ABCDEFGHIJKLMNOPQRSTWXYZAAABACADAEAFAG
1
Cells B12 and B15 have been adjusted to remove discounting factors. Columns M and R use an isoelastic utility function (set in cell R3) instead of a log utility function in the other sheet.
2
3
Key simulation outputsNotesAssumptions ->
Research intensity 2020
R&D production function params
L, K form a system that develops over time give params and H
eta1.5
4
Utility gain from R&D166,414.772.30%lambda0.75
M, N result from that system but don't feed back in
Fraction world GDP invested in R&D for intervention
5
Utility gain from giving to ppl on global average income
79,000.40Population 2020
Annual absolute increase in research intensity
phi-1.3251.00E-05
6
Impact ratio2.11Impact ratio = (utility gain from R&D / utility gain from giving cash to world average income)7.90E+090.05%delta0.0001
Extra researchers in 1st year due to intervention
7
Isoelastic Utility gain from giving to ppl on global average income
9,829.27
Population growth rate 2020-2100
Maximum research intensity
Annual discount
Recent growth rate in # researchers
3%
Total discounted utility, world 2
7.90E+04
Total discounted utility, world 1
8
Isoelastic Cost-Effectiveness in OP units
130.2348189The outputs in the table use a value of exactly 21, so are very slightly different.0.41%30.00%0.20%Initial A64.597826758.62E+128.62E+12
9
Quantities common to world 1 and world 2World 2: no interventionWorld 1: extra spend on R&D in year 1 due to intervention
10
Adjustments to simulation outputSimulation ->YearPopulation
Research intensity
# researchersDiscount
A (level of tech)
dA (tech progress)
Utility per person
Discounted population utility
A (level of tech)
dA (tech progress)
Utility per person
Discounted population utility
11
Convert to OP units5The "Impact ratio" calculated in simulation compares R&D to giving $ to someone on the average GWP/capita, which is ~$10k. OP units compare R&D to giving $ to someone on $50k. So the impact is 5X higher when measured in OP units.20207.90E+092.30%1.82E+08164.597826750.62514025881.7511595131.38E+1064.597826750.62534409791.7511595131.38E+10
12
Will benefits be realised all over the world?
120217.93E+092.35%1.86E+080.99800199871.0%65.222967010.62839597781.7523549111.38732E+1065.223170850.62839337571.7523552981.38732E+10
13
Capital share0.3520227.97E+092.39%1.91E+080.996007989365.851362980.63152200341.7535393381.39E+1065.851564220.63151944631.7535397141.39E+10
14
Boost from capital accumulation1.53820238.00E+092.44%1.95E+080.994017964166.482884990.63452456641.7547126981.40E+1066.483083670.63452205391.7547130641.40E+10
15
R&D share of TFP growth120248.03E+092.48%2.00E+080.992031914867.117409550.63740960011.7558749181.40E+1067.117605720.63740713161.7558752751.40E+10
16
20258.07E+092.53%2.04E+080.990049833767.754819150.64018275221.7570259461.40E+1067.755012850.64018032731.7570262931.40E+10
17
Outputs quoted in table in R&D post.
