Economic returns of research: the Pareto law and its implications
  At what level should government or companies support research? This complex multi-faceted question encompasses such qualitative bonus as satisfying natural human curiosity, the quest for knowledge and the impact on education and culture, but one of its most scrutinized component reduces to the assessment of economic performance and wealth creation derived from research. In certain areas such as biotechnology, semi-conductor physics, optical communications, the impact of basic research is direct while, in other disciplines, the path from discovery to applications is full of surprises. As a consequence, there are persistent uncertainties in the quantification of the exact economic returns of public expenditure on basic research. Here, we suggest that these uncertainties have a fundamental origin to be found in the interplay between the intrinsic ``fat tail'' power law nature of the distribution of economic returns, characterized by a mathematically diverging variance, and the stochastic character of discovery rates. In the regime where the cumulative economic wealth derived from research is expected to exhibit a long-term positive trend, we show that strong fluctuations blur out significantly the short-time scales: a few major unpredictable innovations may provide a finite fraction of the total creation of wealth. In such a scenario, any attempt to assess the economic impact of research over a finite time horizon encompassing only a small number of major discoveries is bound to be highly unreliable. New tools, developed in the theory of self-similar and complex systems to tackle similar extreme fluctuations in Nature can be adapted to measure the economic benefits of research, which is intimately associated to this large variability. 
Didier Sornette (CNRS-University of Nice and UCLA) and Daniel   Zajdenweber (Universite de Parix X - Nanterre)