In Acemoglu's book "Introduction to Modern Economic Growth" there is Proposition 8.3 which states that the impact of a change in the population growth rate on the steady state capital-labour ratio is zero. However, I was not able to prove this, which is asked in Exercise 8.17 as well. It makes more sense that this effect is negative. Does anyone have a solution to Exercise 8.17? Or an explanation to why this effect should be zero?