Regarding your question, yes, you have the right idea. Growth of consumption per capita is growth in consumption technology plus growth in consumption work per capita — thus, while the fraction of workers in the consumption sector declines exponentially, consumption technology grows (due to increasing returns) quickly enough to offset that. This yields positive asymptotic growth of consumption per capita overall (on the specific asymptotic paths you are referring to). Note that the absolute total number of people working consumption *research* is still increasing on the asymptotic path: while the fraction of scientists in the consumption sector declines exponentially, there is still overall population growth. This yields the asymptotic growth in consumption technology (but this growth is slower than what would be feasible, since scientists are being shifted away from consumption). Does that make sense?

Thanks!

Regarding your question, yes, you have the right idea. Growth of consumption per capita is growth in consumption technology plus growth in consumption work per capita — thus, while the fraction of workers in the consumption sector declines exponentially, consumption technology grows (due to increasing returns) quickly enough to offset that. This yields positive asymptotic growth of consumption per capita overall (on the specific asymptotic paths you are referring to). Note that the absolute total number of people working consumption *research* is still increasing on the asymptotic path: while the fraction of scientists in the consumption sector declines exponentially, there is still overall population growth. This yields the asymptotic growth in consumption technology (but this growth is slower than what would be feasible, since scientists are being shifted away from consumption). Does that make sense?