We clarify the different effects of elementary and higher education on human capital accumulation and inequality. The productivity of elementary education plays a significant role in the widening of inequality regardless of the existence of multiple steady states. When the productivity of elementary education is low, the poor cannot afford higher education in the long run because the demand for education by the rich makes the price of education too high for the poor. However, the effect of its productivity on the attainable education level is ambiguous. A rise in the productivity of higher education always increases the education level.
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