I13+F13+C13","v":41.522718837945305},6.0177853388326525,{"$f":"L13/L12-1","v":-8.0158602202282658E-3},{"$f":"C13/C12-1","v":-2.6814638502323795E-2},{"$f":"F13/F12-1","v":1.0299907744292902E-2},{"$f":"I13/I12-1","v":1.742703923880029E-2},null,"Simplification"]
[2022,1.2,19.385220674904559,16.154350562420468,4,19.822228252377556,4.955557063094389,1.7000000000000004,1.2798951813680191,0.7528795184517757,6.9,40.487344108650134,5.8677310302391499,-2.4935138118869937E-2,-4.6682562327912791E-2,-5.2647254934573562E-3,1.4909389111519955E-2,null,null,"We assumed that the emission power at the end of the base year are the emissions in the base year divided by one year."]
[2023,1.2,18.191425678058579,15.15952139838215,4,19.477476193679365,4.8693690484198413,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A15-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A15-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A14-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A14-$A$11)+2*I$8+I$7)","v":1.2960607035590357},0.76238864915237381,6.9,38.96496257529698,5.647096025405359,-3.7601417600219844E-2,-6.1582739596636404E-2,-1.7392194979736431E-2,1.263034850536604E-2]
[2024,1.2,16.860335181254214,14.050279317711846,4,18.949483905085344,4.7373709762713361,1.7000000000000004,1.3097439045035912,0.77043759088446528,6.9,37.11956299084315,5.3796468102671229,-4.7360486511124678E-2,-7.3171312703096514E-2,-2.7107838990215738E-2,1.055753091423961E-2,null,"Input values"]
[2025,1.2,15.470337360456455,12.891947800380379,4,18.285000229655111,4.5712500574137778,1.7000000000000004,1.3210917316294797,0.7771127833114585,6.9,35.076429321741045,5.0835404814117453,-5.5041964518981912E-2,-8.2441885398767067E-2,-3.506605661444484E-2,8.66415723476055E-3,null,"-","reduction rate at the beginnging of 2020 for each country"]
[2026,1.2,14.077593777898727,11.73132814824894,4,17.522440033914222,4.3806100084785555,1.7000000000000004,1.3302441131734497,0.78249653716085255,6.9,32.930277924986399,4.7725040470994777,-6.1185001958692031E-2,-9.0026710478706362E-2,-4.1704139248745942E-2,6.9278925337614705E-3,null,"-","Share that is distributed over the population key"]
[2027,1.2,12.721256075259902,10.601046729383253,4,16.693183355652934,4.1732958389132335,1.7000000000000004,1.3373342622177375,0.78666721306925724,6.9,30.751773693130573,4.4567787961058798,-6.6155051494504624E-2,-9.6347268150912435E-2,-4.7325411110340942E-2,5.32996085009807E-3]
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["∑",null,{"$f":"SUM(C12:C42)","v":228.39056397717752},null,null,{"$f":"SUM(F12:F42)","v":332.98106674128212},null,null,{"$f":"SUM(I12:I42)","v":39.893856784500301},null,null,{"$f":"SUM(L12:L42)","v":601.26548750296001}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A42-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A42-$A$11)+2*C$8+C$7)","v":3.1920685627401761},null,null,{"$f":"F$11*EXP(-F$8*($A42-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A42-$A$11)+2*F$8+F$7)","v":25.083938307595592},null,null,{"$f":"I$11*EXP(-I$8*($A42-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A42-$A$11)+2*I$8+I$7)","v":54.424711017346368},null,null,82.700717887682131]
["∑",null,{"$f":"SUM(C43:C44)","v":231.58263253991771},null,null,{"$f":"SUM(F43:F44)","v":358.06500504887771},null,null,{"$f":"SUM(I43:I44)","v":94.318567801846669},null,null,{"$f":"SUM(L43:L44)","v":683.96620539064213}]
[]
[null,null,null,null,null,"global path 2020 - 2100 sheet \"global path\":",null,null,null,null,null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L45-L47","v":0}]
[]
[]
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["∑",null,{"$f":"SUM(C51:C100)","v":3.191262708953071},null,null,{"$f":"SUM(F51:F100)","v":24.967820899041229},null,null,{"$f":"SUM(I51:I100)","v":38.002363700654968},null,null,{"$f":"SUM(L51:L100)","v":66.161447308649272}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A100-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A100-$A$11)+2*C$8+C$7)","v":8.058537871051027E-4},null,null,{"$f":"F$11*EXP(-F$8*($A100-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A100-$A$11)+2*F$8+F$7)","v":0.11611740855436117},null,null,{"$f":"I$11*EXP(-I$8*($A100-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A100-$A$11)+2*I$8+I$7)","v":16.4223473166914},null,null,{"$f":"I102+F102+C102","v":16.53927057903287}]
["∑",null,{"$f":"SUM(C101:C102)","v":3.1920685627401761},null,null,{"$f":"SUM(F101:F102)","v":25.083938307595592},null,null,{"$f":"SUM(I101:I102)","v":54.424711017346368},null,null,{"$f":"SUM(L101:L102)","v":82.700717887682146}]
[]
["∑",null,{"$f":"C103+C43","v":231.58263253991771},null,null,{"$f":"F103+F43","v":358.06500504887771},null,null,{"$f":"I103+I43","v":94.318567801846669},null,null,{"$f":"SUM(C105:I105)","v":683.96620539064213}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L105-L107","v":0}]

{"sheet":"ESPM","index":14,"n_rows":32,"n_cols":15,"rows_kept":32,"cut":false,"hidden":false,"merged":[[2,2,2,9],[31,1,31,7],[12,2,12,3],[13,2,13,3]]}
[]
[null,"Extended Smooth Pathway Model"]
[null,"ESPM","Wirtschaftsdienst 2021/2: Calculation of Paris-Compatible Emission Paths with the ESPM Using the Example of the EU",null,null,null,null,null,null,null,null,null,"update on:","Zenodo","in German"]
[null,null,"Zeitschrift für Umweltpolitik und Umweltrecht 2021/9: Calculation of Paris-compatible emission targets for the six largest emitters with the ESPM",null,null,null,null,null,null,null,null,null,"update on:","Zenodo","in English"]
[null,null,"inspired by:",{"$f":"'SPF-eq'!B2","v":"Smooth Pathways Formula; based on: Raupach et al. (2014) / Sharing a quota on cumulative carbon emissions / nature climate change DOI: 10.1038/NCLIMATE2384"}]
[]
[]
[]
[]
[]
[null,"For a comprehensive mathematical description of the RM Scenario Types, we refer to:",null,null,null,null,"Zenodo"]
[]
[null,null,"calculation of Paris-compatible emission paths for all countries of the world",null,"web apps","use of the\nRM Scenario Types\nwith a known budget","calculation of global paths"]
[null,"published tools:","Zenodo",null,"here","Zenodo","Zenodo"]
[]
[null,"The following figures show the relationship between SPF and ESPM with the same framework data:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"The course of the reduction rates for SPF corresponds to scenario type RM-5-rad."]

{"sheet":"EPM","index":15,"n_rows":127,"n_cols":44,"rows_kept":127,"cut":false,"hidden":false,"merged":[[108,43,111,45],[118,38,126,40],[118,28,121,28],[123,28,126,28],[1,3,1,4],[14,37,14,38],[14,24,14,26],[3,23,5,31],[14,28,14,30],[14,31,14,33],[14,34,14,36],[2,2,2,18],[113,43,116,45],[103,43,106,45]]}
[]
[null,"Cap Model",null,"input values",null,null,"solver",null,null,"original scenario global path:",null,null,3,null,"choosen scenario global path:",null,null,{"$f":"'global path'!C2","v":3}]
[null,"EPM","cap model; based on: Chakravartya et al. / Sharing global CO2 emission reductions among\none billion high emitters / 11884–11888   PNAS   July 21, 2009   vol. 106   no. 29 / doi 10.1073 pnas.0905232106",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Description"]
[null,"source data:","http://data.worldbank.org/indicator/SI.DST.04TH.20/countries?display=default",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Chakravarty et al. insinuate that the income and emissions distribution correlated. Each person is attributed his emissions or a cap, whatever is the least. The cap is calculated for each year such that the emissions of the global pathway are met."]
[]
[null,"Country A",null,null,null,null,null,null,"Country B",null,null,null,null,null,null,"Country C"]
[null,"Data of the probability density functions",null,null,null,null,null,null,"Data of the probability density functions",null,null,null,null,null,null,"Data of the probability density functions"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"If you change the quantile values of countries, you have to do the following optimization with the help of the Excel solver:"]
[null,null,"G income","G emissions",null,null,null,null,null,"G income","G emissions",null,null,null,null,null,"G income","G emissions",null,null,null,null,null,"- For each country: minimize the target value by adjusting the parameter a (variable)"]
[null,"a",1.5667140078250585,{"$f":"C10","v":1.5667140078250585},null,null,null,null,"a",0.78102068816147474,{"$f":"J10","v":0.78102068816147474},null,null,null,null,"a",2.7860406584318342,{"$f":"Q10","v":2.7860406584318342},null,null,null,null,null,"- Redefine caps for each year. Target = 0 by adjusting the caps of the individual years (variables)."]
[null,"b",{"$f":"C12/C10","v":34866.142836442385},{"$f":"D12/D10","v":11.169875237340747},null,null,null,null,"b",{"$f":"J12/J10","v":15014.718634345252},{"$f":"K12/K10","v":6.2418320972723089},null,null,null,null,"b",{"$f":"Q12/Q10","v":153.42798802110258},{"$f":"R12/R10","v":0.25921607712145089}]
[null,"E",{"$f":"17420000/318.9","v":54625.274380683601},{"$f":"AC19","v":17.5},null,null,null,null,"E",{"$f":"2416635506076/206077898","v":11726.805880347247},{"$f":"AF19","v":4.875},null,null,null,null,"E",{"$f":"8168695870/19110000","v":427.45661276818419},{"$f":"AI19","v":0.72218653017956425},null,null,null,null,null,"Limitations"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"- 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."]
[null,"Data of the Lorenz curve",null,null,null,null,null,null,"Data of the Lorenz curve",null,null,null,null,null,null,"Data of the Lorenz curve",null,null,null,null,null,null,null,"- Actual correlation between emission and income distribution?"]
[null,null,null,"≈ USA",null,null,null,null,null,null,"≈ Brazil",null,null,null,null,null,null,"≈ Niger",null,null,null,null,null,null,"Global",null,null,null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
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[null,60087.801818751963,7.8273044654169554E-6,0.65112145074222227,19.25,2.4432494519117207E-2,0.65112145074222227,null,12899.486468381972,2.4583069518692369E-5,0.67901384214980998,5.3624999999999998,5.913454034641781E-2,0.67901384214980998,null,470.20227404500258,1.3567763645852553E-3,0.64103664089928203,0.79440518319752063,0.80306541987890911,0.64103664089928225,null,null,2100,6.9,{"$f":"'global path'!C88","v":0},0,1.9383052454530348E-3,1.9383045508960669E-3,1.2,2.3259654610752801E-3,1.9361665780948329E-3,4,7.7446663123793315E-3,1.9383051138561602E-3,1.7000000000000004,3.2951186935554731E-3,1.3365750467010084E-2,1.7864328554638027E-4]
[null,65550.329256820318,7.030496708258795E-6,0.69167758869460316,21,2.194530352692169E-2,0.69167758869460338,null,14072.167056416696,2.2307037570041193E-5,0.70648200006125406,5.85,5.3659548584509949E-2,0.70648200006125406,null,512.94793532182098,1.1995102603785635E-3,0.69566425084546069,0.86662383621547701,0.70998083106675525,0.69566425084546069,null,null,"∑",null,{"$f":"SUM(Z20:Z100)","v":683.96620539064213},null,null,null,null,{"$f":"SUM(AE20:AE100)","v":251.67673951787432},null,null,{"$f":"SUM(AH20:AH100)","v":388.58981154055857},null,null,{"$f":"SUM(AK20:AK100)","v":43.807409668045615},"target",{"$f":"SUM(AM20:AM100)","v":1.3260197182857576E-3}]
[null,71012.856694888687,6.2899132678377711E-6,0.72803262235892841,22.75,1.9633613604933743E-2,0.72803262235892841,null,15244.84764445142,2.0272645173574713E-5,0.7314262582731148,6.3374999999999995,4.8765820437265468E-2,0.7314262582731148,null,555.69359659863937,1.0473559250262162E-3,0.74365839126891919,0.9388424892334335,0.61992185864097837,0.74365839126891942]
[null,76475.384132957042,5.6084472957465745E-6,0.76050303839373101,24.5,1.7506455564557693E-2,0.76050303839373101,null,16417.528232486147,1.844774733483673E-5,0.75411049122913054,6.8250000000000002,4.4376031164168953E-2,0.75411049122913054,null,598.43925787545788,9.0485968378055555E-4,0.78534261801000804,1.01106114225139,0.53557943730016044,0.78534261801000815,null,null,null,null,null,null,null,"global path:",{"$f":"'global path'!C2","v":3},{"$f":"AC15","v":"Country A"},null,null,{"$f":"AF15","v":"Country B"},null,null,{"$f":"AI15","v":"Country C"}]
[null,81937.911571025412,4.9863378013582308E-6,0.78941340097734902,26.25,1.5564575460226743E-2,0.78941340097734902,null,17590.208820520871,1.6805936498939658E-5,0.77476439971835998,7.3125,4.0426657427796511E-2,0.77476439971835998,null,641.18491915227628,7.7464115313304093E-4,0.82119164736939376,1.0832797952693463,0.45850409775263878,0.82119164736939376,null,null,null,null,null,null,null,null,2,269.62970205103386,null,null,379.81845048201433,null,null,35.64500914283628,null,{"$f":"AE104+AH104+AK104","v":685.09316167588452},"EPM",null,null,null,"Transfer values for the individual global paths from above."]
