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In this paper, we develop a model characterized by skill-biased technological change and increasing costs of education to investigate income inequality. Irregular workers cannot escape poverty by commencing investment in education because wage inequality between regular and irregular workers widens and the price of education increases with the average level of education. Moreover, if the productivity of elementary education is low relative to that of higher education, middle-income individuals are eventually unable to pursue higher education because the threshold for education expenditure rises with the price of education. Thus, income inequality may widen, even among regular workers.