Using a standard Solow growth model with population growth and fixed productivity, derive the investment rate needed to keep the physical capital per capita constant. How is this investment rate...

Using a standard Solow growth model with population growth and fixed productivity, derive the investment rate needed to keep the physical capital per capita constant. How is this investment rate affected by the productivity level? Would an economy be able to sustain such an investment rate?

How would the output per capita growth predictions (short-run & long-run) and the steady-state output per capita level be affected by a lower labour share of output in a standard Solow growth model with population growth and fixed productivity?