[null,87400.439009093767,4.4220580768652843E-6,0.81508441900276762,28,1.3803207758633385E-2,0.81508441900276762,null,18762.889408555595,1.5325184444214432E-5,0.79358939489921465,7.8,3.6864710370834865E-2,0.79358939489921465,null,683.93058042909468,6.5790743875872022E-4,0.85176032038690375,1.1554984482873027,0.38941031649658431,0.85176032038690375,null,null,null,null,null,null,null,null,1,220.84211947036036,null,null,404.81878572545918,null,null,58.37257419502027,null,{"$f":"AE105+AH105+AK105","v":684.03347939083983},"EPM"]
[null,92862.966447162122,3.9129463701988449E-6,0.83782512117050134,29.75,1.2214043949086392E-2,0.83782512117050145,null,19935.569996590319,1.3986882281458956E-5,0.81076313987521298,8.2874999999999996,3.364542633557694E-2,0.81076313987521298,null,726.67624170591307,5.5487242611821318E-4,0.87763252218258803,1.2277171013052592,0.32842469067926611,0.87763252218258814,null,null,null,null,null,null,null,null,3,251.65867344728332,null,null,388.52702916459572,null,null,43.780478278414826,null,{"$f":"SUM(AE106:AK106)","v":683.96618089029391},"EPM"]
[null,98325.493885230491,3.455653932286262E-6,0.85792794932757566,31.5,1.078663109804716E-2,0.85792794932757566,null,21108.250584625042,1.2775143022611036E-5,0.82644312968158173,8.7750000000000004,3.0730589193811726E-2,0.82644312968158185,null,769.42190298273147,4.6508556979417138E-4,0.89938605839861252,1.2999357543232155,0.27528054595832296,0.89938605839861252,null,null,null,null,null,null,null,null,6,251.60139629882309,null,null,384.800766542058,null,null,47.421772658231703,null,{"$f":"SUM(AE107:AK107)","v":683.82393549911285},"EPM"]
[null,103788.02132329885,3.0464621345654686E-6,0.87566592215953243,33.25,9.5093617137715306E-3,0.87566592215953243,null,22280.93117265977,1.1676282642251356E-5,0.84076956453182605,9.2624999999999993,2.8087282040974302E-2,0.84076956453182605,null,812.16756425954998,3.8768129573961543E-4,0.91756984359427451,1.372154407341172,0.22946555576054967,0.91756984359427463]
[null,109250.54876136722,2.6815049599300951E-6,0.89129125886346117,35,8.3701682393911674E-3,0.89129125886346094,null,23453.611760694494,1.0678425746869667E-5,0.85386769179084865,9.75,2.5686938634101059E-2,0.85386769179084865,null,854.91322553636837,3.215623446093897E-4,0.93269029041372897,1.4443730603591285,0.19033026077950899,0.93269029041372908,null,null,null,null,null,null,null,{"$f":"SUM(AE109:AL109)","v":683.96620539064213},2,{"$f":"$AM109*'input data'!$C$11*$Z$101+(1-$AM109)*'input data'!$C$10*$Z$101","v":318.32593578131457},null,null,{"$f":"$AM109*'input data'!$D$11*$Z$101+(1-$AM109)*'input data'!$D$10*$Z$101","v":328.46271526575771},null,null,{"$f":"$AM109*'input data'!$E$11*$Z$101+(1-$AM109)*'input data'!$E$10*$Z$101","v":37.177554343569845},null,0.11492598734126944,{"$f":"RF!M108","v":"share population key"},null,"solver",null,"Solver must be performed manually for each global path: Minimisation of the quadratic deviation."]
[null,114713.07619943557,2.3569227714884623E-6,0.90503502054355445,36.75,7.3570030335221998E-3,0.90503502054355445,null,24626.292348729217,9.771200310837731E-6,0.86584974056677433,10.237499999999999,2.3504609079627231E-2,0.86584974056677433,null,897.65888681318677,2.6553020319378687E-4,0.94520436009207875,1.5165917133770848,0.15716527033070329,0.94520436009207875,null,null,null,null,null,null,null,683.96620539064213,1,{"$f":"$AM110*'input data'!$C$11*$Z$101+(1-$AM110)*'input data'!$C$10*$Z$101","v":276.21039345281736},null,null,{"$f":"$AM110*'input data'!$D$11*$Z$101+(1-$AM110)*'input data'!$D$10*$Z$101","v":342.83519638873224},null,null,{"$f":"$AM110*'input data'!$E$11*$Z$101+(1-$AM110)*'input data'!$E$10*$Z$101","v":64.920615549092517},null,0.30188682781792603,{"$f":"RF!M109","v":"share population key"},null,"solver"]
[null,120175.60363750393,2.0689660744280265E-6,0.91710744776775177,38.5,6.4581622571403879E-3,0.91710744776775177,null,25798.972936763945,8.9454974319622013E-6,0.87681653838141071,10.725,2.1518381925695499E-2,0.8768165383814106,null,940.40454809000516,2.183744319952509E-4,0.95551727082143367,1.5888103663950413,0.12925413465224378,0.95551727082143367,null,null,null,null,null,null,null,683.96620539064213,{"$f":"AD106","v":3},{"$f":"$AM111*'input data'!$C$11*$Z$101+(1-$AM111)*'input data'!$C$10*$Z$101","v":304.09393198774222},null,null,{"$f":"$AM111*'input data'!$D$11*$Z$101+(1-$AM111)*'input data'!$D$10*$Z$101","v":333.31957319886368},null,null,{"$f":"$AM111*'input data'!$E$11*$Z$101+(1-$AM111)*'input data'!$E$10*$Z$101","v":46.55270020403627},null,0.17810521391180853,"share population key",null,"solver"]
[null,125638.1310755723,1.8140629207486163E-6,0.92769876033568321,40.25,5.6624962736981409E-3,0.92769876033568321,null,26971.653524798669,8.1932794607711875E-6,0.8868588758271756,11.2125,1.9708922617415362E-2,0.8868588758271756,null,983.15020936682356,1.7893091056675665E-4,0.96398332779998519,1.6610290194129977,0.10590781986943922,0.9639833277999853,null,null,null,null,null,null,null,683.96620539064213,{"$f":"AD107","v":6},{"$f":"$AM112*'input data'!$C$11*$Z$101+(1-$AM112)*'input data'!$C$10*$Z$101","v":298.34483488787106},null,null,{"$f":"$AM112*'input data'!$D$11*$Z$101+(1-$AM112)*'input data'!$D$10*$Z$101","v":335.28152797787493},null,null,{"$f":"$AM112*'input data'!$E$11*$Z$101+(1-$AM112)*'input data'!$E$10*$Z$101","v":50.339842524896213},null,0.20362681392802243,"share population key",null,"solver"]
[null,131100.65851364064,1.5888599812696596E-6,0.9369802494290761,42,4.9595378531053086E-3,0.93698024942907621,null,28144.334112833392,7.5074247415095854E-6,0.89605866865390427,11.7,1.8059100021538259E-2,0.89605866865390427,null,1025.895870643642,1.4611717857203874E-4,0.97090872752007074,1.733247672430954,8.6485626094573942E-2,0.97090872752007074]
[null,136563.18595170902,1.3902446814858615E-6,0.9451055395195922,43.75,4.3395712675686439E-3,0.9451055395195922,null,29317.014700868116,6.8816004972145533E-6,0.90448995499046458,12.1875,1.6553680651679215E-2,0.90448995499046458,null,1068.6415319204605,1.1895134796584667E-4,0.97655550132501456,1.8054663254489105,7.0406381399896731E-2,0.97655550132501467,null,null,null,null,null,null,null,null,{"$f":"AD109","v":2},{"$f":"(AE104-AE109)^2/AE104^2","v":3.2617846373206062E-2},null,null,{"$f":"(AH104-AH109)^2/AH104^2","v":1.8282087646901271E-2},null,null,{"$f":"(AK104-AK109)^2/AK104^2","v":1.8485411550537235E-3},null,{"$f":"AE114+AH114+AK114","v":5.2748475175161055E-2},"square deviation",null,null,null,"There is no implicit population weighting that is the same for all countries."]
