The possible non linearity of the income elasticity of child labour has been at the centre of the debate regarding both its causes and the policy instruments to address it. We contribute to this debate providing theoretical and empirical novel results. From a theoretical point of view, for any given transfer size, there is a critical level of household income below which an increase in income has no impact on child labour and education. We estimate the causal impact of an increase in income on child labour and education exploiting the random allocation of the Child Grant Programme, an unconditional cash transfer, in Lesotho. We show that the poorest households do not increase investment in children's human capital, while relatively less poor households reduce child labour and increase education. In policy terms, the results indicate that cash transfers might not be always effective to support the investment in children's human capital of the poorest households. Beside the integration with other measures, making the amount of transfer depends of the level of deprivation of the household might improve cash transfer effectiveness.