Thanks very much for writing this, I found it really interesting. I like the way you follow the formalism with many examples.
I have a very simple question, probably due to my misunderstanding—looking at your simulations, you have the fraction of workers and scientists working on consumption going asymptotically to zero, but the terminal growth rate of consumption is positive. Is this a result of consumption economies of scale growing fast enough to offset the decline in worker fraction?
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 very much for writing this, I found it really interesting. I like the way you follow the formalism with many examples.
I have a very simple question, probably due to my misunderstanding—looking at your simulations, you have the fraction of workers and scientists working on consumption going asymptotically to zero, but the terminal growth rate of consumption is positive. Is this a result of consumption economies of scale growing fast enough to offset the decline in worker fraction?
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?