[null,142025.71338977737,1.2153538734509789E-6,0.95221193228851175,45.5,3.7936593603935054E-3,0.95221193228851175,null,30489.69528890284,6.3101576582956802E-6,0.91221975688603885,12.674999999999999,1.5179075678609226E-2,0.91221975688603896,null,1111.3871931972787,9.6559586202882021E-5,0.98114600764558557,1.877684978466867,5.7152871071022023E-2,0.98114600764558557,null,null,null,null,null,null,null,null,{"$f":"AD110","v":1},{"$f":"(AE105-AE110)^2/AE105^2","v":6.2857652479552606E-2},null,null,{"$f":"(AH105-AH110)^2/AH105^2","v":2.3444022400971248E-2},null,null,{"$f":"(AK105-AK110)^2/AK105^2","v":1.2583606681884397E-2},null,{"$f":"AE115+AH115+AK115","v":9.888528156240825E-2},"square deviation"]
[null,147488.24082784573,1.0615730951132585E-6,0.95842177063050049,47.25,3.313641234040759E-3,0.95842177063050049,null,31662.375876937567,5.7880430227817215E-6,0.91930882906987188,13.1625,1.3923129631848111E-2,0.91930882906987188,null,1154.1328544740973,7.8175944550795383E-5,0.98486756896721517,1.9499036314848235,4.6271735986723003E-2,0.98486756896721517,null,null,null,null,null,null,null,null,3,{"$f":"(AE106-AE111)^2/AE106^2","v":4.3413322194962606E-2},null,null,{"$f":"(AH106-AH111)^2/AH106^2","v":2.0190775262690117E-2},null,null,{"$f":"(AK106-AK111)^2/AK106^2","v":4.0095440093770585E-3},null,{"$f":"AE116+AH116+AK116","v":6.7613641467029778E-2},"square deviation"]
[null,152950.76826591408,9.2652941300448145E-7,0.96384377992050596,49,2.8921099089796298E-3,0.96384377992050596,null,32835.056464972295,5.3107252684986436E-6,0.92581231312040235,13.65,1.2774942422059203E-2,0.92581231312040235,null,1196.8785157509158,6.3137318372077713E-5,0.98787698899666432,2.02212228450278,3.7370489648822967E-2,0.98787698899666432,null,null,null,null,null,null,null,null,6,{"$f":"(AE107-AE112)^2/AE107^2","v":3.4515583568901914E-2},null,null,{"$f":"(AH107-AH112)^2/AH107^2","v":1.6560599684850307E-2},null,null,{"$f":"(AK107-AK112)^2/AK107^2","v":3.7864811875036319E-3},null,{"$f":"AE117+AH117+AK117","v":5.4862664441255857E-2},"square deviation"]
[null,158413.29570398244,8.0808005637997529E-7,0.96857435783222545,50.75,2.5223768457893936E-3,0.96857435783222534,null,34007.737053007018,4.8741321566393911E-6,0.93178031165965125,14.137499999999999,1.1724718284321728E-2,0.93178031165965125,null,1239.624177027734,5.0875550746258247E-5,0.9903047873511257,2.094340937520736,3.0112844377344208E-2,0.9903047873511257]
[null,163875.82314205082,7.0429846109136119E-7,0.97269879437013784,52.5,2.1984283818862185E-3,0.97269879437013784,null,35180.417641041742,4.4745968674340528E-6,0.93725839443905767,14.625,1.0763636688658261E-2,0.93725839443905767,null,1282.3698383045526,4.0908094500583081E-5,0.99225906174629519,2.1665595905386925,2.4213184238803521E-2,0.99225906174629519,null,null,null,null,null,null,null,"Original budgets",{"$f":"AD109","v":2},{"$f":"(AE104-($Z$101*'input data'!C$10))/($Z$101*('input data'!C$11-'input data'!C$10))","v":0.33110007137059072},null,null,{"$f":"(AH104-$Z$101*'input data'!D$10)/($Z$101*('input data'!D$11-'input data'!D$10))","v":0.78297427609357451},null,null,{"$f":"(AK104-$Z$101*'input data'!E$10)/($Z$101*('input data'!E$11-'input data'!E$10))","v":0.10459814584335365},null,"Calculation using the formula for the implicit weighting of the population."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AD110","v":1},{"$f":"(AE105-($Z$101*'input data'!C$10))/($Z$101*('input data'!C$11-'input data'!C$10))","v":0.54767967452424848},null,null,{"$f":"(AH105-$Z$101*'input data'!D$10)/($Z$101*('input data'!D$11-'input data'!D$10))","v":1.1081849094783041},null,null,{"$f":"(AK105-$Z$101*'input data'!E$10)/($Z$101*('input data'!E$11-'input data'!E$10))","v":0.25775949428526052}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,{"$f":"(AE106-($Z$101*'input data'!C$10))/($Z$101*('input data'!C$11-'input data'!C$10))","v":0.41087771226573822},null,null,{"$f":"(AH106-$Z$101*'input data'!D$10)/($Z$101*('input data'!D$11-'input data'!D$10))","v":0.89625765256292156},null,null,{"$f":"(AK106-$Z$101*'input data'!E$10)/($Z$101*('input data'!E$11-'input data'!E$10))","v":0.15942317528015149}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6,{"$f":"(AE107-($Z$101*'input data'!C$10))/($Z$101*('input data'!C$11-'input data'!C$10))","v":0.41113197905714521},null,null,{"$f":"(AH107-$Z$101*'input data'!D$10)/($Z$101*('input data'!D$11-'input data'!D$10))","v":0.84778549345653209},null,null,{"$f":"(AK107-$Z$101*'input data'!E$10)/($Z$101*('input data'!E$11-'input data'!E$10))","v":0.18396190417636896}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Budgets via the solver",{"$f":"AD114","v":2},{"$f":"(AE109-($Z$101*'input data'!C$10))/($Z$101*('input data'!C$11-'input data'!C$10))","v":0.11492598734126948},null,null,{"$f":"(AH109-$Z$101*'input data'!D$10)/($Z$101*('input data'!D$11-'input data'!D$10))","v":0.11492598734126956},null,null,{"$f":"(AK109-$Z$101*'input data'!E$10)/($Z$101*('input data'!E$11-'input data'!E$10))","v":0.11492598734126942}]
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["Allocation per capita starting 2020"]
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[2050,{"$f":"RF!B40","v":1.2},{"$f":"B39/$K39*'global path'!$C38","v":0.77335076918943702},0.64445897432453092,{"$f":"RF!E40","v":4},{"$f":"E39/$K39*'global path'!$C38","v":2.5778358972981237},0.64445897432453092,{"$f":"K39-E39-B39","v":1.7000000000000004},{"$f":"H39/$K39*'global path'!$C38","v":1.0955802563517028},0.64445897432453092,{"$f":"RF!K40","v":6.9},4.4467669228392639,0.64445897432453092]
["∑",null,{"$f":"SUM(C9:C39)","v":114.2197645839727},null,null,{"$f":"SUM(F9:F39)","v":380.73254861324233},null,null,{"$f":"SUM(I9:I39)","v":161.81133316062795},null,null,{"$f":"SUM(L9:L39)","v":656.76364635784307}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C90","v":656.76364635784296}]
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{"sheet":"G-C&C = RF","index":17,"n_rows":52,"n_cols":25,"rows_kept":52,"cut":false,"hidden":false,"merged":[[2,18,2,20],[0,7,0,11],[3,13,3,16],[3,1,3,4],[3,5,3,8],[3,9,3,12]]}
["Comparision of G-C&C and RF",null,null,null,null,null,null,null,null,null,null,null,null,"convergence period: 2020 - 2050"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Comparison to RM"]
[null,"Country A",null,null,null,"Country B",null,null,null,"Country C",null,null,null,"Global",null,null,null,null,"A","B","C","C_t_A - C_t_C"]
[]
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[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"G-C&C ≙ RM"]

{"sheet":"G-LIMITS = RF","index":18,"n_rows":43,"n_cols":18,"rows_kept":43,"cut":false,"hidden":false,"merged":[[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13]]}
["Comparison of RF and G-LIMITS"]
[]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global"]
[]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita","Ct",null,"RM - \nG-LIMITS\nA","RM -\nG-LIMITS\nB","RM - \nG-LIMITS\nC"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t"]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C8/B8","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F8/E8","v":4.875},{"$f":"K8-E8-B8","v":1.7000000000000004},{"$f":"'global path'!$C$7-C8-F8","v":1.2277171013052595},{"$f":"I8/H8","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I8+F8+C8","v":41.727717101305259},{"$f":"L8/K8","v":6.047495232073226},null,null,{"$f":"RF!C9-C8","v":0},{"$f":"RF!F9-F8","v":0},{"$f":"RF!I9-I8","v":0}]
[{"$f":"A8+1","v":2020},{"$f":"B$8*(B$39/B$8)^(($A9-2019)/31)","v":1.2},{"$f":"((1-$N9)*(C$8/$L$8)+$N9*(B9/$K9))*'global path'!$C8","v":20.547215458313012},{"$f":"C9/B9","v":17.122679548594178},{"$f":"E$8*(E$39/E$8)^(($A9-2019)/31)","v":4},{"$f":"((1-$N9)*(F$8/$L$8)+$N9*(E9/$K9))*'global path'!$C8","v":19.12118815478728},{"$f":"F9/E9","v":4.78029703869682},{"$f":"H$8*(H$39/H$8)^(($A9-2019)/31)","v":1.7000000000000004},{"$f":"((1-$N9)*(I$8/$L$8)+$N9*(H9/$K9))*'global path'!$C8","v":1.2247591461788567},{"$f":"I9/H9","v":0.72044655657579793},{"$f":"B9+E9+H9","v":6.9},{"$f":"I9+F9+C9","v":40.89316275927915},{"$f":"L9/K9","v":5.9265453274317608},{"$f":"(RF!C10/RF!L10-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B9/'G-LIMITS = RF'!K9-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":2.4342283372512557E-3},null,{"$f":"RF!C10-C9","v":0},{"$f":"RF!F10-F9","v":0},{"$f":"RF!I10-I9","v":0}]
[{"$f":"A9+1","v":2021},{"$f":"B$8*(B$39/B$8)^(($A10-2019)/31)","v":1.2},{"$f":"((1-$N10)*(C$8/$L$8)+$N10*(B10/$K10))*'global path'!$C9","v":20.030691537716816},16.692242948097348,{"$f":"E$8*(E$39/E$8)^(($A10-2019)/31)","v":4},{"$f":"((1-$N10)*(F$8/$L$8)+$N10*(E10/$K10))*'global path'!$C9","v":18.689050214016273},4.6722625535040683,{"$f":"H$8*(H$39/H$8)^(($A10-2019)/31)","v":1.7000000000000004},{"$f":"((1-$N10)*(I$8/$L$8)+$N10*(H10/$K10))*'global path'!$C9","v":1.2213847938364675},0.71846164343321595,{"$f":"B10+E10+H10","v":6.9},{"$f":"I10+F10+C10","v":39.94112654556956},5.7885690645752979,{"$f":"(RF!C11/RF!L11-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B10/'G-LIMITS = RF'!K10-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":5.3353402110699003E-3},null,{"$f":"RF!C11-C10","v":0},{"$f":"RF!F11-F10","v":0},{"$f":"RF!I11-I10","v":0}]
[2022,1.2,{"$f":"((1-$N11)*(C$8/$L$8)+$N11*(B11/$K11))*'global path'!$C10","v":19.455092518697356},16.212577098914466,4,{"$f":"((1-$N11)*(F$8/$L$8)+$N11*(E11/$K11))*'global path'!$C10","v":18.207488441423497},4.5518721103558741,1.7000000000000004,{"$f":"((1-$N11)*(I$8/$L$8)+$N11*(H11/$K11))*'global path'!$C10","v":1.2176245151336678},0.71624971478451027,6.9,38.88020547525452,5.6348123877180463,{"$f":"(RF!C12/RF!L12-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B11/'G-LIMITS = RF'!K11-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":8.7356323583372558E-3},null,{"$f":"RF!C12-C11","v":0},{"$f":"RF!F12-F11","v":0},{"$f":"RF!I12-I11","v":1.7763568394002505E-15}]
