Five years ago I published a paper  introducing the concept of constant annual increment in real GDP per capita, G(t), as observed in developed countries. In the long run, the GDP growth as a linear function of time:
where G0 is the initial level of GDP per capita at time t0 in a given country, A is the country dependent increment measured in PPP dollars. Therefore, the rate of growth of real GDP per capita, dG/G, has a decelerating nonlinear trend:
dG/G = A/G
This assumption gives excellent statistical results and explains the evolution of real GDP per capita in developed countries, as also was confirmed in our 2008 paper .
Hence, the task now is to track the progress of the economies under study. The figure below presents several important cases, which demonstrate the accuracy of our concept. Since the increment is assumed to be constant, the mean value of the annual GDP increment should coincide with its linear trend (see the paper for details). In reality, the linear regression line is very close to the constant level. In many cases (e.g. France, Italy, Japan), it oscillates around the mean value over time with a small amplitude. The hypothesis of the constant increment looks sound.
Figure. The increment of real GDP per capita vs. real GDP per capita in select developed countries. Thick line – the mean increment. Two solid lines represent two linear trends (also represented by their equations) as associated with the original and population corrected GDP estimates. All data are borrowed from the Conference Board data base (http://www.conference-board.org/economics/database.cfm).
 Kitov, I., (2006). Real GDP per capita in developed countries, MPRA Paper 2738, University Library of Munich, Germany, http://ideas.repec.org/p/pra/mprapa/2738.html
 Kitov, I., (2009). The Evolution of Real GDP Per Capita in Developed Countries, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. IV(1(8)_ Summ), pp. 221-234.