World GDP/capita and energy efficiency - base case - wealth convergence by 2100

Here I'll develop a 'wealth convergence' scenario to act as a base case:

1. GDP/capita in Europe grows at the same annual rate between 2010 and 2100 as it did between 1870 and 2000. The analysis by Broadberry and Klein (1911) gives GDP/capita growth rates (% per year) as follows:

   Region	1870-1913	1913-1950	1950-1990	1990-2000
   NW	1.03	0.95	2.47	2.19
   S	1.15	0.73	3.39	1.57
   C&E	1.12	0.79	2.55	-0.47
   Total	1.08	0.82	2.72	0.96

   Northwestern (NW) includes Scandinavia, Benelux and the UK; Southern (S) covers countries bordering the Mediterranean including Turkey plus Portugal; Central and Eastern (C&E) includes Austria, Germany, Switzerland, Poland and the USSR.
   Since 1870 there have been times of boom and bust, of war and peace but there has been an increase in GDP per capita over the 130 years for all Europe which averages out at 1.5% per year. This is the figure that will be assumed for the remainder of the 21st century.
2. Every nation converges on European GDP/capita by 2100. This implies a slowing in the rate of growth of GDP in the USA compared to Europe but is unlikely to introduce serious errors for global GDP which by 2050 will be dominated by Asia who will be joined by Africa by 2100.
3. The trend in energy efficiency that was achieved by the USA in the last 200 years is achieved by all nations and maintained throughout the 21st century. The evidence from my posting on 16 January 2014 shows that between 1795 and 2005 the USA increased GDP/capita by a factor of 40 whilst increasing energy efficiency by a factor of 20. For my base case I will assume that this rate of improvement in both parameters will be sustained by all nations throughout the 21st century.
   R/R₀ = (W/W₀)^0.8where R is GDP/Mtoe and W is GDP/capita