[2023,1.2,{"$f":"((1-$N12)*(C$8/$L$8)+$N12*(B12/$K12))*'global path'!$C11","v":18.825570883122545},15.687975735935455,4,{"$f":"((1-$N12)*(F$8/$L$8)+$N12*(E12/$K12))*'global path'!$C11","v":17.680813543281147},4.4202033858202867,1.7000000000000004,{"$f":"((1-$N12)*(I$8/$L$8)+$N12*(H12/$K12))*'global path'!$C11","v":1.2135119702526256},0.71383057073683842,6.9,37.719896396656317,5.4666516516893209,{"$f":"(RF!C13/RF!L13-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B12/'G-LIMITS = RF'!K12-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":1.2673459670647404E-2},null,{"$f":"RF!C13-C12","v":0},{"$f":"RF!F13-F12","v":0},{"$f":"RF!I13-I12","v":0}]
[2024,1.2,{"$f":"((1-$N13)*(C$8/$L$8)+$N13*(B13/$K13))*'global path'!$C12","v":18.147689927786825},15.123074939822354,4,{"$f":"((1-$N13)*(F$8/$L$8)+$N13*(E13/$K13))*'global path'!$C12","v":17.113679924786705},4.2784199811966763,1.7000000000000004,{"$f":"((1-$N13)*(I$8/$L$8)+$N13*(H13/$K13))*'global path'!$C12","v":1.2090835031511278},0.71122559008889852,6.9,36.470453355724658,5.2855729501050224,{"$f":"(RF!C14/RF!L14-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B13/'G-LIMITS = RF'!K13-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":1.719396336515298E-2},null,{"$f":"RF!C14-C13","v":0},{"$f":"RF!F14-F13","v":0},{"$f":"RF!I14-I13","v":0}]
[2025,1.2,{"$f":"((1-$N14)*(C$8/$L$8)+$N14*(B14/$K14))*'global path'!$C13","v":17.427341186140875},14.522784321784064,4,{"$f":"((1-$N14)*(F$8/$L$8)+$N14*(E14/$K14))*'global path'!$C13","v":16.511016602839188},4.127754150709797,1.7000000000000004,{"$f":"((1-$N14)*(I$8/$L$8)+$N14*(H14/$K14))*'global path'!$C13","v":1.2043776020944976},0.70845741299676313,6.9,35.142735391074559,5.0931500566774721,{"$f":"(RF!C15/RF!L15-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B14/'G-LIMITS = RF'!K14-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":2.2349942204167004E-2},null,{"$f":"RF!C15-C14","v":0},{"$f":"RF!F15-F14","v":0},{"$f":"RF!I15-I14","v":0}]
[2026,1.2,{"$f":"((1-$N15)*(C$8/$L$8)+$N15*(B15/$K15))*'global path'!$C14","v":16.670658387708748},13.892215323090625,4,{"$f":"((1-$N15)*(F$8/$L$8)+$N15*(E15/$K15))*'global path'!$C14","v":15.877955222150625},3.9694888055376563,1.7000000000000004,{"$f":"((1-$N15)*(I$8/$L$8)+$N15*(H15/$K15))*'global path'!$C14","v":1.1994343375688474},0.70554961033461594,6.9,33.748047947428219,4.891021441656263,{"$f":"(RF!C16/RF!L16-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B15/'G-LIMITS = RF'!K15-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":2.8202890535156414E-2},null,{"$f":"RF!C16-C15","v":0},{"$f":"RF!F16-F15","v":0},{"$f":"RF!I16-I15","v":0}]
[2027,1.2,{"$f":"((1-$N16)*(C$8/$L$8)+$N16*(B16/$K16))*'global path'!$C15","v":15.883929729625063},13.236608108020887,4,{"$f":"((1-$N16)*(F$8/$L$8)+$N16*(E16/$K16))*'global path'!$C15","v":15.219756659231409},3.8049391648078523,1.7000000000000004,{"$f":"((1-$N16)*(I$8/$L$8)+$N16*(H16/$K16))*'global path'!$C15","v":1.1942947891677518},0.7025263465692656,6.9,32.297981178024223,4.6808668373948148,{"$f":"(RF!C17/RF!L17-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B16/'G-LIMITS = RF'!K16-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":3.4824231993493521E-2},null,{"$f":"RF!C17-C16","v":0},{"$f":"RF!F17-F16","v":0},{"$f":"RF!I17-I16","v":0}]
[2028,1.2,{"$f":"((1-$N17)*(C$8/$L$8)+$N17*(B17/$K17))*'global path'!$C16","v":15.073510232180503},12.561258526817086,4,{"$f":"((1-$N17)*(F$8/$L$8)+$N17*(E17/$K17))*'global path'!$C16","v":14.541737696659204},3.6354344241648011,1.7000000000000004,{"$f":"((1-$N17)*(I$8/$L$8)+$N17*(H17/$K17))*'global path'!$C16","v":1.1890004730277324},0.69941204295748949,6.9,30.80424840186744,4.4643838263575999,{"$f":"(RF!C18/RF!L18-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B17/'G-LIMITS = RF'!K17-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":4.2296783820704557E-2},null,{"$f":"RF!C18-C17","v":0},{"$f":"RF!F18-F17","v":0},{"$f":"RF!I18-I17","v":0}]
[2029,1.2,{"$f":"((1-$N18)*(C$8/$L$8)+$N18*(B18/$K18))*'global path'!$C17","v":14.245735901269432},11.871446584391194,4,{"$f":"((1-$N18)*(F$8/$L$8)+$N18*(E18/$K18))*'global path'!$C17","v":13.849199209051289},3.4622998022628222,1.7000000000000004,{"$f":"((1-$N18)*(I$8/$L$8)+$N18*(H18/$K18))*'global path'!$C17","v":1.1835927810678848},0.69623104768699084,6.9,29.278527891388606,4.2432649117954497,{"$f":"(RF!C19/RF!L19-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B18/'G-LIMITS = RF'!K18-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":5.0716494145018776E-2},null,{"$f":"RF!C19-C18","v":0},{"$f":"RF!F19-F18","v":0},{"$f":"RF!I19-I18","v":0}]
[2030,1.2,{"$f":"((1-$N19)*(C$8/$L$8)+$N19*(B19/$K19))*'global path'!$C18","v":13.406841327716663},11.17236777309722,4,{"$f":"((1-$N19)*(F$8/$L$8)+$N19*(E19/$K19))*'global path'!$C18","v":13.14735722442331},3.2868393061058274,1.7000000000000004,{"$f":"((1-$N19)*(I$8/$L$8)+$N19*(H19/$K19))*'global path'!$C18","v":1.1781124426819756},0.69300731922469139,6.9,27.732310994821948,4.0191755064959338,{"$f":"(RF!C20/RF!L20-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B19/'G-LIMITS = RF'!K19-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":6.0194503550852832E-2},null,{"$f":"RF!C20-C19","v":0},{"$f":"RF!F20-F19","v":0},{"$f":"RF!I20-I19","v":0}]
[2031,1.2,{"$f":"((1-$N20)*(C$8/$L$8)+$N20*(B20/$K20))*'global path'!$C19","v":12.562882220532583},10.469068517110486,4,{"$f":"((1-$N20)*(F$8/$L$8)+$N20*(E20/$K20))*'global path'!$C19","v":12.441278113406538},3.1103195283516345,1.7000000000000004,{"$f":"((1-$N20)*(I$8/$L$8)+$N20*(H20/$K20))*'global path'!$C19","v":1.1725990186629716},0.68976412862527725,6.9,26.17675935260209,3.7937332395075489,{"$f":"(RF!C21/RF!L21-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B20/'G-LIMITS = RF'!K20-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":7.0859593204637208E-2},null,{"$f":"RF!C21-C20","v":0},{"$f":"RF!F21-F20","v":0},{"$f":"RF!I21-I20","v":0}]
[2032,1.2,{"$f":"((1-$N21)*(C$8/$L$8)+$N21*(B21/$K21))*'global path'!$C20","v":11.719664203325619},9.7663868361046831,4,{"$f":"((1-$N21)*(F$8/$L$8)+$N21*(E21/$K21))*'global path'!$C20","v":11.735819018392645},2.9339547545981612,1.7000000000000004,{"$f":"((1-$N21)*(I$8/$L$8)+$N21*(H21/$K21))*'global path'!$C20","v":1.1670904360435628},0.68652378590797791,6.9,24.622573657761826,3.5684889359075109,{"$f":"(RF!C22/RF!L22-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B21/'G-LIMITS = RF'!K21-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":8.2861095173318827E-2},null,{"$f":"RF!C22-C21","v":0},{"$f":"RF!F22-F21","v":0},{"$f":"RF!I22-I21","v":0}]
[2033,1.2,{"$f":"((1-$N22)*(C$8/$L$8)+$N22*(B22/$K22))*'global path'!$C21","v":10.882679006500132},9.0688991720834427,4,{"$f":"((1-$N22)*(F$8/$L$8)+$N22*(E22/$K22))*'global path'!$C21","v":11.035574470193419},2.7588936175483547,1.7000000000000004,{"$f":"((1-$N22)*(I$8/$L$8)+$N22*(H22/$K22))*'global path'!$C21","v":1.1616225712519559},0.68330739485409153,6.9,23.079876047945504,3.3449095721660149,{"$f":"(RF!C23/RF!L23-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B22/'G-LIMITS = RF'!K22-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":9.6372356952473731E-2},null,{"$f":"RF!C23-C22","v":0},{"$f":"RF!F23-F22","v":0},{"$f":"RF!I23-I22","v":0}]
[2034,1.2,{"$f":"((1-$N23)*(C$8/$L$8)+$N23*(B23/$K23))*'global path'!$C22","v":10.057048969339537},8.3808741411162817,4,{"$f":"((1-$N23)*(F$8/$L$8)+$N23*(E23/$K23))*'global path'!$C22","v":10.344829956976215},2.5862074892440536,1.7000000000000004,{"$f":"((1-$N23)*(I$8/$L$8)+$N23*(H23/$K23))*'global path'!$C22","v":1.1562288875545534},0.6801346397379725,6.9,21.558107813870304,3.1243634512855514,{"$f":"(RF!C24/RF!L24-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B23/'G-LIMITS = RF'!K23-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":0.11159487234362932},null,{"$f":"RF!C24-C23","v":0},{"$f":"RF!F24-F23","v":0},{"$f":"RF!I24-I23","v":0}]
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[2036,1.2,{"$f":"((1-$N25)*(C$8/$L$8)+$N25*(B25/$K25))*'global path'!$C24","v":8.4582271647522678},7.0485226372935568,4,{"$f":"((1-$N25)*(F$8/$L$8)+$N25*(E25/$K25))*'global path'!$C24","v":9.0072122112256725},2.2518030528064181,1.7000000000000004,{"$f":"((1-$N25)*(I$8/$L$8)+$N25*(H25/$K25))*'global path'!$C24","v":1.1457840893830737},0.67399064081357263,6.9,18.611223465361014,2.6972787630957988,{"$f":"(RF!C26/RF!L26-('G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8))/('G-LIMITS = RF'!B25/'G-LIMITS = RF'!K25-'G-LIMITS = RF'!$C$8/'G-LIMITS = RF'!$L$8)","v":0.14815094636794041},null,{"$f":"RF!C26-C25","v":0},{"$f":"RF!F26-F25","v":0},{"$f":"RF!I26-I25","v":0}]
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["∑",null,{"$f":"SUM(C9:C39)","v":305.50878147574412},null,null,{"$f":"SUM(F9:F39)","v":315.45266303406379},null,null,{"$f":"SUM(I9:I39)","v":35.802201848035104},null,null,{"$f":"SUM(L9:L39)","v":656.76364635784296}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C90","v":656.76364635784296}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L40-L42","v":0}]

{"sheet":"SPF = RF","index":19,"n_rows":108,"n_cols":26,"rows_kept":108,"cut":false,"hidden":false,"merged":[[101,15,101,17],[8,15,8,17],[3,19,3,20],[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13],[5,10,7,13],[101,20,101,22]]}
["Comparision SPF and RF"]
[{"$f":"CONCATENATE(\"SPF-\",ROUND(T8*100,0))","v":"SPF-16"}]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global",null,null,null,null,null,null,null,null,"input value"]
[null,"RBA:",{"$f":"T8*'global path'!C89/K11*B11+(1-T8)*'global path'!C89*C11/L11","v":308.98458991296116},"Gt","RBB:",{"$f":"T8*'global path'!C89/K11*E11+(1-T8)*'global path'!C89*F11/L11","v":331.65057204577687},"Gt","RBC:",{"$f":"T8*'global path'!C89/K11*H11+(1-T8)*'global path'!C89*I11/L11","v":43.331043431904078},"Gt","RB:",{"$f":"C5+F5+I5","v":683.96620539064213},"Gt"]
[null,"TA",{"$f":"C5/C11","v":14.713551900617198},null,"TB",{"$f":"F5/F11","v":17.007721643373173},null,"TC",{"$f":"I5/I11","v":35.293996789517927},null,"Global path ist different to the path in sheet \"global path\"."]