20268.10E+092.58%2.09E+080.988071712968.395001910.6428493991.7581657481.41E+1068.395193180.64284701691.7581660861.41E+10
18
Cost-Effectiveness in OP units16.20388837The outputs in the table use a value of exactly 21, so are very slightly different.20278.13E+092.62%2.13E+080.986097544369.037851310.64541465641.7592943071.41E+1069.03804020.64541231661.7592946361.41E+10
19
$20b to R&D gives same welfare as raising X ppl's income by 10%6.48E+0720288.17E+092.67%2.18E+080.984127320169.683265960.64788339311.7604116221.41E+1069.683452510.6478810951.7604119431.41E+10
20
R&D $ needed to get the same welfare benefit as raising 1 person's income by 10%308.56791220298.20E+092.71%2.23E+080.982161032470.331149350.65026024141.7615177071.42E+1070.331333610.65025798421.761518021.42E+10
21
20308.23E+092.76%2.27E+080.980198673370.98140960.65254960851.7626125881.42E+1070.981591590.65254739161.7626128921.42E+10
22
Average growth 2020-210020318.27E+092.81%2.32E+080.978240235171.63395920.65475568761.7636963021.43E+1071.634138980.65475351031.7636965991.43E+10
23
A0.8%20328.30E+092.85%2.37E+080.976285709872.288714890.65688246771.7647688981.43E+1072.288892490.65688032931.7647691871.43E+10
24
GDP/capita1.19%20338.34E+092.90%2.42E+080.974335089672.945597360.65893374391.7658304331.43E+1072.945772820.65893164381.7658307151.43E+10
25
20348.37E+092.94%2.46E+080.972388366873.60453110.66091312671.7668809741.44E+1073.604704470.66091106411.7668812481.44E+10
26
20358.41E+092.99%2.51E+080.970445533574.265444230.66282405091.7679205941.44E+1074.265615530.66282202511.7679208621.44E+10
27
20368.44E+093.04%2.56E+080.968506582174.928268280.66466978461.7689493751.45E+1074.928437560.6646677951.7689496361.45E+10
28
20378.48E+093.08%2.61E+080.966571504675.592938070.66645343721.7699674031.45E+1075.593105350.6664514831.7699676571.45E+10
29
20388.51E+093.13%2.66E+080.964640293576.25939150.66817796741.770974771.45E+1076.259556840.6681760481.7709750181.45E+10
30
20398.55E+093.17%2.71E+080.962712940976.927569470.66984619071.7719715741.46E+1076.927732880.66984430541.7719718161.46E+10
31
20408.58E+093.22%2.76E+080.960789439277.597415660.67146078651.7729579151.46E+1077.597577190.67145893451.7729581511.46E+10
32
20418.62E+093.27%2.81E+080.958869780678.268876450.67302430491.7739338981.47E+1078.269036120.67302248561.7739341291.47E+10
33
20428.65E+093.31%2.87E+080.956953957578.941900750.67453917331.7748996311.47E+1078.942058610.67453738611.7748998561.47E+10
34
20438.69E+093.36%2.92E+080.955041962279.616439930.67600770251.7758552251.47E+1079.616595990.67600594671.7758554451.47E+10
35
20448.72E+093.40%2.97E+080.953133787180.292447630.67743209251.7768007931.48E+1080.292601940.67743036741.7768010081.48E+10
36
20458.76E+093.45%3.02E+080.951229424580.969879720.67881443821.7777364491.48E+1080.970032310.67881274331.7777366581.48E+10
37
20468.80E+093.50%3.08E+080.949328866881.648694160.68015673461.778662311.49E+1081.648845050.68015506911.7786625141.49E+10
38
20478.83E+093.54%3.13E+080.947432106582.328850890.68146088171.7795784921.49E+1082.329000120.6814592451.7795786921.49E+10
39
20488.87E+093.59%3.18E+080.945539135983.010311780.68272868941.7804851161.49E+1083.010459370.6827270811.7804853111.49E+10
40
20498.91E+093.63%3.24E+080.943649947483.693040460.68396188211.7813822991.50E+1083.693186450.68396030141.781382491.50E+10
41
20508.94E+093.68%3.29E+080.941764533684.377002350.68516210291.7822701621.50E+1084.377146750.68516054921.7822703481.50E+10
42
20518.98E+093.73%3.35E+080.939882886885.062164450.68633091751.7831488241.51E+1085.06230730.68632939031.7831490061.51E+10
43
