This paper develops a dynamic dual-economy model and examines how the long-run outcome of an economy depends on the initial distribution of wealth and sectoral productivity. It is shown that, for fast transformation into a developed economy, the initial distribution must be such that extreme poverty is not prevalent so that most people can take education to acquire basic skills and the size of the “middle class” is large enough so that an adequate number of people can access education to acquire advanced skills. Both conditions seem to have held in successful East Asian nations, where, as in the model economy undergoing such transformation, the fraction of workers with advanced skills rose greatly and inequalities between these workers and others fell over time. In contrast, if the former condition holds but the latter does not, which would be the case for many nations falling into the “middle income trap,” consistent with facts, the fraction of workers with basic skills and the share of the modern sector rise, but inequality between workers with advanced skills and with basic skills worsens and the traditional sector persists for long periods. If the former condition does not hold, which would be true for the poorest economies, the dual structure and high inequality between workers without basic skills and others persist for very long periods. Consistently, Hanushek and Woessmann (2012) [Hanushek, Eric A. and Ludger Woessmann (2012) Do better schools lead to more growth? Cognitive skills, economic outcomes, and causation. Journal of Economic Growth 17, 267–321] find that the share of students with basic skills and that of top performance have significant effects on economic growth that are complementary to each other.