[null,"rA",{"$f":"'SPF-eq'!C7","v":0},null,"rB",{"$f":"'SPF-eq'!F7","v":0.03},null,"rC",{"$f":"'SPF-eq'!I7","v":0.02}]
[null,"mA",{"$f":"(1+SQRT(1+C7*C6))/C6","v":0.13592910899482435},null,"mB",{"$f":"(1+SQRT(1+F7*F6))/F6","v":0.13105311061826475},null,"mC",{"$f":"(1+SQRT(1+I7*I6))/I6","v":6.5339536376087484E-2},null,null,null,null,null,null,"share population key:",null,null,null,0.1563944281631455,"solver: variable",null,null,"global path:",null,{"$f":"'global path'!C2","v":3}]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita",null,null,"RM - \nSPM"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t",null,null,"A","B","C"]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C11/B11","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F11/E11","v":4.875},{"$f":"K11-E11-B11","v":1.7000000000000004},{"$f":"'global path'!$C$7-C11-F11","v":1.2277171013052595},{"$f":"I11/H11","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I11+F11+C11","v":41.727717101305259},{"$f":"L11/K11","v":6.047495232073226},null,null,{"$f":"RF!C9-'SPF = RF'!C11","v":0},{"$f":"RF!F9-'SPF = RF'!F11","v":0},{"$f":"RF!I9-'SPF = RF'!I11","v":0}]
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[{"$f":"A12+1","v":2021},1.2,{"$f":"-C$11*EXP(-C$8*($A13-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A13-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)","v":20.608016746228088},17.173347288523409,4,{"$f":"-F$11*EXP(-F$8*($A13-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A13-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)","v":19.87609134997183},4.9690228374929575,1.7000000000000004,{"$f":"-I$11*EXP(-I$8*($A13-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A13-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)","v":1.2552909923131281},0.73840646606654581,{"$f":"B13+E13+H13","v":6.9},{"$f":"I13+F13+C13","v":41.739399088513046},6.0491882736975429,null,null,{"$f":"RF!C11-'SPF = RF'!C13","v":-0.57732520851127589},{"$f":"RF!F11-'SPF = RF'!F13","v":-1.1870411359555568},{"$f":"RF!I11-'SPF = RF'!I13","v":-3.390619847666021E-2}]
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[2024,1.2,18.35557610079934,15.296313417332783,4,18.642551810666816,4.6606379526667041,1.7000000000000004,1.2661346172794126,0.74478506898788954,6.9,38.264262528745569,5.545545294021097,null,null,{"$f":"RF!C14-'SPF = RF'!C16","v":-0.20788617301251477},{"$f":"RF!F14-'SPF = RF'!F16","v":-1.5288718858801111},{"$f":"RF!I14-'SPF = RF'!I16","v":-5.7051114128285008E-2}]
[2025,1.2,17.375307971334195,14.479423309445163,4,17.881255024143684,4.470313756035921,1.7000000000000004,1.2592075506346134,0.74071032390271363,6.9,36.515770546112492,5.2921406588568827,null,null,{"$f":"RF!C15-'SPF = RF'!C17","v":5.2033214806684214E-2},{"$f":"RF!F15-'SPF = RF'!F17","v":-1.3702384213044958},{"$f":"RF!I15-'SPF = RF'!I17","v":-5.4829948540116025E-2}]
[2026,1.2,16.347712703188222,13.623093919323519,4,17.025717958490702,4.2564294896226755,1.7000000000000004,1.248091411985655,0.73417141881509096,6.9,34.621522073664579,5.0176118947339967,null,null,{"$f":"RF!C16-'SPF = RF'!C18","v":0.32294568452052985},{"$f":"RF!F16-'SPF = RF'!F18","v":-1.1477627363400753},{"$f":"RF!I16-'SPF = RF'!I18","v":-4.8657074416808221E-2}]
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[2028,1.2,14.255680936281294,11.879734113567746,4,15.16338193426941,3.7908454835673524,1.7000000000000004,1.2154686791989491,0.71498157599938161,6.9,30.634531549749653,4.4397871811231377,null,null,{"$f":"RF!C18-'SPF = RF'!C20","v":0.81782929589920883},{"$f":"RF!F18-'SPF = RF'!F20","v":-0.62164423761020338},{"$f":"RF!I18-'SPF = RF'!I20","v":-2.6468206171216035E-2}]
[2029,1.2,13.229174375899589,11.024311979916325,4,14.205813554120425,3.5514533885301063,1.7000000000000004,1.1949205813346069,0.70289445960859209,6.9,28.629908511354621,4.1492621030948724,null,null,{"$f":"RF!C19-'SPF = RF'!C21","v":1.0165615253698448},{"$f":"RF!F19-'SPF = RF'!F21","v":-0.35661434506913459},{"$f":"RF!I19-'SPF = RF'!I21","v":-1.132780026672231E-2}]
[2030,1.2,12.23332075458265,10.194433962152209,4,13.254710457975932,3.313677614493983,1.7000000000000004,1.1721091860778614,0.68947599181050656,6.9,26.660140398636443,3.8637884635704989,null,null,{"$f":"RF!C20-'SPF = RF'!C22","v":1.173520573134013},{"$f":"RF!F20-'SPF = RF'!F22","v":-0.10735323355262238},{"$f":"RF!I20-'SPF = RF'!I22","v":6.003256604114604E-3}]
[2031,1.2,11.276909802470286,9.3974248353919059,4,12.322931154690451,3.0807327886726128,1.7000000000000004,1.1474030091383156,0.6749429465519502,6.9,24.747243966299052,3.5865570965650799,null,null,{"$f":"RF!C21-'SPF = RF'!C23","v":1.2859724180622951},{"$f":"RF!F21-'SPF = RF'!F23","v":0.1183469587160868},{"$f":"RF!I21-'SPF = RF'!I23","v":2.5196009524655949E-2}]
[2032,1.2,10.366001834614877,8.6383348621790645,4,11.420077821128359,2.8550194552820898,1.7000000000000004,1.1211330031575741,0.65949000185739637,6.9,22.907212658900811,3.3198858925943204,null,null,{"$f":"RF!C22-'SPF = RF'!C24","v":1.3536623687107419},{"$f":"RF!F22-'SPF = RF'!F24","v":0.31574119726428407},{"$f":"RF!I22-'SPF = RF'!I24","v":4.5957432885988636E-2}]
[2033,1.2,9.5044795608449277,7.9203996340374401,4,10.553102249693481,2.6382755624233702,1.7000000000000004,1.0935958351856598,0.64329166775627034,6.9,21.151177645724069,3.0653880645976908,null,null,{"$f":"RF!C23-'SPF = RF'!C25","v":1.3781994456552038},{"$f":"RF!F23-'SPF = RF'!F25","v":0.48247222049993965},{"$f":"RF!I23-'SPF = RF'!I25","v":6.8026736066295168E-2}]
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[2035,1.2,7.9368880686165113,6.6140733905137594,4,8.9442925893221883,2.2360731473305471,1.7000000000000004,1.0357530883962731,0.60926652258604286,6.9,17.916933746334973,2.5966570646862279,null,null,{"$f":"RF!C25-'SPF = RF'!C27","v":1.3105924643256319},{"$f":"RF!F25-'SPF = RF'!F27","v":0.72323042586871544},{"$f":"RF!I25-'SPF = RF'!I27","v":0.11518704283790093}]
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[2039,1.2,5.414871730055971,4.5123931083799764,4,6.2713693628411491,1.5678423407102873,1.7000000000000004,0.91476606385283787,0.53809768461931629,6.9,12.601007156749958,1.8262329212681097,null,null,{"$f":"RF!C29-'SPF = RF'!C31","v":0.83271646071897809},{"$f":"RF!F29-'SPF = RF'!F31","v":0.88636224175546552},{"$f":"RF!I29-'SPF = RF'!I31","v":0.21657634238146373}]
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[2041,1.2,4.4333118056242782,3.6944265046868985,4,5.2009169589691524,1.3002292397422881,1.7000000000000004,0.85414164172511775,0.50243625983830442,6.9,10.488370406318548,1.5200536820751518,null,null,{"$f":"RF!C31-'SPF = RF'!C33","v":0.49787561385743295},{"$f":"RF!F31-'SPF = RF'!F33","v":0.85547800689173492},{"$f":"RF!I31-'SPF = RF'!I33","v":0.26860096912893106}]
[2042,1.2,4.0040162125804599,3.3366801771503836,4,4.726801670098979,1.1817004175247448,1.7000000000000004,0.82420748843973257,0.48482793437631316,6.9,9.5550253711191715,1.3847862856694451,null,null,{"$f":"RF!C32-'SPF = RF'!C34","v":0.32148845011866189},{"$f":"RF!F32-'SPF = RF'!F34","v":0.82286265108156265},{"$f":"RF!I32-'SPF = RF'!I34","v":0.29457831238558874}]
[2043,1.2,3.6122312332895206,3.0101926944079338,4,4.2906906131702769,1.0726726532925692,1.7000000000000004,0.79464292715240603,0.46743701597200343,6.9,8.6975647736122035,1.260516633856841,null,null,{"$f":"RF!C33-'SPF = RF'!C35","v":0.14385388409335675},{"$f":"RF!F33-'SPF = RF'!F35","v":0.78258185095222732},{"$f":"RF!I33-'SPF = RF'!I35","v":0.32042296429423467}]
[2044,1.2,3.2553565329017573,2.7127971107514646,4,3.8904006969800662,0.97260017424501655,1.7000000000000004,0.76552095991071667,0.45030644700630384,6.9,7.9112781897925402,1.1465620564916725,null,null,{"$f":"RF!C34-'SPF = RF'!C36","v":-3.2034012892636188E-2},{"$f":"RF!F34-'SPF = RF'!F36","v":0.73714810833653921},{"$f":"RF!I34-'SPF = RF'!I36","v":0.34606449501265657}]
[2045,1.2,2.9308468394063638,2.4423723661719698,4,3.5237117566184537,0.88092793915461343,1.7000000000000004,0.7369038753018593,0.43347286782462302,6.9,7.1914624713266768,1.0422409378734314,null,null,{"$f":"RF!C35-'SPF = RF'!C37","v":-0.20363334933480104},{"$f":"RF!F35-'SPF = RF'!F37","v":0.688778759921016},{"$f":"RF!I35-'SPF = RF'!I37","v":0.37144059386945671}]
[2046,1.2,2.6362399510477807,2.1968666258731506,4,3.1884085970244591,0.79710214925611478,1.7000000000000004,0.70884431166402173,0.41696724215530678,6.9,6.5334928597362616,0.9468830231501828,null,null,{"$f":"RF!C36-'SPF = RF'!C38","v":-0.36884576902975486},{"$f":"RF!F36-'SPF = RF'!F38","v":0.63938459769563449},{"$f":"RF!I36-'SPF = RF'!I38","v":0.39649624559279051}]
[2047,1.2,2.3691767350651034,1.9743139458875862,4,2.8823132675496588,0.72057831688741469,1.7000000000000004,0.68138622866096021,0.40081542862409414,6.9,5.9328762312757224,0.85983713496749592,null,null,{"$f":"RF!C37-'SPF = RF'!C39","v":-0.52599726303712968},{"$f":"RF!F37-'SPF = RF'!F39","v":0.59057037911257915},{"$f":"RF!I37-'SPF = RF'!I39","v":0.42118301473554198}]
[2048,1.2,2.1274147010767805,1.7728455842306505,4,2.6033093330493529,0.65082733326233821,1.7000000000000004,0.65456579455829811,0.38503870268135176,6.9,5.3852898286844315,0.78047678676585963,null,null,{"$f":"RF!C38-'SPF = RF'!C40","v":-0.67381102656117564},{"$f":"RF!F38-'SPF = RF'!F40","v":0.54364462052742946},{"$f":"RF!I38-'SPF = RF'!I40","v":0.44545842439218064}]
[2049,1.2,1.9088364593326137,1.5906970494438448,4,2.3493596206916294,0.58733990517290735,1.7000000000000004,0.62841219597856579,0.36965423292856803,6.9,4.8866082760028089,0.70820409797142159,null,null,{"$f":"RF!C39-'SPF = RF'!C41","v":-0.81137461856832727},{"$f":"RF!F39-'SPF = RF'!F41","v":0.49963640194932912},{"$f":"RF!I39-'SPF = RF'!I41","v":0.46928541623983056}]
[{"$f":"A41+1","v":2050},{"$f":"RF!B40","v":1.2},1.7114541447994505,1.4262117873328755,{"$f":"RF!E40","v":4},2.1185186790482398,0.52962966976205994,{"$f":"K42-E42-B42","v":1.7000000000000004},0.60294837639172805,0.35467551552454585,{"$f":"RF!K40","v":6.9},4.4329212002394183,0.6424523478607852,null,null,{"$f":"RF!C40-'SPF = RF'!C42","v":-0.93810337561001356},{"$f":"RF!F40-'SPF = RF'!F42","v":0.45931721824988347},{"$f":"RF!I40-'SPF = RF'!I42","v":0.49263187995997448}]