20529.02E+093.77%3.40E+080.938004999585.748495370.68746981841.7840184061.51E+1085.748636690.68746831711.7840185841.51E+10
44
20539.06E+093.82%3.46E+080.936130864386.435965190.68858022821.7848790271.51E+1086.436105010.68857875241.7848792011.51E+10
45
20549.09E+093.86%3.51E+080.934260473687.124545410.68966350351.7857308071.52E+1087.124683760.68966205251.7857309781.52E+10
46
20559.13E+093.91%3.57E+080.932393819987.814208920.69072093771.7865738651.52E+1087.814345810.6907195111.7865740321.52E+10
47
20569.17E+093.96%3.63E+080.930530895888.504929860.69175376441.787408321.53E+1088.505065320.69175236151.7874084821.53E+10
48
20579.21E+094.00%3.68E+080.928671693889.196683620.69276316041.7882342881.53E+1089.196817680.69276178081.7882344481.53E+10
49
20589.25E+094.05%3.74E+080.926816206689.889446780.69375024831.7890518881.53E+1089.889579460.69374889151.7890520441.53E+10
50
20599.28E+094.09%3.80E+080.924964426590.583197030.69471609961.7898612361.54E+1090.583328350.6947147651.7898613881.54E+10
51
20609.32E+094.14%3.86E+080.923116346491.277913130.69566173641.7906624461.54E+1091.278043120.69566042371.7906625951.54E+10
52
20619.36E+094.19%3.92E+080.921271958791.973574860.69658813471.7914556341.54E+1091.973703540.69658684341.791455781.54E+10
53
20629.40E+094.23%3.98E+080.919431256192.6701630.69749622611.7922409111.55E+1092.670290390.69749495571.7922410541.55E+10
54
20639.44E+094.28%4.04E+080.917594231293.367659230.69838690031.793018391.55E+1093.367785340.69838565031.793018531.55E+10
55
20649.48E+094.32%4.10E+080.915760876794.066046130.69926100661.7937881821.56E+1094.066170990.69925977671.7937883191.56E+10
56
20659.52E+094.37%4.16E+080.913931185394.765307130.70011935651.7945503961.56E+1094.765430770.70011814621.794550531.56E+10
57
20669.56E+094.42%4.22E+080.912105149595.465426490.70096272511.795305141.56E+1095.465548920.7009615341.7953052711.56E+10
58
20679.60E+094.46%4.28E+080.910282762296.166389210.7017918531.7960525211.57E+1096.166510450.70179068081.796052651.57E+10
59
20689.64E+094.51%4.34E+080.908464016196.868181070.70260744811.7967926451.57E+1096.868301130.70260629421.7967927711.57E+10
60
20699.68E+094.55%4.41E+080.906648903897.570788510.70341018651.7975256151.58E+1097.570907420.70340905071.7975257381.58E+10
61
20709.72E+094.60%4.47E+080.90483741898.27419870.70420071511.7982515351.58E+1098.274316480.70419959691.7982516551.58E+10
62
20719.76E+094.65%4.53E+080.903029551798.978399420.70497965191.7989705051.58E+1098.978516070.7049785511.7989706231.58E+10
63
20729.80E+094.69%4.60E+080.901225297499.683379070.70574758811.7996826251.59E+1099.683494620.70574650411.7996827411.59E+10
64
20739.84E+094.74%4.66E+080.8994246481100.38912670.7065050891.8003879951.59E+10100.38924110.70650402151.8003881081.59E+10
65
20749.88E+094.78%4.73E+080.8976275964101.09563170.70725269531.801086711.60E+10101.09574510.70725164411.8010868221.60E+10
66
20759.92E+094.83%4.79E+080.8958341353101.80288440.70799092431.8017788671.60E+10101.80299680.7079898891.8017789761.60E+10
67
20769.96E+094.88%4.86E+080.8940442575102.51087540.70872027091.802464561.61E+10102.51098670.70871925121.8024646671.61E+10
68
20771.00E+104.92%4.92E+080.8922579559103.21959560.70944120891.8031438811.61E+10103.21970590.70944020441.8031439861.61E+10
69
20781.00E+104.97%4.99E+080.8904752233103.92903680.71015419151.8038169221.61E+10103.92914610.7101532021.8038170251.61E+10
70
20791.01E+105.01%5.06E+080.8886960526104.6391910.71085965251.8044837721.62E+10104.63929930.71085867771.8044838741.62E+10
71
20801.01E+105.06%5.12E+080.8869204367105.35005070.71155800751.8051445211.62E+10105.3501580.7115570471.8051446211.62E+10
72
