This is an advanced macroeconomics question regarding the Solow growth
model as presented in Romers: Advanced Macroeconomics Chapter 1,which
I have been having difficulty with:

Q: (i)The return to capital (r) is roughly constant over time as are the
shares of output going to capital and to labour. Does a Solow economy
on a balanced growth path exhibit these properties? What are the
growth rates of r and w on a balanced growth path?

(ii) Suppose the economy begins with a level of k less than k*. As k
moves towards k*, is w growing at a rate greater than, less than or
equal to it's growth rate on the balanced growth path? what about r?

I need a fairly detailed and most likely mathematical based answer
explained and justified including assumptions - not just simple yes/no
etc.

cheers