["∑",null,{"$f":"SUM(C12:C42)","v":294.78639477853488},null,null,{"$f":"SUM(F12:F42)","v":313.16497631578534},null,null,{"$f":"SUM(I12:I42)","v":31.056795946125455},null,null,{"$f":"SUM(L12:L42)","v":639.00816704044564}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A42-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A42-$A$11)+2*C$8+C$7)","v":14.198195134426141},null,null,{"$f":"F$11*EXP(-F$8*($A42-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A42-$A$11)+2*F$8+F$7)","v":18.485595729991662},null,null,{"$f":"I$11*EXP(-I$8*($A42-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A42-$A$11)+2*I$8+I$7)","v":12.274247485778625},null,null,44.958038350196432]
["∑",null,{"$f":"SUM(C43:C44)","v":308.98458991296104},null,null,{"$f":"SUM(F43:F44)","v":331.65057204577698},null,null,{"$f":"SUM(I43:I44)","v":43.331043431904078},null,null,{"$f":"SUM(L43:L44)","v":683.96620539064202}]
[]
[null,null,null,null,null,"global path 2020 - 2100 sheet \"global path\":",null,null,null,null,null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L45-L47","v":0}]
[]
[]
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[2084,1.2,3.1960969559129859E-2,2.6634141299274883E-2,4,4.7387517466927098E-2,1.1846879366731775E-2,1.7000000000000004,0.11804866333200348,6.9440390195296145E-2,6.9,0.19739715035806044,2.8608282660588468E-2,null,null,{"$f":"RF!C79-'SPF = RF'!C84","v":-3.1960969559129859E-2},{"$f":"RF!F79-'SPF = RF'!F84","v":-4.7387517466927098E-2},{"$f":"RF!I79-'SPF = RF'!I84","v":-0.11804866333200348}]
[2085,1.2,2.8287192408612633E-2,2.3572660340510528E-2,4,4.2154914193807458E-2,1.0538728548451864E-2,1.7000000000000004,0.11203297883795638,6.5901752257621377E-2,6.9,0.18247508544037647,2.64456645565763E-2,null,null,{"$f":"RF!C80-'SPF = RF'!C85","v":-2.8287192408612633E-2},{"$f":"RF!F80-'SPF = RF'!F85","v":-4.2154914193807458E-2},{"$f":"RF!I80-'SPF = RF'!I85","v":-0.11203297883795638}]
[2086,1.2,2.5030982307845701E-2,2.0859151923204752E-2,4,3.7492808260227717E-2,9.3732020650569292E-3,1.7000000000000004,0.10630601548728791,6.2532950286639938E-2,6.9,0.16882980605536133,2.4468087834110336E-2,null,null,{"$f":"RF!C81-'SPF = RF'!C86","v":-2.5030982307845701E-2},{"$f":"RF!F81-'SPF = RF'!F86","v":-3.7492808260227717E-2},{"$f":"RF!I81-'SPF = RF'!I86","v":-0.10630601548728791}]
[2087,1.2,2.2145540969742722E-2,1.8454617474785603E-2,4,3.3339996497114277E-2,8.3349991242785693E-3,1.7000000000000004,0.10085531629667011,5.9326656645100048E-2,6.9,0.1563408537635271,2.265809474833726E-2,null,null,{"$f":"RF!C82-'SPF = RF'!C87","v":-2.2145540969742722E-2},{"$f":"RF!F82-'SPF = RF'!F87","v":-3.3339996497114277E-2},{"$f":"RF!I82-'SPF = RF'!I87","v":-0.10085531629667011}]
[2088,1.2,1.9589220739073931E-2,1.6324350615894944E-2,4,2.9641703714414186E-2,7.4104259286035465E-3,1.7000000000000004,9.5668845036618322E-2,5.6275791198010766E-2,6.9,0.14489976949010644,2.0999966592769048E-2,null,null,{"$f":"RF!C83-'SPF = RF'!C88","v":-1.9589220739073931E-2},{"$f":"RF!F83-'SPF = RF'!F88","v":-2.9641703714414186E-2},{"$f":"RF!I83-'SPF = RF'!I88","v":-9.5668845036618322E-2}]
[2089,1.2,1.7324971293372987E-2,1.4437476077810823E-2,4,2.6348926986176968E-2,6.587231746544242E-3,1.7000000000000004,9.0734982841569778E-2,5.3373519318570442E-2,6.9,0.13440888112111973,1.9479547988568078E-2,null,null,{"$f":"RF!C84-'SPF = RF'!C89","v":-1.7324971293372987E-2},{"$f":"RF!F84-'SPF = RF'!F89","v":-2.6348926986176968E-2},{"$f":"RF!I84-'SPF = RF'!I89","v":-9.0734982841569778E-2}]
[2090,1.2,1.5319843787966067E-2,1.2766536489971723E-2,4,2.3417844038626234E-2,5.8544610096565586E-3,1.7000000000000004,8.604252356546449E-2,5.0613249156155574E-2,6.9,0.12478021139205679,1.8084088607544461E-2,null,null,{"$f":"RF!C85-'SPF = RF'!C90","v":-1.5319843787966067E-2},{"$f":"RF!F85-'SPF = RF'!F90","v":-2.3417844038626234E-2},{"$f":"RF!I85-'SPF = RF'!I90","v":-8.604252356546449E-2}]
[2091,1.2,1.3544546780934863E-2,1.1287122317445719E-2,4,2.0809279886536941E-2,5.2023199716342353E-3,1.7000000000000004,8.1580668055155625E-2,4.7988628267738594E-2,6.9,0.11593449472262743,1.6802100684438756E-2,null,null,{"$f":"RF!C86-'SPF = RF'!C91","v":-1.3544546780934863E-2},{"$f":"RF!F86-'SPF = RF'!F91","v":-2.0809279886536941E-2},{"$f":"RF!I86-'SPF = RF'!I91","v":-8.1580668055155625E-2}]
[2092,1.2,1.197304878569827E-2,9.9775406547485592E-3,4,1.8488226334384072E-2,4.6220565835960181E-3,1.7000000000000004,7.7339017497082496E-2,4.5493539704166162E-2,6.9,0.10780029261716484,1.5623230814081859E-2,null,null,{"$f":"RF!C87-'SPF = RF'!C92","v":-1.197304878569827E-2},{"$f":"RF!F87-'SPF = RF'!F92","v":-1.8488226334384072E-2},{"$f":"RF!I87-'SPF = RF'!I92","v":-7.7339017497082496E-2}]
[2093,1.2,1.0582222772149097E-2,8.8185189767909147E-3,4,1.6423409402442912E-2,4.1058523506107281E-3,1.7000000000000004,7.3307565977371869E-2,4.3122097633748149E-2,6.9,0.10031319815196388,1.453814465970491E-2,null,null,{"$f":"RF!C88-'SPF = RF'!C93","v":-1.0582222772149097E-2},{"$f":"RF!F88-'SPF = RF'!F93","v":-1.6423409402442912E-2},{"$f":"RF!I88-'SPF = RF'!I93","v":-7.3307565977371869E-2}]
[2094,1.2,9.3515283734813826E-3,7.792940311234486E-3,4,1.4586900153949589E-2,3.6467250384873973E-3,1.7000000000000004,6.9476692381473359E-2,4.0868642577337258E-2,6.9,9.3415120908904331E-2,1.3538423320131061E-2,null,null,{"$f":"RF!C89-'SPF = RF'!C94","v":-9.3515283734813826E-3},{"$f":"RF!F89-'SPF = RF'!F94","v":-1.4586900153949589E-2},{"$f":"RF!I89-'SPF = RF'!I94","v":-6.9476692381473359E-2}]
[2095,1.2,8.2627279567221643E-3,6.8856066306018041E-3,4,1.2953764787736924E-2,3.238441196934231E-3,1.7000000000000004,6.5837151746648059E-2,3.8727736321557675E-2,6.9,8.7053644491107141E-2,1.2616470216102484E-2,null,null,{"$f":"RF!C90-'SPF = RF'!C95","v":-8.2627279567221643E-3},{"$f":"RF!F90-'SPF = RF'!F95","v":-1.2953764787736924E-2},{"$f":"RF!I90-'SPF = RF'!I95","v":-6.5837151746648059E-2}]
[2096,1.2,7.2996330825201919E-3,6.0830275687668266E-3,4,1.1501750221893814E-2,2.8754375554734535E-3,1.7000000000000004,6.2380066168949311E-2,3.6694156569970174E-2,6.9,8.118144947336331E-2,1.1765427459907725E-2,null,null,{"$f":"RF!C91-'SPF = RF'!C96","v":-7.2996330825201919E-3},{"$f":"RF!F91-'SPF = RF'!F96","v":-1.1501750221893814E-2},{"$f":"RF!I91-'SPF = RF'!I96","v":-6.2380066168949311E-2}]
[2097,1.2,6.447878215902654E-3,5.3732318465855456E-3,4,1.0211001728834032E-2,2.552750432208508E-3,1.7000000000000004,5.9096915355605795E-2,3.476289138565046E-2,6.9,7.5755795300342488E-2,1.0979100768165577E-2,null,null,{"$f":"RF!C92-'SPF = RF'!C97","v":-6.447878215902654E-3},{"$f":"RF!F92-'SPF = RF'!F97","v":-1.0211001728834032E-2},{"$f":"RF!I92-'SPF = RF'!I97","v":-5.9096915355605795E-2}]
[2098,1.2,5.6947188565521986E-3,4.7455990471268325E-3,4,9.0638094916729584E-3,2.2659523729182396E-3,1.7000000000000004,5.5979526904093024E-2,3.2929133472995892E-2,6.9,7.0738055252318188E-2,1.025189206555336E-2,null,null,{"$f":"RF!C93-'SPF = RF'!C98","v":-5.6947188565521986E-3},{"$f":"RF!F93-'SPF = RF'!F98","v":-9.0638094916729584E-3},{"$f":"RF!I93-'SPF = RF'!I98","v":-5.5979526904093024E-2}]
[2099,1.2,5.0288515366908593E-3,4.1907096139090494E-3,4,8.0443812371916584E-3,2.0110953092979146E-3,1.7000000000000004,5.302006638022505E-2,3.1188274341308844E-2,6.9,6.6093299154107568E-2,9.5787390078416763E-3,null,null,{"$f":"RF!C94-'SPF = RF'!C99","v":-5.0288515366908593E-3},{"$f":"RF!F94-'SPF = RF'!F99","v":-8.0443812371916584E-3},{"$f":"RF!I94-'SPF = RF'!I99","v":-5.302006638022505E-2}]
[2100,1.2,4.4402533888797044E-3,3.7002111573997539E-3,4,7.1386383631542941E-3,1.7846595907885735E-3,1.7000000000000004,5.0211027259600138E-2,2.9535898388000074E-2,6.9,6.1789919011634137E-2,8.9550607263237866E-3,null,null,{"$f":"RF!C95-'SPF = RF'!C100","v":-4.4402533888797044E-3},{"$f":"RF!F95-'SPF = RF'!F100","v":-7.1386383631542941E-3},{"$f":"RF!I95-'SPF = RF'!I100","v":-5.0211027259600138E-2}]
["∑",null,{"$f":"SUM(C51:C100)","v":14.164967570017836},null,null,{"$f":"SUM(F51:F100)","v":18.429828488477757},null,null,{"$f":"SUM(I51:I100)","v":11.403118582197846},null,null,{"$f":"SUM(L51:L100)","v":43.997914640693438},null,null,null,{"$f":"SUM(P12:P100)","v":1.2882989589824019},{"$f":"SUM(Q12:Q100)","v":-0.37254233089525118},{"$f":"SUM(R12:R100)","v":4.4367081415956355E-2},{"$f":"SUM(P101:R101)","v":0.9601237095031071}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A100-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A100-$A$11)+2*C$8+C$7)","v":3.3227564408307424E-2},null,null,{"$f":"F$11*EXP(-F$8*($A100-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A100-$A$11)+2*F$8+F$7)","v":5.5767241513908002E-2},null,null,{"$f":"I$11*EXP(-I$8*($A100-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A100-$A$11)+2*I$8+I$7)","v":0.87112890358077422},null,null,{"$f":"I102+F102+C102","v":0.96012370950298964},null,null,null,{"$f":"P101^2/RF!C98^2+Q101^2/RF!F98^2+R101^2/RF!I98^2","v":1.9598662549407273E-5},null,null,null,"square deviation","solver: target value min"]
["∑",null,{"$f":"SUM(C101:C102)","v":14.198195134426143},null,null,{"$f":"SUM(F101:F102)","v":18.485595729991665},null,null,{"$f":"SUM(I101:I102)","v":12.27424748577862},null,null,{"$f":"SUM(L101:L102)","v":44.958038350196425},null,null,null,{"$f":"P101/RF!C98","v":4.1525927199402559E-3},{"$f":"Q101/RF!F98","v":-1.1247502752783894E-3},{"$f":"R101/RF!I98","v":1.0438261684627618E-3},null,"deviation from RM budget"]
[]
[null,null,{"$f":"C103+C43","v":308.98458991296104},null,null,{"$f":"F103+F43","v":331.65057204577698},null,null,{"$f":"I103+I43","v":43.331043431904078},null,null,{"$f":"SUM(C105:I105)","v":683.96620539064213}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L105-L107","v":0}]

{"sheet":"SPF = C&C_exp","index":20,"n_rows":108,"n_cols":26,"rows_kept":108,"cut":false,"hidden":false,"merged":[[8,15,8,17],[101,15,101,17],[3,19,3,20],[3,1,3,3],[3,4,3,6],[3,7,3,9],[3,10,3,13],[5,10,7,13]]}
["Comparision SPF and C&C exp"]
[{"$f":"CONCATENATE(\"SPF-\",ROUND(T8*100,0))","v":"SPF-50"}]
[]
[null,"Country A",null,null,"Country B",null,null,"Country C",null,null,"Global",null,null,null,null,null,null,null,null,"input value"]
[null,"RBA:",{"$f":"T8*'global path'!C89/K11*B11+(1-T8)*'global path'!C89*C11/L11","v":230.81303194650883},"Gt","RBB:",{"$f":"T8*'global path'!C89/K11*E11+(1-T8)*'global path'!C89*F11/L11","v":358.32764134392352},"Gt","RBC:",{"$f":"T8*'global path'!C89/K11*H11+(1-T8)*'global path'!C89*I11/L11","v":94.825532100209799},"Gt","RB:",{"$f":"C5+F5+I5","v":683.96620539064213},"Gt"]
[null,"TA",{"$f":"C5/C11","v":10.991096759357564},null,"TB",{"$f":"F5/F11","v":18.375776479175563},null,"TC",{"$f":"I5/I11","v":77.237282106272772},null,"Global path ist different to the path in sheet \"global path\"."]
