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This paper explores the relationship between ability and skill acquisition, when technological progress is ability biased and cost of education is a decreasing function of ability. It shows that, if the impact of ability biased technological progress on the productivity of unskilled labour is sufficiently low, the economy will be caught in a steady state where many abler individuals born of poor parents will not acquire skill, while many less able individuals born of rich parents will acquire skill. This is true even when technological progress is not ability biased at all. This result is likely to hold for LDCs like India where ability biased technological progress is confined only to a few pockets of the economy where there is little scope for employment of low-skilled labour.