Both economists and psychologists proved the role of cognitive abilities and competencies in economic achievements. The assumption that more capable and educated individuals achieve better economic results underlies most of these researches. This assumption is evidently true as a general tendency, but it cannot explain modest economic achievements in certain countries with high levels of human capital development. We propose that problem solving is the mediator between human competencies and achievements. Creation of goods and services is based on problem solving in design, production and delivery. The quality of problem solving depends on human competencies and, in turn, determines economic achievements. More importantly, the choice of problems to be solved creates or does not create the possibility for application of highly qualified labor and, as a result, for full-fledged realization of human capital. We propose a mathematical model based on these assumptions. The simulation reproduces most important traits of Lynn and Vanhanen’s (2002) findings. The simulation shows a non-linear growth of economic achievements with national IQ growth as well as an increase of between countries variance. Thereby the proposed model can serve as a satisfactory explanation for empirical data on links between national IQs and economic achievements.