[null,"rA",{"$f":"'SPF-eq'!C7","v":0},null,"rB",{"$f":"'SPF-eq'!F7","v":0.03},null,"rC",{"$f":"'SPF-eq'!I7","v":0.02}]
[null,"mA",{"$f":"(1+SQRT(1+C7*C6))/C6","v":0.18196546202700351},null,"mB",{"$f":"(1+SQRT(1+F7*F6))/F6","v":0.12219898433646989},null,"mC",{"$f":"(1+SQRT(1+I7*I6))/I6","v":3.3600688940035067E-2},null,null,null,null,null,null,"share population key:",null,null,null,0.50341643882091736,"solver: variable",null,null,"global path:",null,{"$f":"'global path'!C2","v":3}]
["Year\nt","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPit","Eit","Per capita","Popu-lation\nPt","Et","Per capita",null,null,"RM - \nSPM"]
[null,"bn","Gt","t","bn","Gt","t","bn","Gt","t","bn","Gt","t",null,null,"A","B","C",null,{"$f":"COUNT($T$8)","v":1}]
[2019,{"$f":"RF!B9","v":1.2},{"$f":"RF!C9","v":21},{"$f":"C11/B11","v":17.5},{"$f":"RF!E9","v":4},{"$f":"RF!F9","v":19.5},{"$f":"F11/E11","v":4.875},{"$f":"K11-E11-B11","v":1.7000000000000004},{"$f":"'global path'!$C$7-C11-F11","v":1.2277171013052595},{"$f":"I11/H11","v":0.72218653017956425},{"$f":"RF!K9","v":6.9},{"$f":"I11+F11+C11","v":41.727717101305259},{"$f":"L11/K11","v":6.047495232073226},null,null,{"$f":"'C&C-exp'!C11-'SPF = C&C_exp'!C11","v":0},{"$f":"'C&C-exp'!F11-'SPF = C&C_exp'!F11","v":0},{"$f":"'C&C-exp'!I11-'SPF = C&C_exp'!I11","v":0},null,{"$f":"{32767;32767;0.000001;0.01;FALSE;FALSE;TRUE;1;1;1;0.0001;TRUE}","v":32767}]
[{"$f":"A11+1","v":2020},{"$f":"B$11*(B$42/B$11)^(($A12-2019)/31)","v":1.2},{"$f":"-C$11*EXP(-C$8*($A12-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A12-$A$11)+2*C$8+C$7)\n  +C$11*EXP(-C$8*($A11-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A11-$A$11)+2*C$8+C$7)","v":20.894100932579619},{"$f":"C12/B12","v":17.411750777149685},{"$f":"E$11*(E$42/E$11)^(($A12-2019)/31)","v":4},{"$f":"-F$11*EXP(-F$8*($A12-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A12-$A$11)+2*F$8+F$7)\n  +F$11*EXP(-F$8*($A11-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A11-$A$11)+2*F$8+F$7)","v":19.724056924744673},{"$f":"F12/E12","v":4.9310142311861682},{"$f":"H$11*(H$42/H$11)^(($A12-2019)/31)","v":1.7000000000000004},{"$f":"-I$11*EXP(-I$8*($A12-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A12-$A$11)+2*I$8+I$7)\n  +I$11*EXP(-I$8*($A11-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A11-$A$11)+2*I$8+I$7)","v":1.2394955180713652},{"$f":"I12/H12","v":0.72911501063021467},{"$f":"B12+E12+H12","v":6.9},{"$f":"I12+F12+C12","v":41.857653375395657},{"$f":"L12/K12","v":6.0663265761442977},null,null,{"$f":"'C&C-exp'!C12-'SPF = C&C_exp'!C12","v":-0.59475275912184955},{"$f":"'C&C-exp'!F12-'SPF = C&C_exp'!F12","v":-0.51828080846807012},{"$f":"'C&C-exp'!I12-'SPF = C&C_exp'!I12","v":0.1485429514734109},null,{"$f":"{0;0;1;100;0;FALSE;TRUE;0.075;0;0;FALSE;30}","v":0}]
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[2022,1.2,19.376041304156388,16.146701086796991,4,19.823339058122656,4.955834764530664,1.7000000000000004,1.2799514106251308,0.75291259448537096,6.9,40.479331772904175,5.8665698221600246,null,null,{"$f":"'C&C-exp'!C14-'SPF = C&C_exp'!C14","v":-0.70336927941463401},{"$f":"'C&C-exp'!F14-'SPF = C&C_exp'!F14","v":-1.3488393624716153},{"$f":"'C&C-exp'!I14-'SPF = C&C_exp'!I14","v":0.45308234423659366}]
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[2032,1.2,7.0757746563420625,5.8964788802850521,4,12.28751053254544,3.07187763313636,1.7000000000000004,1.3470725674977899,0.79239562793987628,6.9,20.710357756385292,3.0015011241138105,null,null,{"$f":"'C&C-exp'!C24-'SPF = C&C_exp'!C24","v":1.3154611800271141},{"$f":"'C&C-exp'!F24-'SPF = C&C_exp'!F24","v":0.58417831509277285},{"$f":"'C&C-exp'!I24-'SPF = C&C_exp'!I24","v":2.0125764062566485}]
[2033,1.2,6.2266351356920495,5.1888626130767079,4,11.444620681421725,2.8611551703554312,1.7000000000000004,1.3443728410507703,0.79080755355927645,6.9,19.015628658164545,2.7558882113281946,null,null,{"$f":"'C&C-exp'!C25-'SPF = C&C_exp'!C25","v":1.2093260796402729},{"$f":"'C&C-exp'!F25-'SPF = C&C_exp'!F25","v":0.76719143527732925},{"$f":"'C&C-exp'!I25-'SPF = C&C_exp'!I25","v":2.0877298748633586}]
[2034,1.2,5.4641881823651701,4.5534901519709754,4,10.633061521273106,2.6582653803182765,1.7000000000000004,1.340380786741008,0.7884592863182398,6.9,17.437630490379284,2.5271928246926496,null,null,{"$f":"'C&C-exp'!C26-'SPF = C&C_exp'!C26","v":1.0759212732991257},{"$f":"'C&C-exp'!F26-'SPF = C&C_exp'!F26","v":0.91197016590232849},{"$f":"'C&C-exp'!I26-'SPF = C&C_exp'!I26","v":2.1325858842895684}]
[2035,1.2,4.7830910102989357,3.9859091752491134,4,9.856777852292339,2.4641944630730848,1.7000000000000004,1.3351847555124152,0.7854027973602441,6.9,15.97505361810369,2.3152251620440127,null,null,{"$f":"'C&C-exp'!C27-'SPF = C&C_exp'!C27","v":0.92934929217883155},{"$f":"'C&C-exp'!F27-'SPF = C&C_exp'!F27","v":1.01712400007494},{"$f":"'C&C-exp'!I27-'SPF = C&C_exp'!I27","v":2.1444167690097569}]
[2036,1.2,4.1773790328906095,3.4811491940755079,4,9.1183924033923347,2.2795981008480837,1.7000000000000004,1.3288686706130903,0.78168745330181766,6.9,14.624640106896035,2.1195130589704396,null,null,{"$f":"'C&C-exp'!C28-'SPF = C&C_exp'!C28","v":0.78234268452710509},{"$f":"'C&C-exp'!F28-'SPF = C&C_exp'!F28","v":1.0827306711493847},{"$f":"'C&C-exp'!I28-'SPF = C&C_exp'!I28","v":2.1215100027884906}]
[2037,1.2,3.6408206433629253,3.0340172028024379,4,8.4194577868025959,2.104864446700649,1.7000000000000004,1.3215122237374004,0.77736013161023532,6.9,13.381790653902922,1.939389949841003,null,null,{"$f":"'C&C-exp'!C29-'SPF = C&C_exp'!C29","v":0.64551008109813779},{"$f":"'C&C-exp'!F29-'SPF = C&C_exp'!F29","v":1.1101880898621825},{"$f":"'C&C-exp'!I29-'SPF = C&C_exp'!I29","v":2.0634126831196111}]
[2038,1.2,3.167171156379716,2.6393092969830967,4,7.7606679819577948,1.9401669954894487,1.7000000000000004,1.3131910630401507,0.77246533120008842,6.9,12.241030201377662,1.774062348025748,null,null,{"$f":"'C&C-exp'!C30-'SPF = C&C_exp'!C30","v":0.52677220571337324},{"$f":"'C&C-exp'!F30-'SPF = C&C_exp'!F30","v":1.1020876521347827},{"$f":"'C&C-exp'!I30-'SPF = C&C_exp'!I30","v":1.9711237132519286}]
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[2040,1.2,2.3845572934471768,1.9871310778726474,4,6.5630381445449615,1.6407595361362404,1.7000000000000004,1.2939380488631258,0.76114002874301501,6.9,10.241533486855264,1.48428021548627,null,null,{"$f":"'C&C-exp'!C32-'SPF = C&C_exp'!C32","v":0.36004873336247423},{"$f":"'C&C-exp'!F32-'SPF = C&C_exp'!F32","v":0.99472780823072426},{"$f":"'C&C-exp'!I32-'SPF = C&C_exp'!I32","v":1.6957054418584643}]
[2041,1.2,2.0643518495306186,1.7202932079421822,4,6.0227434454503879,1.505685861362597,1.7000000000000004,1.2831388587048309,0.75478756394401803,6.9,9.3702341536858373,1.3580049498095417,null,null,{"$f":"'C&C-exp'!C33-'SPF = C&C_exp'!C33","v":0.31275388598830967},{"$f":"'C&C-exp'!F33-'SPF = C&C_exp'!F33","v":0.90526538929926836},{"$f":"'C&C-exp'!I33-'SPF = C&C_exp'!I33","v":1.522071567223231}]
[2042,1.2,1.7846894789517567,1.4872412324597972,4,5.5199084426995242,1.379977110674881,1.7000000000000004,1.2716406054971969,0.74802388558658628,6.9,8.5762385271484778,1.2429331198765909,null,null,{"$f":"'C&C-exp'!C34-'SPF = C&C_exp'!C34","v":0.28566676571150795},{"$f":"'C&C-exp'!F34-'SPF = C&C_exp'!F34","v":0.79935485016028807},{"$f":"'C&C-exp'!I34-'SPF = C&C_exp'!I34","v":1.332694641684709}]
[2043,1.2,1.5409428352177912,1.2841190293481595,4,5.0530641730979156,1.2632660432744789,1.7000000000000004,1.259501277357316,0.74088310432783278,6.9,7.8535082856730227,1.1381896066192787,null,null,{"$f":"'C&C-exp'!C35-'SPF = C&C_exp'!C35","v":0.27371618990076985},{"$f":"'C&C-exp'!F35-'SPF = C&C_exp'!F35","v":0.68274540487860413},{"$f":"'C&C-exp'!I35-'SPF = C&C_exp'!I35","v":1.1344535924996255}]
[2044,1.2,1.3289020848758604,1.1074184040632171,4,4.620583972944118,1.1551459932360295,1.7000000000000004,1.2467757935026285,0.73339752558978133,6.9,7.1962618513226069,1.0429365001916822,null,null,{"$f":"'C&C-exp'!C36-'SPF = C&C_exp'!C36","v":0.27116550924787308},{"$f":"'C&C-exp'!F36-'SPF = C&C_exp'!F36","v":0.56092186320186421},{"$f":"'C&C-exp'!I36-'SPF = C&C_exp'!I36","v":0.9341075564767567}]
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[2046,1.2,0.98511348840227164,0.82092790700189311,4,3.8517441900823641,0.96293604752059103,1.7000000000000004,1.2197715221288021,0.71751266007576575,6.9,6.0566292006134379,0.87777234791499092,null,null,{"$f":"'C&C-exp'!C38-'SPF = C&C_exp'!C38","v":0.27352449972985027},{"$f":"'C&C-exp'!F38-'SPF = C&C_exp'!F38","v":0.32030028463367799},{"$f":"'C&C-exp'!I38-'SPF = C&C_exp'!I38","v":0.55007394901796136}]
[2047,1.2,0.84689915512439651,0.70574929593699709,4,3.5117922993366477,0.87794807483416193,1.7000000000000004,1.2055884549077831,0.70916967935751929,6.9,5.5642799093688273,0.80641737816939518,null,null,{"$f":"'C&C-exp'!C39-'SPF = C&C_exp'!C39","v":0.271207967787362},{"$f":"'C&C-exp'!F39-'SPF = C&C_exp'!F39","v":0.20853179506291264},{"$f":"'C&C-exp'!I39-'SPF = C&C_exp'!I39","v":0.37461268986760721}]
