It's the expected growth rate, so yes it would vary in a real-world instance. I wondered for a while why they've taken the logarithm, but I think it's just because growth models are normally defined exponentially (with the rate being a parameter inside the exponential) - it shouldn't make a difference to the result.
As for varying, that Samuelson article says:
> For N as large as one likes, your growth rate can well (and at times must) turn out to be less than mine - and turn out so much less that my tastes for risk will force me to shun your mode of play.
As for varying, that Samuelson article says:
> For N as large as one likes, your growth rate can well (and at times must) turn out to be less than mine - and turn out so much less that my tastes for risk will force me to shun your mode of play.