20811.02E+105.11%5.19E+080.8851483685106.06160870.71224965421.8057992551.63E+10106.06171510.71224870771.8057993531.63E+10
73
20821.02E+105.15%5.26E+080.8833798409106.77385840.71293497331.8064480611.63E+10106.77396380.71293404071.8064481561.63E+10
74
20831.03E+105.20%5.33E+080.8816148468107.48679330.71361432981.8070910211.63E+10107.48689780.71361341071.8070911151.63E+10
75
20841.03E+105.24%5.40E+080.8798533791108.20040770.71428807311.807728221.64E+10108.20051120.71428716721.8077283121.64E+10
76
20851.03E+105.29%5.47E+080.8780954309108.91469570.71495653791.8083597391.64E+10108.91479840.71495564491.8083598291.64E+10
77
20861.04E+105.34%5.54E+080.8763409951109.62965230.71562004491.8089856581.65E+10109.6297540.71561916471.8089857461.65E+10
78
20871.04E+105.38%5.61E+080.8745900646110.34527230.71627890161.8096060561.65E+10110.34537320.71627803381.8096061431.65E+10
79
20881.05E+105.43%5.68E+080.8728426325111.06155120.71693340231.8102210111.65E+10111.06165120.71693254681.8102210971.65E+10
80
20891.05E+105.47%5.75E+080.8710986917111.77848460.71758382961.81083061.66E+10111.77858380.71758298611.8108306841.66E+10
81
20901.06E+105.52%5.83E+080.8693582354112.49606840.71823045391.8114348971.66E+10112.49616680.71822962221.8114349791.66E+10
82
20911.06E+105.57%5.90E+080.8676212565113.21429890.71887353491.8120339761.67E+10113.21439640.71887271461.8120340571.67E+10
83
20921.06E+105.61%5.97E+080.8658877481113.93317240.71951332111.812627911.67E+10113.93326910.71951251221.812627991.67E+10
84
20931.07E+105.66%6.05E+080.8641577032114.65268580.72015005131.8132167711.67E+10114.65278160.72014925341.8132168491.67E+10
85
20941.07E+105.70%6.12E+080.8624311149115.37283580.72078395411.8138006281.68E+10115.37293090.72078316711.8138007051.68E+10
86
20951.08E+105.75%6.20E+080.8607079764116.09361980.7214152491.8143795511.68E+10116.0937140.72141447281.8143796261.68E+10
87
20961.08E+105.80%6.27E+080.8589882807116.8150350.72204414651.8149536071.69E+10116.81512850.72204338081.8149536811.69E+10
88
20971.09E+105.84%6.35E+080.857272021117.53707920.72267084861.8155228641.69E+10117.53717190.72267009311.8155229361.69E+10
89
20981.09E+105.89%6.42E+080.8555591904118.259750.72329554891.8160873861.70E+10118.2598420.72329480351.8160874571.70E+10
90
20991.10E+105.93%6.50E+080.853849782118.98304560.72391843341.8166472391.70E+10118.98313680.72391769791.8166473091.70E+10
91
21001.10E+105.98%6.58E+080.852143789119.7069640.72453968041.8172024851.70E+10119.70705450.72453895471.8172025541.70E+10
92
21011.10E+106.03%6.63E+080.8504412045120.43150370.72291246821.8177531871.70E+10120.43159340.72291175421.8177532551.70E+10
93
21021.10E+106.07%6.68E+080.8487420219121.15441610.72130481471.8182977221.70E+10121.15450520.72130411221.8182977891.70E+10
94
21031.10E+106.12%6.73E+080.8470462342121.87572090.71971628791.818836211.69E+10121.87580930.71971559661.8188362761.69E+10
95
21041.10E+106.16%6.78E+080.8453538347122.59543720.71814646951.8193687691.69E+10122.59552490.71814578911.8193688331.69E+10
96
21051.10E+106.21%6.83E+080.8436648166123.31358370.71659495441.8198955121.69E+10123.31367070.71659428461.8198955751.69E+10
97
21061.10E+106.26%6.88E+080.8419791732124.03017870.71506135021.820416551.69E+10124.0302650.71506069081.8204166121.69E+10
98
21071.10E+106.30%6.93E+080.8402968977124.745240.71354527661.8209319911.68E+10124.74532570.71354462741.8209320531.68E+10
99
21081.10E+106.35%6.98E+080.8386179833125.45878530.71204636491.8214419411.68E+10125.45887030.71204572571.8214420011.68E+10
100
21091.10E+106.39%7.03E+080.8369424235126.17083170.71056425791.8219465011.68E+10126.1709160.71056362831.821946561.68E+10