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[2049,1.2,0.62423392223048602,0.52019493519207172,4,2.9118506415284493,0.72796266038211233,1.7000000000000004,1.1760804801477889,0.69181204714575795,6.9,4.7121650439067242,0.68292247013140928,null,null,{"$f":"'C&C-exp'!C41-'SPF = C&C_exp'!C41","v":0.25304995982190104},{"$f":"'C&C-exp'!F41-'SPF = C&C_exp'!F41","v":1.2283996937493047E-2},{"$f":"'C&C-exp'!I41-'SPF = C&C_exp'!I41","v":6.6656474957521139E-2}]
[{"$f":"A41+1","v":2050},{"$f":"RF!B40","v":1.2},0.53525654652760757,0.44604712210633968,{"$f":"RF!E40","v":4},2.6483683498831034,0.66209208747077586,{"$f":"K42-E42-B42","v":1.7000000000000004},1.1608363638045418,0.68284491988502438,{"$f":"RF!K40","v":6.9},4.3444612602152528,0.62963206669786265,null,null,{"$f":"'C&C-exp'!C42-'SPF = C&C_exp'!C42","v":0.23809422266182945},{"$f":"'C&C-exp'!F42-'SPF = C&C_exp'!F42","v":-7.0532452584979755E-2},{"$f":"'C&C-exp'!I42-'SPF = C&C_exp'!I42","v":-6.5256107452839052E-2}]
["∑",null,{"$f":"SUM(C12:C42)","v":227.6829764691891},null,null,{"$f":"SUM(F12:F42)","v":333.17263109686911},null,null,{"$f":"SUM(I12:I42)","v":39.938748471663679},null,null,{"$f":"SUM(L12:L42)","v":600.79435603772151}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A42-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A42-$A$11)+2*C$8+C$7)","v":3.1300554773197122},null,null,{"$f":"F$11*EXP(-F$8*($A42-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A42-$A$11)+2*F$8+F$7)","v":25.15501024705447},null,null,{"$f":"I$11*EXP(-I$8*($A42-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A42-$A$11)+2*I$8+I$7)","v":54.886783628546148},null,null,83.171849352920333]
["∑",null,{"$f":"SUM(C43:C44)","v":230.8130319465088},null,null,{"$f":"SUM(F43:F44)","v":358.32764134392357},null,null,{"$f":"SUM(I43:I44)","v":94.825532100209827},null,null,{"$f":"SUM(L43:L44)","v":683.96620539064179}]
[]
[null,null,null,null,null,"global path 2020 - 2100 sheet \"global path\":",null,null,null,null,null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L45-L47","v":0}]
[]
[]
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[2093,1.2,4.6975536129338288E-4,3.9146280107781907E-4,4,2.9885649698986994E-2,7.4714124247467484E-3,1.7000000000000004,0.5131521227946152,0.30185418987918533,6.9,0.54350752785489553,7.8769206935492109E-2,null,null,{"$f":"'C&C-exp'!C90-'SPF = C&C_exp'!C93","v":-4.6975536129338288E-4},{"$f":"'C&C-exp'!F90-'SPF = C&C_exp'!F93","v":-2.9885649698986994E-2},{"$f":"'C&C-exp'!I90-'SPF = C&C_exp'!I93","v":-0.5131521227946152}]
[2094,1.2,3.9656044451237028E-4,3.3046703709364194E-4,4,2.6778322006109606E-2,6.6945805015274015E-3,1.7000000000000004,0.50158076061978818,0.29504750624693415,6.9,0.52875564307041023,7.6631252618900025E-2,null,null,{"$f":"'C&C-exp'!C91-'SPF = C&C_exp'!C94","v":-3.9656044451237028E-4},{"$f":"'C&C-exp'!F91-'SPF = C&C_exp'!F94","v":-2.6778322006109606E-2},{"$f":"'C&C-exp'!I91-'SPF = C&C_exp'!I94","v":-0.50158076061978818}]
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[2096,1.2,2.8247672063939563E-4,2.3539726719949637E-4,4,2.1489582418567521E-2,5.3723956046418803E-3,1.7000000000000004,0.47905045302730187,0.28179438413370694,6.9,0.50082251216650875,7.2582972777754884E-2,null,null,{"$f":"'C&C-exp'!C93-'SPF = C&C_exp'!C96","v":-2.8247672063939563E-4},{"$f":"'C&C-exp'!F93-'SPF = C&C_exp'!F96","v":-2.1489582418567521E-2},{"$f":"'C&C-exp'!I93-'SPF = C&C_exp'!I96","v":-0.47905045302730187}]
[2097,1.2,2.3835351348638965E-4,1.9862792790532473E-4,4,1.9246646973921061E-2,4.8116617434802653E-3,1.7000000000000004,0.46808959002246553,0.2753468176602738,6.9,0.48757459050987301,7.0662984131865655E-2,null,null,{"$f":"'C&C-exp'!C94-'SPF = C&C_exp'!C97","v":-2.3835351348638965E-4},{"$f":"'C&C-exp'!F94-'SPF = C&C_exp'!F97","v":-1.9246646973921061E-2},{"$f":"'C&C-exp'!I94-'SPF = C&C_exp'!I97","v":-0.46808959002246553}]
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[2099,1.2,1.6963349648064987E-4,1.4136124706720822E-4,4,1.5432146145268472E-2,3.8580365363171179E-3,1.7000000000000004,0.44677048256546215,0.26280616621497765,6.9,0.46237226220721123,6.7010472783653796E-2,null,null,{"$f":"'C&C-exp'!C96-'SPF = C&C_exp'!C99","v":-1.6963349648064987E-4},{"$f":"'C&C-exp'!F96-'SPF = C&C_exp'!F99","v":-1.5432146145268472E-2},{"$f":"'C&C-exp'!I96-'SPF = C&C_exp'!I99","v":-0.44677048256546215}]
[2100,1.2,1.4307564369152033E-4,1.1922970307626694E-4,4,1.3815712730967586E-2,3.4539281827418965E-3,1.7000000000000004,0.4364094326611756,0.25671143097716204,6.9,0.45036822103583474,6.5270756671860108E-2,null,null,{"$f":"'C&C-exp'!C97-'SPF = C&C_exp'!C100","v":-1.4307564369152033E-4},{"$f":"'C&C-exp'!F97-'SPF = C&C_exp'!F100","v":-1.3815712730967586E-2},{"$f":"'C&C-exp'!I97-'SPF = C&C_exp'!I100","v":-0.4364094326611756}]
["∑",null,{"$f":"SUM(C51:C100)","v":3.1292884500384615},null,null,{"$f":"SUM(F51:F100)","v":25.038104324534402},null,null,{"$f":"SUM(I51:I100)","v":38.21760065811219},null,null,{"$f":"SUM(L51:L100)","v":66.384993432685036},null,null,null,{"$f":"SUM(P12:P100)","v":16.323049929299398},{"$f":"SUM(Q12:Q100)","v":-5.4532871682706645},{"$f":"SUM(R12:R100)","v":5.9170931592066616},{"$f":"SUM(P101:R101)","v":16.786855920235396}]
["Rest",null,{"$f":"C$11*EXP(-C$8*($A100-$A$11))/C$8^2*((C$7*C$8+C$8^2)*($A100-$A$11)+2*C$8+C$7)","v":7.6702728125196105E-4},null,null,{"$f":"F$11*EXP(-F$8*($A100-$A$11))/F$8^2*((F$7*F$8+F$8^2)*($A100-$A$11)+2*F$8+F$7)","v":0.11690592252005776},null,null,{"$f":"I$11*EXP(-I$8*($A100-$A$11))/I$8^2*((I$7*I$8+I$8^2)*($A100-$A$11)+2*I$8+I$7)","v":16.669182970433962},null,null,{"$f":"I102+F102+C102","v":16.786855920235272},null,null,null,{"$f":"P101^2/'C&C-exp'!C100^2+Q101^2/'C&C-exp'!F100^2+R101^2/'C&C-exp'!I100^2","v":9.554808610865325E-3},null,null,null,"square deviation","solver: target value min"]
["∑",null,{"$f":"SUM(C101:C102)","v":3.1300554773197136},null,null,{"$f":"SUM(F101:F102)","v":25.155010247054459},null,null,{"$f":"SUM(I101:I102)","v":54.886783628546155},null,null,{"$f":"SUM(L101:L102)","v":83.171849352920304},null,null,null,{"$f":"P101/'C&C-exp'!C100","v":6.6049038516830513E-2},{"$f":"Q101/'C&C-exp'!F100","v":-1.5459027712314884E-2},{"$f":"R101/'C&C-exp'!I100","v":7.038005103761609E-2},null,"deviation from C&C exp budget"]
[]
[null,null,{"$f":"C103+C43","v":230.8130319465088},null,null,{"$f":"F103+F43","v":358.32764134392357},null,null,{"$f":"I103+I43","v":94.825532100209841},null,null,{"$f":"SUM(C105:I105)","v":683.96620539064224}]
[]
[null,null,null,null,null,null,null,null,null,"global path:",null,{"$f":"'global path'!C89","v":683.96620539064213}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"L105-L107","v":0}]

{"sheet":"glossary","index":21,"n_rows":21,"n_cols":3,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Country A","≈ developed countries"]
[null,"Country B","≈ emerging countries"]
[null,"Country C","≈ developing countries"]
[]
[]
[null,{"$f":"comparison!B43","v":"C&C-exp"},{"$f":"comparison!C43","v":"C&C: exponential approach"}]
[null,{"$f":"comparison!B44","v":"C&C-lin"},{"$f":"comparison!C44","v":"C&C: linear aproach"}]
[null,{"$f":"CDC!A2","v":"CDC"},{"$f":"CDC!A1","v":"Common but Differentiated Convergence"}]
[null,{"$f":"comparison!B50","v":"EPM"},{"$f":"comparison!C50","v":"Cap Model"}]
[null,"ESPM","Extended Smooth Pathway Model"]
[null,{"$f":"comparison!B42","v":"GQWF"},{"$f":"comparison!C42","v":"General Quadratic Weigthing Formula"}]
[null,{"$f":"comparison!B45","v":"LIMITS"},{"$f":"comparison!C45","v":"LIMITS"}]
[null,{"$f":"comparison!B46","v":"pc20"},{"$f":"comparison!C46","v":"Allocation per capita starting 2020"}]
[null,{"$f":"comparison!B41","v":"RF"},{"$f":"comparison!C41","v":"Regensburg Model resp. Regensburg Formula"}]
[null,{"$f":"comparison!B49","v":"SPF-50"},{"$f":"comparison!C49","v":"Smooth Pathways Formula (spk = 50%)"}]
[null,{"$f":"comparison!B47","v":"SPF-eq"},{"$f":"comparison!C47","v":"Smooth Pathways Formula - equity (spk = 100%)"}]
[null,{"$f":"comparison!B48","v":"SPF-in"},{"$f":"comparison!C48","v":"Smooth Pathways Formula - inertia (spk = 0%)"}]
[null,"spk","share population key; weighting population"]
[]
[null,"2020 - 2050","convergence periond per capita emissions: RF, GQWF, C&C, LIMITS, CDC"]

{"sheet":"imprint","index":22,"n_rows":19,"n_cols":3,"rows_kept":19,"cut":false,"hidden":false,"merged":[[15,2,15,3],[18,2,18,3],[18,1,20,1]]}
[]
[null,"Authors:"]
[]
[null,"Andreas Wolfsteiner, Master of Economics"]
[null,"Günter Wittmann, Master of Mathematics"]
[null,"save-the-climate@online.ms"]
[]
[null,"last update:","2024-05-02"]
[]
[]
[null,"You can download the most recent version of the tool here:"]
[null,"http://downloads.save-the-climate.info"]
[]
[null,"Papers published on this topic:"]
[]
[null,"Distribution of a Global CO2 Budget -","10.5281/zenodo.4540475"]
[null,"A Comparison of Resource Sharing Models"]
[]
[null,"Distribution of a Global CO2 Budget -\nA Mathematical Description of Resource Sharing Models","10.5281/zenodo.4405448"]

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