This note proves that unless the amount of scientists , the proposition 15.12 in Acemoglu (2009) does not hold. Because this is an extremely restrictive requirement, it is not suitable as a proof of why the technological progress must be labor-augmenting on the BGP. Proposition 15.12 Consider the baseline model of directed technological change with the two factors corresponding to labor and capital. Suppose that the innovation possibilities frontier is given by the knowledge spillovers

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... tion with extreme state dependence, that is, δ = 1, and that capital accumulates according to (15.45). Then there exists a unique BGP allocation in which there is only labor-augmenting technological change, the interest rate is constant and consumption and output grow at constant rates. (Acemoglu,2009, chapter 15,p521) , that is , why Proposition 15.12 does not hold, because implies capital accumulation with finite elasticity.